Latest revision as of 03:19, 20 October 2016

MODELING

ABSTRACT
Bonding of proteins is highly depending on structural properties which in turn are determined by the amino acid sequences. Changing the amino acid sequence of one participating partner could consequently diminish its binding ability. Therefore it is important to estimate the influence of mutations on the protein structure. This is particularly true for mutations from natural to non-natural amino acids.
To estimate the influence of O-methyl-l-tyrosine on Colicin E2's immunity protein we applied several molecular dynamics simulations leading to 1300 ns in total simulation time. To do this we estimated O-methyl-l-tyrosine parameters for the CHARMm 22 and the GROMOS36a7 force field. We evaluated our simulations by applying several well documented evaluation methods, like secondary structure analysis, plotting the solvent accesible surface area, and RMSD and RMSF. Our first simulation analysis led to the conclusion that O-methyl-l-tyrosine had no influence on the immunity protein.
To estimate possible influences on the thermodynamics of the system we tried to calculate the binding energy between Colicin E2 and its immunity protein by Alchemistry Free Energy Perturbation experiments. This was not successful due to computational errors and comutational limitations.

THEORETICAL OVERVIEW

Molecular Dynamics Simulation

Introduction

Molecular Dynamics (MD) Simulations is a method to describe atomic and molecular movements. Molecular Dynamics simulations depend on several simplifications that enables the simulation to range from nanoseconds up to severeal milliseconds in systems containg of over one hundred thousand atoms. This enables the possibility to study different biomolecular processes like protein protein binding or enzyme dynamics. Because of the deterministic nature of the system it is possible to calculate thermodynamic properties like free energy or free binding enthalpies [1].

Assumptions

To describe atomistic or molecular behavior the exact system conditions like positions and energies. The energies of an atomic system are described by the Schrödinger equation (eq. \ref{Schrödinger}) with wavefunction $\Psi$ (eq. \ref{wavefunction}), kinetic energies $\hat{T}_{e}$ and $\hat{T}_{N}$ and potential energies $\hat{V}_{e}$, $\hat{V}_{N}$ and $\hat{V}_{eN}$. Terms with subscript $_{e}$ are terms concerning the electrons and terms with subscript $_{N}$ are terms concerning the nuclei[1].

$$ \begin{equation} (\hat{T}_{e} + \hat{T}_{N} + \hat{V}_{e} + \hat{V}_{N} + \hat{V}_{eN})\Psi=i \hbar \frac{\partial}{\partial t}\Psi \label{Schrödinger} \end{equation}$$ $$ \begin{equation} \Psi=\Psi(\vec{r}_{1},..., \vec{r}_{N_{e}},\vec{r}_{1},...,\vec{r}_{N_{N}}) \label{wavefunction} \end{equation}$$

Since there is no possibility to solve these equations numerically, it is necessary to simplify the system description. The first assumption depends on the Born-Oppenheimer approximation that the Schrödinger equation can be split into two parts, one for the electrons and one for the nuclei respectivly. Since the electrons are far more mobile the dynamic of the system can be defined by the nuclei positions.
Molecular Dynamics simulations depend on several simplifications. First, we assume in accord with the Born-Oppenheimer approximation that electronical movement has no influence on the overall atomic momentum since electrons will simply follow the nuclear movements in the simulated time scales. Second, we can describe the potential energy function by a sum of simple terms. These terms are described in the so-called force field which will be described later on. Third, the system potential is evaluated by deriving the forces and applying Newtonian mechanic calculations as shown in equation \ref{newton} and \ref{newton1} [1].

$$ \begin{equation} M_{K}\frac{d\vec{v}_{1}}{dt} = M_{K}\frac{d^{2}\vec{r}_{1}}{dt^{2}} = \vec{F}_{\vec{r}_{1}} = \frac{\partial V\left(\vec{r}_{1},...,\vec{r}_{N}\right)}{\partial \vec{r}_{1}} \label{newton} \end{equation} $$

$$ \begin{equation} F_{ij}=-\frac{\partial}{\partial r_{ij}}V_{force~field} \label{newton1} \end{equation} $$

To solve these terms numerically we have to discretize the trajectory and therefore use an integrator for the small time steps. Several different integrators are developed today, of which the velocity-Verlet algorithm is the most used (eq. \ref{VV1} & \ref{VV2}) [1].

$$ \begin{equation} r_{i}(t_{0} + \Delta t) = r_{i}(t_{0}) + v_{i}(t_{0})\Delta t + \frac{1}{2}a_{i}(t_{0})\Delta t^{2} \label{VV1} \end{equation} $$

$$ \begin{equation} v_{i}(t_{o}+\Delta t) = v_{i}(t_{0}) + \frac{1}{2}[a_{i}(t_{o} + \Delta t)]\Delta t \label{VV2} \end{equation} $$

The temperature of the system is directly correlated to the distribution of kinetic energies. Therefore the temperature of the system can be controlled by manipulating the atom velocities. A possible way to do this was proposed by Berendsen by coupling the system to a heat bath resulting in a NVT ensemble (eq. \ref{Berendsen}) [1].

$$ \begin{equation} a_{i}=\frac{F_{i}}{m_{i}} + \frac{1}{2 \tau_{T}} \left( \frac{T_{B}}{T_{t}} -1 \right) v_{i} \label{Berendsen} \end{equation} $$

Empirical Force Fields

Empirical Force Fields are the backbone of every Molecular Dynamics simulation. Typically the force fields are divided into two parts, bonded and nonbonded interactions. Bonded interactions consist of chemical bond stretching, angle bending, and rotation of dihedrals and impropers. Nonbonded interactions are approximated by Coulomb interactions (ionic) and Lennard-Jones potentials. The overall CHARMm (Chemistry at HARvard Macromolekular mechanics) potential is calculated by summing up these main potentials ($ V_{CHARMm} = V_{bonded} + V_{nonbonded} $) [2,3,4].
In equation \ref{CHARMM_bonded} and \ref{CHARMM_nonbonded} the bonded and nonbonded potentials of the CHARMm force field are displayed. All terms consist of an equilibrium value marked with $0$ and a force constant $K$ [2,3,4].

$$ \begin{equation} V_{bonded} = \sum_{bonds}{K_{b}(b-b_{0})^{2}} + \sum_{angels}{K_{\theta}(\theta-\theta_{0})^{2}} + \sum_{torsions}{K_{\phi}(1+cos(n\phi-\delta))} + \\ \sum_{impropers}{K_{\psi}(\psi-\psi_{0})^{2}} + \sum_{Urey-Bradley}{K_{UB}(r_{1,3}-r_{1,3,o})^{2}} + \sum_{\phi\psi}{V_{CMAP}} \label{CHARMM_bonded} \end{equation} $$ $$ \begin{equation} V_{nonbonded}=\sum_{nonbonded}{\frac{q_{i}q_{j}}{4\pi D r_{ij}}}+ \sum_{nonbonded}{\epsilon_{ij}\left[\left(\frac{R_{min,ij}}{r_{ij}}\right)^{12}-2\left(\frac{R_{min,ij}}{r_{ij}}\right)^{6}\right] } \label{CHARMM_nonbonded} \end{equation} $$

The additional terms CMAP and Urey-Bradley are correctional terms for backbone atoms and 1, 3 interactions respectively [2,3,4].

Simulation Analysis

Since the vast amount of data that is produced by Molecular Dynamics simulations it is essential to process the data into more accesible formats. To perform this task we applied several approaches like comparison of the solvent accesible surface area (SASA) over time.

Root Mean Square Deviation

The Root Mean Square Deviation (RMSD) describes the sum of distances of all selected atoms $n$ between themselves in a selceted timestep $\tau$ and a reference timestep $r$ (eq. \ref{RMSD}). Plotted over time it is possible to detect fluctuations in the whole molecular configuration and therefore it is possible to conclude structures of high stability from plateaus in the RMSD.

$$ \begin{equation} RMSD_{\tau}=\sqrt{\sum_{n=1}^{N}{\left((x_{\tau,n}-x_{r,n})^{2}+(y_{\tau}-y_{r,n})^{2}+(z_{\tau,n}-z_{r,n})^{2}\right)}} \label{RMSD} \end{equation} $$

By choosing the right atom selection it is possible to evaluate the different behaviours of protein subgroups. For example, if the RMSD between Cα atoms is calculated it is possible to plot the backbone movement over time and hence detect configurations that differ from the starting structure. This is important if one wants to search for different thermodynamically stable ensembles of the protein or molecule of interest.

Root Mean Square Fluctuation

Similar to the RMSD the Root Mean Square Fluctuation describes the sum of distances of all selected atoms. In this case the distance per atom between all selected configuartions is calculated and summed over time. Therefore it is possible to spot residues with strong mobility and consequntly residues that are part of fluctuating and disordered protein subunits.

$$ \begin{equation} RMSF_{n}=\sqrt{\sum_{\tau=1}^{T}{\left((x_{n}-x_{0})^{2}+(y_{n}-y_{0})^{2}+(z_{n}-z_{0})^{2}\right)}} \label{RMSF} \end{equation} $$

DSSP

Define Secondary Structures of Proteins (DSSP) by Wolfgang Kabsch and Christian Sander is a standard program to analyse secondary structure properties of proteins. The main idea to discriminate between different secondary structures is based on the presence of H bonds because this can be represented by one energy value. This definition enables the algorithm to distinguish different types of α helices, β sheets, and turns.
The electrostatic interations between two groups are calculated by assigning partial charges to each C ($+q_{1}$), O ($-q_{1}$), N ($-q_{2}$), and H ($+q_{2}$), with $q_{1} = 0.42~e$ and $ q_{2} = 0.20~e$ and r(AB) being the distance between two atoms A and B in Angström. An H bond is defined by $ E < -0.5~\frac{kcal}{mol}$ [5].

$$ \begin{equation} E = q_{1} q_{2} \left( \frac{1}{r(ON)} + \frac{1}{r(CH)} + \frac{1}{r(OH)} + \frac{1}{r(CN)} \right) 332~\frac{kcal}{mol} \label{DSSP} \end{equation} $$

Binding Energy Calculations

Alchemical Free Energy Perturbation (FEP) is a method in computational biology to obtain energy differences from molecular dynamics or Metropolis Monte Carlo simulations between two system states. In here the system is slowly transformed from state $i$ to state $j$ through non-natural intermediates which are sampled by slowly decreasing the intermolecular interactions. The core equation (eq. \ref{FEGG}) for the Helmholtz free energy difference between states $i$ and $j$ $\Delta A_{ij}$ is derived from statistical mechanics. $Q$ represents the canonical partition function, $k_B$ the Boltzman constant, $U$ the corresponding potential system energy in relation to the coordinates and momenta $\vec{q}$, $T$ the temperatur and $\Gamma$ the volume of potential states of $\vec{q}$ [16].

$$ \begin{equation} \Delta A_{ij} = -k_{B} T \frac{Q_{j}}{Q_{i}} = -k_{B} T~ln \left( \frac{\int_{\Gamma_{j}}e^{-\frac{U_{j}(\vec{q})}{k_{B}T}}d \vec{q}}{\int_{\Gamma_{i}}e^{-\frac{U_{i}(\vec{q})}{k_{B}T}}d \vec{q}}\right) \label{FEGG} \end{equation} $$

To calculate free energy differences between states with low state space overlap a thermodynamic cycle can be constructed hence the Helmholtz free energy is a thermodynamic state function. The most straightforward way to calculate state transition free energy changes would be to simulate the naturally occuring process. For example the binding free energy between two proteins can be calculated by separating both proteins. This approach however has high computational costs since simulating the whole water filled box results in large systems.
The alchemical perturbation approach relies on simulating several intermediate states over which Coulomb and Lennard-Jones interactions are slowly decreased. This is controlled via a coupling factor $\lambda$ (eq \ref{lambda}). The resulting potential energy $U$ at state $\lambda$ is subsequently calculated as a sum of the two end states $U_0$, $U_1$ and all not decoupled interacions $U_{unaffected}$ [16].

$$ \begin{equation} U(\lambda,\vec{q}) = (1-\lambda)~U_{0}(\vec{q}) + \lambda~U_{1}(\vec{q}) + U_{unaffected}(\vec{q}) \label{lambda} \end{equation} $$

The overall free energy change $\Delta A_{0,1}$ is consequently calculated as the sum over all free energy changes (eq. \ref{TC}).

$$ \begin{equation} \Delta A_{0,1} = \sum^{1}_{\lambda=0} {\Delta A_{\lambda,\Delta \lambda}} \label{TC} \end{equation} $$

Gibb's free energy differences between two λ states can be calculated by equation \ref{Calc}.

$$ \begin{equation} \Delta G~(\lambda^{'} \rightarrow \lambda^{"}) = -k_{B}T~\Bigg \langle exp \left( -\frac{U(\lambda^{"})-U(\lambda^{'})}{k_{B}T} \right) \Bigg \rangle \label{Calc} \end{equation} $$

Interactions of molecules are represented by Lennard-Jones and Coulomb interactions. This can lead to problems when Lennard-Jones interactions are decoupled and charge interactions are still active. This ensemble will lead to a clashing of the molecules since the charges will attract each other without any form of antagonistic force. To avoid this problem, position restraints are added which have to be considered in the final calculation.
In order to evaluate the simulations of the intermediate states and calculate the free energy difference between the end states several algorithms have been developed (e.g., Exponential Averaging (EXP) or Bennett Acceptance Ratio (BAR)). BAR computes the energy difference between two simulations generating the trajectories $ n_i $ and $ n_j $ with the corresponding potential energy functions $U_i$ and $U_j$. The free energy difference $\Delta A_{ij}$ can then be written as in equation \ref{Bennett} where $f()$ stands for the Fermi function (eq. \ref{Fermi}) [16].

$$ \begin{equation} \Delta A_{ij} = k_B T ~ \left( ln \frac{\sum_j f(U_i - U_j + k_B T~ln \frac{Q_i n_j}{Q_j n_i})}{\sum_i f(U_j - U_i - k_B T~ln \frac{Q_i n_j}{Q_j n_i})} - ln \frac{n_j}{n_i} \right)+ k_B T~ln \frac{Q_i n_j}{Q_j n_i} \label{Bennett} \end{equation} $$

$$ \begin{equation} f(x) = \frac{1}{1 + e^{~\beta x}} \label{Fermi} \end{equation} $$

The Term $k_B T~ln \frac{Q_i n_j}{Q_j n_i}$ has to be approximated since it cannot be computed analytically. Equation \ref{Bennett2} describes the relation used by Bennett et al. to estimate the term. Once it has been determined the free energy difference can be calculated by equation \ref{Bennett3} [16].

$$ \begin{equation} \sum_j f\left(U_i - U_j + k_B T~ln \frac{Q_i n_j}{Q_j n_i}\right) = \sum_i f\left(U_j - U_i - k_B T~ln \frac{Q_i n_j}{Q_j n_i}\right) \label{Bennett2} \end{equation} $$

$$ \begin{equation} \Delta A_{ij} = - k_B T ~ ln \frac{n_j}{n_i} + k_B T~ln \frac{Q_i n_j}{Q_j n_i} \label{Bennett3} \end{equation} $$

Later on Shirts et al. derived the BAR method by applying maximum likelihood techniques [16].
Since common analysis methods in biochemistry often rely on titration, only dissociation ($K_{d}$) respectively association constants ($K_{a}$) can be concluded from experiments. Therefore the dissociation constants were calculated by using equation \ref{gibbs}.

$$ \begin{equation} K_{a/d} = e^{-\frac{\Delta G}{RT}} \label{gibbs} \end{equation} $$

METHODS

Visualisations

Colicin E2

No obtainable 3D model of Colicin E2 was found in the Research Collaboration for Structural Bioinformatics (RCSB) Protein Data Bank (PDB) at the Brookhaven National Laboratory and the Protein Data Bank in Europe (PDBe) at the European Bioinformatics Institue (EMBL-EBI). Crystallographic structures of the DNase subunit of Colicin E2 and its bacterial import subunit were available. Therefore we chose to use homology modeling to obtain a 3D structure of Colicin E2. For homology modeling the Protein Homology/analogY Recognition Engine V 2.0 (PHYRE²) [17] server was used in combination with the amino acid sequence obtained from the Universal Protein Resource (UniProt) Protein Knowledgebase (UniProtKB) entrance P04419.
The obtained model was based on the known subunits of Colicin E2 and Colicin E3, a close relative. Afterwards a CHARMm topology was produced via the pdb2gmx module of GROMACs 5.1.3 [6-15], the model was solvated in TIP3P water and energy minimized using the steepest descend algorithm. Afterwards we used PyMOL [18] to create molecular images.

Force Field Parametrization

A 3D model of O-methyl-l-tyrosine was created using Avogadro 1.1.1, and energy minimized using the steepest descend algorithm in vacuum. The so obtained model was subsequently parsed to the SwissParam [19] topology server. The created topology was then used to derive parameters for the CHARMm residue force field [2,3,4] so that for any protein with O-methyl-l-tyrosine a topology could be created. Since O-methyl-l-tyrosine is very similar to tyrosine most parameters could be adopted.
CHARMm is an atom type based force field, meaning that every parameter is not dependend on the residue but on the assigned atom types taking part in the interactions. As a result we had to define several new atom types to account for the changed properties of the methyl ether since no other benzyl ether atoms could be found in the force field parameter files.

Figure 1: Used atom names and types for the implementation.

To implement the newly derived parameters we had to update several force field parameter files that we gathered from the GROMACS 5.0.4 software suite [6-15]. This was due to the case that all parameter files had to be compatible to the GROMACS software suite. First we had to implement the new amino acid in the aminoacids.rtp file which basically serves as a register for all known residues. The amino acid entry contains a three letter code by which it will be identified, all atoms with name, type and charge, all bonds between these atoms as well as impropers and CMAPs. Since the last two entries only concern the backbone atoms, we simply copied those entries. Atom charges were duplicated from tyrosine for all atoms that were not involved in the ether bond. The ether methyl group was represented by a standard methyl group with CT3 carbon and HA hydrogen. This atom classes represent alanin's Cβ and the Cδ atom of methionin.
A new atom class named OE was introduced to represent the ether oxygen since there are no ether oxygen parameters for amino acid residues in the CHARMm force field files. We used parameters from the generated topology file to derive parameters for all interactions from the OE atom type. To implement these parameters we updated the bondtypes, angletypes, and dihedrals in the ffbonded.itp file. Similarly, we updated the ffnonbonded.itp file sections atomtypes, and pairtypes. Subsequently we added an OE entry to the atomtypes.atp file.
CHARMm simulates aromaticity through dummy atoms which will be calculated automatically. To achieve this for our new amino acid we updated the aminoacids.vsd file and inserted every bond length and angle. Finally we had to assign a three letter code to represent our amino acid in the topology and structure files. We chose OMT. This resulted in the empirical force field CHARMm 27 OMT.

Molecular Dynamics Simulations

3D structures of the Colicin E2 DNase subunit (miniColicin) and its immunity protein were obtained from the RCSB PDB entrance 3U43 [20]. Since the main binding occurs between the DNase subunit and the immunity protein only this Colicin E2 subunit was simulated. Furthermore we established a minimized Colicin E2 in another project part and wanted to test its operational capability.
To insert mutations inside the immunity protein we inserted the energy minimized structure of OMT at the desired position. Positions of backbone atoms were fitted to those of the replaced amino acid so that the backbone integrity was preserved. This was achieved through the implementation of Kabsch's algorithm for structural alignments in the Bio3D package [21-23] for the statistical computing language R [24]. Additionaly we used Bio3D's pdb processing package to separate Colicin E2 DNase subunit and its immunity protein.
All molecular dynamics simulations were performed with the GROningen MAchine for Chemical Simulations (GROMACS) 5.0.3 [6-15] software suite. As empirical force field CHARMm 27 OMT was used. An explicit water model with TIP3P water was chosen. The box was subsequently filled with water and the system was neutralized through insertions of chloride ions. After neutralization the system was energy minimized with the steepest descent algorithm until it converted. To generate velocity and temperate the system a small equilibration run of about 500 ps was performed. The end temperature was set to 298 K and the Berendsen thermostat and the velocity-Verlet integrator with a stepsize of 2 fs were used. After this equilibration run a NVT ensemble was achieved. To achieve a NPT ensemble the equilibration run was repeated with applied pressure coupling to 1 bar. Subsequently the final MD production run was performed. Every 5000st step was saved resulting in a trajectory of 10001 conformations ranging over 100 ns simulation time.

Molecular Dynamics Simulations Analysis

Simulation Analysis was performed using the R [24] package Bio3D [21,22,23]. All plots were created using the R package ggplot2 [25]. For visualization of protein structures and trajectories the PyMOL visualization system [18] was used. To compensate for eventual jumps due to translations across the PBC barriers a GROMACS internal fitting program was applied (gmx trjconv -center -pbc nojump). To exclude translational and rotational movement of the simulated protein we applied the GROMACS internal fitting algorithms gmx trjconv -fit rot+trans. These trajectory manipulations were performed because several analysis methods like RMSD and RMSF rely on distance calculations between atom positions over time. In these analyses the translational and rotational movements are not of interest since we only want to visualize the movement of atoms in relation to the simulated protein to test for different configuarations and structural flexibility. Additionally the crossing of PBC barriers would increase the distance between two atom positions drastically since the atom would be relocated to the opposing site of the simulated system.

Binding Energy Calculations

Binding energies were calculated by using alchemical Free Energy Perturbation (FEP) in combination with Bennett Acceptence Ratio (BAR). A thermodynamical cycle was constructed (see fig. 2) and accordingly two simulation sets were performed. First, Colicin E2's immunity protein was simulated in TIP3P water with 0.6 nm space between the box and the protein. Furthermore, Lennard-Jones potential and Coulomb interactions were decoupled over ten simulations, each resulting in 20 simulations in total. The simulations were energy minimized over approximately 300 steps, NVT equilibrated over 10 ps and NPT equilibrated over 100 ps. The production run was performed for 2 ns. Second, the binding complex consisting of Colicin E2 and its immunity protein was simulated under similar conditions i.e. equilibration and simulation times, and steps were chosen alike. In contrast to the immunity protein simulations additional restraint decoupling steps were performed over ten simulations before the other steps. All simulations were evaluated using the BAR scripts from the pyMBAR python library.

RESULTS & CONCLUSION

Molecular Dynamcis Simulations

Three amino acid positions were chosen for O-methyl-l-tyrosine (OMT) exchange evaluation (tyrosine 8 (Y8), phenylalanine 13 (F13) and phenylalanine 16 (F16)). These positions were selected because of their small deviation in regard to OMT and were therefore expected to cause the smallest structural differences. All molecular dynamics steps were performed on these mutation variants, as well as on the wildtype protein for comparison. All simulations were performed over 100 ns, leading to 10001 conformations each. These conformations were evaluated using RMSD, RMSF, SASA and the amount of secondary structures over time.
Figure 2 displays the RMSD in regard to the initial conformation. It can be observed that the mutational variant Y8O exhibits similar curve characteristics as the wildtype variant. The mutational variant F16O on the contrary shows a more severe deviation from the wildtype.

Figure 2: RMSD of the mutation variants Y8O (green), F16O (blue) and the wildtype (red).

The solvent accessible surface area (SASA) was calculated for every simulation step using DSSP and is displayed in figure 3. The little to no fluctuation in the SASA of all simulated variants is an argument for the high structural stability of the wildtype and the mutational variants. The disparity between the mutational variants and the wildtype can be traced back to the DSSP algorithm since it is based solely on natural amino acids. Therefore it cannot evaluate a non-natural amino acid and would cause a discrepancy between surface areas if non-natural amino acids like OMT are involved.

Figure 3: SASA of the mutation variants Y8O (green), F16O (blue) and the wildtype (red).

Additionally we evaluated the RMSF and the amount of secondary structures over time which exhibited no differences between the mutational variants and the wildtype. Therefore the results of these evaluation methods are not shown on this wiki.
Closing up we can conclude that the mutational variant Y8O does fit our demands best, since its behavior exhibits the least disparity in our applied evaluation methods towards the wildtype. Therefore Y8O was chosen for further analyses.

Furthermore we evaluated the stability of our designed miniColicin by performing 100 ns of MD simulations with different force fields (CHARMm27, AMBER03, GROMOS56a7). The RMSD of these simulations is displayed in figure 4. It can be observed that some deviations between the different force fields occur. The simulation run with the GROMOS56a7 shows the biggest discrepancy towards the AMBER and CHARMm simulations which display little to no fluctuations over time. This behavior can be traced to the different parametrization approach in the force fields as well as to the fact that the GROMOS56a7 force field is a united atom force field, in which all CH₃ and CH₂ groups are described as one group.

Figure 4: RMSD of miniColicin simulated using the the force fields CHARMm27 (red), AMBER03 (blue) and GROMOS56a7 (green).

Binding Energy Calculations

To obtain the binding energy between miniColicin and the immunity protein we simulated 20 λ states per thermodynamic step. The coupling factor λ has been variated ina range of 0 to 1 in steps of 0.2 for Coulomb, 0.05 and 0.1 for the Lennard-Jones interactions respectively. Unfortunatly, a computation of a full set of simulations could not be achieved. This was due to unknown errors, inferior debugging abilities, malformed error messages recieved from the GROMACS simulation package [6-15] and temporal as well as computational limitations. In this context it was only possible to evaluate a scaling of Lennard-Jones potentials in the range from 0.9 to 1.0 with completely coupled Coulomb interactions. We tested simulations for different immunity protein variants on different computer systems (workstation and server) with the results being the same. Therefore, it seems appropriate to assume that the unknown error occured due to systematic problems. For example, instabilities in the simulated systems or badly implemented features could account for thus errors. Because of insufficient debug information provided by error messages we have not been able to debug the error and are consequently unable to present calculated data.
It should be evaluated wether this behavior is a singular event or an indication for a major underlying fault within the implemtation. If so an evaluation of the configuration space seems to be in order. Furthermore, a comparison against alternative simulation frameworks is most likely imperative for future work.

References

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Theoretical Overview
Methods
Results & Conclusion

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-<!-- END -->
 <body>
-  <div class="vviki" id="vviki">
+	<div class="vviki" id="vviki">
-    <div id="head">
+<div id="head">
-      <div id="title">
+		<div id="title">
-        <img id="logoleiste" src="https://static.igem.org/mediawiki/2016/8/83/T--TU_Darmstadt--titel.png" alt="iGEM TU Darmstadt 2016"/>
+			<img id="logoleiste" src="https://static.igem.org/mediawiki/2016/8/83/T--TU_Darmstadt--titel.png" alt="iGEM TU Darmstadt 2016"/>
-      </div>
+		</div>
-      </html>{{Team:TU_Darmstadt/MainMenu}}<html>
+		</html>{{Team:TU_Darmstadt/MainMenu}}<html>
-      <div class="banner">
+		<div class="banner"><img id="banner" src="https://static.igem.org/mediawiki/2016/8/86/T--TU_Darmstadt--team.jpg" alt="teamphoto"></img>
-        <img id="banner" src="https://static.igem.org/mediawiki/2016/8/86/T--TU_Darmstadt--team.jpg" alt="teamphoto"></img>
+		</div>
-      </div>
+		<div id="mainHeader">
-      <div id="mainHeader">
+			<h1>MODELING</h1>
-        <h1>ROBOTICS</h1>
+	    </div>
-      </div>
+</div>
-    </div>
+		<div class="page">
-    <div class="page">
+			<div class="abstract">
-      <div class="abstract">
+			    <p><b>ABSTRACT</b><br/>
-        <p><b>ABSTRACT</b><br/>
+				Bonding of proteins is highly depending on structural properties which in turn are determined by the amino acid sequences. Changing the amino acid sequence of one participating partner could consequently diminish its binding ability. Therefore it is important to estimate the influence of mutations on the protein structure. This is particularly true for mutations from natural to non-natural amino acids.<br/>To estimate the influence of <i>O</i>-methyl-<span style="font-variant: small-caps;">l</span>-tyrosine on Colicin E2's immunity protein we applied several molecular dynamics simulations leading to 1300&nbsp;ns in total simulation time. To do this we estimated <i>O</i>-methyl-<span style="font-variant: small-caps;">l</span>-tyrosine parameters for the CHARMm&nbsp;22 and the GROMOS36a7 force field. We evaluated our simulations by applying several well documented evaluation methods, like secondary structure analysis, plotting the solvent accesible surface area, and RMSD and RMSF. Our first simulation analysis led to the conclusion that <i>O</i>-methyl-<span style="font-variant: small-caps;">l</span>-tyrosine had no influence on the immunity protein.<br/>To estimate possible influences on the thermodynamics of the system we tried to calculate the binding energy between Colicin E2 and its immunity protein by Alchemistry Free Energy Perturbation experiments. This was not successful due to computational errors and comutational limitations.</p>
-          <b>One task of our project is to monitor and to keep alive manipulated <i>E.&nbsp;Coli</i> before they die, since they aren't able to survive on their own due to their dependence on non-natural amino acid. To catch the moment before the bacteria dies, a flourescent protein was implemented in such a way that it emits light as a warn signal.<br>
+			</div>
-            Therefore, our team decided to build a fully automatized pipetting robot that's able to locate a set of samples, detect potential light emission and pipet a specific amount of nonnatural amino acid onto the fluorescent sample.<br>
+			<div class="content">
-            The foundation for the robot lays a 3D-printer due to the easy handling of movements in three dimensions. By controlling these movements with an optical system the autonomy of the robot should be be increased even more.</b></p>
+			    <div class="verlinked" id="ThOv"><h2 style="border-bottom:3px solid #019ac8; padding-top:80px;">THEORETICAL OVERVIEW</h2></div>
-          </div>
+					<h5 id="MD" style="padding-top:0;">Molecular Dynamics Simulation</h5>
+<p><h6>Introduction</h6></p>
-          <div class="content">
+<p>Molecular Dynamics (MD) Simulations is a method to describe atomic and molecular movements. Molecular Dynamics simulations depend on several simplifications that enables the simulation to range from nanoseconds up to severeal milliseconds in systems containg of over one hundred thousand atoms. This enables the possibility to study different biomolecular processes like protein protein binding or enzyme dynamics. Because of the deterministic nature of the system it is possible to calculate thermodynamic properties like free energy or free binding enthalpies [1].</p>
-            <div class="verlinked" id="intro"><h5>INTRODUCTION</h5></div>
+<h6>Assumptions</h6><br/>
-            <p><h6>Development of 3D printers &amp; possibilities</h6>
+<p>To describe atomistic or molecular behavior the exact system conditions like positions and energies. The energies of an atomic system are described by the Schr&ouml;dinger equation (eq. \ref{Schrödinger}) with wavefunction \(\Psi\) (eq. \ref{wavefunction}), kinetic energies \(\hat{T}_{e}\) and \(\hat{T}_{N}\) and potential energies \(\hat{V}_{e}\), \(\hat{V}_{N}\) and \(\hat{V}_{eN}\). Terms with subscript \(_{e}\) are terms concerning the electrons and terms with subscript \(_{N}\) are terms concerning the nuclei[1].
-              <br>
+					</p><p>
-              In the 80s Chuck Hull invented the first standardized 3D printer, based on a procedure which is known as stereolithography (SLA, [1]). Moving from SLA to full deposit modeling (FDM) techniques, the 3D printing idea became alive in the Do&#8209;It&#8209;Yourself community. Ever since that time, basic 3D printers are accessible for little money and due to the open source idea of projects like REPRAP [2] affordable for many. In last years project, iGEM TU Darmstadt build already a fully working SLA printer, capable of feeding it with biological engineered plastics [3].<br>
+					<center>
-              So now, the hardware branch decided to rebuild a clone of the Ultimaker 2 FDM printer [4] and exchange the extruder with a camera and a pipette to create a pipetting robot. Using several open&#8209;source parts and software, it is the idea to establish an easy manageable robot to help the daily biologist's work.
+					$$
-            </p>
+						\begin{equation}
-            <p>
+							(\hat{T}_{e} + \hat{T}_{N} + \hat{V}_{e} + \hat{V}_{N} + \hat{V}_{eN})\Psi=i \hbar \frac{\partial}{\partial t}\Psi
-              <h6>Lab 3.0</h6>
+							\label{Schrödinger}
-              <br>
+						\end{equation}$$
-              Following the concept of the industry 3.0, the automation of simple tasks by robots (refers to the 4th stage of industrial revolution)  let us introduce the laboratory 3.0, which enables scientists to concentrate on actual science by the automation of simple, repeating work. This task is fulfilled with intelligent robots, which are enabled to detect, react and response to the experimenter.
+					$$
-            </p>
+						\begin{equation}
-            <p>
+							\Psi=\Psi(\vec{r}_{1},..., \vec{r}_{N_{e}},\vec{r}_{1},...,\vec{r}_{N_{N}})
-              <h6>Connection to our team</h6>
+							\label{wavefunction}
-              <br>
+						\end{equation}$$
-              iGEM TU DARMSTADT is a young and dynamic team of engaged researches. We have limited resources, namely time and money and we have to invent our lab work every day again, to reach more and stayfocus on science. We have the possibilities, thanks to iGEM, to experiment on our own ideas and to try reaching the sky (or actual the biologist's equivalent to something really cool).
+					</center>
-              Interdisciplinary opens our mind and sharpens our knowledge for the important things. It is really helpful, if we work together and benefit from each other.
+					</p><p>
-            </p>
+					Since there is no possibility to solve these equations numerically, it is necessary to simplify the system description. The first assumption depends on the Born-Oppenheimer approximation that the Schr&ouml;dinger equation can be split into two parts, one for the electrons and one for the nuclei respectivly. Since the electrons are far more mobile the dynamic of the system can be defined by the nuclei positions. <br/>Molecular Dynamics simulations depend on several simplifications. First, we assume in accord with the Born-Oppenheimer approximation that electronical movement has no influence on the overall atomic momentum since electrons will simply follow the nuclear movements in the simulated time scales. Second, we can describe the potential energy function by a sum of simple terms. These terms are described in the so-called force field which will be described later on. Third, the system potential is evaluated by deriving the forces and applying Newtonian mechanic calculations as shown in equation \ref{newton} and \ref{newton1} [1].</p>
+					<p>
-            <p>
+					<center>
-              References:
+					$$
-              <br>
+					\begin{equation}
-              <ol>
+						M_{K}\frac{d\vec{v}_{1}}{dt} = M_{K}\frac{d^{2}\vec{r}_{1}}{dt^{2}} = \vec{F}_{\vec{r}_{1}} = \frac{\partial V\left(\vec{r}_{1},...,\vec{r}_{N}\right)}{\partial \vec{r}_{1}}
-                <li><a href="http://edition.cnn.com/2014/02/13/tech/innovation/the-night-i-invented-3d-printing-chuck-hall/">http://edition.cnn.com/2014/02/13/tech/innovation/the-night-i-invented-3d-printing-chuck-hall</a></li>
+						\label{newton}
-                <li><a href="https://2015.igem.org/Team:TU_Darmstadt/Project/Tech">https://2015.igem.org/Team:TU_Darmstadt/Project/Tech</a></li>
+					\end{equation}
-                <li><a href="http://reprap.org/wiki/About">http://reprap.org/wiki/About</a></li>
+					$$
-                <li><a href="http://www.thingiverse.com/thing:811271">http://www.thingiverse.com/thing:811271, jasonatepaint</a></li>
+					</center>
-              </ol>
+					</p>
-            </p>
+					<p>
+					<center>
-            <div class="verlinked" id="goals"><h5>GOALS</h5></div>
+					$$
-            <p>
+					\begin{equation}
-              The main task is to develop a machine which is capable to monitor our organisms and their health condition in order to keep them alive. Therefore the machine has to measure the light emittance of the organisms and be capable of dropping liquids into our containers. This has to be independent of the exact position of the container, which requires an automatic tracking system.<br>
+						F_{ij}=-\frac{\partial}{\partial r_{ij}}V_{force~field}
-              The idea is that one places a container somewhere under the machines working area and click a run button of a program. The machine starts its routine by tracking the new container and measuring the light emittance of the organisms. Based on the measurement the machine decides whether to feed the organisms with non&#8209;natural amino acid or not. After a period of time it repeats this routine until the stop button of the program is clicked.<br>
+						\label{newton1}
-              These are only the minimum requirements for our project needs. We decided to go one step further ans designed our machine in such a way, that it serves as a multi purpose platform which is adaptable and easy to modify. Our aim is that it is possible to add new features and software, inviting other scientists to improve our platform and share their ideas with the community.<br>
+					\end{equation}
-              For example our liquid system can be upgraded to be able to prepare 96-well plates with probes and monitor routines, by using the optic.
+					$$
-              Or our measuring head can be changed back to a printer head which allows to 3D print again with just a few changes.<br>
+					</center>
-              One has a vast room of possibilities, just using the concept of the accurate positioning of a probe in the 3D space.<br>
+					</p>
-              Due to the fact that we try to stick to widely used open-source software and standard commercial parts, our machine can be easily combined with the most DIY products, making it reusable, flexible and cheap.<br>
+					<p>To solve these terms numerically we have to discretize the trajectory and therefore use an integrator for the small time steps. Several different integrators are developed today, of which the velocity-Verlet algorithm is the most used (eq. \ref{VV1} & \ref{VV2}) [1].</p>
-              In the special case of the TU Darmstadt and the next generations of iGEM competitors we have the idea to develop our technical equipment further from year to year and combining them. Our SLA printer from the last years competition was upgraded and is nearly ready for use again, giving us the possibility to manufacture parts for prototyping in our lab. Also this years project will serve as a starting point for the next years technical development team. New ideas and possibilities have been already discussed and we are looking forward to the next years competition.<br>
+					<p>
-            </p>
+					<center>
+					$$
-            <div class="verlinked" id="setup"><h5>SETUP OVERVIEW</h5></div>
+					\begin{equation}
-            <div class="this-is-printer">
+						r_{i}(t_{0} + \Delta t) = r_{i}(t_{0}) + v_{i}(t_{0})\Delta t + \frac{1}{2}a_{i}(t_{0})\Delta t^{2}
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+						\label{VV1}
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+						\begin{equation}
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+							\label{VV2}
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-      <div class="description abstract"></div>
-      <!-- Hier kommen die Texte (ruhig auch HTML) fuer die einzelnen Parts rein (zwischen die tags <li data-part=PART> und </li>) -->
-      <ul class="description-text" style="display:none;">
-        <li data-part="default">Default Text</li>
-        <li data-part="x-y-axis">Text fuer x-y</li>
-        <li data-part="z-axis"><span style="color: red;"><b>Text fuer z</b></span></li>
-        <li data-part="optics">Text fuer optics</li>
-        <li data-part="syringepump">Text fuer syringepump</li>
-        <li data-part="chassis">Text fuer chassis</li>
-        <li data-part="electronics">Text fuer electronics</li>
-        <div class="verlinked" id="func"><h5>FUNCTIONALITY</h5></div>
-        The functionality of the pipetting robot comprises the three&#8209;dimensional agility of a 3D-printer, the possibility to pipet a specific amount of non natural amino acid (short:&nbsp;nnAA) using a syringe pump as well as intelligent visual object recognition so that it is able to distinguish between samples that require more nnAA from samples that still contain a sufficient amount.
-        With that said it is capable to autonomously keep alive the modified <i>E.&nbsp;coli</i> bacteria, given that it is activated and connected to a reliable power supply.<br>
-        To fulfill the task of keeping alive the bacteria it loops through a specially designed procedure. Initially the robot scans the internal space for samples by lighting the downside of the shelf space using infrared LEDs and monitoring the shadows of the placed reservoirs with a camera. If the contrast is sufficiently high, which is given due to isolation from light sources from outside, it is able to detect the edges of the mentioned reservoirs, fit a circle onto it and compute the distance between the reservoir and the camera itself. Furthermore it is possible to put an entire rack of reservoirs under observation due to its ability to recognize even rectangles.<br>
-        Shortly after the detection of the samples the distance data is transferred to the 3D control and the head of the robot moves in direction of the first reservoir. To check whether the bacteria needs more nnAA the robot uses the fluorescence of the protein mVenus that has been inserted into the bacteria. Therefore the robot excites the protein via high power LEDs and detects the emitted photons. To exclude reflected light from the LEDs that would disturb the measurement a longpass filter cuts of the spectrum below the emission peak of the protein. In dependence of the fluorescence signal the robot decides whether it is necessary to pipet nnAA onto the sample. If that's the case the robot moves the samples in z-range just so that the syringe reaches the sample and is able to securely add the nnAA.<br>
-        Eventually the robot recommences the procedure described above, except for the scanning of the individual positions of the samples, which are saved temporarily until all samples are checked. As long as the robot is activated, connected to a power supply and the syringe pump does not run out on nnAA the robot will loop through this whole process and keep the bacteria alive without a need of human interaction.
-        Nevertheless it is possible to check what the robot is doing via a livestream of the camera visible on the graphical user interface, since there is no other opportunity to look inside the robot itself while it is working.
-        <br>
-        <div class="verlinked" id="achie"><h5>ACHIEVEMENTS</h5></div>
-        <p><ul>
-          <li>Successfully redesign a 3D printer chassis to meet our requirements</li>
-          <li>Construct a unique base platform with integrated IR LEDs for measuring and positioning purposes</li>
-          <li>Design a measuring probe with a camera device with an integrated optical filter system and LEDs</li>
-          <li>Construct a syringe pump system to add liquids down to µl accuracy</li>
-          <li>Implementing a unique GUI to run our program featuring a multi threading system optimizing the overall performance</li>
-          <li>Implementing an automatic object tracking system including a vector based feedback system for positioning</li>
-          <li>Connecting a Raspberry Pi with an Arduino Micro controller by establishing a serial connection between the two devices, allowing a variety of different tasks</li>
-          <li>Data of all CADs designed by the TU Darmstadt technical department</li>
-          <li>A complete <a href="#build">build instruction</a> including a <a href="#bom">BOM</a> (Bill of Materials incl. prices) and a step by step video tutorial</li>
-        </ul></p>
-        <div class="verlinked" id="mech"><h5>Mechanics</h5></div>
-        <div class="verlinked" id="optics"><h5>Optics</h5></div>
-        <p>
-          <div class="verlinked" id="wave"><h6>Operating range of wavelengths</h6></div>
-          The robot optics consists of two big components, a camera head, and a lightbox.
-          The camera head is responsible for two tasks, which are the detection and localization of cuvettes, and the fluorescence measurements.
-          The light table illuminates the sample table uniformly from below, thereby aiding the camera to reliably do the detection work.
-          The fluorescence measurement and object detection are separated in terms of their operating range of wavelengths.
-          All the detection occurs at wavelengths above 860nm, which is near infrared.
-          The light table radiates uniform infrared light, while the camera chip is capable of capturing this wavelength.
-          There is nothing special to the camera chip. Actually all commercially available CCD-Chips can potentially capture near infrared, but this is usually an undesirable feature for photographic purposes,
-          since it falsifies image colors, at least from a human point of view. This is why camera lenses are usually equipped with an infrared filter.
-          In our case, we use our own lens system, where we removed the infrared filter.
-          The reason why we chose the detection to operate at infrared is because we are mainly dealing with GFP, which does not absorb infrared.
-          Otherwise, over a long time of illumination during periods of detection the fluorescent proteins would bleach out unnecessarily.
-          Now, if we take a look at the camera head, there is also a slight spectral separation: The GFP’s are stimulated at wavelengths lower than the emission wavelengths.
-          The stimulation occurs at a central wavelength of 465&nbsp;nm, while the emission takes place at a central wavelength of 525&nbsp;nm.
-          The reason for this separation is, that we use continuous rather than pulsed stimulation.<br></p>
-          <p>
-            <div class="verlinked" id="fluor"><h6>Fluorescence measurement and filtering</h6></div>
-            For pulse measurements there is a need for advanced high frequency circuitry, which is capable of forcing the LEDs to emit pulse lengths of picoseconds.
-            LEDs have rise and fall times in the nanosecond region, if they are used in a simple on/off manner.
-            For continuous measurements there are just two interconnected selections to be made: The wavelength of stimulation, and a corresponding optical filter.
-            In our case it is a long pass filter with a cutoff wavelength of 515nm.
-            It is capable of blocking most of the stimulation light, while letting GFP emission pass. The camera captures a long-exposed image to be further analyzed.
-            To get rid of the residual stimulation light appearing in that image, the image is digitally color-filtered, and segmented into regions of interest (ROI).
-            The determination of ROIs occurs simultaneously with the detection of cuvettes.
-            The filtering is very strong, and does indeed block some of the already weak GFP fluorescence.
-            This is why we use an exposure time of 10 seconds for a fluorescence capture, to make sure enough data is collected.</p><p>
-            <div class="verlinked" id="cam"><h6>Optical Hardware - Camera Head</h6></div>
-            We are using the 8 megapixels PiCamera, because we have access to its capturing settings like framerate,
-            exposure time, gains, light sensitivity etc. over existing Programming interface [1],
-            which is absolutely necessary since detection and measurement have totally different requirements.
-            Another benefit is, that we are able to capture directly in grayscale (Y part of YUV) for fast detection purposes, and switch to RGB when doing
-            fluorescence measurements. We don't have these degrees of freedom with an usual USB camera. The bad thing is, the stock camera itself is equipped
-            with a very minimal lens system. Since detection and measurement not only occur at different wavelengths, but also at different distances to the vessels
-            (fluorescence images are taken from each single cuvette, while the camera head is directly placed over its opening), there is a need for adjusting the focus.
-            We have therefore developed a focusing system consisting of a so called voice coil, which inhabits a 3D printed adapter socket for the PiCamera.
-            The adapter socket also harbors the optical longpass filter. The voice coil holds a suspended lens, which can be adjusted in its distance to the camera chip.
-            This method is used in most smartphones. In our case, we salvaged our voice coil out of an old webcam.
-            The voice coil is fed with a PWM signal provided directly by the Raspberry Pi's hardware PWM channel.
-            We use a simple L297 H-Bridge Stepperdriver to amplify the PWM signal, and to decouple the Raspberry Pi's precious hardware PWM pin.
-            Different duty cycles mean different focal positions. The coil current is tuned with a potentiometer.
-            In this way we are able to automatically focus the lens by evaluating simple Sobel-filter-based sharpness measurements.
-            Our autofocus is finding best sharpness within 2 seconds, using a robust global search algorithm.
-            It is applied every time a new set of racks and cuvettes is placed into the robot, i.e. prior to each new session.
-            Also, to adjust the focus for individual fluorescence captures, the sharpness of the individual cuvette corners is considered.
-            The camera head also harbors the stimulating LEDs, which are 4 high Power Cree XTE, driven by a 0.9 amp
-            current source and a PWM signal delivered by the Raspberry Pi.
-            <br>
-            <div class="verlinked" id="lightbox"><h6>Optical Hardware - Lightbox</h6></div>
-            The lightbox is an essential part of the detection. All applied detection algorithms rely on thresholding the image,
-            or filtered versions of it. The thresholding is basically doing a binary selection of relevant vs. irrelevant image information.
-            But with thresholding there is always a loss of relevant image information. If there is less clutter in the image,
-            then there is no need to use strong thresholds, therefore conserving more of the relevant image information.
-            The lightbox is acting as a clean background, creating only low amount of static noise and clutter due to its uniform radiation of light,
-            allowing to use less strict thresholds. It also emphasizes the vessel corners. This enhances detection reliability beyond comparison.
-            The heart of the lightbox is a Plexiglas panel called “Endlighten”.
-            Light is laterally injected, and reflected off systematic impurities inside the panel [2].
-            The light then leaves the panel uniformly in all directions.
-            Light leaving the panel back side is mirrored to the front side by a white reflective Plexiglas,
-            and additionally diffused by a diffusor plate, also made of Plexiglas. All Plexiglas panels are products of Evonik, the original.
-            The light is injected by flat-end infrared LEDs which are mounted on 3d printed rails and tightly clamped to the sides of the
-            Endlighten panel. The LEDs are driven by constant current sources to give them a hopefully long lifetime.
-          </p>
-          <p>References<br>
-            [1]: <a href="https://picamera.readthedocs.io/en/release-1.12/">https://picamera.readthedocs.io/en/release-1.12/</a><br>
-            [2]: <a href="https://www.plexiglas-shop.com/pdfs/en/212-15-PLEXIGLAS-LED-edge-lighting-en.pdf">https://www.plexiglas-shop.com/pdfs/en/212-15-PLEXIGLAS-LED-edge-lighting-en.pdf</a>
-          </p>
-          <div class="verlinked" id="cool"><h5>Cooling</h5></div>
-          All electronic components produce a significant amount of heat, especially the motor parts, power supply, and the Raspberry Pi.
-          Since the robot chassis is meant to be completely enclosed to keep light out, heat is going to pile up in the upper part of the interior sooner or later.
-          To protect the probes from temperatures above room temperature, it is necessary to include a cooling system, which ensures proper air circulation, and does not let in ambient light.
-          To fulfill these two requirements we decided to adapt a double-walled cooling system. The simplest implementation of it is based on the fact that warm air rises naturally, and incorporates the power supply as the air intake.
-          The power supply is placed on the bottom of the robot, and sucks in fresh air. The air, which is getting warmed up by the interior rises to the top and is being sucked out by a radial fan through an extractor hood, made of a laser&nbsp;cutted MDF grid.
-          The warm air in between the MDF grid and the outer wall is directed through a 3D&nbsp;printed exhaust tunnel. Thus, ambient light is being held out.
-          <div class="verlinked" id="softw"><h5>Software</h5></div>
-          <div class="verlinked" id="marl"><h6>Marlin</h6></div>
-          <div class="verlinked" id="opencv"><h6>OpenCV</h6></div>
-          <div class="verlinked" id="pyqt"><h6>PyQt</h6></div>
-          <p>Qt is a software tool to develop a GUI (Graphical User Interface). It is available under a commercial license and a open-source license. The software is a cross-platform application framework, which means it runs on the most computer systems like Unix or Windows. The underlying programming language is C++ and Qt can use already existing programming languages like Javascript, making it a powerful tool.<br>
-            The main idea of Qt is to use a system of signals and slots to have an easy framework to connect displayed elements with underlying functions. Also the re usability of already existing code is enhanced. Every graphical element, for example a button, emits its own signal when its pressed or used. The signal then can be used to trigger an action, for example closing a window. If the signal is not connected to a function nothing will happen, however the signal will be emitted with no consequences. Now it is possible to connect the emitted signal with a desired action, called slot, and the program gets its unique behavior.<br>
-            Qt is widely used by companies like the European Space Agency, Samsung, DreamWorks, Volvo and many more.
-            To be able to combine the possibilities of Qt with the simplicity of the Python programming language, PyQt was developed. PyQt is a binding for Python to be able to use the Qt methods within the Python syntax. <br>
-            To be able to get a direct preview of the constructed GUI, Qt Designer is a helpful tool. It is basically a constructing tool in which it is possible to use the objects as visible ones, making it possible to move them around and arranging them in the desired manner. To later work with the code itself, PyQt uses a method called pyuic(number) which is executed through the terminal. The number in the brackets stands for the version number.<br>
-            After converting the code one can open the GUI as a regular python script and work with it as usual. </p>
-            <p>
-              References:<br>
-              <a href="https://riverbankcomputing.com/software/pyqt/intro<br>">https://riverbankcomputing.com/software/pyqt/intro<br></a>
-              <a href="https://www.qt.io/">https://www.qt.io/</a><br>
-              <a href="https://en.wikipedia.org/wiki/Qt_(software)">https://en.wikipedia.org/wiki/Qt_(software)</a><br>
-            </p>
-            <div class="verlinked" id="develop"><h5>FURTHER DEVELOPMENTS</h5></div>
-            <p>Due to a tight time schedule from start to the end of iGEM it wasn't possible for us to to realize all ideas and planned developments in respect of improvement of the robot itself and further applications other than its current very specialized task.
-              First of all it should be mentioned that the current model of the robot is designed to work with only one kind of bacteria culture in virtue of the not solved problem of sterility. For a working process with more kinds of bacteria cultures it is absolutely indispensable to develop a system that is able to avoid all sorts of contamination between the different bacteria. Therefore it would be an option to have an extra reservoir filled with ethanol in which the tip of the syringe can be sterilized between the checks of different samples.
-              Another modification that would be useful for working with individual bacteria cultures is make the power LED's changeable. This is necessary if the the wavelength of the LED's does not overlap with absorption spectrum of the fluorescent proteins or overlaps with a part of the spectrum that has a very low absorption efficiency.
-              <br>Moreover, apart from the latter developments it may be useful to add one more syringe pump to the current setup, just so that it would be possible to remove liquid from the samples. Of course, this only makes sense, if the above mentioned idea of a sterility progress is implemented, due to the fact that the tip of the removing syringe has to be inserted into the liquid. And thus a contamination, in case of different bacteria cultures, would occur.
-              <br>Besides, a usage of the robot except for its “normal” tasks of observing bacteria would be a neat extension. For example a useful modification of the robot to a functional 3D-printer would be convenient, due to its setup that resembles an <i>Ultimaker 3D-printer</i>. Essential alterations would be to replace the sample stage with a heatbed and to replace the current head with a printhead hotend. Since the current head can be clipped it wouldn't be too much of a challenge. Furthermore, a change of the syringe extruder is necessary, if the printer should work with plastics.
-              An alternative approach is a kind of paste 3D-printer. In this case it wouldn't even be needed to change the head and the syringe, because of the already viscous properties of the paste.
-            </p>
-            <div class="verlinked" id="build"><h5>BUILDING INSTRUCTIONS</h5></div>
-            <div class="verlinked" id="vid"><h6>Construction Video</h6></div>
-            <div class="verlinked" id="bom"><h6>Bill Of Materials</h6></div>
-          </div>
-        </div>
-        <div class="rechts">
-          <div class="scrollbox">
-            <div class="highlights">
-              <a href="#intro">Introduction</a><br/>
-              <a href="#goals">Goals</a><br/>
-              <a href="#setup">Setup Overview</a><br/>
-              <a href="#mech">Mechanics</a><br/>
-              <a href="#optics">Optics</a><br/>
-              <a href="#cool">Cooling</a><br/>
-              <a href="#softw">Software</a><br/>
-              <a href="#achie">Achievements</a><br/>
-              <a href="#develop">Further Developments</a><br/>
-              <a href="#build">Building Instructions</a>
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-          }
-          function setDescription(group) {
+					<br/>The temperature of the system is directly correlated to the distribution of kinetic energies. Therefore the temperature of the system can be controlled by manipulating the atom velocities. A possible way to do this was proposed by Berendsen by coupling the system to a heat bath resulting in a NVT ensemble (eq. \ref{Berendsen}) [1].</p>
-            var desc = $('.description-text').find('[data-part='+ group +']').html();
+					<p>
-            $('.description').html(desc);
+					<center>
-          }
+					$$
+						\begin{equation}
+							a_{i}=\frac{F_{i}}{m_{i}} + \frac{1}{2 \tau_{T}} \left( \frac{T_{B}}{T_{t}} -1 \right) v_{i}
+							\label{Berendsen}
+						\end{equation}
+					$$
+					</center>
+					</p>
+					<h5 id="FFs">Empirical Force Fields</h5>
+					<p>Empirical Force 	Fields are the backbone of every Molecular Dynamics simulation. Typically the force fields are divided into two parts, bonded and nonbonded interactions. Bonded interactions consist of chemical bond stretching, angle bending, and rotation of dihedrals and impropers. Nonbonded interactions are approximated by Coulomb interactions (ionic) and Lennard-Jones potentials. The overall CHARMm (Chemistry at HARvard Macromolekular mechanics) potential is calculated by summing up these main potentials (\( V_{CHARMm} = V_{bonded} + V_{nonbonded} \)) [2,3,4].
+					<br/>
+					In equation \ref{CHARMM_bonded} and \ref{CHARMM_nonbonded} the bonded and nonbonded potentials of the CHARMm force field are displayed. All terms consist of an equilibrium value marked with \(0\) and a force constant \(K\) [2,3,4].</p>
+					<p>
+					<center>
+					$$
+						\begin{equation}
+						V_{bonded} = \sum_{bonds}{K_{b}(b-b_{0})^{2}} + \sum_{angels}{K_{\theta}(\theta-\theta_{0})^{2}} + \sum_{torsions}{K_{\phi}(1+cos(n\phi-\delta))} + \\ \sum_{impropers}{K_{\psi}(\psi-\psi_{0})^{2}} + \sum_{Urey-Bradley}{K_{UB}(r_{1,3}-r_{1,3,o})^{2}} + \sum_{\phi\psi}{V_{CMAP}}
+						\label{CHARMM_bonded}
+						\end{equation}
+					$$
+					$$
+						\begin{equation}
+							V_{nonbonded}=\sum_{nonbonded}{\frac{q_{i}q_{j}}{4\pi D r_{ij}}}+ \sum_{nonbonded}{\epsilon_{ij}\left[\left(\frac{R_{min,ij}}{r_{ij}}\right)^{12}-2\left(\frac{R_{min,ij}}{r_{ij}}\right)^{6}\right] }
+							\label{CHARMM_nonbonded}
+						\end{equation}
+					$$
+					</center>
+					</p>
+					<p>The additional terms CMAP and Urey-Bradley are correctional terms for backbone atoms and 1, 3 interactions respectively [2,3,4].</p>
+<h5 id="SimAn">Simulation Analysis</h5>
+					<p>Since the vast amount of data that is produced by Molecular Dynamics simulations it is essential to process the data into more accesible formats. To perform this task we applied several approaches like comparison of the solvent accesible surface area (SASA) over time.</p>
+					<h6 id="RMSD">Root Mean Square Deviation</h6>
+					<p>The Root Mean Square Deviation (RMSD) describes the sum of distances of all selected atoms \(n\) between themselves in a selceted timestep \(\tau\) and a reference timestep \(r\) (eq. \ref{RMSD}). Plotted over time it is possible to detect fluctuations in the whole molecular configuration and therefore it is possible to conclude structures of high stability from plateaus in the RMSD.</p>
+					<p>
+					<center>
+					$$
+						\begin{equation}
+							RMSD_{\tau}=\sqrt{\sum_{n=1}^{N}{\left((x_{\tau,n}-x_{r,n})^{2}+(y_{\tau}-y_{r,n})^{2}+(z_{\tau,n}-z_{r,n})^{2}\right)}}
+							\label{RMSD}
+						\end{equation}
+					$$
+					</center>
+					</p>
+					<p>
+					By choosing the right atom selection it is possible to evaluate the different behaviours of protein subgroups. For example, if the RMSD between C&alpha; atoms is calculated it is possible to plot the backbone movement over time and hence detect configurations that differ from the starting structure. This is important if one wants to search for different thermodynamically stable ensembles of the protein or molecule of interest.
+					</p>
+					<h6 id="RMSF">Root Mean Square Fluctuation</h6>
+					<p>Similar to the RMSD the Root Mean Square Fluctuation describes the sum of distances of all selected atoms. In this case the distance per atom between all selected configuartions is calculated and summed over time. Therefore it is possible to spot residues with strong mobility and consequntly residues that are part of fluctuating and disordered protein subunits.</p>
+					<p>
+					<center>
+					$$
+						\begin{equation}
+							RMSF_{n}=\sqrt{\sum_{\tau=1}^{T}{\left((x_{n}-x_{0})^{2}+(y_{n}-y_{0})^{2}+(z_{n}-z_{0})^{2}\right)}}
+							\label{RMSF}
+						\end{equation}
+					$$
+					</center>
+					</p>
+					<h6 id="DSSP">DSSP</h6>
+					<p><i>Define Secondary Structures of Proteins</i> (DSSP) by Wolfgang Kabsch and Christian Sander is a standard program to analyse secondary structure properties of proteins. The main idea to discriminate between different secondary structures is based on the presence of H&nbsp;bonds because this can be represented by one energy value. This definition enables the algorithm to distinguish different types of &alpha;&nbsp;helices, &beta;&nbsp;sheets, and turns.<br/>The electrostatic interations between two groups are calculated by assigning partial charges to each C (\(+q_{1}\)), O (\(-q_{1}\)), N (\(-q_{2}\)), and H (\(+q_{2}\)), with \(q_{1} = 0.42~e\) and \( q_{2} = 0.20~e\) and r(AB) being the distance between two atoms A and B in Angstr&ouml;m. An H&nbsp;bond is defined by \( E < -0.5~\frac{kcal}{mol}\) [5].</p><p>
+					$$
+						\begin{equation}
+							E = q_{1} q_{2} \left( \frac{1}{r(ON)} + \frac{1}{r(CH)} + \frac{1}{r(OH)} + \frac{1}{r(CN)} \right) 332~\frac{kcal}{mol}
+							\label{DSSP}
+						\end{equation}
+					$$
+					</p>
+<h5 id="BEC">Binding Energy Calculations</h5>
+<p>Alchemical Free Energy Perturbation (FEP) is a method in computational biology to obtain energy differences from molecular dynamics or Metropolis Monte Carlo simulations between two system states. In here the system is slowly transformed from state \(i\) to state \(j\) through non-natural intermediates which are sampled by slowly decreasing the intermolecular interactions. The core equation (eq. \ref{FEGG}) for the Helmholtz free energy difference between states \(i\) and \(j\) \(\Delta A_{ij}\) is derived from statistical mechanics. \(Q\) represents the canonical partition function, \(k_B\) the Boltzman constant, \(U\) the corresponding potential system energy in relation to the coordinates and momenta \(\vec{q}\), \(T\) the temperatur and \(\Gamma\) the volume of potential states of \(\vec{q}\) [16].</p>
-          function resetDescription(group) {
+<p>
-            setDescription('default');
+					$$
-          }
+					\begin{equation}
+						\Delta A_{ij} = -k_{B} T \frac{Q_{j}}{Q_{i}} = -k_{B} T~ln \left( \frac{\int_{\Gamma_{j}}e^{-\frac{U_{j}(\vec{q})}{k_{B}T}}d \vec{q}}{\int_{\Gamma_{i}}e^{-\frac{U_{i}(\vec{q})}{k_{B}T}}d \vec{q}}\right)
+						\label{FEGG}
+					\end{equation}
+					$$
+					<p>
+					To calculate free energy differences between states with low state space overlap a thermodynamic cycle can be constructed hence the Helmholtz free energy is a thermodynamic state function. The most straightforward way to calculate state transition free energy changes would be to simulate the naturally occuring process. For example the binding free energy between two proteins can be calculated by separating both proteins. This approach however has high computational costs since simulating the whole water filled box results in large systems.<br/>The alchemical perturbation approach relies on simulating several intermediate states over which Coulomb and Lennard-Jones interactions are slowly decreased. This is controlled via a coupling factor \(\lambda\) (eq \ref{lambda}). The resulting potential energy \(U\) at state \(\lambda\) is subsequently calculated as a sum of the two end states \(U_0\), \(U_1\) and all not decoupled interacions \(U_{unaffected}\) [16].
+					<p>
+					$$
+					\begin{equation}
+					U(\lambda,\vec{q}) = (1-\lambda)~U_{0}(\vec{q}) + \lambda~U_{1}(\vec{q}) + U_{unaffected}(\vec{q})
+					\label{lambda}
+					\end{equation}
+					$$
+					</p>
+					The overall free energy change \(\Delta A_{0,1}\) is consequently calculated as the sum over all free energy changes (eq. \ref{TC}).
+					</p>
+					<p>
+					$$
+					\begin{equation}
+					\Delta A_{0,1} = \sum^{1}_{\lambda=0} {\Delta A_{\lambda,\Delta \lambda}}
+					\label{TC}
+					\end{equation}
+					$$
+					</p>
+					<p>
+					Gibb's free energy differences between two &lambda; states can be calculated by equation \ref{Calc}.
+					</p><p>
+					$$
+					\begin{equation}
+					\Delta G~(\lambda^{'} \rightarrow \lambda^{"}) = -k_{B}T~\Bigg \langle exp \left( -\frac{U(\lambda^{"})-U(\lambda^{'})}{k_{B}T} \right) \Bigg \rangle
+					\label{Calc}
+					\end{equation}
+					$$
+					</p><p>
+					Interactions of molecules are represented by Lennard-Jones and Coulomb interactions. This can lead to problems when Lennard-Jones interactions are decoupled and charge interactions are still active. This ensemble will lead to a clashing of the molecules since the charges will attract each other without any form of 	antagonistic force. To avoid this problem, position restraints are added which have to be considered in the final calculation.<br/>In order to evaluate the simulations of the intermediate states and calculate the free energy difference between the end states several algorithms have been developed (e.g., Exponential Averaging (EXP) or Bennett Acceptance Ratio (BAR)). BAR computes the energy difference between two simulations generating the trajectories \( n_i \) and \( n_j \) with the corresponding potential energy functions \(U_i\) and \(U_j\). The free energy difference \(\Delta A_{ij}\) can then be written as in equation \ref{Bennett} where \(f()\) stands for the Fermi function (eq. \ref{Fermi}) [16].
+					</p><p>
+					$$
+					\begin{equation}
+						\Delta A_{ij} = k_B T ~ \left( ln \frac{\sum_j f(U_i - U_j + k_B T~ln \frac{Q_i n_j}{Q_j n_i})}{\sum_i f(U_j - U_i - k_B T~ln \frac{Q_i n_j}{Q_j n_i})} - ln \frac{n_j}{n_i} \right)+ k_B T~ln \frac{Q_i n_j}{Q_j n_i}
+						\label{Bennett}
+					\end{equation}
+					$$
+					</p>
+					<p>
+					$$
+					\begin{equation}
+						f(x) = \frac{1}{1 + e^{~\beta x}}
+						\label{Fermi}
+					\end{equation}
+					$$
+					</p>
+					<p>
+					The Term \(k_B T~ln \frac{Q_i n_j}{Q_j n_i}\) has to be approximated since it cannot be computed analytically. Equation \ref{Bennett2} describes the relation used by Bennett et al. to estimate the term. Once it has been determined the free energy difference can be calculated by equation \ref{Bennett3} [16].
+					</p>
+					<p>
+					$$
+					\begin{equation}
+						\sum_j f\left(U_i - U_j + k_B T~ln \frac{Q_i n_j}{Q_j n_i}\right) = \sum_i f\left(U_j - U_i - k_B T~ln \frac{Q_i n_j}{Q_j n_i}\right)
+						\label{Bennett2}
+					\end{equation}
+					$$
+					</p>
+					<p>
+					$$
+					\begin{equation}
+						\Delta A_{ij} = - k_B T ~ ln \frac{n_j}{n_i} + k_B T~ln \frac{Q_i n_j}{Q_j n_i}
+						\label{Bennett3}
+					\end{equation}
+					$$
+					</p><p>Later on Shirts et al. derived the BAR method by applying maximum likelihood techniques [16].<br/>Since common analysis methods in biochemistry often rely on titration, only dissociation (\(K_{d}\)) respectively association constants (\(K_{a}\)) can be concluded from experiments. Therefore the dissociation constants were calculated by using equation \ref{gibbs}.
+					</p>
+					<p>
+					$$
+					\begin{equation}
+						K_{a/d} = e^{-\frac{\Delta G}{RT}}
+						\label{gibbs}
+					\end{equation}
+					$$
+					</p>
+				<div class="verlinked" id="Mod_m"><h2 style="border-bottom:3px solid #019ac8; padding-top:80px;">METHODS</h2></div>
+					<h5 style="padding-top:0;">Visualisations</h5>
+					<h6>Colicin E2</h6>
+					<p>No obtainable 3D model of Colicin E2 was found in the Research Collaboration for Structural Bioinformatics (RCSB) Protein Data Bank (PDB) at the Brookhaven National Laboratory and the Protein Data Bank in Europe (PDBe) at the European Bioinformatics Institue (EMBL-EBI). Crystallographic structures of the DNase subunit of Colicin E2 and its bacterial import subunit were available. Therefore we chose to use homology modeling to obtain a 3D structure of Colicin E2. For homology modeling the <a href="http://www.sbg.bio.ic.ac.uk/phyre2/html/page.cgi?id=index">Protein Homology/analogY Recognition Engine V 2.0</a> (PHYRE<sup style="font-size: 12pt; vertical-align:baseline; position: relative; top: -0.4em">2</sup>) [17] server was used in combination with the amino acid sequence obtained from the Universal Protein Resource  (UniProt) Protein Knowledgebase (UniProtKB) entrance <a href="http://www.uniprot.org/uniprot/P04419">P04419</a>.<br/>The obtained model was based on the known subunits of Colicin E2 and Colicin E3, a close relative. Afterwards a CHARMm topology was produced via the pdb2gmx module of GROMACs 5.1.3 [6-15], the model was solvated in TIP3P water and energy minimized using the steepest descend algorithm. Afterwards we used PyMOL [18] to create molecular images.</p>
-          function hookClick(group) {
+					<h5>Force Field Parametrization</h5>
-            $(selectPart(group)).on('click', function() {
+					<p>A 3D model of <i>O</i>-methyl-<span style="font-variant: small-caps;">l</span>-tyrosine was created using Avogadro 1.1.1, and energy minimized using the steepest descend algorithm in vacuum. The so obtained model was subsequently parsed to the <a href="http://www.swissparam.ch/">SwissParam</a> [19] topology server. The created topology was then used to derive parameters for the CHARMm residue force field [2,3,4] so that for any protein with <i>O</i>-methyl-<span style="font-variant: small-caps;">l</span>-tyrosine a topology could be created. Since <i>O</i>-methyl-<span style="font-variant: small-caps;">l</span>-tyrosine is very similar to tyrosine most parameters could be adopted.<br/>CHARMm is an atom type based force field, meaning that every parameter is not dependend on the residue but on the assigned atom types taking part in the interactions. As a result we had to define several new atom types to account for the changed properties of the methyl ether since no other benzyl ether atoms could be found in the force field parameter files.</p><p>
-              if ((' ' + $(selectPart(group)).attr('class') + ' ').indexOf(' ' + 'selected' + ' ') > -1 ) {
+					<center><div class="bild" style="width: 80%;"><img src="https://static.igem.org/mediawiki/2016/f/f4/T--TU_Darmstadt--forec_field_style.png" width=100%><b>Figure 1:</b> Used atom names and types for the implementation.</div></center></p><p>
-                resetClasses();
+					To implement the newly derived parameters we had to update several force field parameter files that we gathered from the GROMACS&nbsp;5.0.4 software suite [6-15]. This was due to the case that all parameter files had to be compatible to the GROMACS software suite. First we had to implement the new amino acid in the <b>aminoacids.rtp</b> file which basically serves as a register for all known residues. The amino acid entry contains a three letter code by which it will be identified, all atoms with name, type and charge, all bonds between these atoms as well as impropers and CMAPs. Since the last two entries only concern the backbone atoms, we simply copied those entries. Atom charges were duplicated from tyrosine for all atoms that were not involved in the ether bond. The ether methyl group was represented by a standard methyl group with <i>CT3</i> carbon and <i>HA</i> hydrogen. This atom classes represent alanin's C&beta; and the C&delta; atom of methionin.<br/>A new atom class named <i>OE</i> was introduced to represent the ether oxygen since there are no ether oxygen parameters for amino acid residues in the CHARMm force field files. We used parameters from the generated topology file to derive parameters for all interactions from the <i>OE</i> atom type. To implement these parameters we updated the <i>bondtypes</i>, <i>angletypes</i>, and <i>dihedrals</i> in the <b>ffbonded.itp</b> file. Similarly, we updated the <b>ffnonbonded.itp</b> file sections <i>atomtypes</i>, and <i>pairtypes</i>. Subsequently we added an <i>OE</i> entry to the <b>atomtypes.atp</b> file.<br/>CHARMm simulates aromaticity through dummy atoms which will be calculated automatically. To achieve this for our new amino acid we updated the <b>aminoacids.vsd</b> file and inserted every bond length and angle. Finally we had to assign a three letter code to represent our amino acid in the topology and structure files. We chose <b>OMT</b>. This resulted in the empirical force field CHARMm&nbsp;27&nbsp;OMT.
-                resetDescription();
+					</p>
-              } else {
-                resetClasses();
-                setDescription(group);
-                $('[id^=printer_]').not(selectPart(group)).attr("class", "not-selected");
-                $(selectPart(group)).attr("class", "selected");
-              }
-            });
-          }
-          function hookHover(group) {
+					<h5 id="MDS">Molecular Dynamics Simulations</h5>
-            $(selectPart(group)).on('mouseover', function() {
+					<p>3D structures of the Colicin E2 DNase subunit (miniColicin) and its immunity protein were obtained from the RCSB PDB entrance <a href="http://www.ebi.ac.uk/pdbe/entry/pdb/3U43">3U43</a> [20]. Since the main binding occurs between the DNase subunit and the immunity protein only this Colicin E2 subunit was simulated. Furthermore we established a minimized Colicin E2 in <a href="">another project part</a> and wanted to test its operational capability. <br/>To insert mutations inside the immunity protein we inserted the energy minimized structure of OMT at the desired position. Positions of backbone atoms were fitted to those of the replaced amino acid so that the backbone integrity was preserved. This was achieved through the implementation of Kabsch's algorithm for structural alignments in the <a href="http://thegrantlab.org/bio3d/index.php">Bio3D package</a> [21-23] for the <a style="padding-right:0;" href="https://www.r-project.org/">statistical computing language R</a> [24]. Additionaly we used Bio3D's pdb processing package to separate Colicin E2 DNase subunit and its immunity protein.<br/>All molecular dynamics simulations were performed with the <a href="http://www.gromacs.org/">GROningen MAchine for Chemical Simulations</a> (GROMACS) 5.0.3 [6-15] software suite. As empirical force field CHARMm&nbsp;27&nbsp;OMT was used. An explicit water model with TIP3P water was chosen. The box was subsequently filled with water and the system was neutralized through insertions of chloride ions. After neutralization the system was energy minimized with the steepest descent algorithm until it converted. To generate velocity and temperate the system a small equilibration run of about 500&nbsp;ps was performed. The end temperature was set to 298&nbsp;K and the Berendsen thermostat and the velocity-Verlet integrator with a stepsize of 2&nbsp;fs were used. After this equilibration run a NVT ensemble was achieved. To achieve a NPT ensemble the equilibration run was repeated with applied pressure coupling to 1&nbsp;bar. Subsequently the final MD production run was performed. Every 5000st step was saved resulting in a trajectory of 10001 conformations ranging over 100&nbsp;ns simulation time.</p>
-              addClass($(selectPart(group)), 'hovered');
-            });
-            $(selectPart(group)).on('mouseout', function() {
-              removeClass($(selectPart(group)), 'hovered');
-            });
-          }
-          function init(){
+					<h5>Molecular Dynamics Simulations Analysis</h5>
-            resetClasses();
+					<p>Simulation Analysis was performed using the R [24] package Bio3D [21,22,23]. All plots were created using the R package ggplot2 [25]. For visualization of protein structures and trajectories the PyMOL visualization system [18] was used. To compensate for eventual jumps due to translations across the PBC barriers a GROMACS internal fitting program was applied (<i>gmx trjconv -center -pbc nojump</i>). To exclude translational and rotational movement of the simulated protein we applied the GROMACS internal fitting algorithms <i>gmx trjconv -fit rot+trans</i>. These trajectory manipulations were performed because several analysis methods like <a href="Theory.html#RMSD">RMSD</a> and <a href="Theory.html#RMSF">RMSF</a> rely on distance calculations between atom positions over time. In these analyses the translational and rotational movements are not of interest since we only want to visualize the movement of atoms in relation to the simulated protein to test for different configuarations and structural flexibility. Additionally the crossing of PBC barriers would increase the distance between two atom positions drastically since the atom would be relocated to the opposing site of the simulated system.</p>
-            resetDescription();
-            parts.forEach(hookClick);
-            parts.forEach(hookHover);
-          }
-          init();
+					<h5>Binding Energy Calculations</h5>
-        });
+					<p>Binding energies were calculated by using <a href="#BEC">alchemical Free Energy Perturbation</a> (FEP) in combination with Bennett Acceptence Ratio (BAR). A thermodynamical cycle was constructed (see fig. 2) and accordingly two simulation sets were performed. First, Colicin E2's immunity protein was simulated in TIP3P water with 0.6&nbsp;nm space between the box and the protein. Furthermore, Lennard-Jones potential and Coulomb interactions were decoupled over ten simulations, each resulting in 20 simulations in total. The simulations were energy minimized over approximately 300&nbsp;steps, NVT equilibrated over 10&nbsp;ps and NPT equilibrated over 100&nbsp;ps. The production run was performed for 2&nbsp;ns. Second, the binding complex consisting of Colicin E2 and its immunity protein was simulated under similar conditions i.e. equilibration and simulation times, and steps were chosen alike. In contrast to the immunity protein simulations additional restraint decoupling steps were performed over ten simulations before the other steps. All simulations were evaluated using the BAR scripts from the <a style="padding-right:0;" href="https://github.com/choderalab/pymbar">pyMBAR python library</a>.</p></p>
-      </script>
+				</p>
-    </body>
+				<div class="verlinked" id="Mod_r"><h2 style="border-bottom:3px solid #019ac8; padding-top:80px;">RESULTS &amp; CONCLUSION</h2></div>
-    </html>
+<h5>Molecular Dynamcis Simulations</h5>
+<p>Three amino acid positions were chosen for <i>O</i>-methyl-<span style="font-variant: small-caps;">l</span>-tyrosine (OMT) exchange evaluation (tyrosine 8 (Y8), phenylalanine 13 (F13) and phenylalanine 16 (F16)). These positions were selected because of their small deviation in regard to OMT and were therefore expected to cause the smallest structural differences. All molecular dynamics steps were performed on these mutation variants, as well as on the wildtype protein for comparison. All simulations were performed over 100&nbsp;ns, leading to 10001 conformations each. These conformations were evaluated using RMSD, RMSF, SASA and the amount of secondary structures over time.<br/>Figure 2 displays the RMSD in regard to the initial conformation. It can be observed that the mutational variant Y8O exhibits similar curve characteristics as the wildtype variant. The mutational variant F16O on the contrary shows a more severe deviation from the wildtype.</p>
+<p>
+<center><div class="bild" style="width:70%;"><img src="https://static.igem.org/mediawiki/2016/8/81/T--TU_Darmstadt--RMSDc.png" width=100%><b>Figure 2:</b> RMSD of the mutation variants Y8O (green), F16O (blue) and the wildtype (red).</div></center>
+</p>
+<p>
+The solvent accessible surface area (SASA) was calculated for every simulation step using DSSP and is displayed in figure 3. The little to no fluctuation in the SASA of all simulated variants is an argument for the high structural stability of the wildtype and the mutational variants. The disparity between the mutational variants and the wildtype can be traced back to the DSSP algorithm since it is based solely on natural amino acids. Therefore it cannot evaluate a non-natural amino acid and would cause a discrepancy between surface areas if non-natural amino acids like OMT are involved.
+</p>
+<center><div class="bild" style="width:70%;"><img src="https://static.igem.org/mediawiki/2016/1/16/T--TU_Darmstadt--SASAc.png" width=100%><b>Figure 3:</b> SASA of the mutation variants Y8O (green), F16O (blue) and the wildtype (red).</div></center>
+</p>
+<p>
+Additionally we evaluated the RMSF and the amount of secondary structures over time which exhibited no differences between the mutational variants and the wildtype. Therefore the results of these evaluation methods are not shown on this wiki.<br/>Closing up we can conclude that the mutational variant Y8O does fit our demands best, since its behavior exhibits the least disparity in our applied evaluation methods towards the wildtype. Therefore Y8O was chosen for further analyses.
+</p>
+<p>
+Furthermore we evaluated the stability of our designed miniColicin by performing 100&nbsp;ns of MD simulations with different force fields (CHARMm27, AMBER03, GROMOS56a7). The RMSD of these simulations is displayed in figure 4. It can be observed that some deviations between the different force fields occur. The simulation run with the GROMOS56a7 shows the biggest discrepancy towards the AMBER and CHARMm simulations which display little to no fluctuations over time. This behavior can be traced to the different parametrization approach in the force fields as well as to the fact that the GROMOS56a7 force field is a united atom force field, in which all CH<sub>3</sub> and CH<sub>2</sub> groups are described as one group.
+</p>
+<p>
+<center><div class="bild" style="width:76%;"><img src="https://static.igem.org/mediawiki/2016/3/31/T--TU_Darmstadt--RMSD.png" width=100%><b>Figure 4:</b> RMSD of miniColicin simulated using the the force fields CHARMm27 (red), AMBER03 (blue) and GROMOS56a7 (green).</div></center>
+</p>
+<h5>Binding Energy Calculations</h5>
+<p>To obtain the binding energy between miniColicin and the immunity protein we simulated 20 &lambda; states per thermodynamic step. The coupling factor &lambda; has been variated ina range of 0 to 1 in steps of 0.2 for Coulomb, 0.05 and 0.1 for the Lennard-Jones interactions respectively. Unfortunatly, a computation of a full set of simulations could not be achieved. This was due to unknown errors, inferior debugging abilities, malformed error messages recieved from the GROMACS simulation package [6-15] and temporal as well as computational limitations. In this context it was only possible to evaluate a scaling of Lennard-Jones potentials in the range from 0.9 to 1.0 with completely coupled Coulomb interactions. We tested simulations for different immunity protein variants on different computer systems (workstation and server) with the results being the same. Therefore, it seems appropriate to assume that the unknown error occured due to systematic problems. For example, instabilities in the simulated systems or badly implemented features could account for thus errors. Because of insufficient debug information provided by error messages we have not been able to debug the error and are consequently unable to present calculated data.<br/>It should be evaluated wether this behavior is a singular event or an indication for a major underlying fault within the implemtation. If so an evaluation of the configuration space seems to be in order. Furthermore, a comparison against alternative simulation frameworks is most likely imperative for future work.</p>
+			    <p>
+		    </div>
+<div class="references"><h6>References</h6>
+            <ul><li>[1] Gonz&agrave;lez, Force fields and molecular dynamics simulations, Les journ&eacute;es de la Diffusion Neutronique (JDN), vol. 12,pp. 2011</li>
+<li>[2] R. B. Best et al., Optimization of the Additive CHARMM All-Atom Protein Force Field Targeting Improved Sampling of the Backbone phi, psi and Side-Chain chi1 and chi2 Dihedral Angles, Journal of Chemical Theory and Computation, 8: 3257-3273., 2012</li>
+<li>[3] A.D. Jr. MacKerell, M. Feig, C.L. III Brooks, Extending the treatment of backbone energetics in protein force fields: limitations of gas-phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations, Journal of Computational Chemistry, 25: 1400-1415., 2004</li>
+<li>[4] A.D. Jr. MacKerell et al. All-atom empirical potential for molecular modeling and dynamics Studies of proteins, Journal of Physical Chemistry B,  102, 3586-3616.,1998</li>
+<li>[5] Wolfgang Kabsch and Christian Sander, Dictionary of Protein Secondary Structure: Patter Recognition of Hydrogen-Bonded and Geometrical Features, Biopolymers, Vol.22, 2577-2637, 1983</li>
+<li>[6] Berendsen, et al., GROMACS: A message-passing parallel molecular dynamics implementation, Comp. Phys. Comm. 91: 43-56.1995, 1995</li>
+<li>[7] Lindahl, et al., GROMACS 3.0: a package for molecular simulation and trajectory analysis,  J. Mol. Model. 7: 306-317., 2001</li>
+<li>[8] van der Spoel, et al., GROMACS: Fast, flexible, and free, J. Comput. Chem. 26: 1701-1718., 2005</li>
+<li>[9] Hess, et al., GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation, J. Chem. Theory Comput. 4: 435-447., 2008</li>
+<li>[10] Pronk, et al., GROMACS 4.5: a high-throughput and highly parallel open source molecular simulation toolkit, Bioinformatics 29 845-854, 2013</li>
+<li>[11] P&agrave;ll, et al., Tackling Exascale Software Challenges in Molecular Dynamics Simulations with GROMACS, Proc. of EASC 2015 LNCS, 2015</li>
+<li>[12] Abraham, et al., GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers, SoftwareX 1-2 19-25, 2015</li>
+<li>[13] Wennberg et al., Lennard-Jones Lattice Summation in Bilayer Simulations Has Critical Effects on Surface Tension and Lipid Properties, J. Chem. Theory Comput., 9 3527–3537, 2013</li>
+<li>[14] Wennberg et al., Direct-Space Corrections Enable Fast and Accurate Lorentz–Berthelot Combination Rule Lennard-Jones Lattice Summation, J. Chem. Theory Comput., 12 5737–5746, 2015</li>
+<li>[15] P&agrave;ll, Hess, A flexible algorithm for calculating pair interactions on SIMD architectures, Comp. Phys. Comm.,184 2641-2650, 2013</li>
+<li>[16] Gerhard K&ouml;nig, Stefan Bruckner, Stefan Boresch, Unorthodox Uses of Bennett’s Acceptance Ratio Method, J. Comput. Chem., vol. 30, 1712-1718, 2009</li>
+<li>[17] Lawrence A Kelley,	Stefans Mezulis, Christopher M Yates, Mark N Wass & Michael J E Sternberg, The Phyre2 web portal for protein modeling, prediction and analysis, Nature Protocols, vol. 10, 845-858, 2015</li>
+<li>[18] The PyMOL Molecular Graphics System, Version 1.8 Schrödinger, LLC.</li>
+<li>[19] V. Zoete, M. A. Cuendet, A. Grosdidier, O. Michielin, SwissParam, a Fast Force Field Generation Tool For Small Organic Molecules, J. Comput. Chem, vol. 32(11), 2359-68., 2011</li>
+<li>[20] J.A. Wojdyla , S.J. Fleishman, D. Baker, C. Kleanthous, Structure of the ultra-high-affinity colicin E2 DNase--Im2 complex, J. Mol. Biol, vol. 417, 79-94, 2012</li>
+<li>[21] Grant, Rodrigues, ElSawy, McCammon, Caves, Bio3D: An R package for the comparative analysis of protein structures., Bioinformatics, vol. 22, 2695-2696 2006</li>
+<li>[22] Skj&aelig;rven, Yao, Scarabelli, Grant, Integrating protein structural dynamics and evolutionary analysis with Bio3D., BMC Bioinformatics vol., 15, 399, 2014</li>
+<li>[23] Skj&aelig;rven, Jariwala, Yao, Grant, Online interactive analysis of protein structure ensembles with Bio3D-web., Bioinformatics In press., 2016</li>
+<li>[24] R Core Team, R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria, <a href="http://www.R-project.org/.">URL</a>, 2014</li>
+<li>[25] H. Wickham, ggplot2: elegant graphics for data analysis, Springer New York, 2009</li>
+</ul></div>
+	    </div>
+		<div class="rechts">
+			<div class="scrollbox"><div class="highlights"><a href="#ThOv">Theoretical Overview</a><br/><a href="#Mod_m">Methods</a><br/><a href="#Mod_r">Results &amp; Conclusion</a></div>
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Difference between revisions of "Team:TU Darmstadt/Model"

Latest revision as of 03:19, 20 October 2016

MODELING

THEORETICAL OVERVIEW

Molecular Dynamics Simulation

Introduction

Assumptions

Empirical Force Fields

Simulation Analysis

Root Mean Square Deviation

Root Mean Square Fluctuation

DSSP

Binding Energy Calculations

METHODS

Visualisations

Colicin E2

Force Field Parametrization

Molecular Dynamics Simulations

Molecular Dynamics Simulations Analysis

Binding Energy Calculations

RESULTS & CONCLUSION

Molecular Dynamcis Simulations

Binding Energy Calculations

References