Team:Jilin China/Model
Model
In the modeling parts, we use bioinformatics tools (SignalP 4.1 Server, TMpred program and TMHMM) to assess the ability of Tmp1 and Sec2 to deliver apoptin across the cell membrane and simulate the three-dimensional structure of our proteins. Besides, we have applied two ecological models to study the interspecies relation between tumor cells and somatic cells, as well as the interspecies relation between tumor cells and bifidobacteria. Finally, we have established an ecological model to estimate the population curve of tumor cells and somatic cells when bifidobacteria are introduced into the tissue.
1.Models of signal peptides and protein structures
Prediction of signal peptides:
Through literature searching, we have identified two signal peptides, Tmp1 and Sec2, which might have the potential to facilitate the transmembrane of apoptin, and multiple bioinformatics tools have been applied to assess the ability of Tmp1 and Sec2 to deliver apoptin across the cell membrane (Figure 1).
Figure 1. The amino acid sequence of Tmp1 and Sec2Model
First, the presences of signal peptides and the location of signal peptide cleavage sites in Tmp1 and Sec2 are analyzed with the SignalP 4.1 Server. According to the analysis, the Tmp1 and Sec2 sequences that we chose are indeed signal peptides, which could deliver proteins across the cell membrane. Moreover, the location of cleavage sites in Tmp1 is between amino acid 26 and 27, and the location of cleavage site in Sec2 is between amino acid 34 and 35 (Figure 2).
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Next, the membrane-spanning regions and their orientation in Tmp1 and Sec2 were identified with TMpred program. Since the presence of transmembrance helixes is a classical feature of signal peptides, the presence of such structure in Tmp1 and Sec2 should be helpful to deliver apoptin across cell membranes. According to the results from TMpred analysis, Tmp1 and Sec2 both have possible transmembrane helixes. For Tmp1, the possible transmembrane helix is from amino acid 18 to 36. For Sec2, the possible transmembrane helix is from amino acid 12 to 28. Furthermore, the orientation of transmembrane for Tmp1 and Sec2 is predicted to be from bifidobacterium to extracellular environment (Figure 3).
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In addition, the hydrophobic domains in Tmp1 and Sec2 were analyzed with the TMHMM. Theoretically, all signal peptides should have highly hydrophobic domains. Therefore, presence of the hydrophobic domain of proteins is another important feature of signal peptides. The results from the analysis show that both Tmp1 and Sec2 have hydrophobic domains (Figure 4).
In summary, Tmp1 and Sec2 have multiple features as signal peptides that should have the ability to deliver apoptin across the cell membrane.
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1.2 Prediction of protein structures:
The protein structures of Tmp1-TAT-Linker-apoptin and Sec2-TAT-Linker-apoptin were constructed and simulated by the Phyre2 web portal and Hyperchem 8.0 for Molecular Dynamic Simulation. The Tmp1 and Sec2 domains are well separated from apoptin domain, which indicates that apoptin should not interference the function of Tmp1 and Sec2 as signal peptides.
2.Ecological Models
We assume that a part of human’s tissue can be considered as a miniature ecosystem, and tumor cells, normal somatic cells and bifidobacteria are three different species in such ecosystem. While normal somatic cells of the tissue can be viewed as the original species of the ecosystem, tumor cells can be treated as an invasive species. Based on the Lotka-Volterra Model, we can apply an ecology model to analyze the competition relation between tumor cells and somatic cells, and show the curve of population change with time. Based on the Holling Ⅱ Type Functional Reacting Model, we can apply an ecology model to study the predation relation between tumor cells and bifidobacteria, and show the curve of population change with time. Combining all of the relations among tumor cells, bifidobacteria and somatic cells, we can establish an ecological model to estimate the curves of population change of tumor cells and somatic cells when bifidobacteria are introduced into the tissue.
Model
2.1 The somatic cells - tumor cells relation model
Considering that the tumor cells act as an invasive species in the ecosystem and compete with somatic cell for resources, the competition model is an appropriate model to simulate the relation between tumor cells and somatic cells. Based on the Lotka-Volterra Model, we set〖 x〗_1 as the population of tumor cells, x_3 as the population of somatic cells. The differential equations show as follows.
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The modeling result shows that when ecological system is healthy, and the immune system can limit environmental capacity of tumor cells (N_1 in the equations above) in a low scope, somatic cells is the dominant species in body ecosystem, and tumors cannot expand. When the body ecosystem is defected and the body's immune system is weak, the value of N_1 increases and somatic cells have a lower survival advantage than tumor cell. Gradually, the number of somatic cells will decrease, and tumor cells become the dominant species. In that case, tumors expand.
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2.2 Bifidobacteria-tumor cells relation model
When the genetically engineered bifidobacteria is introduced into the tumor tissues, they secrete apoptin to induce the apoptosis of tumor cells. For tumor cells, bifidobacterium is as a predator in the tissue ecosystem. However, bifidobacterium is strictly anaerobic bacterium. When tumor cell population decreases, which is likely to cause the increasing of oxygen concentration in tissues, the growth of bifidobacterium is suppressed. Therefore, the relation between bifidobacteria and tumor cells is more likely to be a parasitic relation. Based on the Holling Ⅱ Type Functional Reacting Model, we establish a differential equations as follows.
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In this model, with the appropriate parameter, bifidobacteria can reduce the amount of tumor cells at the beginning. However, the population of bifidobacteria gradually drop as population of tumor cells decreases at the late phase, which indicates that bifidobacteria will not stay in the body ecosystem very long after tumor cells are eliminated.
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2.3 Tumor cell - bifidobacterium-somatic cell model
This model estimates the population curve of tumor cells and somatic cells after bifidobacteria are introduced into the tissue. We consider the tumor tissue as a homogeneous environment, which contains a great number of tumor cells and a small number of somatic cells. When a small amount of genetically engineered bifidobacteria parasitize in such tumor tissue, the relations among these three kinds of cells can be summarized as follows
(1) Tumor cells compete with somatic cells, and bifidobacteria prey on tumor cells.
(2) Bifidobacteria compete with somatic cells, restricted by oxygen.
(3) Somatic cells compete with tumor cells and bifidobacteria.
We establish differential equations as follows.
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From this model, tumor cells are killed by bifidobacteria and the population of tumor cells decreases. Then the growth of bifidobacteria will be restrained by the rising of oxygen concentration. When the population of competitors declines and the improvement of the environment, the population of somatic cells will constantly increase and reach to normal level finally. In this model, bifidobacteria can be used to kill the tumor cells and they will not stay for a long time in the tissue after tumor cells are eliminated.
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2.4 Parameters List
t: time
x_1: the population of tumor cells
x_2: the population of bifidobacteria
x_3: the population of somatic cells
r_1: the natural growth rate of tumor cells
r_2: the natural growth rate of bifidobacteria in best hypoxia condition
r_3: the natural growth rate of somatic cells
R_2: the death rate of bifidobacteria in nontumorous condition (the oxygen concentration is high )
N_1: the environmental capacity of tumor cells
N_2: the environmental capacity of bifidobacteria
N_3: the environmental capacity of somatic cells
m_1: the coefficient competition of somatic cells to tumor cells
n_1: the coefficient competition of bifidobacteria to tumor cells
n_2: the coefficient competition of tumor cells to bifidobacteria
L_2: the coefficient competition of somatic cells to bifidobacteria
L_3: the coefficient competition of bifidobacteria to somatic cells
m_3: the coefficient competition of tumor cells to somatic cells
a: the predation coefficient of bifidobacteria to tumor cells (related to the ability of apoptin to kill tumor cells)
b: unit adjust factor（adjustment for unit difference, take 1×10^9 as unit）
3. Cooperation with BIT-China team
This year we help BIT-China team construct and optimize model. The modeling part in the project of BIT-China team is to simulate the protein expression process by establishing the functional relations among protein concentration, time and other factors, such as the concentration of inductor, plasmid and so on.
Model
BIT-China team shares us the model structure and the original differential equations. We help BIT-China team finish the model optimization and establish two differential equations. In addition, we have simplified the differential equations to make the differential equations solvable. The original differential equations, simplified equations and the analytic solutions of two differential equations are shown as follows.
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The final analytic solutions:
