Difference between revisions of "Team:NCTU Formosa/Model"

The aim of this modeling was to predict and simulate the degradation rate of Pantide. Practically, the results would be integrated into our device to promote automatic control system. Once Pantide degraded below the effective level, it will spray the solution to replenish.

After discussion and experimental verification, we show that UV radiolytic oxidation contributes to the degradation of Pantide. We tried to build a model for simulating the relationship between applied UV light and degradation rate and then combined with UV intensity sensor to calculate the period of spraying Pantide.

For the proteins used as Pantide, the inhibitor cystine knot (ICK) is significant to their function. Pantide with several disulfide bonds is often more stable in solution. If “native protein” is denatured, it loses disulfide bonds and becomes a less stable form, normally called “linear protein,” which is easily degradable.

Recent research shows that the spider toxin proteins containing ICK structure, for example, ω-hexatoxin-Hv1a (Hv1a), have high stability against temperature, pH, solvents and protease. In contrast, when Hv1a is denatured to linear form, it loses its stability and then degrades rapidly. ^[1]

There are many possible processes of Pantide degradation we discussed below. (Figure 1) Pantide may have a chance to be reduced to a linear form by reductants or reductases. For both native form and linear form proteins, it may suffer hydrolysis and proteolysis, resulting in denaturing or amino acid cleavage. Also, UV light of sun also leads to Pantide degradation. Though the energy of UV light may not be not enough to break the covalent bonds efficiently, proteins still could undergo radiolytic oxidation.

Figure 1. Pantide degradation process

According to this degradation process, we attempted to build up our model. The degradation rate of Pantide is contributed by hydrolysis, proteolysis, UV radiolytic oxidation and the reduction to linear form. We considered that the rate Pantide transformed to linear form is a part of degradation rate because linear form protein loses its function and it is also likely to be degraded.

However, since the whole process is too complex to verify, we divided the experiment into three parts, hydrolysis test, proteolysis test and UV radiolytic oxidation test, and further summarized the results to conclude. The purpose is to find out the degradation rate of Pantide and to verify the less stable linear form protein has.

On the other hand, because ICK structure domain mainly contributes the stability of these proteins; we could assume that the degradation processes of three target proteins are roughly the same, for the reason that, we chose Hv1a and Hv1a with lectin (Hv1a-lectin) to demonstrate.

i. Theory

Like the reverse direction of polypeptide formation, proteins can be hydrolyzed into their constituent amino acids. The mechanism undergoes an E2 elimination since a nucleotide attach to sp2 hybridized acyl carbon (amide). [2] Therefore, the reaction rate depends on the concentration of both nucleotides and the protein:

Where, [P ] is the concentration of Pantide, K_h is the reaction constant of hydrolysis, and k_A , k_N , k_B are the three contributing components of overall hydorlysis which are dependent to condition.

For Pantide, we would apply the protein solution in the farm at a constant pH. Thus, the rate of hydrolysis is proportional to the concentration of Pantide by a constant K_h , and the concentration of Pantide undergoes an exponential decay as time goes on.

ii. Experimental proof

We tested the chemical stability of both native and linear types of Hv1a and Hv1a-lectin in neutral PBS solvent (phosphate buffered saline, pH=7.4) in 4 ℃; for one day and seven days. SDS-PAGE showed the remained protein concentration and calculated by software ImageJ. (Figure 2, Figure 3)

Figure 2. SDS-PAGE gel and the concentrations of hydrolysis test to Hv1a (5.3 kDa). The samples were marked on the top of the gel.

Figure 3. SDS-PAGE gel and the concentrations of hydrolysis test to Hv1a-lectin (HL, 17.1 kDa). The samples were marked on the top of the gel.

The difference of the concentration of native Hv1a was not significant during seven days (1 day: 98%, seven days: 87%), while linear Hv1a only remained 9% after one day, and almost all degraded after seven days.

The test to Hv1a-lectin showed the similar result. Native Hv1a-lectin nearly did not degrade in 7 days (1 day: 110% , 7 days: 105%), but linear Hv1a-lectin remained 16% after 1 day, 3% after 7 days.

So, we could conclude that native proteins dissolved in neutral PBS solvent did not undergo hydrolysis (or at a very slow rate) in 4℃ for seven days, on the other side, linear form proteins degrade as time went on, and remained merely little after seven days.

i. Theory

To simulate the degradation by protease, we used Michaelis-Menten kinetics model to express the rate equation. It is useful to describe enzymatic reactions, especially the one without ligand participation, such as proteolysis with proteases whose mechanism is first to find out the specific active site and then react to break it down. [3]

The proteolysis process is irreversible in vivo because the product, linear form protein, is degraded quickly. We used differential equation to describe the major proteolysis process:

Where [P ]: the concentation of Pantide, V_m,p : the maximum reaction rate of proteolysis, which is equal to the product of the concentration of total enzyme and turnover number k_cat of specific protease and substrate, K_M,p : Michaelis constant, which is the substrate concentration at which the reaction rate is half of V_m,p

We had assumed that the V_m,p is a constant because the proteases in vivo are in active and in equilibrium, and V_m,p represents the equivalent value for all kinds of protease in environment.

ii. Experimental proof

We designed two experiments to test the enzymatic stability towards protease of Hv1a and Hv1a-lectin. One was to observe the degrade level of both native and linear types of proteins applied by protease for one day, and the other one was to obtain the curve of the degradation rate of only linear form proteins in the period of four hours, because of the resistance against the protease.

For the first experiment, we dissolved the protein solutions in neutral PBS (pH=7.5) solvent, applied with 0.25% trypsin-EDTA(1:250), a serine protease, and then incubated the samples in work temperature 37℃ for one day. (Figure 4, Figure 5)

Figure 4. SDS-PAGE gel and the concentrations of trypsin resistance test to Hv1a (5.3 kDa). The samples were marked on the top of the gel.

Figure 5. SDS-PAGE gel and the concentrations of trypsin resistance test to Hv1a-lectin (HL, 17.1 kDa). The samples were marked on the top of the gel.

Compared with the sample incubated for one day without trypsin treatment, native Hv1a and Hv1a-lectin showed the resistance to trypsin protease (111% and 100%), but linear proteins were degraded by proteolysis (67% and 18%).

We next tested the proteolysis rate of only linear proteins in the period of four hours, and we drew the Lineweaver–Burk plot (also called “double reciprocal plot”) (Figure 6) to obtain V_m,p and K_M,p for linear form Hv1a and Hv1a-lectin. (Table 1)

Figure 6. Lineweaver–Burk plot of proteolysis test of linear Hv1a (blue line) and Hv1a-lectin (orange line). The horizontal axis represents the reciprocal of substrate concentration, and the longitudinal axis represents the reciprocal of rate. The straight line’s x-intercept means the reciprocal of -K_M,p , and y-intercept means the reciprocal of V_m,p .

Table 1. TheV_m,p and K_M,p of linear form Hv1a and Hv1a-lectin.

i. Theory

In nature, proteins are also probable to degrade under the sunlight, and the reason is that the energy of light excites the solvent (almost water) and initially generate radicals, which afterward propagate and attack protein to break it down until termination.

Ionizing radiation causes the radiolysis of water is, the major process is shown below. (Figure 7)

Figure 7. The radiolysis process of water.

Though the real mechanism that radicals attack to protein is quite complex, we can simply indicate the rate of protein been attacked by an unknown power, n, of the total concentration of radicals. Then we derived the rate formula as differential equations.

Where [radical ]: the total concentation of radicals, [P ]: the concentation of Pantide, G_γ : the dose rate of absorbing γ-ray (radiation energy absorption rate per mass, for water, 1.42 Gy/s) [5], A_γ : the number of radicals created per energy (for water, 0.045 μmol/J) [5], I : the intensity of UVB from sunlight measured by UV Sensor (UVM30A), R_T : the rate constant of radicals termination, which is equal to 2.365×10^-7 mol^-1 s^-1 [6], K_UV : the rate const ant of UV radiolytic oxidation to protiens, which is set to 44 mol^-1 s^-1 at the beginning [6]

We then used software MATLAB to simulate the degradation rate by UV radiolytic oxidation on the intensity of UVB from sunlight. The results showed that the degradation rate increases as rising intensity whatever n is, and eventually it tends to be fully degraded. (Figure 8)

Figure 8. The simulation of degradation rate by UV radiolytic oxidation on the intensity of UVB from sunlight.

ii. Experimental proof

We applied the four kinds of native protein solutions to the UVB light from UV transilluminator (302 nm, 50 mW/m² ) in the period of 2 hours, where the environment temperature was 36.8℃ in average. The results showed the six proteins degraded under UVB light treatment and the tendency of the reduction of proteins corresponded to our model. (Figure 9)

Figure 9. The degradation rate of four proteins by UV radiolytic oxidation as time goes on.

The degradation rates are obviously different between the protein with and without fusing to lectin. The possible reason we concerned was the difference in amino length; the longer protein has a relatively high probability to be attacked.

To determine the relation between the UVB light intensity and the degradation, we fit the result from experiments to our model. We calculated the parameter n in formula (4) must be equal to 0.78. The rate constant K_UV for Hv1a, Sf1a, OAIP 7.8 15.7and Hv1a-lectin are 2.4, 7.8, 15.7 and 90.3.

We also applied native Hv1a-lectin with another UV transilluminator (286 nm, 36.4 mW/m² ), and compared with the prediction from our model. (Figure 10)

Figure 10. The model prediction compared with the experiment data.

The figure showed our model is on the right way, but to accomplish our purpose; we still need more experiment data to correct the parameters.

The whole equation of degradation rate could be expressed by the summation of the rates of three possible degrade processes, that is hydrolysis, proteolysis, and UV radiolytic oxidation, and the rate that proteins transfer from native form to linear form indicated as R_SS

However, according to the previous experiments, if we only considered about the protein in native form, because of the high chemical stability and protease resistance, K_h and V_m,p is much smaller than K_UV , and the first two terms on the right side of the equal sign is relative insignificant. As for the reduction of disulfide bonds, since proteins are most stable in their favorable dimensional structure, it does not tend to break this strong bond down, so we assumed that R_SS is not contributed a lot for degradation in the nature. Then the equation was simplified to only one term.

and

As results, the degradation rate of Pantide mainly related to UV intensity expressed by (6) and (7). To verify our degradation rate model, and the practical use of our device, we had done the UV radiolytic oxidation test outdoor.

We put the samples on a wide square in a transparent and closed acrylic box outdoor for 4 hours at a different time in a day. Combined with UV intensity sensor, we got the remained protein concentration with the average UVB light intensity in each period. (Figure 11)

Figure 11. The remained protein concentration and the average UVB light intensity in each 4 hours at a different time in a day.

[1] Volker Herzig and Glenn F. King (2015). The Cystine Knot Is Responsible for the Exceptional Stability of the Insecticidal Spider Toxin ω-Hexatoxin-Hv1a. Toxins, 7, 4366-4380.

[2] Anonymous. (n.d.). HYDROLYSIS. Retrieved October 16, 2016 , from https://zh.scribd.com/document/79207692/Hydrolysis-2006

[3] Hedstrom, L. (2002, May 14). Serine Protease Mechanism and Specificity. Chem. Rev. 2002, 102, 4501-4523.

[4] Guozhong Xu & Mark R. Chance (2005). Radiolytic Modification of Sulfur-Containing Amino Acid Residues in Model Peptides: Fundamental Studies for Protein Footprinting. Anal. Chem, 77, 2437-2449.

[5] Mary E. Dzaugis, Arthur J. Spivack, Steven D'Hondt (2015, April 10). A quantitative model of water radiolysis and chemical production rates near radionuclide-containing solids. Radiation Physics and Chemistry, 115, 127-134.

[6] Bachari, T. S. (n.d.). Theoretical Investigation on The Kinetics of Free Radical Reactions of Styrene Emulsion Polymerization . Retrieved from http://www.iasj.net/iasj?func=fulltext&aId=13996