The computational chemistry study with the software GaussView and Gaussian provided us with these interesting results. The photos and difference between its complex is available at the Model page.

Table 1: Complexes between Cu, Glutathione, and Thiosulfate

Complex	ΔG (kcal/mol)	K constant
Cu-1	-81.76	4 * 1057
Cu-2	-69.07	5 * 1048
Cu-3	-48.62	2 * 1034
Cu-4	-29.90	1 * 1021

For the reaction: Thiosulfate-Cu + GS^- 🡪 GS-Cu + Thiosulfate

ΔG = -51.78 kcal/mol, K = 4 * 10³⁶

Table 2: Complexes between Ag, Glutathione, and Thiosulfate

Complex	ΔG (kcal/mol)	K constant
Ag-1	-26.74	7 * 1018
Ag-2	-29.53	7 * 1020
Ag-3	-41.44	2 * 1029
Ag-4	-5.83	1 * 104

For the reaction: Thiosulfate-Ag + GS^- 🡪 GS-Ag + Thiosulfate

ΔG = -35.61 kcal/mol, K = 1 * 10²⁵

Table 3: Complexes between Au, Glutathione, and Thiosulfate

Complex	ΔG (kcal/mol)	K constant
Au-1	-35.88	2 * 1025
Au-2	-63.49	7 * 1020
Au-3	-83.63	9 * 1058
Au-4	-61.48	2 * 1043
Au-5	-34.82	4 * 1024
Au-6	-19.74	8 * 1013

For the reaction: Thiosulfate-Au + GS^- 🡪 GS-Au + Thiosulfate

ΔG = -48.81 kcal/mol, K = 3 * 10³⁴

In addition to the previous research, we explored the effect of the oxidation of gold.

Table 4: Complex of Au(III) and Glutathione

Complex	ΔG (kcal/mol)	K constant
Au-7	-407.64	3 * 10287

For the reaction: Thiosulfate-Au + GS^- 🡪 GS-Au + Thiosulfate

ΔG = -48.81 kcal/mol, K = 3 * 10³⁴

In addition to the previous research, we explored the effect of the oxidation of gold.

The results and the comparisons are clear in the graph below.

Graph 1: Comparison of ΔG for each metal in pH 7 and 11

Results and Discussion

This study aimed to model and simulate the production and transport of Glutathione (GSH) between two containers connected by selective membranes with differing pore sizes. The system was designed to investigate the concentration dynamics of GSH under various experimental conditions, including production rates, membrane pore sizes, and fouling probabilities. By doing so, we hoped to gain insight into the behavior of small biomolecules in a controlled environment, which could provide valuable information for optimizing biochemical production processes.

Experimental Setup

The system consists of two 1-liter containers, A and B, each connected by membranes with specific pore sizes. Container A is linked to a membrane with a pore size of 0.65 nanometers, which allows GSH and smaller amino acids to pass through. Container B, on the other hand, is connected to a membrane with a smaller pore size of 0.45 nanometers, effectively blocking the passage of GSH while allowing amino acids to move freely between containers.

In this experiment, GSH is continuously produced in Container A at a rate of 0.00025 mol/L per minute. The system was designed to simulate the transport of GSH from Container A to Container B, based on the selective permeability of the membranes. The membranes’ fouling probabilities were also incorporated into the model, with fouling rates of 0.001/min for Membrane A and 0.0005/min for Membrane B. This setup allowed us to explore the dynamics of molecular transport and fouling under varying conditions.

Parameter Variation and Exploration

To explore the impact of different system parameters, we conducted experiments by varying the pore sizes of the membranes, fouling rates, and production rates of GSH. Initially, the base case involved a pore size of 0.65 nm for Membrane A and 0.45 nm for Membrane B, with a production rate of 0.00025 mol/L/min. We then experimented with different pore sizes and production rates to understand how these factors influenced GSH transport and membrane fouling.

For example, when we increased the pore size of Membrane A to 0.75 nm, we observed a faster accumulation of GSH in Container B due to the increased flux rate, while reducing the pore size to 0.55 nm slowed down the transport process significantly. Similarly, altering the fouling rates for both membranes helped us understand the long-term effects of membrane degradation on the system's efficiency. Higher fouling rates resulted in a slower accumulation of GSH in Container B over time, as the membranes became increasingly clogged and less effective in transporting molecules.

Membrane Fouling Probability Results

The first graph below illustrates the fouling probabilities of both Membrane A and Membrane B over time. As expected, Membrane A showed a higher fouling probability compared to Membrane B, owing to its higher base fouling rate of 0.001/min. Fouling probability for both membranes increased linearly over time, but at different rates. After 100 minutes, the fouling probability of Membrane A reached approximately 0.09, while Membrane B exhibited a fouling probability of around 0.06.

The linear growth of fouling probability is consistent with our model, which accounts for membrane degradation over time due to continuous usage. As fouling increases, the effectiveness of the membranes in transporting GSH and other molecules diminishes. This result suggests that the system will need maintenance or membrane replacement after extended periods of operation, especially in cases where high production rates are maintained.

GSH Concentration Dynamics

The second graph demonstrates the change in GSH concentration in both Container A and Container B over time. As shown, Container A experiences a rapid increase in GSH concentration due to the constant production of the molecule at a rate of 0.00025 mol/L/min. Initially, GSH concentrations in both containers start at zero, but as time progresses, Container A accumulates GSH at a much faster rate compared to Container B.

This discrepancy can be attributed to the selective permeability of the membranes, which favors the retention of GSH in Container A. After 120 minutes, the concentration of GSH in Container A reaches approximately 0.021 mol/L, while the concentration in Container B lags behind at 0.007 mol/L. These results align with our hypothesis that the membrane pore sizes and fouling effects significantly impact the overall efficiency of GSH transport between the containers.

Achievements and Insights

The key achievements of this study include the successful development of a dynamic model that accurately describes the transport and production of GSH in a membrane-based system. By experimenting with different parameters such as membrane pore size, fouling rates, and production rates, we were able to better understand the factors that influence the efficiency of GSH transport.

One of the main insights gained from this work is the critical role that membrane pore size plays in controlling molecular flux rates. Larger pore sizes lead to faster transport but may also increase the risk of membrane fouling, which can compromise the long-term functionality of the system. Moreover, the fouling rates for each membrane provide valuable information for predicting system maintenance needs, especially in large-scale industrial applications.

Overall, the results of this study have important implications for the design of biochemical systems involving selective molecular transport. By optimizing membrane characteristics and monitoring fouling over time, it is possible to enhance the efficiency and sustainability of systems used in industrial applications, such as bioremediation, biochemical production, and molecular separation processes.

Results and Discussion

This analysis aims to elucidate the dynamic behavior of the glutathione biosynthesis pathway by comparing the outcomes generated by two methodologies RRE and SSA. The python script implements the simulation of the chemical system we study, the glutathione biosynthesis, with reaction rate equation and stochastic simulation algorithm. the python script below simulates the evolution of the system over time assuming random numbers of molecules of the chemical species at the initial state. The number of molecules at the initial state at t=0s is a parameter that can be changed.

The goal here is to show the simulation process. This code can be very useful for wet lab members to simulate the system and calculate useful data (i.e. concentrations of the chemical species involved in GSH biosynthesis) saving resources and time. Also, this code can easily be transformed to simulate any other chemical system.

The plot above shows the evolution of the GSH biosynthesis chemical system over time. The left-hand side plot depicts the implementation of SSA algorithm for the chemical system and the right-hand side plot depicts the deterministic approach solving the RRE. The number of molecules of chemical species are initialized randomly with the values L-Glu=100, Cys=80, γ-GC=0, Gly=50.

At the right-hand plot that implements the deterministic approach, the lines are smoother than those from the left-hand plot. This is because of the RRE models the system using continuous, averaged concentrations of species, which are governed by ordinary differential equations (ODEs). The SSA models the system as a series of discrete reaction events that happen at random times. Instead of tracking continuous concentrations, the SSA tracks the exact number of molecules of each species, and reactions occur with certain probabilities.

Insights

The developed Python script successfully implements both the Stochastic Simulation Algorithm (SSA) and the Reaction Rate Equation (RRE) to simulate the biosynthesis of glutathione, capturing the dynamic behavior of the system with high fidelity. The script provides a comparative analysis between the deterministic and stochastic approaches, demonstrating the distinct advantages of each method. In particular, the RRE yields smooth, continuous curves, reflecting the average behavior of the system in scenarios where molecular populations are large, while the SSA captures the inherent randomness and fluctuations typical in smaller-scale systems. The simulation offers valuable insights into the kinetics of glutathione biosynthesis, highlighting the exponential-like behavior in product formation during the early stages due to enzyme-substrate interactions. Additionally, the script enhances our understanding of reaction dynamics, particularly how substrate availability and enzyme saturation influence the overall reaction rates. By combining both stochastic and deterministic frameworks, this tool provides a robust platform for exploring the complex biochemical pathways involved in glutathione production.

Results and Discussion

In this study, the aim is to investigate the thermostability of the glutathione synthetase enzyme (GshF) using computational approaches. By employing Python scripts, we calculate key structural properties such as B-factors and loop depths, which are critical indicators of protein flexibility and stability. These computational analyses are designed to provide insights into the relationship between the dynamic behavior of the enzyme's loops and its overall thermostability. The ultimate goal of this research is to identify structural features that could enhance the thermal resilience of GshF, which has potential implications for improving its functionality in industrial applications.

The depth of the loops,shown at the bar chart, has been calculated by comparing the spatial positions of residues in the loops to the overall center of mass of the protein. Firstly, we calculated the center of mass of the entire protein structure based on its atomic coordinates and then we calculated as the Euclidean distance between the center of the loop and the center of mass of the protein. The more buried the loops are, the more stable tend to be and play important role at the structure of the gshF.

The line chart shows the b-factors of residues in gshF. The b-factor for individual atoms within a residue can vary. By examining the b-factors of all atoms in a residue, one can assess the overall stability of that residue. The b-factor as a measurement for displacement of atoms within th crystal structure provide insights into the dynamic behaviour of the position of atoms in the residue. Low b-factor values indicate that the residue is relatively well-ordered and stable, while high b-factors indicate that the residue is more flexible and possibly unstable. Here we observe from the line chart that the b-factors show slight deviation and the values mainly are in the range from 0.7 Ų to 0.95 Ų

Below are shown arithmetic data, calculated from the python scripts, for the b-factor and the depth of the loops.

B-factors of loops of gshF enzyme

Loop Start Residue	Loop End Residue	Average B-Factor(Ų)
1	5	0.14
11	11	0.81
36	42	0.86
47	47	0.90
72	73	0.79
92	92	0.87
99	103	0.91
114	119	0.81
134	135	0.83
139	142	0.91
150	150	0.86
162	165	0.84
193	197	0.91
209	210	0.79
223	223	0.73
228	230	0.83
257	257	0.80
264	264	0.89
275	277	0.87
282	286	0.91
294	295	0.92
312	317	0.70
335	335	0.87
340	341	0.86
362	364	0.81
380	380	0.86
384	384	0.87
427	427	0.87
441	442	0.91
475	475	0.80
496	502	0.90
522	522	0.80
543	544	0.86
559	560	0.86
567	570	0.87
590	591	0.92
600	600	0.81
624	628	0.85
639	640	0.85
645	646	0.82
654	659	0.85
663	664	0.93
674	674	0.85
689	689	0.91
705	706	0.83
712	713	0.87
723	723	0.94
729	729	0.89
734	737	0.90

Depth of loops

Loop Start Residue	Loop End Residue	Estimated Depth (Å)
1	5	0.76
11	11	8.96
36	42	14.2
47	47	16
72	73	3.29
92	92	8.03
99	103	2.52
114	119	24.43
134	135	19.59
139	142	8.14
150	150	0.35
162	165	6.26
193	197	0.61
209	210	4.19
223	223	15.3
228	230	14.1
257	257	14.37
264	264	13.84
275	277	10.33
282	286	2.36
294	295	5.21
312	317	1.93
335	335	5.49
340	341	11.38
362	364	16.67
380	380	18.48
384	384	11.21
427	427	4.12
441	442	12.85
475	475	11.88
496	502	3.53
522	522	9.53
543	544	19.66
559	560	17.36
567	570	6.77
590	591	14.42
600	600	25.62
624	628	21.02
639	640	26.12
645	646	24.42
654	659	16.2
663	664	12.94
674	674	9.17
689	689	11.96
705	706	9.6
712	713	3.85
723	723	1.42
729	729	0.99
734	737	5.63

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It is easily understood from the charts and the tables above, that wild-type gshF is a very stable enzyme.

Insights and Future Goals

The insights gained from this study will pave the way for future investigations into the impact of single-point mutations on the thermostability and melting temperatures of the GshF enzyme. By systematically introducing mutations, we can explore how specific alterations in the protein structure affect its thermal resilience and stability. This research not only enhances our understanding of the relationship between amino acid composition and enzyme performance under thermal stress but also provides a framework for designing more robust enzymes for various applications. Ultimately, the findings could inform directed evolution strategies aimed at optimizing GshF for industrial processes, thereby contributing to advancements in enzyme engineering and biotechnological applications. The computational method we are gonna use to make single point mutations is to use Rosetta program to calculate the ΔΔG between the mutated enzyme and the wild-type. Negative ΔΔG leads to a more stable enzyme while positive ΔΔG mean that the mutation destabilized the enzyme’s structure and thus the thermostability did not possibly enhanced. Unfortunately, in the current stage we could not access to Rosetta to make single point mutations.