In our project, we have identified two main points which may affect the rate of activity in our system. The first point is the branching of pyruvate [as substrate] into two different cycles (Krebs and Isobutanol pathway). The other point is in gene expression (transcription, translation)of RuBisCO which is our rate controlling step [1]. Along with this we have also mathematically modeled ODEs for certain crucial steps in our cycle. RuBisCO reaction being the rate controlling reaction, plays an important role and the maintenance of its structure is a priority. As we have modified our genes of interest by codon optimization, we wanted to ensure that the structure of our insert has not changed from the native form of RuBisCO. To accomplish this, we have computationally modeled both the native and modified form of RuBisCO and compared their structure.
Our team has used COPASI to model enzyme kinetics due to the ease of adding user defined functions and altering resulting graphs. In our project RECOVER, one of the major points where rate is decided is the point where pyruvate
branches into two different cycles:
1) Krebs cycle and
2) Our engineered Isobutanol producing pathway.
Here, while there is one substrate, pyruvate, there are two enzymes. This means there exists competition for the substrate from two different enzymes. For general enzyme kinetics, we have many different kinds of inhibitory models such as competitive inhibition, non-competitive inhibition, un-competitive inhibition, etc. All these models describe competition between substrate or substrate like molecules. But, these are all studies on multiple enzymes competing for the same substrate[2]. We found literature stating that when multiple enzymes compete on the same substrate, the reaction velocity will be additive in nature[3]. Therefore we used the equation:
The following equation was added as a user defined function on COPASI for modeling purposes. There were three reactions modeled in total:
Note: While the pyruvate molecule variable is assigned as a separate entity in the enzyme competition equation, the pyruvate molecule defined in both the traditional equations are common and separate from the one
used in additive enzyme model. This was done to ensure proper comparison between the traditional system and the new additive model.
These reactions were used to target two key enzymes, pyruvate dehydrogenase producing
Acetyl CoA for krebs cycle and acetolactate synthase producing acetolactate for the isobutanol pathway.
The values for K and V were taken from sources such as literature papers as well as databases such as BRENDA.
| ENZYME | K cat[-] | Km[mM] | SPECIFIC ACTIVITY [mol/mg.min] | REFERENCES |
|---|---|---|---|---|
| Pyruvate Dehydrogenase | 0.515 | - | 0.445 | BRENDA |
| Acetolactate Synthase | 121 | 13.6 | - | Atsumi et al[4] |
Note: Values such as Km and Vmax required for the kinetic equations were calculated using the values found in the above mentioned references.
Red – [Acetolactate]; Light blue – [AcetyleCoA]; Green – [Pyruvate] Dark blue – [Pyruvate(OldM)]; Purple – [Acetolactate(OldM)]; Yellow – [AcetylCoA(OldM)]
From the above graph, we can come to the following conclusions:
RuBisCO being the slowest reaction in the Calvin cycle, is our rate controlling step. Therefore to more closely observe it, we have implemented a simple dynamic model of our gene expression using Simbiology in MATLAB. We have also included a provision regulatory mechanism (feedback inhibition) to control the gene expression[6]. This allows us to simulate various conditions and view our rate of expression and production. We also implemented a model with values both observed and calculated from existing literature.
In the above model we have considered that all the transcription, translation and degradation reactions are governed by 'mass action' laws. Most equations are irreversible forward reactions with the only exceptions being the regulatory mechanism reactions [k3 and rk3].
The above model was simulated on Model Analyzer in Simbiology and a plot was derived.
| MOLECULES | TRANSCRIPTION RATE [1/sec] | TRANSLATION RATE [1/sec] | AMOUNT [Molecules] | REFERENCES |
|---|---|---|---|---|
| DNA | 0.208 | - | 7 | Paul, J. H.[7] |
| mRNA | - | 104.16 | 0.25 | Paul, J. H.[7] |
Note: Some rates were derived through calculation from the values present in the literature work mentioned above.
A model with the above values was simulated on Model Analyzer in Simbiology and
a plot was derived.
From the above graph we can come to the following conclusion:
$${V= {V_{\text{max1}} \cdot [Xylose] \over (K_{\text{m1}} + [Xylose])}}$$
$${V_2 ={V_{\text{max2}}\cdot [Ru5P]\over (K_{\text{m1}} + [Ru5P])}}$$
The overall reaction rate, \(V_{overall}\), can be calculated as the product of the rates of these two consecutive reactions: \[V_{overall} = V_1 \cdot V_2\]
Now, substitute the rate equations for \(V_1\) and \(V_2\) into the overall rate equation:
$$V_{\text{overall}} = {V_{\text{max1}} \cdot [Xylose] \over {K_{m1} + [Xylose]}} \cdot {V_{\text{max2}} \cdot [Ru5P] \over {K_{m2} + [Ru5P]}}$$
This equation represents the overall reaction rate for the entire pathway from xylose to RuBP, considering both the xylose isomerase and PRK steps. The overall rate depends on the concentrations of xylose and Ru5P, as well as the kinetic parameters (\(V_{max1}\), \(K_{m1}\), \(V_{max2}\), and \(K_{m2}\)) of the enzymes involved.
This is the combined enzyme kinetics equation for the entire pathway, and you can use it to calculate the overall rate at specific substrate concentrations when you have the numerical values for \(V_{max}\) and \(K_m\).
To set up a differential equation to describe the change in the concentration of ribulose-1,5- bisphosphate (RuBP) over time, you need to consider the enzymatic reaction catalyzed by phosphoribulokinase (PRK), which converts ribulose-5-phosphate (Ru5P) to RuBP. The rate of change of RuBP concentration (\([RuBP]\)) over time can be described as:
$${d[RuBP]\over{dt}} = Rate$$
Where:\({d[RuBP] \over{dt}}\) is the rate of change of RuBP concentration with respect to time.
Based on the Michaelis-Menten equation for this step, you can express \({Rate}\) as follows: $${Rate} = {V_{\text{max}}\cdot [Ru5P] \over{K_{\text{m}} + [Ru5P]}}$$ Here, Rate is the rate of the enzymatic conversion of Ru5P to RuBP by PRK. So, the differential equation describing the change in the concentration of RuBP over time is: $${d[RuBP]\over {dt}} = {V_{\text{max}}\cdot [Ru5P] \over{K_{\text{m}} + [Ru5P]}}$$ This equation represents how the concentration of RuBP changes with time because of the enzymatic conversion from Ru5P catalyzed by PRK.
\[CO2 + RuBP \xrightarrow{k_1} 2(3-phosphoglycerate) (3-PGA)\]
Simplified model for CO2 uptake that includes some key equations: 1. Rubisco Reaction - Rubisco catalyzes the carboxylation of ribulose-1,5-bisphosphate (RuBP) using CO2: \[CO2 + RuBP \xrightarrow{k_1} 2(3-phosphoglycerate) (3-PGA)\] where \(k_1\) is the rate constant for this reaction. 2. RuBP Regeneration: - Part of the 3-PGA produced in the Rubisco reaction is used to regenerate RuBP: \[3-PGA \xrightarrow{k_2} RuBP\] where \(k_2\) is the rate constant for RuBP regeneration. 3. Carbon Uptake Rate: - The rate of carbon dioxide (CO2) uptake by Rubisco can be defined as: \[Rate_{CO2\ uptake} = k_1 \cdot [CO2] \cdot [RuBP] - k_2 \cdot [3-PGA]\] where: - \([CO2]\) is the concentration of CO2. - \([RuBP]\) is the concentration of RuBP. - \([3-PGA]\) is the concentration of 3-phosphoglycerate. - \(k_1\) and \(k_2\) are rate constants. 4. Change in CO2 Concentration: - Assuming steady-state conditions, the change in CO2 concentration in the system can be represented as: \[d[CO2]/dt = -Rate_{CO2\ uptake}\] This equation describes how the concentration of CO2 changes over time due to Rubisco activity.
Ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO) is a pivotal enzyme in photosynthesis, responsible for fixing carbon dioxide in plants and algae. It operates as a complex assembly of large (L) and small (S) subunits, forming an L8S8 hexadecameric structure. Understanding the interactions between these subunits is crucial for elucidating RuBisCO's function and assembly. In this study, molecular docking of RuBisCO's large and small subunits (whose coding gene was obtained from Synechococcus elongatus (PCC7942) was performed using PyMOL.
This docking software was chosen for its vast range of molecule rendering capacity and universal format of file (PDB) for importing and exporting docs with ease This was followed by a structural analysis to assess any changes resulting from the docking process. The key findings are as follows:
1. Molecular Docking: Molecular docking simulations were conducted using PyMOL to predict the binding interactions between RuBisCO's large and small subunits. The docking process aimed to determine how these subunits come together to form the functional enzyme.
2. Alignment with Protein Sequences: Subsequently, the resulting docked structure was aligned with the individual large and small subunit protein sequences. This alignment was conducted to verify whether the overall structure of RuBisCO had undergone significant alterations because of the docking process.
3. Structural Consistency: The alignment analysis indicated that the structure of RuBisCO remained largely consistent with the known structure of the enzyme. This suggests that the docking process did not induce substantial structural changes in the large and small subunits.
The structural analysis of RuBisCO's large and small subunits following molecular docking using PyMOL demonstrates that the overall enzyme structure remains stable and consistent with the native enzyme structure. These findings provide insights into the interactions between the subunits in the assembly of the functional RuBisCO enzyme.
In the rigorous pursuit of engineering the Calvin cycle within E.Coli, we currently find ourselves at a point of substantial significance. Our investigations have yielded a revelation of considerable importance: the branching points within our system, namely, the production of RuBisCO, the acknowledged rate-limiting step, and the nexus of two enzymes engaged in competition around a common substrate, exhibit a state of remarkable stasis. They appear to exert minimal influence upon our engineered Calvin cycle.
Our computational modeling using PyMol has allowed us to replicate the native as well as engineered RuBisCO and ensure its structural fidelity of RuBisCO compared to its native archetype. We are compelled to initiate additional experimental investigations. Through each methodical examination, our goal is to enhance not only the precision of our models, particularly within the context of our specific biosystem, but also to provide scholarly insights that elucidate the wider landscape of scientific understanding.
Collectively, we endeavor to advocate for the pursuit of knowledge acquisition and its dissemination, aiming to inspire the academic community with our steadfast commitment to the quest for enlightenment.