Integrating Kinetic and Constraint-Based Models for Better Metabolic Predictions

Metabolic models are tools that help scientists understand the chemical processes that occur in living organisms. These models can simulate how an organism grows and how important genes work. They are useful in various scientific studies and biotechnological developments.

Two common types of models used in metabolism research are Kinetic Models and constraint-based models. Kinetic models focus on how quickly reactions happen based on the amounts of substances involved. They provide specific details about the rates of reactions. On the other hand, constraint-based models look at the overall structure of metabolic reactions without going into the details of how fast they occur. They only define limits on how much reaction can happen based on mass balance and the number of substances involved.

These models are analyzed differently. Kinetic models use differential equations to track how the amounts of substances change over time, giving precise details on concentrations and reaction rates. Constraint-based models use linear programming to find the best possible distribution of reaction rates.

Building kinetic models can be challenging because they need a lot of detailed information about how reactions work. Consequently, kinetic models tend to be smaller and often focus on key pathways in metabolism. In contrast, constraint-based models can become quite large because they only require stoichiometric information and can easily incorporate many reactions, resulting in genome-scale models for various organisms. However, a downside of constraint-based models is that they lack the precision that kinetic models provide.

#Citramalate: An Important Metabolite

Citramalate, also known by its chemical names like 2-hydroxy-2-methylbutanedioate, is a dicarboxylic acid. Even though citramalate is not very common, it can be found in some bacteria and fungi. It plays a role in important pathways, such as the biosynthesis of an amino acid called isoleucine.

Certain bacteria, like Methanocaldococcus jannaschii, can produce citramalate using a specific enzyme. This enzyme helps convert acetyl-CoA, pyruvate, and water into citramalate, along with releasing other substances.

Citramalate has the potential to replace fossil fuels in creating industrial products. For example, it can be transformed into methacrylic acid, which is a precursor to a widely used compound in industries like dentistry, electronics, and paints. This process of producing materials from citramalate is more environmentally friendly compared to traditional methods that rely on petroleum and natural gas, which can lead to environmental harm and greenhouse gas emissions.

For large-scale production of citramalate, scientists can use genetically modified organisms in controlled environments called Bioreactors. E. coli is often used as it grows quickly and is easy to modify genetically. With specific conditions, E. coli can produce citramalate efficiently, which can lead to replacing fossil fuel sources in manufacturing.

#Aims and Objectives

The goal is to connect kinetic and constraint-based models to improve their accuracy. Specifically, the aim is to merge kinetic data obtained from detailed kinetic models into larger constraint-based models to create a more realistic model. This process is done in three steps: mapping reactions between both types of models, running simulations to get flow rates from the kinetic model, and transferring these rates to the constraint-based model. To assist in mapping and transferring flow rates, visual representations called Petri nets can be used.

We will show this approach using models of E. coli. Enhancing the constraint-based model using kinetic data leads to changes in how reactions behave and better activation of some processes. Moreover, we extended these models to simulate citramalate production. A challenge observed in the extended model is a bifurcation, which can lead to allocating all resources either for growth or citramalate production. By fixing the growth rate, we can solve this issue, resulting in a more accurate prediction of citramalate output.

#Materials and Methods

#Kinetic Model

The chosen kinetic model of E. coli covers essential carbon pathways. It includes numerous reactions and metabolites spread across different parts of the cell. This model operates under glucose-limited conditions and uses equations to describe the reactions. Many of the reactions include parameters that can vary based on enzyme levels.

The kinetic model is analyzed by solving the set of equations until reaching steady conditions, where changes stop occurring.

#Constraint-Based Model

A constraint-based model is defined by a collection of reactions, metabolites, a matrix representing the chemical relationships, and limits on flow rates for each reaction. A well-known model used in this study is called iJO1366, which encompasses a large set of reactions and metabolites also organized in different compartments.

#Petri Nets for Metabolic Networks

Petri nets are a way to visualize and represent dynamic systems, particularly metabolic networks. In this representation, the substances (metabolites) are shown as places, while reactions are shown as transitions. This structure helps to connect reactants and products visually.

#FBA and FVA Simulations

Flux Balance Analysis (FBA) is a method to calculate steady-state flow rates in a metabolic network. The aim is to optimize a specific goal while following the rules of mass balance. This involves setting up a linear problem to find the most efficient flow distribution that meets the necessary conservation laws.

Flux Variability Analysis (FVA) builds on FBA by examining the range of possible flow values for each reaction while fixing the optimized goal. This helps scientists understand the flexibility of the metabolic network under various conditions.

#Translating Fluxes Between Models

#Translation of Fluxes

To transfer flow rates from the kinetic to the constraint-based model, each reaction in the constraint-based model is analyzed for its flow limits based on the data from the kinetic model. These limits establish the degrees of uncertainty and help convert units between the two models.

#Mapping of Reactions

Reactions in the kinetic model must be matched with corresponding reactions in the constraint-based model. Since the two models may not perfectly align, adjustments must be made based on various categories of differences, such as variations in chemical species or differences in reaction reversibility.

For some categories, bounds from the kinetic model can be applied directly, while others might require new calculations due to structural differences.

#Subnetworks with Different Structures

When reactions are structured differently in each model, it becomes necessary to consider them separately for establishing flow limits. Each subnetwork is analyzed to ensure that the overall flow rates meet the constraints and reactant/product relationships established by each model.

#Assessing the Enhanced Constraint-Based Model

To see how changes in specific reactions affect the model, researchers sequentially added kinetic bounds to the constraint-based model. After each step, they analyzed the flow distribution and the number of inactive (dead) reactions, as well as the variability of reactions.

Adding kinetic constraints to the model often reduces the number of dead reactions and provides a more realistic representation of how the metabolic network behaves. This change suggests that the integration of kinetic information leads to a better understanding of the system's reaction dynamics.

#Kinetic Bound Uncertainty

Changing the level of uncertainty in the kinetic bounds impacts the model. As uncertainty increases, there may be different behaviors observed in the output of the model, such as the growth rate and the number of dead reactions. Lower uncertainty typically leads to more constrained models, while higher uncertainty allows for additional responsiveness in the system.

#Effect of Varying Kinetic Bounds

As the uncertainty of the kinetic bounds is adjusted, the model's predictions of citramalate production change based on the integration of kinetic information. The findings suggest that the inclusion of realistic kinetic constraints can lead to better predictions that align more closely with experimental results, showcasing the importance of proper modeling techniques.

#Enriched Constraint-Based Model to Simulate Citramalate Production

#Inclusion of Citramalate Production

To address the challenge of competing objectives (growth versus citramalate production) in the constraint-based model, we added new reactions related to citramalate synthesis and transport. By enforcing a relationship between biomass production and citramalate synthesis, the model can now better reflect the reality of how these processes interact.

#Modeling Citramalate Production in the Kinetic Model

A new reaction was added to the kinetic model to represent the synthesis of citramalate. This reaction follows established kinetic laws, allowing the model to simulate citramalate production more accurately.

#Effect of Kinetic Bounds on Citramalate Production

The integrating of kinetic constraints into the model allows for more accurate predictions of citramalate output. Observations show a decrease in the number of dead reactions and an increase in the overall variability of flux values. This suggests that integrating kinetic information improves the model's accuracy and responsiveness.

#Validation of Citramalate Efficiency in the Kinetically Constrained Model

To validate the improved model, the calculated efficiency of converting glucose to citramalate was compared with experimental data. The results demonstrate that as kinetic constraints were added, the model's predictions regarding conversion efficiency tended to align closer with real-world observations.

In summary, while constraint-based models are relatively simple to create, they often lack the details necessary for precision. By combining the strengths of both kinetic and constraint-based models, a more realistic representation of metabolic processes emerges. The enhanced model is better at predicting behaviors in metabolic networks, leading to more effective applications in biotechnology and beyond.