Sensitivity and network topology in chemical reaction systems

Inferring networks of chemical reactions by curvature analysis of kinetic trajectories

Quantifying interaction networks of chemical reactions allows description, prediction, and control of a range of phenomena in chemistry and biology. The challenge lies in unambiguously assigning contributions to changes in rates from different interactions. We propose that the curvature change of kinetic trajectories due to a systematic perturbation of a node in a network can identify the coupling strength and topology. Specifically, the coupling strength can be calculated as the ratio of the curvature change measured from the coupled node and the rate change of a perturbed node. We verified the methodology in numerical simulations with a network with complex ordinary differential equations and experiments with electrochemical networks. The experiments show excellent network inference (without false positive or negative links) of various systems with large heterogeneity in local dynamics and network structure without any a priori knowledge of the kinetics. The theory and the experiments also clarify the influence of local perturbations on response amplitude and timing through network-wide up-regulation. A major advantage of our technique is its independence from hidden/unobserved nodes. This makes our method highly suitable for applications with high temporal and low spatial resolution data from interacting chemical and biochemical systems including neuronal activity monitoring with multi-electrode arrays.

BayesianSSA: a Bayesian statistical model based on structural sensitivity analysis for predicting responses to enzyme perturbations in metabolic networks

BACKGROUND

Chemical bioproduction has attracted attention as a key technology in a decarbonized society. In computational design for chemical bioproduction, it is necessary to predict changes in metabolic fluxes when up-/down-regulating enzymatic reactions, that is, responses of the system to enzyme perturbations. Structural sensitivity analysis (SSA) was previously developed as a method to predict qualitative responses to enzyme perturbations on the basis of the structural information of the reaction network. However, the network structural information can sometimes be insufficient to predict qualitative responses unambiguously, which is a practical issue in bioproduction applications. To address this, in this study, we propose BayesianSSA, a Bayesian statistical model based on SSA. BayesianSSA extracts environmental information from perturbation datasets collected in environments of interest and integrates it into SSA predictions.

RESULTS

We applied BayesianSSA to synthetic and real datasets of the central metabolic pathway of Escherichia coli. Our result demonstrates that BayesianSSA can successfully integrate environmental information extracted from perturbation data into SSA predictions. In addition, the posterior distribution estimated by BayesianSSA can be associated with the known pathway reported to enhance succinate export flux in previous studies.

CONCLUSIONS

We believe that BayesianSSA will accelerate the chemical bioproduction process and contribute to advancements in the field.

Patterns of change in regulatory modules of chemical reaction systems induced by network modification

Cellular functions are realized through the dynamics of chemical reaction networks formed by thousands of chemical reactions. Numerical studies have empirically demonstrated that small differences in network structures among species or tissues can cause substantial changes in dynamics. However, a general principle for behavior changes in response to network structure modifications is not known. The chemical reaction system possesses substructures called buffering structures, which are characterized by a certain topological index being zero. It was proven that the steady-state response to modulation of reaction parameters inside a buffering structure is localized in the buffering structure. In this study, we developed a method to systematically identify the loss or creation of buffering structures induced by the addition of a single degradation reaction from network structure alone. This makes it possible to predict the qualitative and macroscopic changes in regulation that will be caused by the network modification. This method was applied to two reaction systems: the central metabolic system and the mitogen-activated protein kinases signal transduction system. Our method enables identification of reactions that are important for biological functions in living systems.

A structural approach to understanding enzymatic regulation of chemical reaction networks

In living cells, chemical reactions are connected by sharing their products and substrates, and form complex systems, i.e. chemical reaction network. One of the largest missions in modern biology is to understand behaviors of such systems logically based on information of network structures. However, there are series of obstacles to study dynamical behaviors of complex network systems in biology. For example, network structure does not provide sufficient information to determine details of the dynamical behaviors. In this review, I will introduce a novel mathematical theory, structural sensitivity analysis, by which the responses of reaction systems upon the changes in enzyme activities/amounts are determined from network structure alone. The patterns of responses exhibit characteristic features, localization and hierarchy, depending on the topology of the network. The theory also shows that ranges of enzymatic regulations are governed by a mathematical law characterized by local topology of substructures. These findings imply that the network topology is one of the origins of biological robustness.

Flux-augmented bifurcation analysis in chemical reaction network systems

The dynamics of biochemical reaction networks are considered to be responsible for biological functions in living systems. Since real networks are immense and complicated, it is difficult to determine which reactions can cause a significant change of dynamical behaviors, namely, bifurcations. Also to what extent numerical results of network systems depend on the chosen kinetic rate parameters is not known. In this paper, an analytical setting that splits the information of the dynamics into the network structure and reaction kinetics is introduced. This setting possesses a factorization structure for some class of network systems which allows one to determine which subnetworks are responsible for the occurrence of a bifurcation. Subsequently, the bifurcation criteria are reformulated in a manner that allows the efficient determination of relevant reactions for bifurcations.

Sensitivity analysis for reproducible candidate values of model parameters in signaling hub model

Mathematical models for signaling pathways are helpful for understanding molecular mechanism in the pathways and predicting dynamic behavior of the signal activity. To analyze the robustness of such models, local sensitivity analysis has been implemented. However, such analysis primarily focuses on only a certain parameter set, even though diverse parameter sets that can recapitulate experiments may exist. In this study, we performed sensitivity analysis that investigates the features in a system considering the reproducible and multiple candidate values of the model parameters to experiments. The results showed that although different reproducible model parameter values have absolute differences with respect to sensitivity strengths, specific trends of some relative sensitivity strengths exist between reactions regardless of parameter values. It is suggested that (i) network structure considerably influences the relative sensitivity strength and (ii) one might be able to predict relative sensitivity strengths specified in the parameter sets employing only one of the reproducible parameter sets.

Structural bifurcation analysis in chemical reaction networks

In living cells, chemical reactions form complex networks. Dynamics arising from such networks are the origins of biological functions. We propose a mathematical method to analyze bifurcation behaviors of network systems using their structures alone. Specifically, a whole network is decomposed into subnetworks, and for each of them the bifurcation condition can be studied independently. Further, parameters inducing bifurcations and chemicals exhibiting bifurcations can be determined on the network. We illustrate our theory using hypothetical and real networks.