134,890 research outputs found
A network dynamics approach to chemical reaction networks
A crisp survey is given of chemical reaction networks from the perspective of
general nonlinear network dynamics, in particular of consensus dynamics. It is
shown how by starting from the complex-balanced assumption the reaction
dynamics governed by mass action kinetics can be rewritten into a form which
allows for a very simple derivation of a number of key results in chemical
reaction network theory, and which directly relates to the thermodynamics of
the system. Central in this formulation is the definition of a balanced
Laplacian matrix on the graph of chemical complexes together with a resulting
fundamental inequality. This directly leads to the characterization of the set
of equilibria and their stability. Both the form of the dynamics and the
deduced dynamical behavior are very similar to consensus dynamics. The
assumption of complex-balancedness is revisited from the point of view of
Kirchhoff's Matrix Tree theorem, providing a new perspective. Finally, using
the classical idea of extending the graph of chemical complexes by an extra
'zero' complex, a complete steady-state stability analysis of mass action
kinetics reaction networks with constant inflows and mass action outflows is
given.Comment: 18 page
On the Mathematical Structure of Balanced Chemical Reaction Networks Governed by Mass Action Kinetics
Motivated by recent progress on the interplay between graph theory, dynamics, and systems theory, we revisit the analysis of chemical reaction networks described by mass action kinetics. For reaction networks possessing a thermodynamic equilibrium we derive a compact formulation exhibiting at the same time the structure of the complex graph and the stoichiometry of the network, and which admits a direct thermodynamical interpretation. This formulation allows us to easily characterize the set of positive equilibria and their stability properties. Furthermore, we develop a framework for interconnection of chemical reaction networks, and we discuss how the formulation leads to a new approach for model reduction
Reactive SINDy: Discovering governing reactions from concentration data
The inner workings of a biological cell or a chemical reaction can be rationalized by the network of reactions, whose structure reveals the most important functional mechanisms. For complex systems, these reaction networks are not known a priori and cannot be efficiently computed with ab initio methods, therefore an important approach goal is to estimate effective reaction networks from observations, such as time series of the main species. Reaction networks estimated with standard machine learning techniques such as least-squares regression may fit the observations, but will typically contain spurious reactions. Here we extend the sparse identification of nonlinear dynamics
(SINDy) method to vector-valued ansatz functions, each describing a particular reaction process. The resulting sparse tensor regression method “reactive SINDy” is able to estimate a parsimonious reaction network. We illustrate that a gene regulation network can be correctly estimated from observed time series
Automated Exploration of Reaction Network and Mechanism via Meta-dynamics Nanoreactor
We developed an automated approach to construct the complex reaction network
and explore the reaction mechanism for several reactant molecules. The
nanoreactor type molecular dynamics was employed to generate possible chemical
reactions, in which the meta-dynamics was taken to overcome reaction barriers
and the semi-empirical GFN2-xTB method was used to reduce computational cost.
The identification of reaction events from trajectories was conducted by using
the hidden Markov model based on the evolution of the molecular connectivity.
This provided the starting points for the further transition state searches at
the more accurate electronic structure levels to obtain the reaction mechanism.
Then the whole reaction network with multiply pathways was obtained. The
feasibility and efficiency of this automated construction of the reaction
network was examined by two examples. The first reaction under study was the
HCHO + NH3 biomolecular reaction. The second example focused on the reaction
network for a multi-species system composed of dozens of HCN and H2O compounds.
The result indicated that the proposed approach was a valuable and effective
tool for the automated exploration of reaction networks
Power-law Kinetics and Determinant Criteria for the Preclusion of Multistationarity in Networks of Interacting Species
We present determinant criteria for the preclusion of non-degenerate multiple
steady states in networks of interacting species. A network is modeled as a
system of ordinary differential equations in which the form of the species
formation rate function is restricted by the reactions of the network and how
the species influence each reaction. We characterize families of so-called
power-law kinetics for which the associated species formation rate function is
injective within each stoichiometric class and thus the network cannot exhibit
multistationarity. The criterion for power-law kinetics is derived from the
determinant of the Jacobian of the species formation rate function. Using this
characterization we further derive similar determinant criteria applicable to
general sets of kinetics. The criteria are conceptually simple, computationally
tractable and easily implemented. Our approach embraces and extends previous
work on multistationarity, such as work in relation to chemical reaction
networks with dynamics defined by mass-action or non-catalytic kinetics, and
also work based on graphical analysis of the interaction graph associated to
the system. Further, we interpret the criteria in terms of circuits in the
so-called DSR-graphComment: To appear in SIAM Journal on Applied Dynamical System
Algebraic Aspects of (Bio) Nano-chemical Reaction Networks and Bifurcations in Various Dynamical Systems
The dynamics of (bio) chemical reaction networks have been studied by different methods. Among these methods, the chemical reaction network theory has been proven to successfully predicate important qualitative properties, such as the existence of the steady state and the asymptotic behavior of the steady state. However, a constructive approach to the steady state locus has not been presented. In this thesis, with the help of toric geometry, we propose a generic strategy towards this question. This theory is applied to (bio)nano particle configurations. We also investigate Hopf bifurcation surfaces of various dynamical systems
Uncoupled Analysis of Stochastic Reaction Networks in Fluctuating Environments
The dynamics of stochastic reaction networks within cells are inevitably
modulated by factors considered extrinsic to the network such as for instance
the fluctuations in ribsome copy numbers for a gene regulatory network. While
several recent studies demonstrate the importance of accounting for such
extrinsic components, the resulting models are typically hard to analyze. In
this work we develop a general mathematical framework that allows to uncouple
the network from its dynamic environment by incorporating only the
environment's effect onto the network into a new model. More technically, we
show how such fluctuating extrinsic components (e.g., chemical species) can be
marginalized in order to obtain this decoupled model. We derive its
corresponding process- and master equations and show how stochastic simulations
can be performed. Using several case studies, we demonstrate the significance
of the approach. For instance, we exemplarily formulate and solve a marginal
master equation describing the protein translation and degradation in a
fluctuating environment.Comment: 7 pages, 4 figures, Appendix attached as SI.pdf, under submissio
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