Photocaged and Water‐Soluble Glucose Functionalization for Spatiotemporal Acidification Pathways

Self-regulating bioinspired supramolecular photonic hydrogels based on chemical reaction networks for monitoring activities of enzymes and biofuels

Research has been conducted on the current problem of developing a methodology for determining the level of process control in complex systems, taking into account risk-oriented factors influencing it. For the first time, the study proposes stages of risk management in the process of assessing the level of controllability of complex systems, formalizes the input data used to assess risks using fuzzy models for various complex systems, constructs generalized step-by-step algorithms for risk-oriented assessment of controllability in complex systems. An experimental approbation has been made of the research on the problem of determining the level of process control in the airline system, taking into account risk-oriented factors influencing it. The study will be a useful tool to support decision-making to improve process control in various complex systems by taking into account the risks and threats to its operation for managers from safe time to pandemics as COVID-19. © 2021 Copyright for this paper by its authors.

We show that adding new chemical species into the reactions of a chemical reaction network (CRN) in such a way that the rank of the network remains unchanged preserves its capacity for multiple nondegenerate equilibria and/or periodic orbits. One consequence is that any bounded nondegenerate behaviours which can occur in a CRN can occur in a CRN with bounded stoichiometric classes. The main result adds to a family of theorems which tell us which enlargements of a CRN preserve its capacity for nontrivial dynamical behaviours. It generalises some earlier claims, and complements similar claims involving the addition of reactions into CRNs. The result gives us information on how ignoring some chemical species, as is common in biochemical modelling, might affect the allowed dynamics in differential equation models of CRNs. We demonstrate the scope and limitations of the main theorem via several examples. These illustrate how we can use the main theorem to predict multistationarity and oscillation in CRNs enlarged with additional species; but also how the enlargements can introduce new behaviours such as additional periodic orbits and new bifurcations.

Stochastic chemical reaction networks (CRNs) are complex systems that combine the features of concurrent transformation of multiple variables in each elementary reaction event and nonlinear relations between states and their rates of change. Most general results concerning CRNs are limited to restricted cases where a topological characteristic known as deficiency takes a value 0 or 1, implying uniqueness and positivity of steady states and surprising, low-information forms for their associated probability distributions. Here we derive equations of motion for fluctuation moments at all orders for stochastic CRNs at general deficiency. We show, for the standard base case of proportional sampling without replacement (which underlies the mass-action rate law), that the generator of the stochastic process acts on the hierarchy of factorial moments with a finite representation. Whereas simulation of high-order moments for many-particle systems is costly, this representation reduces the solution of moment hierarchies to a complexity comparable to solving a heat equation. At steady states, moment hierarchies for finite CRNs interpolate between low-order and high-order scaling regimes, which may be approximated separately by distributions similar to those for deficiency-zero networks and connected through matched asymptotic expansions. In CRNs with multiple stable or metastable steady states, boundedness of high-order moments provides the starting condition for recursive solution downward to low-order moments, reversing the order usually used to solve moment hierarchies. A basis for a subset of network flows defined by having the same mean-regressing property as the flows in deficiency-zero networks gives the leading contribution to low-order moments in CRNs at general deficiency, in a 1/n expansion in large particle numbers. Our results give a physical picture of the different informational roles of mean-regressing and non-mean-regressing flows and clarify the dynamical meaning of deficiency not only for first-moment conditions but for all orders in fluctuations.

Steady state equivalence in speciation: Reaction networks in acid–base aqueous solutions

The dynamics of a chemical reaction network (CRN) is often modeled under the assumption of mass action kinetics by a system of ordinary differential equations (ODEs) with polynomial right-hand sides that describe the time evolution of concentrations of chemical species involved. Given an arbitrarily large integer K in {mathbb N}, we show that there exists a CRN such that its ODE model has at least K stable limit cycles. Such a CRN can be constructed with reactions of at most second-order provided that the number of chemical species grows linearly with K. Bounds on the minimal number of chemical species and the minimal number of chemical reactions are presented for CRNs with K stable limit cycles and at most second order or seventh-order kinetics. We also show that CRNs with only two chemical species can have K stable limit cycles, when the order of chemical reactions grows linearly with K.

It is common that probability theory and stochastic process, especially Markov chains, have long been used to study and explain the behaviors of chemical reaction networks (CRNs). Nonetheless, this paper sees things from a reverse angle, devoting itself in synthesizing common probability theory and stochastic process with CRNs. The main motivation is to imitate and explore the evolution of large-scale and complex practical systems based on CRNs, by making use of the inherent parallelism and randomness. In our conference paper, a preliminary but concise approach has been put forward to synthesize the stand-alone examples such as law of total probability, Bayes’ theorem, and n-step transition of Markov chains. To make this methodology systematic and theoretically sound, we enrich and offer more solid foundation for the previous version. Rigorous stability analysis based on ordinary differential equations (ODEs) are provided. This paper further deeply discusses and distinguishes building stochastic models for CRNs and utilizing CRNs to solve stochastic problems. A joint distribution of Markov chains are implemented using molecular reactions as a showcase. In order to enhance the clearness of the results, all the simulations are done according to deterministic mass action. It is worth noting that an already mathematically proven conclusion, which states that nearly an arbitrary set of bimolecular or unimolecular reactions can be implemented by DNA strand displacement reactions, ensures the meaningfulness of our work. It is also believed that, though in its infancy, the proposed approach is also valid for other molecular synthesis than DNA, as long as the kinetics constraints are met.

Understanding the algorithmic behaviors that are in principle realizable in a chemical system is necessary for a rigorous understanding of the design principles of biological regulatory networks. Further, advances in synthetic biology herald the time when we'll be able to rationally engineer complex chemical systems, and when idealized formal models will become blueprints for engineering.

Understanding the algorithmic behaviors that are in principle realizable in a chemical system is necessary for a rigorous understanding of the design principles of biological regulatory networks. Further, advances in synthetic biology herald the time when we will be able to rationally engineer complex chemical systems and when idealized formal models will become blueprints for engineering. Coupled chemical interactions in a well-mixed solution are commonly formalized as chemical reaction networks (CRNs). However, despite the widespread use of CRNs in the natural sciences, the range of computational behaviors exhibited by CRNs is not well understood. Here, we study the following problem: What functions f : ℝ k → ℝ can be computed by a CRN, in which the CRN eventually produces the correct amount of the “output” molecule, no matter the rate at which reactions proceed? This captures a previously unexplored but very natural class of computations: For example, the reaction X 1 + X 2 → Y can be thought to compute the function y = min ( x 1 , x 2 ). Such a CRN is robust in the sense that it is correct whether its evolution is governed by the standard model of mass-action kinetics, alternatives such as Hill-function or Michaelis-Menten kinetics, or other arbitrary models of chemistry that respect the (fundamentally digital) stoichiometric constraints (what are the reactants and products?). We develop a reachability relation based on a broad notion of “what could happen” if reaction rates can vary arbitrarily over time. Using reachability, we define stable computation analogously to probability 1 computation in distributed computing and connect it with a seemingly stronger notion of rate-independent computation based on convergence in the limit t → ∞ under a wide class of generalized rate laws. Besides the direct mapping of a concentration to a nonnegative analog value, we also consider the “dual-rail representation” that can represent negative values as the difference of two concentrations and allows the composition of CRN modules. We prove that a function is rate-independently computable if and only if it is piecewise linear (with rational coefficients) and continuous (dual-rail representation), or non-negative with discontinuities occurring only when some inputs switch from zero to positive (direct representation). The many contexts where continuous piecewise linear functions are powerful targets for implementation, combined with the systematic construction we develop for computing these functions, demonstrate the potential of rate-independent chemical computation.

Network measures have proven very successful in identifying structural patterns in complex systems (e.g., a living cell, a neural network, the Internet). How such measures can be applied to understand the rational and experimental design of chemical reaction networks (CRNs) is unknown. Here, we develop a procedure to model CRNs as a mathematical graph on which network measures and a random graph analysis can be applied. We used an enzymatic CRN (for which a mass-action model was previously developed) to show that the procedure provides insights into its network structure and properties. Temporal analyses, in particular, revealed when feedback interactions emerge in such a network, indicating that CRNs comprise various reactions that are being added and removed over time. We envision that the procedure, including the temporal network analysis method, could be broadly applied in chemistry to characterize the network properties of many other CRNs, promising data-driven analysis of future molecular systems of ever greater complexity.

State-of-the-art biochemical systems for medical applications and chemical computing are application-specific and cannot be re-programmed or trained once fabricated. The implementation of adaptive biochemical systems that would offer flexibility through programmability and autonomous adaptation faces major challenges because of the large number of required chemical species as well as the timing-sensitive feedback loops required for learning. Currently, biochemistry lacks a systems vision on how the user-level programming interface and abstraction with a subsequent translation to chemistry should look like. By developing adaptation in chemistry, we could replace multiple hard-wired systems with a single programmable template that can be (re)trained to match a desired input-output profile benefiting smart drug delivery, pattern recognition, and chemical computing. I aimed to address these challenges by proposing several approaches to learning and adaptation in Chemical Reaction Networks (CRNs), a type of simulated chemistry, where species are unstructured, i.e., they are identified by symbols rather than molecular structure, and their dynamics or concentration evolution are driven by reactions and reaction rates that follow mass-action and Michaelis-Menten kinetics. Several CRN and experimental DNA-based models of neural networks exist. However, these models successfully implement only the forward-pass, i.e., the input-weight integration part of a perceptron model. Learning is delegated to a non-chemical system that computes the weights before converting them to molecular concentrations. Autonomous learning, i.e., learning implemented fully inside chemistry has been absent from both theoretical and experimental research. The research in this thesis offers the first constructive evidence that learning in CRNs is, in fact, possible. I have introduced the original concept of a chemical binary perceptron that can learn all 14 linearly-separable logic functions and is robust to the perturbation of rate constants. That shows learning is universal and substrate-free. To simplify the model I later proposed and applied the "asymmetric" chemical arithmetic providing a compact solution for representing negative numbers in chemistry. To tackle more difficult tasks and to serve more complicated biochemical applications, I introduced several key modular building blocks, each addressing certain aspects of chemical information processing and learning. These parts organically combined into gradually more complex systems. First, instead of simple static Boolean functions, I tackled analog time-series learning and signal processing by modeling an analog chemical perceptron. To store past input concentrations as a sliding window I implemented a chemical delay line, which feeds the values to the underlying chemical perceptron. That allows the system to learn, e.g., the linear

Chemical Reaction Networks (CRNs) are a standard formalism used in chemistry and biology to model complex molecular interaction systems. In the perspective of systems biology, they are a central tool to analyze the high-level functions of the cell in terms of their low-level molecular interactions. In the perspective of synthetic biology, they constitute a target programming language to implement in chemistry new functions either in vitro , in artificial vesicles, or in living cells. In this paper, we describe the CRN synthesis tool part of our CRN modeling and analysis software BIOCHAM (Biochemical Abstract Machine). This compiler transforms any elementary (resp. algebraic) real function into a formal finite CRN to compute it (resp. with absolute functional robustness), through a pipeline of symbolic computation steps, among which quadratization optimization plays a key role to restrict to elementary reactions with at most two reactants and a minimum number of molecular species.

We study the response of chemical reaction networks driven far from equilibrium to logarithmic perturbations of reaction rates. The response of the mean number of a chemical species is observed to be quantitively limited by number fluctuations and the maximum thermodynamic driving force. We prove these trade-offs for linear chemical reaction networks and a class of nonlinear chemical reaction networks with a single chemical species. Numerical results for several model systems support the conclusion that these trade-offs continue to hold for a broad class of chemical reaction networks, though their precise form appears to sensitively depend on the deficiency of the network.

Chemical reaction networks taken with mass-action kinetics are dynamical systems that arise in chemical engineering and systems biology. In general, determining whether a chemical reaction network admits multiple steady states is difficult, as this requires determining existence of multiple positive solutions to a large system of polynomials with unknown coefficients. However, in certain cases, various easy criteria can be applied. One such test is the Jacobian criterion, due to Craciun and Feinberg, which gives sufficient conditions for ruling out the possibility of multiple steady states. A chemical reaction network is said to pass the Jacobian criterion if all terms in the determinant expansion of its parametrized Jacobian matrix have the same sign. In this article, we present a procedure which simplifies the application of the Jacobian criterion, and as a result, we identify a new class of networks for which multiple steady states is precluded: those in which all chemical species have total moleculari...

Reaction networks and kinetics of biochemical systems