Stochastic reaction networks with mass-action kinetics provide a useful framework for understanding processes-biochemical and otherwise-in homogeneous environments. However, cellular reactions are often compartmentalized, either at the cell level or within cells, and hence non-homogeneous. We investigate a model of compartmentalization in which the rate of fragmentation of a compartment depends on the abundance of some designated species inside that compartment. The particular model of study is part of a general framework for compartmentalized chemistry with dynamic compartments that was proposed in Duso and Zechner (2020). This paper builds on Anderson and Howells (2023) where the special case where the compartment dynamics do not depend on their contents was studied mathematically. In particular, we demonstrate that the explosivity characterization from Anderson and Howells (2023) fails in this setting and provide new sufficient conditions for non-explosivity and positive recurrence, under the assumption that the underlying CRN admits a linear Lyapunov function. These results extend the theoretical foundation for modeling content-mediated compartment dynamics, with implications for systems such as cell division and intracellular transport.

An optimized fast repetition rate fluorometry method reveals photochemical flux bottlenecks in C3 photosynthesis that limit carboxylation and growth.

Biochemical interactions at membranes are starting points for cell signaling. But reaction kinetics are difficult to measure on two-dimensional (2D) membranes and are usually measured in volumetric assays. Membrane tethering produces confinement and steric effects that will significantly impact binding rates; these cannot be determined by volumetric measurements. Additionally, because of the properties of 2D diffusion, bimolecular reactions may not conform to simple mass action kinetics. Here, we show how simulations using the SpringSaLaD software can be used to estimate a 2D rate constant based on a known 3D rate constant and coarse-grained molecular structures for the reactants; this approach accounts for confinement of the reaction to the near-membrane space as well as the steric environment and flexibility of the membrane-anchored binding sites. The approach is validated using theoretical solutions for dimerization in an idealized system containing a binding site at the end of a single stiff membrane anchor. With this ideal system, we also assess whether simple mass action rate constants can correctly describe the reaction rate, considering the diffusivity of the membrane anchors, the initial membrane densities of the reactants, and the desired level of completion of the reaction. We explore how factors such as molecular reach, steric effects, disordered domains, and diffusion affect the kinetics. We then apply our approach to epidermal growth factor receptor (EGFR)-mediated activation of the membrane-bound small GTPase Ras. The analysis reveals how binding of Ras to the allosteric site of SOS, a guanine nucleotide exchange factor that is recruited to EGFR, significantly accelerates Ras binding to the SOS catalytic site. A biochemical network model parametrized with the derived 2D rate constants demonstrates how recruitment of SOS via EGFR can significantly enhance Ras activation. Thus, we offer a novel method to more rigorously parameterize receptor-mediated steps in cell signaling.

Reaction networks are a general framework widely used in modeling diverse phenomena in different science disciplines. The dynamical process of a reaction network endowed with mass-action kinetics is a mass-action system which is an ODE defined by a directed graph, the so-called "reaction graph". Endotacticity is a graph property used to study persistence and permanence of mass-action systems. In this paper, we provide a detailed characterization of first-order endotactic reaction graphs. Besides, we provide a sufficient condition for endotacticity of reaction networks which are not necessarily of first-order. Such a characterization of a first-order endotactic reaction graph yields the spectral property of the adjacency matrix of the reaction graph. As a consequence, we prove that every first-order endotactic mass-action system as a linear ODE has a weakly reversible deficiency zero realization, and has a unique equilibrium which is exponentially globally asymptotically stable (and is positive) in each (positive) stoichiometric compatibility class. Using a stability result for asymptotically autonomous differential equations, examples are constructed to illustrate that the global stability results can be extended to mass-action systems of higher-order reaction networks modeled by nonlinear ODEs, which are not necessarily endotactic. Different from the classical approaches for proving global asymptotic stability, the proof does not rely on the construction of a Lyapunov function. This paper may serve as a starting point of characterizing higher-order endotactic reaction graphs and studying global stability of mass-action systems in general.

The purpose of this study is to characterize absolutely complex balanced (ACB) systems with mass action kinetics (MAK) using zero deficiency decomposition (ZDD). To do this, we first introduce the mass action, Tˆ−independent kinetic (MA-TIK) and mass action, non-Tˆ−independent kinetic (MA-NTIK) systems, that is, MAK systems that are also PL-TIK and non-PL-TIK systems, respectively. Then, we develop an algorithm that can generate the ZDD of both MA-TIK and MA-NTIK systems. We show that for both MA-TIK and MA-NTIK systems, ZDD implies a PL-TIK decomposition, wherein each subnetwork is a PL-TIK system. We show the existence of ACB systems for non-zero deficiency MA-NTIK systems via their weakly reversible, zero deficiency, C−decomposition. On the other hand, we also show the non-existence of ACB systems for non-zero deficiency MA-TIK systems. Lastly, we apply the results to the mathematical model of a mechanism for human dihydrofolate reductase (DHFR) catalysis.

Bistability in the regulatory system of the intrinsic apoptotic pathway arising from the Bax and Bcl-xL interactions.

To investigate the mechanisms governing energy and redox balance in skeletal muscle, we developed a computational model describing the coupled biochemical reaction network of glycolysis and mitochondrial oxidative phosphorylation (OxPhos) in fast-twitch oxidative glycolytic (FOG) muscle fibres. The model was identified against dynamic in vivo recordings of phosphocreatine (PCr), inorganic phosphate (Pi) and pH in rodent hindlimb muscle and verified against independent data from in vivo experiments and muscle biopsies. Step response testing reveals that mass action kinetics in combination with feedback control are sufficient to accomplish myoplasmic ATP homeostasis over a 100-fold range of ATP turnover rates. This vital emergent property of the metabolic model is associated with intermediary metabolite dynamics typical of a second-order underdamped system, which has been previously reported for the glycolytic pathway. Lactate dehydrogenase (LDH) knockout simulations suggest that the contribution of the LDH reaction to redox balance is more fundamental to muscle function than its role in counteracting myoplasmic acidification across the physiological range of ATP demands in this myofibre phenotype. Furthermore, LDH knockout simulations confirm that mitochondrial uptake of myoplasmic NADH and H+ in and by itself is sufficient to maintain redox balance and proton balance over ATP turnover rates in the range of mitochondrial ATP synthesis. We conclude that aerobic lactate production in working muscles is a by-product of the metabolic flexibility of FOG myofibres afforded by expression of high levels of LDH and OxPhos enzymes to support continual myoplasmic redox balance and ATP synthesis under conditions of high-intensity mechanicalwork. KEY POINTS: Feedback regulation suffices to accomplish myoplasmic ATP homeostasis over a 100-fold range of ATP turnover. Second-order underdamped behaviour is predicted to arise as a generic trait of the ATP metabolic network in mammalian cells. Aerobic lactate is a by-product of the metabolic and functional flexibility. LDH's role in maintaining redox balance is more important than its role in counteracting cellular acidification.

ABSTRACT Controlling the quasiparticle population density in 2D materials is crucial for designing next‐generation devices. In this study, we explore how optical pumping effectively controls the population and dynamics of quasiparticles (excitons, trions, and biexcitons) in exfoliated and CVD‐grown WS 2 monolayers at room temperature. Photoluminescence analysis reveals that the emission profile primarily consists of excitons and trions in the low‐pump power regime. The densities of the unbound electrons follow the law of mass action, and the trion population increases with increasing pump power. Furthermore, the excitation‐energy‐dependent conversion efficiency is systematically investigated and found to be consistent with pump energy. In the high‐power regime, photoluminescence spectra reveal the formation of biexcitons and defect states, as confirmed by Raman measurements. Additionally, lifetime measurements are performed to assess variations in the radiative and non‐radiative contributions by varying the pump power, which are correlated with steady‐state measurements. Spectral diffusion and bleaching experiments reveal a higher purity of the exfoliated monolayer compared to the CVD‐grown samples. These findings are crucial for designing high‐performing 2D material‐based devices.

The Law of Mass action predicts that all adverse drug reactions are related to the concentration of the drug at the site of action, and therefore to the administered dose. In other words, there is no such thing as a non-dose-related adverse drug reaction. That being so, there are three types of adverse drug reactions in relation to the dose or concentration of the drug with which the reaction is associated, determined by the relation between the concentration of the drug at the site of action, determining the adverse reaction, and the range of concentrations expected to be associated with therapeutic benefit: those three types are hypersusceptibility reactions (at concentrations below therapeutic), collateral reactions (at concentrations in the therapeutic range), and toxic reactions (at concentrations above therapeutic). Different types of reactions also imply different degrees of predictability. Artificial intelligence (AI) is generally of no value in predicting adverse drug reactions of the different types in an individual, but it may be used in studies of the susceptibility factors that are likely to be associated with risks of harms. AI may also be useful in analysing large databases, such as Vigibase, Eudravigilance, and the US FDA Adverse Event Reporting System (FAERS). There is also as yet unrealised scope for using AI to analyse data in pharmaceutical companies’ clinical study reports and in clinical datasets, such as claims and complaints databases, electronic health records from hospitals and general practice records, and information from poisons centres.

DNA strand displacement (DSD) has enabled significant advances in chaotic secure communication. However, DSD-based drive-response systems often suffer from limited complexity and rigid dynamic control, reducing their adaptability under complex biochemical conditions. To address these limitations, this paper proposes a Dislocated Perturbation Secure Communication (DPSC) scheme based on DSD mechanisms. First, a hyperchaotic system is designed according to the dual-rail representation and law of mass action, integrating emergence, catalysis, fasciation, and annihilation modules. The Chen hyperchaotic system is employed as a parameter perturbation source, and an active perturbation strategy is introduced to emulate nonlinear biochemical fluctuations. Subsequently, a DSD-based Dislocated Perturbation Controller (DPC) is constructed to achieve dislocated projective synchronization, ensuring system stability and accurate dynamic mapping between the drive and response states. Finally, the perturbation-driven hyperchaotic signal is utilized for secondary encryption of the drive signal, significantly enhancing communication security. Numerical simulations confirm that the DPSC-encrypted signal exhibits enhanced complexity and improved resilience to external disturbances as compared to traditional chaotic masking techniques. Furthermore, the receiver is capable of reconstructing the initial signal with high fidelity and without distortion.

The classical and extended deficiency one theorems by Feinberg apply to reaction networks with mass-action kinetics that have independent linkage classes or subnetworks, each with a deficiency of at most one and exactly one absorbing strong component. The theorems assume the existence of a positive equilibrium and guarantee the existence of a unique positive equilibrium in every stoichiometric compatibility class. In our work, we use the monomial dependency which extends the concept of deficiency. First, we provide a dependency one theorem for parametrized systems of polynomial equations that are essentially univariate and decomposable. As our main result, we present a corresponding theorem for mass-action systems, which permits subnetworks with arbitrary deficiency and arbitrary number of absorbing strong components. Finally, to complete the picture, we derive the extended deficiency one theorem as a special case of our more general dependency one theorem.

The study of the mechanisms and causes of critical phenomena and chaotic oscillations in the kinetics of homogeneous chemical reactions, as well as the search for appropriate examples of such reactions, is a relevant area of development of ideas about self-organization processes that play an important role in the evolution of living nature. It is known that the main condition for the existence of complex-periodic and chaotic undamped oscillations is the transition of a dynamic chemical system to such an unstable stationary state in which stable stationary states are inaccessible (absolute instability). The literature contains the necessary conditions for the emergence of unstable stationary states (the Bendixson-Dulac criterion, etc.). The exact conditions for the birth and death of chaotic regimes are still unknown. Dynamic models of chemical reactions are systems of ordinary differential equations based on reaction mechanisms and the corresponding kinetic laws associated with the reaction environment (ideal, non-ideal). At present, examples of chaotic dynamics models are known for homogeneous chemical reactions proceeding according to nonlinear stage schemes with classical kinetics of the law of mass action. In this paper, the possibility of describing chaotic oscillations in homogeneous chemical reactions proceeding according to linear stage schemes in an isothermal reactor of ideal mixing with a new kinetic law, which is called "polymorphic", is investigated. Polymorphic kinetics generalizes the known kinetic laws - the ideal law of Hulbert-Waage mass action and the non-ideal kinetic law of Marcelin-De Donde. Unlike these laws, polymorphic kinetics takes into account the possible mutual influence of reagents in each elementary stage of a chemical reaction. It is shown that polymorphic kinetics allows describing complex oscillatory and chaotic dynamics of chemical reactions by simple linear mechanisms with respect to key (determining the dynamics) reagents. Examples of reactions are given for which, within the framework of polymorphic kinetics, the existence of experimentally observed chaos has been numerically reproduced and proven using the Shilnikov criterion and Lyapunov exponents. For citation: Kol'tsov N.I. Polymorphic kinetics: chaos in linear homogeneous chemical reactions. ChemChemTech [Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol.]. 2026. V. 69. N 2. P. 50-58. DOI: 10.6060/ivkkt.20266902.7208.

Current studies were carried out to evaluate the synergistic effect of selected essential oils when combined or mixed with alpha cypermethrin to reduce the insecticide dose as well increase the mixture efficacy in controlling adult Bactrocera zonata. Essential oil tested included Parthenium hysterophorus (PH), Eucalyptus obliqua (EO), Cannabis sativa (CS) each one used at five different concentrations selected as multiple (0.25, 0.5, 1, 2, 4) of their LC 50 values determined on the basis of preliminary trials. Constant ratio combination design was used for mixing the individual components. Different component mixtures included combinations of (PH + CS), (PH+EO), (EO+CS), (PH+CS+EO) each mixed at five concentration levels (same levels). Similarly, each of the essential oil was mixed with alpha Cypermethrin in combinations of multiple (0.25, 0.5, 1, 2, 4) of their LC 50 values. Toxicity of individual components as well as mixtures was determined by using dry film residue method. The response to Toxicity response exposure was estimated using the median-effect equation, as described by Chou and Talalay (1984). Interactions of these mixtures were studied using the combination-index (CI) equation method using the software Compusyn that is based on general equation of dose and effect and its theorem of combination index developed by using the approach of merging the physicochemical principle of the mass-action law with the mathematical principle of induction and deduction. LC values of individual essential oils as determined by the model were 0.55, 0.398 and 0.572 for C. sativa, P. hysterophorus and E. obliqua respectively. Cypermethrin exhibited LC50 value of 0.00353. When binary combination of cypermethrin and c. sativa were tested, the value of CI ranged between 0.53-1.74. (<1 being synergism) was observed only for the mixture combining 0.25(LC50) but the effect size was small (fa=0.6). All the binary combinations of cypermethrin alpha and P. hysterophorus showed antagonistic effect only. Cypermethrin when combined with E. obliqua indicated synergism at 0.25(LC50) and 4(LC50) with effect size of 0.68% and 0.9% respectively. In combination mixing all the three Eos with pyrethroids showed synergism only at highest concentration 4(LC50) with a very high effect size (fa=0.99). When Eos were mixed to see their synergistic effect, combination of P. hysterophorus with E. obliqua. Showed a moderate synergism (CI= 0.77) at the lowest concentration tested 0.25 (LC50) but the effect size was relatively smaller (fa=0.52). All the combination of C. sativa and E. obliqua showed antagonism (CI=1.26-2.09). In a binary combination of P. hysterophorus and C. sativa, a high level of synergism was observed at the highest concentration combination 4(LC50) with a very high effect size (fa=0.99). When all the three Eos were combined, Synergism was observed at 2(LC50) and 4(LC50) combinations with a high affect size (fa=>0.98).

Abstract Signalling pathways are sequences of events that manage information flow within an organism in response to both external and internal stimuli. The hypothalamic–pituitary–adrenal (HPA) axis is the main stress-responding neuroendocrine subsystem. It is characterized by a vast array of signalling pathways, networks and feedback loops occurring at various temporal and spatial scales. Comprehending the complexities of signalling mechanisms, as well as the involvement of signalling actors, is vital for elucidating their implications in stress-related disorders and overall health. Herein, we elaborate on the regulatory signalling mechanisms of the human HPA axis, determined by integrating published experimental findings with insights from reaction network modelling, deterministic mass-action chemical kinetics and stoichiometric network analysis (SNA). A simplification of the complex interplay between signalling pathways governed by the hypothalamic corticotropin-releasing hormone (CRH) and arginine vasopressin (AVP) was of particular interest. Our findings highlight the importance of multiple parallel signalling pathways in maintaining homeostasis and generating optimal adaptive responses to stress. Their potential to support an organism’s self-protective capacity is also indicated. The proposed interdisciplinary approach, which provides distinctive insights, can be useful in designing and interpreting the corresponding real experiments.

Abstract Modeling gas‐phase atmospheric chemistry is computationally challenging because the underlying dynamics are high‐dimensional (requiring many state variables) and stiff (characterized by Jacobian eigenvalues that span many orders of magnitude). Previous work has demonstrated the promise of machine learning (ML) to accelerate air quality model simulations, but such models commonly suffer from dynamical instability or runaway error propagation. Here, to address this limitation, we introduce a physics‐informed parsimonious machine‐learning framework for atmospheric chemistry. This Sparse Identification of Mass Action Dynamics (SIMADy) framework operates by (a) using a linear autoencoder to create an interpretably‐compressed low‐dimensional state representation, and (b) representing the underlying dynamics of that state constrained by the law of mass action and therefore ensuring boundedness. Using the full Master Chemical Mechanism—one of the most detailed atmospheric chemical mechanisms—as the reference model, the root mean square (RMS) error of the ML model prediction for ozone () concentration over 10 days is 25% of the RMS reference model concentration across all simulations in testing data set when using six state variables. As expected, the ML model predictions remain bounded and exhibit no numerical divergence in all tested simulations. The surrogate model is 5,300 times faster on a CPU (for one simulation) and approximately 1.1 million times faster on a GPU (for many simulations in parallel) compared to the reference model. In future work, the fast, stable, and relatively accurate surrogate models learned by SIMADy can be used to accelerate 3D models of air quality and climate.

Accurate, efficient, and explainable modeling of the dynamics of acute respiratory infections (ARIs) remains, in many aspects, a significant challenge. While compartmental models such as SIR (Susceptible–Infected–Recovered) remain widely used for that purpose due to their simplicity, they cannot capture the complicated multiscale nature of disease progression which unites individual-level interactions affecting the initial phase of an outbreak and mass action laws governing the disease transmission in its general phase. Individual-based models (IBMs) offer a detailed representation capable of capturing these transmission nuances but have high computational demands. In this work, we explore hybrid and surrogate approaches to accelerate forecasting of acute respiratory infection dynamics performed via detailed epidemic models. The hybrid approach combines IBMs and compartmental models, dynamically switching between them with the help of statistical and ML-based methods. The surrogate approach, on the other hand, replaces IBM simulations with trained autoencoder approximations. Our results demonstrate that the usage of machine learning techniques and hybrid modeling allows us to obtain a significant speed–up compared to the original individual-based model—up to 1.6–2 times for the hybrid approach and up to times in case of a surrogate model—without compromising accuracy. Although the suggested approaches cannot fully replace the original model, under certain scenarios they make forecasting with fine-grained epidemic models much more feasible for real-time use in epidemic surveillance.

Alzheimer’s disease (AD) is characterized by the accumulation of amyloid beta, which is strongly associated with disease progression and cognitive decline. Despite the approval of monoclonal antibodies targeting Aβ, optimizing treatment strategies while minimizing side effects remains a challenge. This study develops a mathematical framework to model Aβ aggregation dynamics, capturing the transition from monomers to higher-order aggregates, including protofibrils, toxic oligomers, and fibrils, using mass-action kinetics and coarse-grained modeling. Parameter estimation, sensitivity analysis, and data-driven calibration ensure model robustness. An optimal control framework is introduced to identify the optimal dose of the drug as a control function that reduces toxic oligomers and fibrils while minimizing adverse effects, such as amyloid-related imaging abnormalities (ARIA). The results indicate that Donanemab achieves the most significant reduction in fibrils. These findings provide a quantitative basis for optimizing AD treatments, providing valuable insight into the balance between therapeutic efficacy and safety.

This work addresses multistationarity of fully open reaction networks equipped with mass action kinetics. We improve upon existing results relating existence of positive feedback loops in a reaction network and multistationarity; and we provide a novel deterministic operation to generate new non-multistationary networks. This is interesting because while there were many operations to create infinitely many new multistationary networks from a multistationary example, this is the first such operation for the non-multistationary counterpart. Such tools for the generation of example networks have a use-case in the application of data science to reaction network theory. We demonstrate this by using new data, along with a novel graph representation of reaction networks that is unique up to a permutation on the name of species of the network, to train a graph attention neural network model to predict multistationarity of reaction networks. This is the first time machine learning tools are used for studying classification problems of reaction networks.

Abstract Apoptosis, traditionally regarded as a straightforward cell‐suicide process triggered by cellular stress, plays a vital role in development, immune function, and disease progression. This research presents a synthetic model of the intrinsic (mitochondrial) apoptosis pathway, focusing on programmed cell death initiated by severe DNA damage. Through an in vitro approach, the study quantitatively analyzes apoptotic behavior using mathematical formulations of key regulatory proteins, modeled with ordinary differential equations using Law of Mass Action. A comprehensive system model is developed to capture the full signaling cascade of apoptosis. Furthermore, a novel cytomorphic model is introduced, employing Metal Oxide Semiconductor (MOS) technology to simulate molecular dynamics by drawing parallels with electron flow in transistors. The analytical output of the model reveals time‐dependent protein activity profiles, accurately representing the distinct phases of apoptosis. Notably, simulations show a rapid rise in Caspase‐3 activity following an apoptotic trigger, consistent with its role as an executioner caspase. The electronic circuit model is validated against experimental data from cell culture studies, reinforcing its accuracy and biological relevance. Additionally, the hardware implementation of the apoptosis‐based cytomorphic system is realized using the NI myRIO 1900 tool, demonstrating practical feasibility and integration potential. These findings demonstrate that MOS‐based electronic analogs of apoptosis pathways can effectively mimic protein behavior, offering a faster, more cost‐effective, and safer platform for pharmaceutical research and drug development.

This paper investigates the centre bifurcation of the smallest bimolecular mass-action system. A three-dimensional reaction network, consisting of three species and four reactions, governed by mass-action kinetics with a positive equilibrium point, is considered. In addition to the stability analysis of the equilibrium point, the dynamic directions of the model in its planes are examined. In \cite{Banaji2023}, it is shown that the equilibrium point is classified as a centre when the reaction rate constants satisfy a specific condition, leading to a vertical Andronov-Hopf bifurcation. It is demonstrated that only one limit cycle can bifurcate from the centre equilibrium point using a bifurcation technique.