Search Results (21)

This paper analyses several mathematical games developed 50 years ago by Manfred Eigen and Ruthild Winkler in their famous book “Laws of the Game: How the Principles of Nature Govern Chance,” published for the first time in German in 1975. These games are intended to represent the essential aspects of chemical selection processes via symmetry breaking in biological systems. Special attention is paid to games that model biochemical kinetics, in which a chessboard is used to represent different types of substrates. The time-dependent statistical outcomes of several games are studied by Monte Carlo techniques. Analytical stochastic models applied to these games relate game rules to partial differential equation problems with appropriate initial and boundary conditions: rationalizing their outcomes, they confirm the intuitions of the original authors and add new insights. The potential impact of game-based models on current research on biological homochirality is discussed. Full article

With the increasing emphasis on energy-efficient computing, edge devices accelerated by graphics processing units (GPUs) are gaining attention for their potential in scientific workloads. These platforms support compute-intensive simulations under strict energy and resource constraints, yet their computational efficiency across architectures remains an open question. This study evaluates the performance of GPU-based edge platforms for executing the stochastic simulation algorithm (SSA), a widely used and inherently compute-intensive method for modeling biochemical and physical systems. Execution time, floating point throughput, and the trade-offs between cost and power consumption are analyzed, with a focus on how variations in core count, clock speed, and architectural features impact SSA scalability. Experimental results show that the Jetson Orin NX consistently outperforms Xavier NX and Orin Nano in both speed and efficiency, reaching up to 4.86 million iterations per second while operating under a 20 W power envelope. At the largest workload scale, it achieves 2102.7 ms/W in energy efficiency and 105.3 ms/USD in cost-performance—substantially better than the other Jetson devices. These findings highlight the architectural considerations necessary for selecting edge GPUs for scientific computing and offer practical guidance for deploying compute-intensive workloads beyond artificial intelligence (AI) applications. Full article

Biochemical reaction systems in a cell exhibit stochastic behaviour, owing to the unpredictable nature of the molecular interactions. The fluctuations at the molecular level may lead to a different behaviour than that predicted by the deterministic model of the reaction rate equations, when some reacting species have low population numbers. As a result, stochastic models are vital to accurately describe system dynamics. Sensitivity analysis is an important method for studying the influence of the variations in various parameters on the output of a biochemical model. We propose a finite-difference strategy for approximating second-order parametric sensitivities for stochastic discrete models of biochemically reacting systems. This strategy utilizes adaptive tau-leaping schemes and coupling of the perturbed and nominal processes for an efficient sensitivity estimation. The advantages of the new technique are demonstrated through its application to several biochemical system models with practical significance. Full article

Excessive nitrogen (N) fertilization harms the diversity, structure, and function of the soil microbiome. Yet, whether such adverse effects can be repaired through reducing the subsequent N fertilization rate remains not completely clear so far. Here, using a long-term N-overfertilized wheat-maize cropping field, we assessed the effect of reducing various proportions of the subsequent N fertilization rate over six years on crop productivity, soil physicochemical and biochemical properties, and microbiome. Five treatments were employed in our field experiment: the farmers’ conventional N fertilization rate (zero reduction, as a control) and the reduction in the farmers’ N rate by 20%, 40%, 60%, and 100%. The results showed that moderate N reduction (20–40%) enhanced crop productivity and soil fertility but did not affect soil enzyme activity. Soil bacterial and fungal community diversity were insensitive to N fertilization reduction, whereas their community structures changed significantly, with more prominent alteration in the fungal community. Functional prediction indicated that average relative abundance of arbuscular mycorrhizal fungi increased with N fertilization reduction but that of ectomycorrhizal fungi decreased. Moderate N reduction (20–40%) enhanced species interactions and, thus, provided a more complex cross-kingdom microbial co-occurrence network. Both bacterial and fungal community assembly were governed by stochastic processes, and this was not altered by N fertilization reduction. Overall, the response of the soil microbiome to N fertilization reduction was greatly dependent on the reduced N proportion. The findings obtained here shed light on the importance of optimal N fertilization rate in the intensively cultivated, high-input grain production system. Full article

Cell polarity refers to the asymmetric distribution of proteins and other molecules along a specified axis within a cell. Polarity establishment is the first step in many cellular processes. For example, directed growth or migration requires the formation of a cell front and back. In many cases, polarity occurs in the absence of spatial cues. That is, the cell undergoes symmetry breaking. Understanding the molecular mechanisms that allow cells to break symmetry and polarize requires computational models that span multiple spatial and temporal scales. Here, we apply a multiscale modeling approach to examine the polarity circuit of yeast. In addition to symmetry breaking, experiments revealed two key features of the yeast polarity circuit: bistability and rapid dismantling of the polarity site following a loss of signal. We used modeling based on ordinary differential equations (ODEs) to investigate mechanisms that generate these behaviors. Our analysis revealed that a model involving positive and negative feedback acting on different time scales captured both features. We then extend our ODE model into a coarse-grained reaction–diffusion equation (RDE) model to capture the spatial profiles of polarity factors. After establishing that the coarse-grained RDE model qualitatively captures key features of the polarity circuit, we expand it to more accurately capture the biochemical reactions involved in the system. We convert the expanded model to a particle-based model that resolves individual molecules and captures fluctuations that arise from the stochastic nature of biochemical reactions. Our models assume that negative regulation results from negative feedback. However, experimental observations do not rule out the possibility that negative regulation occurs through an incoherent feedforward loop. Therefore, we conclude by using our RDE model to suggest how negative feedback might be distinguished from incoherent feedforward regulation. Full article

Biophysical factors play a fundamental role in human embryonic development. Traditional in vitro models of organogenesis focused on the biochemical environment and did not consider the effects of mechanical forces on developing tissue. While most human tissue has a Young’s modulus in the low kilopascal range, the standard cell culture substrate, plasma-treated polystyrene, has a Young’s modulus of 3 gigapascals, making it 10,000–100,000 times stiffer than native tissues. Modern in vitro approaches attempt to recapitulate the biophysical niche of native organs and have yielded more clinically relevant models of human tissues. Since Clevers’ conception of intestinal organoids in 2009, the field has expanded rapidly, generating stem-cell derived structures, which are transcriptionally similar to fetal tissues, for nearly every organ system in the human body. For this reason, we conjecture that organoids will make their first clinical impact in fetal regenerative medicine as the structures generated ex vivo will better match native fetal tissues. Moreover, autologously sourced transplanted tissues would be able to grow with the developing embryo in a dynamic, fetal environment. As organoid technologies evolve, the resultant tissues will approach the structure and function of adult human organs and may help bridge the gap between preclinical drug candidates and clinically approved therapeutics. In this review, we discuss roles of tissue stiffness, viscoelasticity, and shear forces in organ formation and disease development, suggesting that these physical parameters should be further integrated into organoid models to improve their physiological relevance and therapeutic applicability. It also points to the mechanotransductive Hippo-YAP/TAZ signaling pathway as a key player in the interplay between extracellular matrix stiffness, cellular mechanics, and biochemical pathways. We conclude by highlighting how frontiers in physics can be applied to biology, for example, how quantum entanglement may be applied to better predict spontaneous DNA mutations. In the future, contemporary physical theories may be leveraged to better understand seemingly stochastic events during organogenesis. Full article

During the development of the nervous system, neuronal cells extend axons and dendrites that form complex neuronal networks, which are essential for transmitting and processing information. Understanding the physical processes that underlie the formation of neuronal networks is essential for gaining a deeper insight into higher-order brain functions such as sensory processing, learning, and memory. In the process of creating networks, axons travel towards other recipient neurons, directed by a combination of internal and external cues that include genetic instructions, biochemical signals, as well as external mechanical and geometrical stimuli. Although there have been significant recent advances, the basic principles governing axonal growth, collective dynamics, and the development of neuronal networks remain poorly understood. In this paper, we present a detailed analysis of nonlinear dynamics for axonal growth on surfaces with periodic geometrical patterns. We show that axonal growth on these surfaces is described by nonlinear Langevin equations with speed-dependent deterministic terms and gaussian stochastic noise. This theoretical model yields a comprehensive description of axonal growth at both intermediate and long time scales (tens of hours after cell plating), and predicts key dynamical parameters, such as speed and angular correlation functions, axonal mean squared lengths, and diffusion (cell motility) coefficients. We use this model to perform simulations of axonal trajectories on the growth surfaces, in turn demonstrating very good agreement between simulated growth and the experimental results. These results provide important insights into the current understanding of the dynamical behavior of neurons, the self-wiring of the nervous system, as well as for designing innovative biomimetic neural network models. Full article

This paper aims to explain the transition to multicellularity as a consequence of the evolutionary response to stress. The proposed model is composed of three parts. The first part details stochastic biochemical kinetics within a reactor (potentially compartmentalized), where kinetic rates are influenced by random stress parameters, such as temperature, toxins, oxidants, etc. The second part of the model is a feedback mechanism governed by a genetic regulation network (GRN). The third component involves stochastic dynamics that describe the evolution of this network. We assume that the organism remains viable as long as the concentrations of certain key reagents are maintained within a defined range (the homeostasis domain). For this model, we calculate the probability estimate that the system will stay within the homeostasis domain under stress impacts. Under certain assumptions, we show that a GRN expansion increases the viability probability in a very sharp manner. It is shown that multicellular organisms increase their viability due to compartment organization and stem cell activity. By the viability probability estimates, an explanation of the Peto paradox is proposed: why large organisms are stable with respect to cancer attacks. Full article

Stochastic modeling of biochemical processes at the cellular level has been the subject of intense research in recent years. The Chemical Master Equation is a broadly utilized stochastic discrete model of such processes. Numerous important biochemical systems consist of many species subject to many reactions. As a result, their mathematical models depend on many parameters. In applications, some of the model parameters may be unknown, so their values need to be estimated from the experimental data. However, the problem of parameter value inference can be quite challenging, especially in the stochastic setting. To estimate accurately the values of a subset of parameters, the system should be sensitive with respect to variations in each of these parameters and they should not be correlated. In this paper, we propose a technique for detecting collinearity among models’ parameters and we apply this method for selecting subsets of parameters that can be estimated from the available data. The analysis relies on finite-difference sensitivity estimations and the singular value decomposition of the sensitivity matrix. We illustrated the advantages of the proposed method by successfully testing it on several models of biochemical systems of practical interest. Full article

This study discusses the calculation of entropy of discrete-time stochastic biological systems. First, measurement methods of the system entropy of discrete-time linear stochastic networks are introduced. The system entropy is found to be characterized by system matrices of the discrete-time biological systems. Secondly, the system entropy of nonlinear discrete-time stochastic biological systems is discussed and is calculated based on a global linearization method. The approximation of the values of system entropy of nonlinear stochastic systems needs to solve an optimization problem that is constrained by a kind of linear matrix inequality (LMI). Finally, a practical biochemical system is provided to verify the effectiveness of the proposed calculation method. Full article

The parameter estimation (PE) of biochemical reactions is one of the most challenging tasks in systems biology given the pivotal role of these kinetic constants in driving the behavior of biochemical systems. PE is a non-convex, multi-modal, and non-separable optimization problem with an unknown fitness landscape; moreover, the quantities of the biochemical species appearing in the system can be low, making biological noise a non-negligible phenomenon and mandating the use of stochastic simulation. Finally, the values of the kinetic parameters typically follow a log-uniform distribution; thus, the optimal solutions are situated in the lowest orders of magnitude of the search space. In this work, we further elaborate on a novel approach to address the PE problem based on a combination of adaptive swarm intelligence and dilation functions (DFs). DFs require prior knowledge of the characteristics of the fitness landscape; therefore, we leverage an alternative solution to evolve optimal DFs. On top of this approach, we introduce surrogate Fourier modeling to simplify the PE, by producing a smoother version of the fitness landscape that excludes the high frequency components of the fitness function. Our results show that the PE exploiting evolved DFs has a performance comparable with that of the PE run with a custom DF. Moreover, surrogate Fourier modeling allows for improving the convergence speed. Finally, we discuss some open problems related to the scalability of our methodology. Full article

The Chemical Master Equation is a standard approach to model biochemical reaction networks. It consists of a system of linear differential equations, in which each state corresponds to a possible configuration of the reaction system, and the solution describes a time-dependent probability distribution over all configurations. The Stochastic Simulation Algorithm (SSA) is a method to simulate sample paths from this stochastic process. Both approaches are only applicable for small systems, characterized by few reactions and small numbers of molecules. For larger systems, the CME is computationally intractable due to a large number of possible configurations, and the SSA suffers from large reaction propensities. In our study, we focus on catalytic reaction systems, in which substrates are converted by catalytic molecules. We present an alternative description of these systems, called SiCaSMA, in which the full system is subdivided into smaller subsystems with one catalyst molecule each. These single catalyst subsystems can be analyzed individually, and their solutions are concatenated to give the solution of the full system. We show the validity of our approach by applying it to two test-bed reaction systems, a reversible switch of a molecule and methyltransferase-mediated DNA methylation. Full article

Living systems are open systems, where the laws of nonequilibrium thermodynamics play the important role. Therefore, studying living systems from a nonequilibrium thermodynamic aspect is interesting and useful. In this review, we briefly introduce the history and current development of nonequilibrium thermodynamics, especially that in biochemical systems. We first introduce historically how people realized the importance to study biological systems in the thermodynamic point of view. We then introduce the development of stochastic thermodynamics, especially three landmarks: Jarzynski equality, Crooks’ fluctuation theorem and thermodynamic uncertainty relation. We also summarize the current theoretical framework for stochastic thermodynamics in biochemical reaction networks, especially the thermodynamic concepts and instruments at nonequilibrium steady state. Finally, we show two applications and research paradigms for thermodynamic study in biological systems. Full article

Individual (bio)chemical entities could show a very heterogeneous behaviour under the same conditions that could be relevant in many biological processes of significance in the life sciences. Conventional detection approaches are only able to detect the average response of an ensemble of entities and assume that all entities are identical. From this perspective, important information about the heterogeneities or rare (stochastic) events happening in individual entities would remain unseen. Some nanoscale tools present interesting physicochemical properties that enable the possibility to detect systems at the single-entity level, acquiring richer information than conventional methods. In this review, we introduce the foundations and the latest advances of several nanoscale approaches to sensing and imaging individual (bio)entities using nanoprobes, nanopores, nanoimpacts, nanoplasmonics and nanomachines. Several (bio)entities such as cells, proteins, nucleic acids, vesicles and viruses are specifically considered. These nanoscale approaches provide a wide and complete toolbox for the study of many biological systems at the single-entity level. Full article

Inference of biochemical network models from experimental data is a crucial problem in systems and synthetic biology that includes parameter calibration but also identification of unknown interactions. Stochastic modelling from single-cell data is known to improve identifiability of reaction network parameters for specific systems. However, general results are lacking, and the advantage over deterministic, population-average approaches has not been explored for network reconstruction. In this work, we study identifiability and propose new reconstruction methods for biochemical interaction networks. Focusing on population-snapshot data and networks with reaction rates affine in the state, for parameter estimation, we derive general methods to test structural identifiability and demonstrate them in connection with practical identifiability for a reporter gene in silico case study. In the same framework, we next develop a two-step approach to the reconstruction of unknown networks of interactions. We apply it to compare the achievable network reconstruction performance in a deterministic and a stochastic setting, showing the advantage of the latter, and demonstrate it on population-snapshot data from a simulated example. Full article