The infectious propagation of SARS-CoV-2 is continuing worldwide, and specifically, Japan is facing severe circumstances. Medical resource maintenance and action limitations remain the central ...measures. An analysis of long-term follow-up reports in Japan shows that the infection number follows a unique wavy oscillation, increasing and decreasing over time. However, only a few studies explain the infection wavy oscillation. This study introduces a novel nonlinear mathematical model of the new infection wavy oscillation by applying the macromolecule diffusion theory. In this model, the diffusion coefficient that depends on population density gives nonlinearity in infection propagation. As a result, our model accurately simulated infection wavy oscillations, and the infection wavy oscillation frequency and amplitude were closely linked with the recovery rate of infected individuals. In conclusion, our model provides a novel nonlinear contact infection analysis framework.
•The entropy production rate per signal molecule is conserved in the nonlinear signal transduction system.•We obtained a condition in which the Onsager’s reciprocity theorem holds even in the ...nonlinear signal transduction system.•Fluctuation circulation was newly introduced to describe the signal transduction amount.
Cell signal transduction is an example of a nonequilibrium phenomenon. In this study, a nonequilibrium nonlinear thermodynamic model was formulated. First, we obtained a condition in which the Onsager’s reciprocity theorem holds in the signal transduction. Second, it was found that the entropy production rate per signal molecule is conserved through signal transduction. Finally, it was determined that when Onsager’s reciprocity theorem does not hold, fluctuation circulation is given by the phosphorylation rate of signal molecules. The simple relation implies that the fluctuation circulation can be an essential quantity of the signal transduction amount. These results expand the limit of nonequilibrium thermodynamics and can be used to provide ideas for signal transduction quantification.
Recent advancements in information thermodynamics have revealed that information can be directly converted into mechanical work. Specifically, RNA transcription and nanopore sequencing serve as prime ...examples of this conversion, by reading information from a DNA template. This paper introduces an information thermodynamic model in which these molecular motors can move along the DNA template by converting the information read from the template DNA into their own motion. This process is a stochastic one, characterized by significant fluctuations in forward movement and is described by the Fokker-Planck equation, based on drift velocity and diffusion coefficients. In the current study, it is hypothesized that by utilizing the sequence information of the template DNA as mutual information, the fluctuations can be reduced, thereby biasing the forward movement on DNA and, consequently, reducing reading errors. Further research into the conversion of biological information by molecular motors could unveil new applications, insights, and important findings regarding the characteristics of information processing in biology.
Queuing networks (QNs) are essential models in operations research, with applications in cloud computing and healthcare systems. However, few studies have analyzed the cell's biological signal ...transduction using QN theory. This study entailed the modeling of signal transduction as an open Jackson's QN (JQN) to theoretically determine cell signal transduction, under the assumption that the signal mediator queues in the cytoplasm, and the mediator is exchanged from one signaling molecule to another through interactions between the signaling molecules. Each signaling molecule was regarded as a network node in the JQN. The JQN Kullback-Leibler divergence (KLD) was defined using the ratio of the queuing time (λ) to the exchange time (μ), λ/μ. The mitogen-activated protein kinase (MAPK) signal-cascade model was applied, and the KLD rate per signal-transduction-period was shown to be conserved when the KLD was maximized. Our experimental study on MAPK cascade supported this conclusion. This result is similar to the entropy-rate conservation of chemical kinetics and entropy coding reported in our previous studies. Thus, JQN can be used as a novel framework to analyze signal transduction.
Immunoglobulin A (IgA) promotes health by regulating the composition and function of gut microbiota, but the molecular requirements for such homeostatic IgA function remain unknown. We found that a ...heavily glycosylated monoclonal IgA recognizing ovalbumin coats
(
), a prominent gut symbiont of the phylum Bacteroidetes. In vivo, IgA alters the expression of polysaccharide utilization loci (PUL), including a functionally uncharacterized molecular family provisionally named Mucus-Associated Functional Factor (MAFF). In both mice and humans, MAFF is detected predominantly in mucus-resident bacteria, and its expression requires the presence of complex microbiota. Expression of the MAFF system facilitates symbiosis with other members of the phylum Firmicutes and promotes protection from a chemically induced model of colitis. Our data reveal a novel mechanism by which IgA promotes symbiosis and colonic homeostasis.
A biological signal is transmitted by interactions between signaling molecules in the cell. To date, there have been extensive studies regarding signaling pathways using numerical simulation of ...kinetic equations that are based on equations of continuity and Fick's law. To obtain a mathematical formulation of cell signaling, we propose a stability kinetic model of cell biological signaling of a simple two-parameter model based on the kinetics of the diffusion-limiting step. In the present model, the signaling is regulated by the binding of a cofactor, such as ATP. Non-linearity of the kinetics is given by the diffusion fluctuation in the interaction between signaling molecules, which is different from previous works that hypothesized autocatalytic reactions. Numerical simulations showed the presence of a critical concentration of the cofactor beyond which the cell signaling molecule concentration is altered in a chaos-like oscillation with frequency, which is similar to a discontinuous phase transition in physics. Notably, we found that the frequency is given by the logarithm function of the difference of the outside cofactor concentration from the critical concentration. This implies that the outside alteration of the cofactor concentration is transformed into the oscillatory alteration of cell inner signaling. Further, mathematical stability kinetic analysis predicted a discontinuous dynamic phase transition in the critical state at which the cofactor concentration is equivalent to the critical concentration. In conclusion, the present model illustrates a unique feature of cell signaling, and the stability analysis may provide an analytical framework of the cell signaling system and a novel formulation of biological signaling.
A model of signal transduction from the perspective of informational thermodynamics has been reported in recent studies, and several important achievements have been obtained. The first achievement ...is that signal transduction can be modelled as a binary code system, in which two forms of signalling molecules are utilised in individual steps. The second is that the average entropy production rate is consistent during the signal transduction cascade when the signal event number is maximised in the model. The third is that a Szilard engine can be a single-step model in the signal transduction. This article reviews these achievements and further introduces a new chain of Szilard engines as a biological reaction cascade (BRC) model. In conclusion, the presented model provides a way of computing the channel capacity of a BRC.
Kullback-Leibler divergence (KLD) is a type of extended mutual entropy, which is used as a measure of information gain when transferring from a prior distribution to a posterior distribution. In this ...study, KLD is applied to the thermodynamic analysis of cell signal transduction cascade and serves an alternative to mutual entropy. When KLD is minimized, the divergence is given by the ratio of the prior selection probability of the signaling molecule to the posterior selection probability. Moreover, the information gain during the entire channel is shown to be adequately described by average KLD production rate. Thus, this approach provides a framework for the quantitative analysis of signal transduction. Moreover, the proposed approach can identify an effective cascade for a signaling network.
•When the whole entropy production rate in the cell signal transduction is minimized, the entropy production rate per signaling molecule is found to be conserved during the signal cascade.•The signal ...transduction system is carried out with a balance between the entropy production.•Non- equilibrium thermodynamics gives a theoretical framework for cell signal cascades.
Studies have reported that bio-cellular signal transduction can be investigated based on thermodynamics. This short article aims to consider signal transduction carried out by signaling molecules from the perspective of non-equilibrium thermodynamics. Under conditions in which total entropy production rate was minimized, the entropy production rate per signaling molecule was conserved independently of the steps during signal transduction. Accordingly, the conserved production rate can be defined as the channel capacity of the given signal transduction cascade. Non- equilibrium thermodynamics provides a theoretical framework for cell signal transduction.
Many studies have been performed to quantify cell signaling. Cell signaling molecules are phosphorylated in response to extracellular stimuli, with the phosphorylation sequence forming a signal ...cascade. The information gain during a signal event is given by the logarithm of the phosphorylation molecule ratio. The average information gain can be regarded as the signal transduction quantity (ST), which is identical to the Kullback-Leibler divergence (KLD), a relative entropy. We previously reported that if the total ST value in a given signal cascade is maximized, the ST rate (STR) of each signaling molecule per signal duration (min) approaches a constant value. To experimentally verify this theoretical conclusion, we measured the STR of the epidermal growth factor (EGF)-related cascade in A431 skin cancer cells following stimulation with EGF using antibody microarrays against phosphorylated signal molecules. The results were consistent with those from the theoretical analysis. Thus, signaling transduction systems may adopt a strategy that prioritizes the maximization of ST. Furthermore, signal molecules with similar STRs may form a signal cascade. In conclusion, ST and STR are promising properties for quantitative analysis of signal transduction.
PDF
