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Large deviation theory (LDT) provides a mathematical framework to quantify the probabilities of rare events in stochastic systems. In this study, we applied LDT to model a chemical reaction system and demonstrated that the fluctuation theorem for nonequilibrium reaction systems can be derived from the symmetry of the cumulant generating function defined through the rate function. Notably, this derivation does not depend on the assumption of local detailed balance. Furthermore, we redefined heat using this rate function based on information theory and evaluated Landauer's principle, which addresses the minimum energy cost associated with information erasure. These findings show the utility of LDT as a comprehensive framework for analyzing a wide range of nonequilibrium systems.

We study pattern formation of skin cancers by means of numerical simulation of a binary system consisting of cancer and healthy cells. We extend the conventional Model H for macrophase separations by considering a logistic growth of cancer cells and also a mechanical friction between dermis and epidermis. Importantly, our model exhibits a microphase separation due to the proliferation of cancer cells. By numerically solving the time evolution equations of the cancer composition and its velocity, we show that the phase separation kinetics strongly depends on the cell proliferation rate as well as on the strength of hydrodynamic interactions. A steady state diagram of cancer patterns is established in terms of these two dynamical parameters and some of the patterns correspond to clinically observed cancer patterns. Furthermore, we examine in detail the time evolution of the average composition of cancer cells and the characteristic length of the microstructures. Our results demonstrate that different sequence of cancer patterns can be obtained by changing the proliferation rate and/or hydrodynamic interactions., Comment: Supplementaly materials (Movies) are not included

It is generally difficult to predict the positions of mutations in genomic DNA at the nucleotide level. Retroviral DNA insertion is one mode of mutation, resulting in host infections that are difficult to treat. This mutation process involves the integration of retroviral DNA into the host-infected cellular genomic DNA following the interaction between host DNA and a pre-integration complex consisting of retroviral DNA and integrase. Here, we report that retroviral insertion sites around a hotspot within the Zfp521 and N-myc genes can be predicted by a periodic function that is deduced using the diffraction lattice model. In conclusion, the mutagenesis process is described by a biophysical model for DNA-DNA interactions.

A cell has the ability to convert an environmental change into the expression of genetic information through a chain of intracellular signal transduction reactions. Here, we aimed to develop a method for quantifying this signal transduction. We showed that the channel capacities of individual steps in a given general model cascade were equivalent in an independent manner, and were given by the entropy production rate. Signal transduction was transmitted by fluctuation of the entropy production rate and quantified transduction was estimated by the work done in individual steps. If the individual step representing the modification to demodification of the signal molecules is considered to be a Szilard engine, the maximal work done is equivalent to the chemical potential change of the messenger that is consumed during the modification reaction. Our method was applicable to calculate the channel capacity of the MAPK cascade. In conclusion, our method is suitable for quantitative analyses of signal transduction.

Cells can be considered as systems that utilize changes in thermodynamic entropy as information. Therefore, they serve as useful models for investigating the relationships between entropy production and information transmission, i.e., signal transduction. Based on the hypothesis that cells apply a chemical reaction cascade for the most efficient transduction of information, we adopted a coding design that minimizes the number of bits per concentration of molecules that are employed for information transduction. As a result, the average rate of entropy production is uniform across all cycles in a cascade reaction. Thus, the entropy production rate can be a valuable measure for the quantification of intracellular signal transduction., Comment: This article is retitled as "Quantifying the information transduction of biochemical reaction cascades: transcription of mRNA from ligand stimulation " (arXiv:1701.01511)

Protein assembly plays an important role in the regulation of biological systems. The cytoskeleton assembly activity is provided by the binding cofactors GTP (guanidine triphosphate) or ATP(adenosine triphosphate) to monomeric protein, and is initiated by assembling the monomeric proteins. The binding GTP or ATP is hydrolyzed to GDP (guanidine diphosphate) or ADP (adenosine diphosphate) by the monomeric enzymatic activity. This self-limited assembly is characteristic of the cytoskeleton. To quantitatively evaluate the assembly kinetics, we propose a nonlinear and non-equilibrium kinetic model, with the nonlinearity provided by the fluctuation in monomer concentrations during the diffusion. Numerical simulations suggest that the assembly and disassembly oscillates in a chaos-like manner. We use a kinetic analysis of the center manifold around the critical point to show that minimal increases in ATP/GTP concentrations may lead to some attenuation in the amplification of these fluctuations. The present model and our application of center manifold theory illustrate a unique feature of protein assemblies, and our stability analysis provides an analytical methodology for the biological reaction system.

The field of information science has greatly developed, and applications in various fields have emerged. In this paper, we evaluated the coding system in the theory of Tsallis entropy for transmission of messages and aimed to formulate the channel capacity by maximization of the Tsallis entropy within a given condition of code length. As a result, we obtained a simple relational expression between code length and code appearance probability and, additionally, a generalized formula of the channel capacity on the basis of Tsallis entropy statistics. This theoretical framework may contribute to data processing techniques and other applications.

Living organisms are non-equilibrium, fluctuating, dynamic systems containing multi-step biological signaling cascades (BSC) with the ability to transduce changes in the concentration of extracellular molecules such as cytokines into changes in gene expression. Here, we derived basic equations that describe the channel capacity and information density of BSC in terms of the average entropy production rate deduced using the fluctuation theorem., Comment: Another article arXiv:1205.0382 [q-bio.MN] "The channel capacity and information density of biochemical signaling cascades " is the revised version of this article

Many physical, chemical and biological systems exhibit a cooperative or sigmoidal response with respect to the input. In biochemistry, such behavior is called an allosteric effect. Here we demonstrate that a system with such properties can be used to discriminate the amplitude or frequency of an external periodic perturbation or input. Numerical simulations performed for a model sigmoidal kinetics illustrate that there exists a narrow range of frequencies and amplitudes within which the system evolves toward significantly different states. Therefore, observation of system evolution should provide information about the characteristics of the perturbation. The discrimination properties for periodic perturbation are generic. They can be observed in various dynamical systems and for different types of periodic perturbation. \end{abstract}, Comment: 13 pages of text, 7 figures, 19 references

Living cell signaling systems include multistep biochemical signaling reaction cascades (BSCs) comprising modifications of molecular signaling proteins. Substantial data on BSCs have been accumulated in the field of molecular biology and the analysis of signaling systems requires qualitative evaluation. However, quantification of the information and channel capacity of BSCs has not been focused on from the perspective of information theory. In the current study, we aimed to derive basic equations for describing the channel capacity and information density of BSCs using the fluctuation theorem. From the results, channel capacity and information density can be described using the average entropy production rate when the signaling system is minimally redundant. The channel capacity could actually be calculated for the mitogen-activated protein kinase BSC when it was minimally redundant. This quantitative method of examination is applicable to the quantitative analysis of BSCs.