Diversity, Stability, Recursivity, and Rule Generation in Biological System: Intra-inter Dynamics Approach

Basic problems for the construction of a scenario for the Life are discussed. To study the problems in terms of dynamical systems theory, a scheme of intra-inter dynamics is presented. It consists of internal dynamics of a unit, interaction among the units, and the dynamics to change the dynamics itself, for example by replication (and death) of units according to their internal states. Applying the dynamics to cell differentiation, isologous diversification theory is proposed. According to it, orbital instability leads to diversified cell behaviors first. At the next stage, several cell types are formed, first triggered by clustering of oscillations, and then as attracting states of internal dynamics stabilized by the cell-to-cell interaction. At the third stage, the differentiation is determined as a recursive state by cell division. At the last stage, hierarchical differentiation proceeds, with the emergence of stochastic rule for the differentiation to sub-groups, where regulation of the probability for the differentiation provides the diversity and stability of cell society. Relevance of the theory to cell biology is discussed.Comment: 19 pages, Int.J. Mod. Phes. B (in press

Poisson-Boltzmann Theory of Charged Colloids: Limits of the Cell Model for Salty Suspensions

Thermodynamic properties of charge-stabilised colloidal suspensions are commonly modeled by implementing the mean-field Poisson-Boltzmann (PB) theory within a cell model. This approach models a bulk system by a single macroion, together with counterions and salt ions, confined to a symmetrically shaped, electroneutral cell. While easing solution of the nonlinear PB equation, the cell model neglects microion-induced correlations between macroions, precluding modeling of macroion ordering phenomena. An alternative approach, avoiding artificial constraints of cell geometry, maps a macroion-microion mixture onto a one-component model of pseudo-macroions governed by effective interactions. In practice, effective-interaction models are usually based on linear screening approximations, which can accurately describe nonlinear screening only by incorporating an effective (renormalized) macroion charge. Combining charge renormalization and linearized PB theories, in both the cell model and an effective-interaction (cell-free) model, we compute osmotic pressures of highly charged colloids and monovalent microions over a range of concentrations. By comparing predictions with primitive model simulation data for salt-free suspensions, and with predictions of nonlinear PB theory for salty suspensions, we chart the limits of both the cell model and linear-screening approximations in modeling bulk thermodynamic properties. Up to moderately strong electrostatic couplings, the cell model proves accurate in predicting osmotic pressures of deionized suspensions. With increasing salt concentration, however, the relative contribution of macroion interactions grows, leading predictions of the cell and effective-interaction models to deviate. No evidence is found for a liquid-vapour phase instability driven by monovalent microions. These results may guide applications of PB theory to soft materials.Comment: 27 pages, 5 figures, special issue of Journal of Physics: Condensed Matter on "Classical density functional theory methods in soft and hard matter

Cell Dynamics Simulation of Kolmogorov-Johnson-Mehl-Avrami Kinetics of Phase Transformation

In this study, we use the cell dynamics method to test the validity of the Kormogorov-Johnson-Mehl-Avrami (KJMA) theory of phase transformation. This cell dynamics method is similar to the well-known phase-field model, but it is a more simple and efficient numerical method for studying various scenarios of phase transformation in a unified manner. We find that the cell dynamics method reproduces the time evolution of the volume fraction of the transformed phase predicted by the KJMA theory. Specifically, the cell dynamics simulation reproduces a double-logarithmic linear KJMA plot and confirms the integral Avrami exponents $n$ predicted from the KJMA theory. Our study clearly demonstrates that the cell dynamics approach is not only useful for studying the pattern formation but also for simulating the most basic properties of phase transformation.Comment: 16 page, 8 figure

Spectral Representation Theory for Dielectric Behavior of Nonspherical Cell Suspensions

Recent experiments revealed that the dielectric dispersion spectrum of fission yeast cells in a suspension was mainly composed of two sub-dispersions. The low-frequency sub-dispersion depended on the cell length, while the high-frequency one was independent of it. The cell shape effect was simulated by an ellipsoidal cell model but the comparison between theory and experiment was far from being satisfactory. Prompted by the discrepancy, we proposed the use of spectral representation to analyze more realistic cell models. We adopted a shell-spheroidal model to analyze the effects of the cell membrane. It is found that the dielectric property of the cell membrane has only a minor effect on the dispersion magnitude ratio and the characteristic frequency ratio. We further included the effect of rotation of dipole induced by an external electric field, and solved the dipole-rotation spheroidal model in the spectral representation. Good agreement between theory and experiment has been obtained.Comment: 19 pages, 5 eps figure

Diffusion and the physics of chemoreception

This review provides a manual which enables the reader to perform calculations on the rate with which a biological cell can capture certain chemical compounds (ligands) which are essential to its survival and which diffuse in its environment. After a discussion of spatial diffusion and the capture of ligands by a single receptor in the cell membrane, the theory of one-stage chemoreception is developed for the general case in which the cell is spherical and arbitrary forces act between the ligand and the cell. Our method can also be applied to cells with other shapes. Next we discuss membrane diffusion and develop a theory of two-stage chemoreception. Some hydrodynamic effects are also discussed

A physical model of cell metabolism

Cell metabolism is characterized by three fundamental energy demands: to sustain cell maintenance, to trigger aerobic fermentation and to achieve maximum metabolic rate. The transition to aerobic fermentation and the maximum metabolic rate are currently understood based on enzymatic cost constraints. Yet, we are lacking a theory explaining the maintenance energy demand. Here we report a physical model of cell metabolism that explains the origin of these three energy scales. Our key hypothesis is that the maintenance energy demand is rooted on the energy expended by molecular motors to fluidize the cytoplasm and counteract molecular crowding. Using this model and independent parameter estimates we make predictions for the three energy scales that are in quantitative agreement with experimental values. The model also recapitulates the dependencies of cell growth with extracellular osmolarity and temperature. This theory brings together biophysics and cell biology in a tractable model that can be applied to understand key principles of cell metabolism

A theory of a saliency map in primary visual cortex (V1) tested by psychophysics of color-orientation interference in texture segmentation

It has been proposed that V1 creates a bottom-up saliency map, where saliency of any location increases with the firing rate of the most active V1 output cell responding to it, regardless the feature selectivity of the cell. Thus, a red vertical bar may have its saliency signalled by a cell tuned to red colour, or one tuned to vertical orientation, whichever cell is the most active. This theory predicts interference between colour and orientation features in texture segmentation tasks where bottom-up processes are significant. The theory not only explains existing data, but also provides a prediction. A subsequent psychophysical test confirmed the prediction by showing that segmentation of textures of oriented bars became more difficult as the colours of the bars were randomly drawn from more colour categories

Statistics of correlated percolation in a bacterial community

Signal propagation over long distances is a ubiquitous feature of multicellular communities, but cell-to-cell variability can cause propagation to be highly heterogeneous. Simple models of signal propagation in heterogenous media, such as percolation theory, can potentially provide a quantitative understanding of these processes, but it is unclear whether these simple models properly capture the complexities of multicellular systems. We recently discovered that in biofilms of the bacterium Bacillus subtilis, the propagation of an electrical signal is statistically consistent with percolation theory, and yet it is reasonable to suspect that key features of this system go beyond the simple assumptions of basic percolation theory. Indeed, we find here that the probability for a cell to signal is not independent from other cells as assumed in percolation theory, but instead is correlated with its nearby neighbors. We develop a mechanistic model, in which correlated signaling emerges from cell division, phenotypic inheritance, and cell displacement, that reproduces the experimentally observed correlations. We find that the correlations do not significantly affect the spatial statistics, which we rationalize using a renormalization argument. Moreover, the fraction of signaling cells is not constant in space, as assumed in percolation theory, but instead varies within and across biofilms. We find that this feature lowers the fraction of signaling cells at which one observes the characteristic power-law statistics of cluster sizes, consistent with our experimental results. We validate the model using a mutant biofilm whose signaling probability decays along the propagation direction. Our results reveal key statistical features of a correlated signaling process in a multicellular community. More broadly, our results identify extensions to percolation theory that do or do not alter its predictions and may be more appropriate for biological systems.P50 GM085764 - NIGMS NIH HHS; Howard Hughes Medical Institute; R01 GM121888 - NIGMS NIH HHSPublished versio