Does sex induce a phase transition?

We discovered a dynamic phase transition induced by sexual reproduction. The dynamics is a pure Darwinian rule applied to diploid bit-strings with both fundamental ingredients to drive Darwin's evolution: (1) random mutations and crossings which act in the sense of increasing the entropy (or diversity); and (2) selection which acts in the opposite sense by limiting the entropy explosion. Selection wins this competition if mutations performed at birth are few enough, and thus the wild genotype dominates the steady-state population. By slowly increasing the average number m of mutations, however, the population suddenly undergoes a mutational degradation precisely at a transition point m_c. Above this point, the “bad” alleles (represented by 1-bits) spread over the genetic pool of the population, overcoming the selection pressure. Individuals become selectively alike, and evolution stops. Only below this point, m < m_c, evolutionary life is possible. The finite-size-scaling behaviour of this transition is exhibited for large enough “chromosome” lengths L, through lengthy computer simulations. One important and surprising observation is the L-independence of the transition curves, for large L. They are also independent on the population size. Another is that m_c is near unity, i.e. life cannot be stable with much more than one mutation per diploid genome, independent of the chromosome length, in agreement with reality. One possible consequence is that an eventual evolutionary jump towards larger L enabling the storage of more genetic information would demand an improved DNA copying machinery in order to keep the same total number of mutations per offspring.     

Loss- and Gain-of-Function Mutations in Cancer: Mass-action, Spatial and Hierarchical Models

We study the stochastic dynamics of the two most common patterns in cancer initiation and progression: loss-of-function and gain-of-function mutations. We consider three stochastic models of cell populations with a constant size: a mass-action model, a spatial model and a hierarchical model. For gain-of-function mutations, we calculate the probability of mutant fixation starting from one mutant cell. For loss-of-function mutations, we calculate the rate of production of double-hit mutants. It turns out that the results are different in all models. This suggests that simple mass-action models are often misleading when studying cancer dynamics. Moreover, our results also allow us to think about various types of tissue architecture and its protective role against cancer. In particular, we show that hierarchical tissue organization lowers the risk of cancerous transformations. Also, cellular motility and long-range signaling can decrease the risk of cancer in solid tissues.     

Monte Carlo simulations of parapatric speciation

Parapatric speciation is studied using an individual-based model with sexual reproduction. We combine the theory of mutation accumulation for biological ageing with an environmental selection pressure that varies according to the individuals geographical positions and phenotypic traits. Fluctuations and genetic diversity of large populations are crucial ingredients to model the features of evolutionary branching and are intrinsic properties of the model. Its implementation on a spatial lattice gives interesting insights into the population dynamics of speciation on a geographical landscape and the disruptive selection that leads to the divergence of phenotypes. Our results suggest that assortative mating is not an obligatory ingredient to obtain speciation in large populations at low gene flow.     

Entropy production in a cell and reversal of entropy flow as an anticancer therapy

The entropy production rate of cancer cells is always higher than healthy cells in the case where no external field is applied. Different entropy production between two kinds of cells determines the direction of entropy flow among cells. The entropy flow is the carrier of information flow. The entropy flow from cancerous cells to healthy cells takes along the harmful information of cancerous cells, propagating its toxic action to healthy tissues. We demonstrate that a low-frequency and lowintensity electromagnetic field or ultrasound irradiation may increase the entropy production rate of a cell in normal tissue than that in cancer and consequently reverse the direction of entropy current between two kinds of cells. The modification of the PH value of cells may also cause the reversal of the direction of entropy flow between healthy and cancerous cells. Therefore, the biological tissue under the irradiation of an electromagnetic field or ultrasound or under the appropriate change of cell acidity can avoid the propagation of harmful information from cancer cells. We suggest that this entropy mechanism possibly provides a basis for a novel approach to anticancer therapy.      

Cancer cell recognition--mechanical phenotype

The major characteristics of cancer metastasis is the ability of the primary tumor cells to migrate by way of the blood or lymph vessels and to form tumors at multiple, distant sites. There are evidences that cancer progression is characterized by disruption and/or reorganization of cytoskeleton (i.e. cellular scaffold). This is accompanied by various molecular alterations influencing the overall mechanical resistance of cells. Current approach in diagnosis focuses mainly on microbiological, immunological, and pathological aspects rather than on the biomechanics of diseases. The determination of mechanical properties of an individual living cell has became possible with the development of local measurement techniques, such as atomic force microscopy, magnetic or optical tweezers. The advantage of them lies in the capability to measure living cells at a single cell level and in liquid conditions, close to natural environment. Here, we present the studies on mechanical properties of single cells originating from various cancers. The results show that, independently of the cancer type (bladder, melanoma, prostate, breast and colon), single cells are characterized by the lower Young's modulus, denoting higher deformability of cancerous cells. However, the obtained Young's modulus values were dependent on various factors, like the properties of substrates used for cell growth, force loading rate, or indentation depth. Their influence on elastic properties of cells was considered. Based on these findings, the identification of cancerous cells based on their elastic properties was performed. These results proved the AFM capability in recognition of a single, mechanically altered cell, also in cases when morphological changes are not visible. The quantitative analysis of cell deformability carried out using normal (reference) and cancerous cells and, more precisely, their characterization (qualitative and quantitative) can have a significant impact on the development of methodological approaches toward precise identification of pathological cells and would allow for more effective detection of cancer-related changes.     

Toward understanding of the role of reversibility of phenotypic switching in the evolution of resistance to therapy

Reversibility of state transitions is intensively studied topic in many scientific disciplines over many years. In cell biology, it plays an important role in epigenetic variation of phenotypes, known as phenotypic plasticity. More interestingly, the cell state reversibility is probably crucial in the adaptation of population phenotypic heterogeneity to environmental fluctuations by evolving bet-hedging strategy, which might confer to cancer cells resistance to therapy. In this article, we propose a formalization of the evolution of highly reversible states in the environments of periodic variability. Two interrelated models of heterogeneous cell populations are proposed and their behavior is studied. The first model captures selection dynamics of the cell clones for the respective levels of phenotypic reversibility. The second model focuses on the interplay between reversibility and drug resistance in the particular case of cancer. Overall, our results show that the threshold dependencies are emergent features of the investigated model with eventual therapeutic relevance. Presented examples demonstrate importance of taking into account cell to cell heterogeneity within a system of clones with different reversibility quantified by appropriately chosen genetic and epigenetic entropy measures.     

Semiconservative replication, genetic repair, and many-gened genomes: Extending the quasispecies paradigm to living systems

Quasispecies theory has emerged as an important tool for modeling the evolutionary dynamics of biological systems. We review recent advances in the field, with an emphasis on the quasispecies dynamics of semiconservatively replicating genomes. Applications to cancer and adult stem cell growth are discussed. Additional topics, such as genetic repair and many-gene genomes, are covered as well.     

On the Role of Physics in the Growth and Pattern Formation of Multi-Cellular Systems: What can we Learn from Individual-Cell Based Models?

We demonstrate that many collective phenomena in multi-cellular systems can be explained by models in which cells, despite their complexity, are represented as simple particles which are parameterized mainly by their physical properties. We mainly focus on two examples that nevertheless span a wide range of biological sub-disciplines: Unstructured cell populations growing in cell culture and growing cell layers in early animal development. While cultured unstructured cell populations would apriori been classified as particularly suited for a biophysical approach since the degree to which they are committed to a genetic program is expected to be modest, early animal development would be expected to mark the other extreme—here the degree of determinism according to a genetic program would be expected to be very high. We consider a number of phenomena such as the growth kinetics and spatial structure formation of monolayers and multicellular spheroids, the effect of the presence of another cell type surrounding the growing cell population, the effect of mutations and the critical surface dynamics of monolayers. Different from unstructured cell populations, cells in early development and at tissue interfaces usually form highly organized structures. An example are tissue layers. Under certain circumstances such layers are observed to fold. We show that folding pattern again can largely be explained by physical mechanisms either by a buckling instability or active cell shape changes. The paper combines new and published material and aims at an overview of a wide range of physical aspects in unstructured populations and growing tissue layers.     

Relationship between measures of fitness and time scale in evolution

The notion of fitness is central in evolutionary biology. We use a simple spatially extended predator-prey or host-pathogen model to show a generic case where the average number of offspring of an individual as a measure of fitness fails to characterize the evolutionary dynamics. Mutants with high initial reproduction ratios have lineages that eventually go extinct due to local overexploitation. We propose general quantitative measures of fitness that reflect the importance of time scale in evolutionary processes.     

Exact solution of an evolutionary model without aging

We introduce an age-structured asexual population model containing all the relevant features of evolutionary aging theories. Beneficial as well as deleterious mutations, heredity, and arbitrary fecundity are present and managed by natural selection. An exact solution without aging is found. We show that fertility is associated with generalized forms of the Fibonacci sequence, while mutations and natural selection are merged into an integral equation which is solved by Fourier series. Average survival probabilities and Malthusian growth exponents are calculated and indicate that the system may exhibit mutational meltdown. The relevance of the model in the context of fissile reproduction groups like many protozoa and coelenterates is discussed.     

Evolutionary game theory in growing populations

Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We present here a generic stochastic model which combines the growth dynamics of the population and its internal evolution. Our model thereby accounts for the fact that both evolutionary and growth dynamics are based on individual reproduction events and hence are highly coupled and stochastic in nature. We exemplify our approach by studying the dilemma of cooperation in growing populations and show that genuinely stochastic events can ease the dilemma by leading to a transient but robust increase in cooperation.     

Coupled map lattices as cellular automata

We approach the problem of the complex dynamics of coupled map lattices (CML) by proposing a reduction to deterministic cellular automata (CA) with more than two states per site. The reduction scheme replaces the local map by an approximation in terms of a step function based on a straightforward analysis of the local dynamics. The variation of the spatial coupling in the CML then translates itself as a path in the spaces of rules for the equivalent deterministic CA. The transition to turbulence via spatiotemporal intermittency in the CML is then interpreted as a transition in the space of rules. The observed nonuniversality of this transition can be traced back to the nature of the rules involved on both sides of the transition region and to the character of the escape process from the turbulent state, either strongly deterministic or quasiprobabilistic. The relation between CML, deterministic, and probabilistic CA and the possibility of a mean-field treatment of the dynamics of CML are discussed at a more formal level.     

Emergent properties of gene evolution: Species as attractors in phenotypic space

The question how the observed discrete character of the phenotype emerges from a continuous genetic distance metrics is the core argument of two contrasted evolutionary theories: punctuated equilibrium (stable evolution scattered with saltations in the phenotype) and phyletic gradualism (smooth and linear evolution of the phenotype). Identifying phenotypic saltation on the molecular levels is critical to support the first model of evolution. We have used DNA sequences of ∼1300 genes from 6 isolated populations of the budding yeast Saccharomyces cerevisiae. We demonstrate that while the equivalent measure of the genetic distance show a continuum between lineage distance with no evidence of discrete states, the phenotypic space illustrates only two (discrete) possible states that can be associated with a saltation of the species phenotype. The fact that such saltation spans large fraction of the genome and follows by continuous genetic distance is a proof of the concept that the genotype-phenotype relation is not univocal and may have severe implication when looking for disease related genes and mutations. We used this finding with analogy to attractor-like dynamics and show that punctuated equilibrium could be explained in the framework of non-linear dynamics systems.     

Size Matters!

Asexual reproduction by division in higher organisms is rare, because a prerequisite is the ability to regenerate an entire organism from a piece of the original body. Freshwater planarians are one of the few animals that can reproduce this way, but little is known about the regulation of their reproduction cycles or strategies. We have previously shown that a planarian??s reproduction strategy is randomized to include fragmentations, producing multiple offspring, as well as binary fissions, and can be partially explained by a maximum relative entropy principle. In this study we attempt to decompose the factors controlling their reproduction cycle. Based on recent studies on the cell cycle of budding yeast, which suggest that molecular noise in gene expression and cell size at birth together control cell cycle variability, we investigated whether the variability in planarian reproduction waiting times could be similarly regulated. We find that such a model can indeed explain the observed distribution of waiting times between birth and next reproductive event, suggesting that birth size and a stochastic noise term govern the reproduction dynamics of asexual planarians.     

基于符号向量动力学的耦合映像格子参数估计

本文,将符号动力学推广到耦合映像格子中,以Logistic映射下耦合映像格子为研究对象,研究控制参数对符号向量序列动力学特性的影响.通过研究耦合映像格子逆函数,给出耦合映像格子的遍历条件.进一步,将给出系统初始向量,禁止字以及控制参数的符号向量序列描述方法,并最终给出基于符号向量动力学的耦合映像格子控制参数估计方法.实验结果表明,根据本文算法可以有效建立符号序列和耦合映像格子控制参数之间的对应关系,能够更好地刻画了实际模型的物理过程. 关键词： 符号向量动力学 耦合映像格子 参数估计 遍历性     

Cancer detection on a cell-by-cell basis using a fractal dimension analysis

We show that the application of imaging and pattern recognition techniques developed for basic heavy ion research has useful applications in medical imaging. In particular, we utilize the fractal dimension of the perimeter surface of cell sections as a new observable to characterize cells of different types. We propose that it is possible to distinguish cancerous from healthy cells with the aid of this new approach. As a first application we show in an exploratory study that it is possible to perform this distinction between patients with hairy-cell lymphocytic leukemia and those with normal blood lymphocytes.     

Manipulation with heterogeneity within a species population formulated as an inverse problem

Dependence of the evolutionary dynamics on the population’s heterogeneity has been reliably recognized and studied within the frame of evolutionary optimization theory. As the causal relation between the heterogeneity and dynamics of environment has been revealed, the possibility to influence convergence rate of evolutionary processes by purposeful manipulation with environment emerges.For the above purposes we formulate the task as the inverse problem meaning that desired population heterogeneity, quantified by Tsallis information entropy, represents the model’s input and dynamics of environment leading to desired population heterogeneity is looked for. Here the presented abstract model of evolutionary motion within the inverse model of replicating species is case-independent and it is relevant for the broad range of phenomena observed at cellular, ecological, economic and social scales. We envision relevance of the model for anticancer therapy, in which the effort is to circumvent heterogeneity as it typically correlates with the therapy efficiency.     

Effects of migration on the evolutionary game dynamics in finite populations with community structures

We investigate the impacts of migration on the evolutionary game dynamics in finite populations with community structures in the framework of evolutionary game theory. In contrast to deterministic dynamics, our model incorporates stochastic factors induced by the finite population size. Based on the analysis of the stationary distribution of the evolutionary process in the limit of rare mutations, we prove that it is most likely to find the population in the community where all individuals have the lower migration rate. Furthermore, we show that reducing the difference between the migration rates of distinct communities can increase the first hitting time to the homogeneous absorbing state and can prolong the coexistence time of different species, promoting the conservation of biodiversity.     

Genetic demixing and evolution in linear stepping stone models

Results for mutation, selection, genetic drift, and migration in a one-dimensional continuous population are reviewed and extended. The population is described by a continuous limit of the stepping stone model, which leads to the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation with additional terms describing mutations. Although the stepping stone model was first proposed for population genetics, it is closely related to "voter models" of interest in nonequilibrium statistical mechanics. The stepping stone model can also be regarded as an approximation to the dynamics of a thin layer of actively growing pioneers at the frontier of a colony of micro-organisms undergoing a range expansion on a Petri dish. The population tends to segregate into monoallelic domains. This segregation slows down genetic drift and selection because these two evolutionary forces can only act at the boundaries between the domains; the effects of mutation, however, are not significantly affected by the segregation. Although fixation in the neutral well-mixed (or "zero-dimensional") model occurs exponentially in time, it occurs only algebraically fast in the one-dimensional model. An unusual sublinear increase is also found in the variance of the spatially averaged allele frequency with time. If selection is weak, selective sweeps occur exponentially fast in both well-mixed and one-dimensional populations, but the time constants are different. The relatively unexplored problem of evolutionary dynamics at the edge of an expanding circular colony is studied as well. Also reviewed are how the observed patterns of genetic diversity can be used for statistical inference and the differences are highlighted between the well-mixed and one-dimensional models. Although the focus is on two alleles or variants, q-allele Potts-like models of gene segregation are considered as well. Most of the analytical results are checked with simulations and could be tested against recent spatial experiments on range expansions of inoculations of Escherichia coli and Saccharomyces cerevisiae.