Coarsening and self-organization in dilute diblock copolymer melts and mixtures

This paper explores the evolution of a sharp interface model for phase separation of copolymers in the limit of low volume fraction. Particles both exchange material as in usual Ostwald ripening, and migrate because of an effectively repulsive nonlocal energetic term. Coarsening via mass diffusion only occurs while particle radii are small, and they eventually approach a finite equilibrium size. Migration, on the other hand, is responsible for producing self-organized patterns.We construct approximations based upon an ansatz of spherical particles similar to the classical LSW theory to derive finite dimensional dynamics for particle positions and radii. For large systems, kinetic-type equations which describe the evolution of a probability density are constructed. For systems larger than the screening length, we obtain an analog of the homogenization result of Niethammer & Otto [B. Niethammer, F. Otto, Ostwald ripening: The screening length revisited, Calc. Var. Partial Differential Equations 13-1 (2001) 33-68]. A separation of timescales between particle growth and migration allows for a variational characterization of spatially inhomogeneous quasi-equilibrium states.     

Coevolution of quasispecies: B-cell mutation rates maximize viral error catastrophes

Coevolution of two coupled quasispecies is studied, motivated by the competition between viral evolution and adapting immune response. In this coadaptive model, besides the classical error catastrophe for high virus mutation rates, a second "adaptation" catastrophe occurs, when virus mutation rates are too small to escape immune attack. Maximizing both regimes of viral error catastrophes is a possible strategy for an optimal immune response, reducing the range of allowed viral mutation rates to a minimum. From this requirement, one obtains constraints on B-cell mutation rates and receptor lengths, yielding an estimate of somatic hypermutation rates in the germinal center in accordance with observation.     

Adaptation dynamics of the quasispecies model

We study the adaptation dynamics of an initially maladapted population evolving via the elementary processes of mutation and selection. The evolution occurs on rugged fitness landscapes which are defined on the multi-dimensional genotypic space and have many local peaks separated by low fitness valleys. We mainly focus on the Eigen’s model that describes the deterministic dynamics of an infinite number of self-replicating molecules. In the stationary state, for small mutation rates such a population forms a quasispecies which consists of the fittest genotype and its closely related mutants. The quasispecies dynamics on rugged fitness landscape follow a punctuated (or steplike) pattern in which a population jumps from a low fitness peak to a higher one, stays there for a considerable time before shifting the peak again and eventually reaches the global maximum of the fitness landscape. We calculate exactly several properties of this dynamical process within a simplified version of the quasispecies model.      

Error threshold for spatially resolved evolution in the quasispecies model.

The error threshold for quasispecies in 1, 2, 3, and infinity dimensions is investigated by stochastic simulation and analytically. The results show a monotonic decrease in the maximal sustainable error probability with decreasing diffusion coefficient, independently of the spatial dimension. It is thereby established that physical interactions between sequences are necessary in order for spatial effects to enhance the stabilization of biological information. The analytically tractable behavior in an infinity-dimensional (simplex) space provides a good guide to the spatial dependence of the error threshold in lower dimensional Euclidean space.     

The comparative analysis of prebiological evolution models

Several models of prebiological systems are described and analyzed. The following models are characterized: a quasispecies model, a hypercycle model, a syser model (the term "syser" is an abbreviation of SYstem of SElf-Reproduction), a stochastic corrector model, a model of the origin of a primordial genome through spontaneous symmetry breaking. The quasispecies model analyzes the Darwinian evolution of information chains; this evolution is similar to the evolution of RNA molecules. Rather general estimates of the speed and efficiency of evolutionary processes can be obtained in the framework of the quasispecies model. We briefly describe the method for obtaining these estimates and the corresponding results. The hypercycle model considers the interaction of RNA chains and enzymes. The syser model characterizes a rather general scheme of the self-reproducing system, which is similar to the self-reproducing systems of biological cells. Syser includes a polynucleotide sequence, a replication enzyme, a translation enzyme, and other enzymes; these macromolecules are located inside the protocell. The stochastic corrector model describes the process of using a relatively small number of molecules of competing and cooperating replicators in protocells. The model of the origin of a primordial genome through spontaneous symmetry breaking characterizes an interesting and important process of the appearance of genotypes in protocells. This model was proposed and investigated by Takeuchi, Hogeweg, and Kaneko in 2017; we call it further “the THK model.” The current article characterizes and compares all these models.     

Selective advantage of topological disorder in biological evolution

We examine a model of biological evolution of Eigen's quasispecies in a so-called holey fitness landscape, where the fitness of a site is either 0 (lethal site) or a uniform positive constant (viable site). The evolution dynamics is therefore determined by the topology of the genome space which is modelled by the random Bethe lattice. We use the effective medium and single-defect approximations to find the criteria under which the localized quasispecies cloud is created. We find that shorter genomes, which are more robust to random mutations than average, represent a selective advantage which we call “topological”. A way of assessing empirically the relative importance of reproductive success and topological advantage is suggested. Received 9 August 2002 / Received in final form 7 November 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: slanina@fzu.cz     

随机化的Eigen模型研究

为了使Eigen模型能够更真实地描述物种的演化过程,将确定性Eigen模型改造成随机模型.以Eigen模型为理论框架,把基因序列中每一个位点的突变率看作一个高斯随机变量,从而导出随机性Eigen模型.对于此随机性Eigen模型,当突变率的涨落强度较小时,准物种的误差阈位置几乎没有改变,仍是个相变点;而当突变率的涨落强度变大时,误差阈由一个相变点变为一个转变区域.在真实的物种演化过程中,误差阈应是一个转变区域,而且在解决实际问题时应考虑该转变区域的上限.     

Theoretical study on non-sequential double ionization of carbon disulfide with different bond lengths in linearly polarizedlaser fields

By using a two-dimensional Monte-Carlo classical ensemble method, we investigate the double ionization(DI) process of the CS_2 molecule with different bond lengths in an 800-nm intense laser field. The double ionization probability presents a "knee" structure with equilibrium internuclear distance R = 2.9245 a.u.(a.u. is short for atomic unit). As the bond length of CS increases, the DI probability is enhanced and the "knee" structure becomes less obvious. In addition,the momentum distribution of double ionized electrons is also investigated, which shows the momentum mostly distributed in the first and third quadrants with equilibrium internuclear distance R = 2.9245 a.u. As the bond length of CS increases,the electron momentum becomes evenly distributed in the four quadrants. Furthermore, the energy distributions and the corresponding trajectories of the double-ionized electrons versus time are also demonstrated, which show that the bond length of CS in the CS_2 molecule plays a key role in the DI process.     

Sigma-Boundary Statistics by Length and Number

This paper presents a rationale for comparative use of length fraction and number fraction statistics in grain boundary analysis from orientation maps generated by electron back-scatter diffraction (EBSD). The length and number fraction statistics for 3 ⁿ coincidence site lattice (CSL) boundaries were measured and compared. The length fraction of 3 boundaries was 0.48 whereas the number fraction was significantly less, 0.36. A simple model was generated to estimate both the length fraction and number fraction of annealing twins (a subset of 3). The model showed that the number fraction of twins is 0.68, 0.75, 0.79 and 0.82 of the length fraction for 1, 2, 3 and 4 twins-per-grain respectively. For the experimental data the number fraction was 0.76 of the length fraction, implying that there were on average two twins-per-grain. In contrast to the 3 case, the length fraction for 9 and 27 boundaries was less than the number fraction. There are more inaccuracies involved in obtaining the number fraction than in obtaining the length fraction from EBSD maps, therefore the length fraction should be recommended as the standard reporting method. However a knowledge of the distribution in the microstructure of 3 ⁿ segments is often crucial to the inquiry in addition to the length fraction.     

Phase diagrams of quasispecies theory with recombination and horizontal gene transfer

We consider how transfer of genetic information between individuals influences the phase diagram and mean fitness of both the Eigen and the parallel, or Crow-Kimura, models of evolution. In the absence of genetic transfer, these physical models of evolution consider the replication and point mutation of the genomes of independent individuals in a large population. A phase transition occurs, such that below a critical mutation rate an identifiable quasispecies forms. We show how transfer of genetic information changes the phase diagram and mean fitness and introduces metastability in quasispecies theory, via an analytic field theoretic mapping.     

Reconstructing the free-energy landscape of a mechanically unfolded model protein

The equilibrium free-energy landscape of an off-lattice model protein as a function of an internal (reaction) coordinate is reconstructed from out-of-equilibrium mechanical unfolding manipulations. This task is accomplished via two independent methods: by employing an extended version of the Jarzynski equality (EJE) and the protein inherent structures (ISs). In a range of temperatures around the "folding transition" we find a good quantitative agreement between the free energies obtained via EJE and IS approaches. This indicates that the two methodologies are consistent and able to reproduce equilibrium properties of the examined system. Moreover, for the studied model the structural transitions induced by pulling can be related to thermodynamical aspects of folding.     

Effects of spatial competition on the diversity of a quasispecies

The diversity harbored by populations of RNA viruses results from high mutation rates, as well as from the characteristics of the environment where they evolve. By means of a simple model for structured quasispecies, we quantify how competition for space among phenotypic types shapes their distribution at the mutation-selection equilibrium. We introduce a general framework to treat this problem and relate mutation rate and competition strength to the quasispecies composition. For diffusion limited competition, diversity typically increases and the asymptotic growth rate of the population diminishes as diffusion decreases. Limited mobility confers a relative advantage to worse competitors. The stationary state is characterized by an over-production of viral particles. Empirical data allow an estimation of mutation rates compatible with the diversity observed in viral populations infecting cellular monolayers.     

Polymer Transport in Random Flow

The dynamics of polymers in a random smooth flow is investigated in the framework of the Hookean dumbbell model. The analytical expression of the time-dependent probability density function of polymer elongation is derived explicitly for a Gaussian, rapidly changing flow. When polymers are in the coiled state the pdf reaches a stationary state characterized by power-law tails both for small and large arguments compared to the equilibrium length. The characteristic relaxation time is computed as a function of the Weissenberg number. In the stretched state the pdf is unstationary and exhibits multiscaling. umerical simulations for the two-dimensional Navier–Stokes flow confirm the relevance of theoretical results obtained for the -correlated model.     

Of Dogs and Fleas: The Dynamics of N Uncoupled Two-State Systems

The historical Ehrenfest model dating back to 1907 describes the process of equilibration together with fluctuations around the thermal equilibrium. This approach represents a special case in the dynamics of N uncoupled two-state systems. In this article we present a generalization of the original model by introducing an additional parameter p which denotes the probability of a single state change. Analytical solutions for the probability distribution of the system's state as well as the fluctuation distribution are derived. Interestingly, close inspection of the fluctuation distribution reveals an intrinsic time scale. Sampling the system's state at much slower rates yields the familiar macroscopic exponential distribution for equilibrium processes. For faster measurements a power law extends roughly over log₁₀ N orders of magnitude followed by an exponential tail. At some point, further increases of the sampling rate merely result in a shift of the fluctuation distribution towards higher values leaving plateau at small fluctuation sizes behind. Since the generic solution is rather unwieldy, we derive and discuss simple and intuitive analytical solutions in the limit of small p and large N. Furthermore, we relax the quantization of time by considering a complementary approach in continuous time. Finally we demonstrate that the fluctuation distributions resulting from the two different approaches bear identical characteristic features.     

Dynamical arrest in attractive colloids: the effect of long-range repulsion

We study gelation in suspensions of model colloidal particles with short-ranged attractive and long-ranged repulsive interactions by means of three-dimensional fluorescence confocal microscopy. At low packing fractions, particles form stable equilibrium clusters. Upon increasing the packing fraction the clusters grow in size and become increasingly anisotropic until finally associating into a fully connected network at gelation. We find a surprising order in the gel structure. Analysis of spatial and orientational correlations reveals that the gel is composed of dense chains of particles constructed from face-sharing tetrahedral clusters. Our findings imply that dynamical arrest occurs via cluster growth and association.     

单峰高斯分布适应面上的误差阈

在Eigen的单峰适应面模型基础上,提出了生物体的适应值为高斯分布的随机适应面模型。 利用系综平均的方法, 计算了在单峰高斯分布适应面上准物种的浓度分布和误差阈。 结果表明, 对于小的适应面涨落, 准物种分布和误差阈与确定情形相比变化极小,误差阈对于小的涨落是稳定的。 然而, 当适应值涨落较大时,从准物种到误差灾变的转变不再明显。 误差阈变宽, 并且在涨落增加时向大的突变率方向移动。 Based on the Eigen model with a single peak fitness landscape, the fitness values of all sequence types are assumed to be random with Gaussian distribution. By ensemble average method, the concentration distribution and error threshold of quasispecies on single peak Gaussian distributed fitness landscapes were evaluated. It is shown that the concentration distribution and error threshold change little in comparing with deterministic case for small fluctuations, which implies that the error threshold is stable against small perturbation. However, as the fluctuation increases, the situation is quite different. The transition from quasi species to error catastrophe is no longer sharp. The error threshold becomes a narrow band which broadens and shifts toward large values of error rate with increasing fluctuation.     

Maternal effects in molecular evolution

We introduce a model of molecular evolution in which the fitness of an individual depends both on its own and on the parent's genotype. The model can be solved by means of a nonlinear mapping onto the standard quasispecies model. The dependency on the parental genotypes cancels from the mean fitness, but not from the individual sequence concentrations. For finite populations, the position of the error threshold is very sensitive to the influence from parent genotypes. In addition to biological applications, our model is important for understanding the dynamics of self-replicating computer programs.     

飞行器FPGA检测点优化设置方法

,针对诱发宇宙空间环境下航空航天飞行器工作异常和故障的FPGA单粒子效应,分析了FPGA电路的特点,从空间和时间维度上,提出基于“运算单元 存储器/触发器”进行FPGA电路层次模块的划分;结合节点所在位置的重要性、节点与其它节点的关联程度以及节点本身的单粒子软错误翻转概率,提出了重要度分析模型,从而建立基于重要度排序的对测试点设置优化方法。测试实验表明,该方法是一种可行的检测点优化设置方法。     

Darwinian demons, evolutionary complexity, and information maximization

Natural selection is shown to be an extended instance of a Maxwell's demon device. A demonic selection principle is introduced that states that organisms cannot exceed the complexity of their selective environment. Thermodynamic constraints on error repair impose a fundamental limit to the rate that information can be transferred from the environment (via the selective demon) to the genome. Evolved mechanisms of learning and inference can overcome this limitation, but remain subject to the same fundamental constraint, such that plastic behaviors cannot exceed the complexity of reward signals. A natural measure of evolutionary complexity is provided by mutual information, and niche construction activity--the organismal contribution to the construction of selection pressures--might in principle lead to its increase, bounded by thermodynamic free energy required for error correction.     

Genome mapping by random anchoring: A discrete theoretical analysis

As a part of the international human genome project, large-scale genomic maps of human and other model organisms are being generated. More recently, mapping using various anchoring (as opposed to the traditional fingerprinting) strategies have been proposed based largely on mathematical models. In all of the theoretical work dealing with anchoring, an anchor has been idealized as a point on a continuous, infinite-length genome. In general, it is not desirable to make these assumptions, since in practice they may be violated under a variety of actual biological situations. Here we analyze a discrete model that can be used to predict the expected progress made when mapping by random anchoring. By virtue of keeping all three length scales (genome length, clone length, and probe length) finite, our results for the random anchoring strategy are derived in full generality, which contain previous results as special cases and hence can have broad application for planning mapping experiments or assessing the accuracy of the continuum models. Finally, we pose a challenging nonrandom anchoring model corresponding to a more efficient mapping scheme.