Detecting autocatalytic, self-sustaining sets in chemical reaction systems

The ability of systems of molecular reactions to be simultaneously autocatalylic and sustained by some ambient 'food source' of simple molecules may have been an essential step in the origin of life. In this paper we first describe a polynomial-time algorithm that determines whether any given set of molecules, reactions and catalysations contains a subsystem that is both autocatalytic and able to be sustained from a given subset of the molecules. We also describe some combinatorial properties of this algorithm, and show how it can be used to find irreducible auto-catalysing and sustaining subsystems. In the second part of the paper we use the algorithm to investigate random catalytic networks-in particular, a model described by Kauffman. Using simulations and some analytic techniques we investigate the rate of catalysis that is required for the emergence of autocatalytic and sustaining subsystems.     

The origin of large molecules in primordial autocatalytic reaction networks

Large molecules such as proteins and nucleic acids are crucial for life, yet their primordial origin remains a major puzzle. The production of large molecules, as we know it today, requires good catalysts, and the only good catalysts we know that can accomplish this task consist of large molecules. Thus the origin of large molecules is a chicken and egg problem in chemistry. Here we present a mechanism, based on autocatalytic sets (ACSs), that is a possible solution to this problem. We discuss a mathematical model describing the population dynamics of molecules in a stylized but prebiotically plausible chemistry. Large molecules can be produced in this chemistry by the coalescing of smaller ones, with the smallest molecules, the 'food set', being buffered. Some of the reactions can be catalyzed by molecules within the chemistry with varying catalytic strengths. Normally the concentrations of large molecules in such a scenario are very small, diminishing exponentially with their size. ACSs, if present in the catalytic network, can focus the resources of the system into a sparse set of molecules. ACSs can produce a bistability in the population dynamics and, in particular, steady states wherein the ACS molecules dominate the population. However to reach these steady states from initial conditions that contain only the food set typically requires very large catalytic strengths, growing exponentially with the size of the catalyst molecule. We present a solution to this problem by studying 'nested ACSs', a structure in which a small ACS is connected to a larger one and reinforces it. We show that when the network contains a cascade of nested ACSs with the catalytic strengths of molecules increasing gradually with their size (e.g., as a power law), a sparse subset of molecules including some very large molecules can come to dominate the system.     

Mutation rate and pattern of microsatellites in common carp (<Emphasis Type="Italic">Cyprinus carpio</Emphasis> L.)

Microsatellites are popular molecular markers in genetic and evolutionary studies. Their mutational dynamics have been extensively studied in humans and fruit flies, but few data were available in fish. By genotyping 55 individuals of a F1 pedigree, we investigated the mutation rates and patterns of 49 microsatellites in one of the most important fresh water fish species, the common carp (Cyprinus carpio L.). The overall mutation rate of the 49 loci was 5.56×10⁻⁴/locus/generation (95% confidence interval 1.52×10⁻⁴ and 1.63×10⁻³). The change of allele size was between +2 to −5 repeat units, assuming that the mutation allele arose from the parental allele most similar in size to the mutant.     

Mutation load and mutation-selection-balance in quantitative genetic traits

Haldane (1937) showed that the reduction of equilibrium mean fitness in an infinite population due to recurrent deleterious mutations depends only on the mutation rate but not on the harmfulness of mutants. His analysis, as well as more recent ones (cf. Crow 1970), ignored back mutation. The purpose of the present paper is to extend these results to arbitrary mutation patterns among alleles and to quantitative genetic traits. We derive first-order approximations for the equilibrium mean fitness (and the mutation load) and determine the order of the error term. For a metric trait under mutation-stabilizing-selection balance our result differs qualitatively from that of Crow and Kimura (1964), whose analysis is based on a Gaussian assumption. Our general approach also yields a mathematical proof that the variance under the usual mutation-stabilizing-selection model is, to first order, µ/s (the house-of-cards approximation) as µ/s tends to zero. This holds for arbitrary mutant distributions and does not require that the population mean coincide with the optimum. We show how the mutant distribution determines the order of the error term, and thus the accuracy of the house-of-cards approximation. Upper and lower bounds to the equilibrium variance are derived that deviate only to second order as µ/s tends to zero. The multilocus case is treated under the assumption of global linkage equilibrium.     

Bistability and oscillations in chemical reaction networks

Bifurcation theory is one of the most widely used approaches for analysis of dynamical behaviour of chemical and biochemical reaction networks. Some of the interesting qualitative behaviour that are analyzed are oscillations and bistability (a situation where a system has at least two coexisting stable equilibria). Both phenomena have been identified as central features of many biological and biochemical systems. This paper, using the theory of stoichiometric network analysis (SNA) and notions from algebraic geometry, presents sufficient conditions for a reaction network to display bifurcations associated with these phenomena. The advantage of these conditions is that they impose fewer algebraic conditions on model parameters than conditions associated with standard bifurcation theorems. To derive the new conditions, a coordinate transformation will be made that will guarantee the existence of branches of positive equilibria in the system. This is particularly useful in mathematical biology, where only positive variable values are considered to be meaningful. The first part of the paper will be an extended introduction to SNA and algebraic geometry-related methods which are used in the coordinate transformation and set up of the theorems. In the second part of the paper we will focus on the derivation of bifurcation conditions using SNA and algebraic geometry. Conditions will be derived for three bifurcations: the saddle-node bifurcation, a simple branching point, both linked to bistability, and a simple Hopf bifurcation. The latter is linked to oscillatory behaviour. The conditions derived are sufficient and they extend earlier results from stoichiometric network analysis as can be found in (Aguda and Clarke in J Chem Phys 87:3461–3470, 1987; Clarke and Jiang in J Chem Phys 99:4464–4476, 1993; Gatermann et al. in J Symb Comput 40:1361–1382, 2005). In these papers some necessary conditions for two of these bifurcations were given. A set of examples will illustrate that algebraic conditions arising from given sufficient bifurcation conditions are not more difficult to interpret nor harder to calculate than those arising from necessary bifurcation conditions. Hence an increasing amount of information is gained at no extra computational cost. The theory can also be used in a second step for a systematic bifurcation analysis of larger reaction networks. We have added a dedication of the paper to K. Gatermann.     

Mutation in evolutionary games can increase average fitness at equilibrium

We study game dynamical interactions between two strategies, A and B, and analyse whether the average fitness of the population at equilibrium can be increased by adding mutation from A to B. Classifying all two by two games with payoff matrix [(a,b),(c,d)], we show that mutation from A to B enhances the average fitness of the whole population (i) if both a and d are less than (b + c)/2 and (ii) if c is less than b. Furthermore, we study conditions for maximizing the productivity of strategy A, and we analyse the effect of mutations in both directions. Depending on the biological system, a mutation in an evolutionary game can be interpreted as a genetic alteration, a cellular differentiation, a change in gene expression, an accidental or deliberate modification in cultural transmission, or a learning error. In a cultural context, our results indicate that the equilibrium payoff of the population can be increased if players sometimes choose the strategy with lower payoff. In a genetic context, we have shown that for frequency-dependent selection mutation can enhance the average fitness of the population at equilibrium.     

Loop analysis and qualitative modeling: limitations and merits

Richard Levins has advocated the scientific merits of qualitative modeling throughout his career. He believed an excessive and uncritical focus on emulating the models used by physicists and maximizing quantitative precision was hindering biological theorizing in particular. Greater emphasis on qualitative properties of modeled systems would help counteract this tendency, and Levins subsequently developed one method of qualitative modeling, loop analysis, to study a wide variety of biological phenomena. Qualitative modeling has been criticized for being conceptually and methodologically problematic. As a clear example of a qualitative modeling method, loop analysis shows this criticism is indefensible. The method has, however, some serious limitations. This paper describes loop analysis, its limitations, and attempts to clarify the differences between quantitative and qualitative modeling, in content and objective. Loop analysis is but one of numerous types of qualitative analysis, so its limitations do not detract from the currently underappreciated and underdeveloped role qualitative modeling could have within science.

Developmental selection and self-organization

Developmental selection is the differential survival and proliferation of developmental units, such as cellular lineages. This type of internal selection has been proposed as an explanation for diverse examples of self-organization, from the wiring of brains to the formation of pores on leaf surfaces. A general understanding of developmental selection has been slowed by failure to understand its relationship to familiar forms of genetical selection and evolution. I show the formal analogies between models of developmental selection and genetical selection. The general method I outline for the analysis of selective systems partitions self-organizing selective systems into generative rules that create variation and selective filters that move the population toward a target design. The method also emphasizes aggregate statistical measures of evolving systems, such as the covariance between particular traits and fitness. The identification of useful aggregate measures is a crucial step in the analysis of selective systems. I apply these concepts to a model of self-organization in ant colonies.     

Autocatalysis in cultural ecology: model ecosystems and the dynamics of biocultural evolution

Using a well-known mathematical model frequently applied in theoretical population dynamics, certain ecological mechanisms are investigated that are inherent in the organic evolution of cultural capacities in man. Culture is argued to involve ecological interactions exhibiting analogies to the interaction of chemical species in autocatalytic biomolecular reactions. In the model, biocultural evolution proceeds by more and more broadening ecological niches and, thus, releasing competitive selection pressure on the populations involved. This, in turn, facilitates the maintenance of polymorphism in these populations as well as the individual acquisition of organic traits through learning and cultural transmission. The result is that the genetic variance in phenotypic expressions decreases at an accelerated rate.     

Exploring multiplicity conditions in enzymatic reaction networks

In this work, a novel algorithmic approach to detect multiplicity of steady states in enzymatic reaction networks is presented. The method exploits the structural properties of networks derived from the Chemical Reaction Network Theory. In first instance, the space of parameters is divided in different regions according to the qualitative behavior induced by the parameters in the long term dynamics of the network. Once the regions are identified, a condition for the appearance of multiplicities is checked in the different regions by solving a given optimization problem. In this way, the method allows the characterization of the whole parameter space of biochemical networks in terms of the appearance or not of multistability. The approach is illustrated through a well‐known case of enzymatic catalysis with substrate inhibition. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

A Petri net approach to the study of persistence in chemical reaction networks

Persistence is the property, for differential equations in R(n), that solutions starting in the positive orthant do not approach the boundary of the orthant. For chemical reactions and population models, this translates into the non-extinction property: provided that every species is present at the start of the reaction, no species will tend to be eliminated in the course of the reaction. This paper provides checkable conditions for persistence of chemical species in reaction networks, using concepts and tools from Petri net theory, and verifies these conditions on various systems which arise in the modeling of cell signaling pathways.     

先天性缝性白内障一家系中晶体蛋白基因的突变筛查

目的：对一中国常染色体显性先天性缝性白内障家系进行晶体蛋白基因（CRYAA、CRYAB、CRYBB2、CRYGC、CRYGD）的突变筛查。方法：对一中国先天性白内障家系进行研究,通过直接测序,筛查此家系中全部患者的CRYAA、CRYAB、CRYBB2、CRYGC和CRYGD基因外显子以及临近的内含子的剪接位点。结果：直接测序后发现该缝性白内障家系基因的外显子及其临近的内含子中．均未发现任何突变。结论：CRYAA、CRYAB、CRYBB2、CRYGC和CRYGD为该先天性白内障家系的非致病基因。     

Detecting autocatalytic dynamics in data modeled by a compartmental model

Modeling growth or reaction dynamics within a compartment in a compartmental model is often based on theoretical or first principle considerations. This approach is frequently applied due to the inability to observe or collect data directly from the compartment. When the internal dynamics are difficult to surmise, it is often the case that several competing models are constructed and compared in some way. In this paper, the dynamics which characterize the data of an autocatalytic process are used to describe a quantitative data analysis strategy to both recognize the presence of the autocatalytic process and to obtain some estimates of important parameters in the process. The compartmental model structure serves to communicate this dynamical information to the downstream compartments. This method has been applied to examine the dynamics of the engraftment of blood cells following hematopoietic stem cell transplantation in a clinical setting [Modeling the time to engraftment of white blood cells and platelets following autologous peripheral blood stem cell transplantation (2001)].     

小鼠白内障基因突变方式、分布及基因定位

哺乳动物发育相关的功能基因的鉴定多来源于自发或诱发突变的小鼠。小鼠白内障作为较易鉴定的性状,目前业已明确的突变多达140余个。自发突变的小鼠主要来源于大规模饲养,诱发突变主要通过X射线与ENU处理获得,基因敲除与转基因小鼠亦可获得白内障性状。已知的白内障相关基因分布于小鼠20条染色体,其中以1号染色体最多,并常于小鼠胚胎时期起始表达。小鼠白内障表型多由单基因突变引起,突变的确定主要通过F2代家系全基因组扫描、精细定位、单倍型分型与测序验证等程序。本文从小鼠白内障基因突变来源、基因分布、基因定位与基因表达等角度较为全面的阐述了小鼠先天性白内障的研究进展。     

宫内感染中HBV前S/S区基因种系进化树及变异特点的研究

目的:通过HBV前S/S区基因变异研究探讨HBV宫内感染的机制。方法:将HBsAg阳性母亲按照随访其新生儿是否发生宫内感染,分为病例组和对照组,经PCR扩增HBV DNA,基因克隆、测序,构建种系进化树分析前S/S基因的突变。结果:共得到60株HBV序列,来源于同一组的序列较为集中在树中的某枝,而且进化距离从病例组母亲、病例组患儿到对照组母亲存在由近及远的特征。结论:各组病毒株在基因序列进化上存在差异,某些突变位点在非宫内感染组母亲中的发生率较高,突变的发生可能使其所在的编码区功能发生变化而影响宫内感染的发生。     

Sensitivity and control analysis of periodically forced reaction networks using the Green's function method

A general sensitivity and control analysis of periodically forced reaction networks with respect to small perturbations in arbitrary network parameters is presented. A well-known property of sensitivity coefficients for periodic processes in dynamical systems is that the coefficients generally become unbounded as time tends to infinity. To circumvent this conceptual obstacle, a relative time or phase variable is introduced so that the periodic sensitivity coefficients can be calculated. By employing the Green's function method, the sensitivity coefficients can be defined using integral control operators that relate small perturbations in the network's parameters and forcing frequency to variations in the metabolite concentrations and reaction fluxes. The properties of such operators do not depend on a particular parameter perturbation and are described by the summation and connectivity relationships within a control-matrix operator equation. The aim of this paper is to derive such a general control-matrix operator equation for periodically forced reaction networks, including metabolic pathways. To illustrate the general method, the two limiting cases of high and low forcing frequency are considered. We also discuss a practically important case where enzyme activities and forcing frequency are modulated simultaneously. We demonstrate the developed framework by calculating the sensitivity and control coefficients for a simple two reaction pathway where enzyme activities enter reaction rates linearly and specifically.     

Asymptotically exact analysis of stochastic metapopulation dynamics with explicit spatial structure

We describe a mathematically exact method for the analysis of spatially structured Markov processes. The method is based on a systematic perturbation expansion around the deterministic, non-spatial mean-field theory, using the theory of distributions to account for space and the underlying stochastic differential equations to account for stochasticity. As an example, we consider a spatial version of the Levins metapopulation model, in which the habitat patches are distributed in the d-dimensional landscape Rd in a random (but possibly correlated) manner. Assuming that the dispersal kernel is characterized by a length scale L, we examine how the behavior of the metapopulation deviates from the mean-field model for a finite but large L. For example, we show that the equilibrium fraction of occupied patches is given by p(0)+c/L(d)+O(L(-3d/2)), where p(0) is the equilibrium state of the Levins model and the constant c depends on p(0), the dispersal kernel, and the structure of the landscape. We show that patch occupancy can be increased or decreased by spatial structure, but is always decreased by stochasticity. Comparison with simulations show that the analytical results are not only asymptotically exact (as L-->infinity), but a good approximation also when L is relatively small.     

胚胎移植技术对特种突变小鼠的净化研究

目的通过净化特种突变小鼠来建立SPF级种子库。方法利用胚胎移植技术对四种突变无毛小鼠和一种白内障小鼠的桑葚胚进行子宫内移植。结果四种突变无毛小鼠和白内障小鼠均产出仔鼠,获得移植成功,其中白内障小鼠的产仔率最高为25.5%。结论建立了SPF级特种突变小鼠种群,为进一步研究与开发利用提供了可靠保证。