A model-independent approach to infer hierarchical codon substitution dynamics

<p>Abstract</p> <p>Background</p> <p>Codon substitution constitutes a fundamental process in molecular biology that has been studied extensively. However, prior studies rely on various assumptions, e.g. regarding the relevance of specific biochemical properties, or on conservation criteria for defining substitution groups. Ideally, one would instead like to analyze the substitution process in terms of raw dynamics, independently of underlying system specifics. In this paper we propose a method for doing this by identifying groups of codons and amino acids such that these groups imply closed dynamics. The approach relies on recently developed spectral and agglomerative techniques for identifying hierarchical organization in dynamical systems.</p> <p>Results</p> <p>We have applied the techniques on an empirically derived Markov model of the codon substitution process that is provided in the literature. Without system specific knowledge of the substitution process, the techniques manage to "blindly" identify multiple levels of dynamics; from amino acid substitutions (via the standard genetic code) to higher order dynamics on the level of amino acid groups. We hypothesize that the acquired groups reflect earlier versions of the genetic code.</p> <p>Conclusions</p> <p>The results demonstrate the applicability of the techniques. Due to their generality, we believe that they can be used to coarse grain and identify hierarchical organization in a broad range of other biological systems and processes, such as protein interaction networks, genetic regulatory networks and food webs.</p

Bistability versus Bimodal Distributions in Gene Regulatory Processes from Population Balance

In recent times, stochastic treatments of gene regulatory processes have appeared in the literature in which a cell exposed to a signaling molecule in its environment triggers the synthesis of a specific protein through a network of intracellular reactions. The stochastic nature of this process leads to a distribution of protein levels in a population of cells as determined by a Fokker-Planck equation. Often instability occurs as a consequence of two (stable) steady state protein levels, one at the low end representing the “off” state, and the other at the high end representing the “on” state for a given concentration of the signaling molecule within a suitable range. A consequence of such bistability has been the appearance of bimodal distributions indicating two different populations, one in the “off” state and the other in the “on” state. The bimodal distribution can come about from stochastic analysis of a single cell. However, the concerted action of the population altering the extracellular concentration in the environment of individual cells and hence their behavior can only be accomplished by an appropriate population balance model which accounts for the reciprocal effects of interaction between the population and its environment. In this study, we show how to formulate a population balance model in which stochastic gene expression in individual cells is incorporated. Interestingly, the simulation of the model shows that bistability is neither sufficient nor necessary for bimodal distributions in a population. The original notion of linking bistability with bimodal distribution from single cell stochastic model is therefore only a special consequence of a population balance model

Time-dependent propagators for stochastic models of gene expression: an analytical method

The inherent stochasticity of gene expression in the context of regulatory networks profoundly influences the dynamics of the involved species. Mathematically speaking, the propagators which describe the evolution of such networks in time are typically defined as solutions of the corresponding chemical master equation (CME). However, it is not possible in general to obtain exact solutions to the CME in closed form, which is due largely to its high dimensionality. In the present article, we propose an analytical method for the efficient approximation of these propagators. We illustrate our method on the basis of two categories of stochastic models for gene expression that have been discussed in the literature. The requisite procedure consists of three steps: a probability-generating function is introduced which transforms the CME into (a system of) partial differential equations (PDEs); application of the method of characteristics then yields (a system of) ordinary differential equations (ODEs) which can be solved using dynamical systems techniques, giving closed-form expressions for the generating function; finally, propagator probabilities can be reconstructed numerically from these expressions via the Cauchy integral formula. The resulting &lsquo;library&rsquo; of propagators lends itself naturally to implementation in a Bayesian parameter inference scheme, and can be generalised systematically to related categories of stochastic models beyond the ones considered here

Speed, Sensitivity, and Bistability in Auto-activating Signaling Circuits

Cells employ a myriad of signaling circuits to detect environmental signals and drive specific gene expression responses. A common motif in these circuits is inducible auto-activation: a transcription factor that activates its own transcription upon activation by a ligand or by post-transcriptional modification. Examples range from the two-component signaling systems in bacteria and plants to the genetic circuits of animal viruses such as HIV. We here present a theoretical study of such circuits, based on analytical calculations, numerical computations, and simulation. Our results reveal several surprising characteristics. They show that auto-activation can drastically enhance the sensitivity of the circuit's response to input signals: even without molecular cooperativity, an ultra-sensitive threshold response can be obtained. However, the increased sensitivity comes at a cost: auto-activation tends to severely slow down the speed of induction, a stochastic effect that was strongly underestimated by earlier deterministic models. This slow-induction effect again requires no molecular cooperativity and is intimately related to the bimodality recently observed in non-cooperative auto-activation circuits. These phenomena pose strong constraints on the use of auto-activation in signaling networks. To achieve both a high sensitivity and a rapid induction, an inducible auto-activation circuit is predicted to acquire low cooperativity and low fold-induction. Examples from Escherichia coli's two-component signaling systems support these predictions

On the Evolution of the Standard Genetic Code: Vestiges of Critical Scale Invariance from the RNA World in Current Prokaryote Genomes

Herein two genetic codes from which the primeval RNA code could have originated the standard genetic code (SGC) are derived. One of them, called extended RNA code type I, consists of all codons of the type RNY (purine-any base-pyrimidine) plus codons obtained by considering the RNA code but in the second (NYR type) and third (YRN type) reading frames. The extended RNA code type II, comprises all codons of the type RNY plus codons that arise from transversions of the RNA code in the first (YNY type) and third (RNR) nucleotide bases. In order to test if putative nucleotide sequences in the RNA World and in both extended RNA codes, share the same scaling and statistical properties to those encountered in current prokaryotes, we used the genomes of four Eubacteria and three Archaeas. For each prokaryote, we obtained their respective genomes obeying the RNA code or the extended RNA codes types I and II. In each case, we estimated the scaling properties of triplet sequences via a renormalization group approach, and we calculated the frequency distributions of distances for each codon. Remarkably, the scaling properties of the distance series of some codons from the RNA code and most codons from both extended RNA codes turned out to be identical or very close to the scaling properties of codons of the SGC. To test for the robustness of these results, we show, via computer simulation experiments, that random mutations of current genomes, at the rates of 10−10 per site per year during three billions of years, were not enough for destroying the observed patterns. Therefore, we conclude that most current prokaryotes may still contain relics of the primeval RNA World and that both extended RNA codes may well represent two plausible evolutionary paths between the RNA code and the current SGC

Generalized coherent states for the double-well potential

We construct generalized coherent states for the one-dimensional double-well potential and calculate their Mandel parameter, uncertainty relation and Wigner functions. The singularities of their autocorrelation function undergo bifurcations as the mean energy of the system is varied, and we analyse their structure. In the high-energy regime these states consist of a coherent superposition of two minimum-uncertainty Gaussians (they are Schrodinger catlike states).36215773578

Information : currency of life?

Original article can be found at : HFSP Publishing http://hfspj.aip.org/ copyright [Full text of this article is not available in the UHRA]In biology, the exception is mostly the rule, and the rule is mostly the exception. However, recent results indicate that known universal concepts in biology such as the genetic code or the utilization of ATP as a source of energy may be complemented by a large class of principles based on Shannon's concept of information. The present position paper discusses various promising pathways toward the formulation of such generic informational principles and their relevance for the realm of biology.Peer reviewe

Modeling the genetic code: p-adic approach. In: Trends in Biomathematics: Modeling Cells, Flows

Abstract and Figures The genetic code (GC) plays a central role in all living organisms. From a mathematical point of view, the GC is a map from a set of 64 elements (which are codons) onto a set of 21 elements (which are 20 amino acids and 1 stop signal). The GC is the result of evolution, experimentally deciphered as early as the mid-1960s, but its satisfactory theoretical understanding does not yet exist. There are many papers on the GC modeling, its origin and evolution, but also many unsolved issues. In this contribution we provide a brief overview of genetic code modeling, highlighting the p-adic approach, which can describe many properties of the GC. Our primary mathematical tool is a p-adic distance, which simply and adequately describes similarities within the GC. We also point how one could apply this mathematical method to other sequences with a bioinformatic content