Moisés Santillán

Influence of Catabolite Repression and Inducer Exclusion on the Bistable Behavior of the lac Operon

A mathematical model of the lac operon which includes all of the known regulatory mechanisms, including external-glucose-dependent catabolite repression and inducer exclusion, as well as the time delays inherent to transcription and translation, is presented. With this model we investigate the influence of external glucose, by means of catabolite repression and the regulation of lactose uptake, on the bistable behavior of this system.

Dynamics and bistability in a reduced model of the lac operon

It is known that the lac operon regulatory pathway is capable of showing bistable behavior. This is an important complex feature, arising from the nonlinearity of the involved mechanisms, which is essential to understand the dynamic behavior of this molecular regulatory system. To find which of the mechanisms involved in the regulation of the lac operon is the origin of bistability, we take a previously published model which accounts for the dynamics of mRNA, lactose, allolactose, permease and beta-galactosidase involvement and simplify it by ignoring permease dynamics (assuming a constant permease concentration). To test the behavior of the reduced model, three existing sets of data on beta-galactosidase levels as a function of time are simulated and we obtain a reasonable agreement between the data and the model predictions. The steady states of the reduced model were numerically and analytically analyzed and it was shown that it may indeed display bistability, depending on the extracellular lactose concentration and growth rate.

Quantitative approaches to the study of bistability in the lac operon of Escherichia coli.

In this paper, the history and importance of the lac operon in the development of molecular and systems biology are briefly reviewed. We start by presenting a description of the regulatory mechanisms in this operon, taking into account the most recent discoveries. Then we offer a survey of the history of the lac operon, including the discovery of its main elements and the subsequent influence on the development of molecular and systems biology. Next the bistable behaviour of the operon is discussed, both with respect to its discovery and its molecular origin. A review of the literature in which this bistable phenomenon has been studied from a mathematical modelling viewpoint is then given. We conclude with some brief remarks.

Antagonism influences assembly of a Bacillus guild in a local community and is depicted as a food-chain network

Understanding the principles that govern community assemblages is a central goal of ecology. There is limited experimental evidence in natural settings showing that microbial assembly in communities are influenced by antagonistic interactions. We, therefore, analyzed antagonism among bacterial isolates from a taxonomically related bacterial guild obtained from five sites in sediments from a fresh water system. We hypothesized that if antagonistic interactions acted as a shaping force of the community assembly, then the frequency of resistance to antagonism among bacterial isolates originating from a given site would be higher than the resistance to conspecifics originating from a different assemblage. Antagonism assays were conducted between 78 thermoresistant isolates, of which 72 were Bacillus spp. Sensitive, resistant and antagonistic isolates co-occurred at each site, but the within-site frequency of resistance observed was higher than that observed when assessed across-sites. We found that antagonism results from bacteriocin-like substances aimed at the exclusion of conspecifics. More than 6000 interactions were scored and described by a directed network with hierarchical structure that exhibited properties that resembled a food chain, where the different Bacillus taxonomic groups occupied specific positions. For some tested interacting pairs, the unidirectional interaction could be explained by competition that inhibited growth or completely excluded one of the pair members. This is the first report on the prevalence and specificity of Bacillus interactions in a natural setting and provides evidence for the influence of bacterial antagonist interactions in the assemblage of a taxonomically related guild in local communities.

Local stability analysis of an endoreversible Curzon-Ahborn-Novikov engine working in a maximum-power-like regime

A local stability analysis of an endoreversible Curzon–Ahborn–Novikov (CAN) engine, working in a maximum-power-like regime, is presented. The CAN engine in the present work consists of a Carnot engine that exchanges heat with the heat reservoirs T1 and T2 (T1 >T 2) through a couple of thermal conductors, both having the same conductance (α). In addition, the working fluid has the same heat capacity (C) in the two isothermal branches of the cycle. From the local stability analysis we conclude that the CAN engine is stable for every value of α, C and τ = T2/T1; that after a perturbation the system state exponentially decays to the steady state with either of two different relaxation times; that both relaxation times are proportional to C/α; and that only one of them depends on τ , being a monotonically decreasing function of τ . Finally, when comparing with the system steady-state energetic properties, we find that as τ increases, the system stability is improved, while the system power and efficiency decrease; this suggests a compromise between the stability and energetic properties, driven by τ .

Dynamic robustness and thermodynamic optimization in a non-endoreversible Curzon-Ahlborn engine

Abstract In this work we analyze the stability of a non-endoreversible Curzon–Ahlborn engine, taking into account the engines implicit time delays. When comparing the systems dynamic stability with its thermodynamic properties (efficiency and power output), we find that the temperature ratio τ = T 2/T 1 (T 1 > T 2 being the temperatures of the external heat reservoirs) represents a trade-off between stability and energetic properties. This result is in agreement with previous studies of the endoreversible Curzon–Ahlborn engine. The only dierence is that, in the non-endoreversible case, τ can only increase up to R (with R < 1, a parameter measuring the degree of internal irreversibilities), while in the endoreversible case it can grow up to one. Finally, we demonstrate that the total time delay does not destabilize the system steady-state, regardless of its length, and thus it does not seem to play a role in the dynamic-thermodynamic property trade-off.

Thermodynamic optimality in some biochemical reactions

SummaryIn this short communication we discuss the possibility that anaerobic glycolisis and (aerobic) respiration, both for adenosine triphosphate (ATP) production, be chemical reactions that follow different thermodynamic-optimization criteria. The former reaction maximizing power output and the latter maximizing a function that represents an advantageous compromise between high power output and low entropy production. Our approach is by means of finite-time thermodynamics (FTT).

A proposed mechanism for the interaction of the segmentation clock and the determination front in somitogenesis.

Background Recent discoveries in the field of somitogenesis have confirmed, for the most part, the feasibility of the clock and wavefront model. There are good candidates for both the clock (various genes expressed cyclically in the tail bud of vertebrate embryos have been discovered) and the wavefront (there are at least three different substances, whose expression levels vary along the presomitic mesoderm [PSM], that have important effects on the formation of somites). Nevertheless, the mechanisms through which the wavefront interacts with the clock to arrest the oscillations and induce somite formation have not yet been fully elucidated. Principal Findings In this work, we propose a gene regulatory network which is consistent with all known experimental facts in embryonic mice, and whose dynamic behaviour provides a potential explanation for the periodic aggregation of PSM cells into blocks: the first step leading to the formation of somites. Significance To our knowledge, this is the first proposed mechanism that fully explains how a block of PSM cells can stop oscillating simultaneously, and how this process is repeated periodically, via the interaction of the segmentation clock and the determination front.

Irreversible thermodynamics in multiscale stochastic dynamical systems.

This work extends the results of a recently developed theory of a rather complete thermodynamic formalism for discrete-state, continuous-time Markov processes with and without detailed balance. We investigate whether and in what way the thermodynamic structure is invariant in a multiscale stochastic system, that is, whether the relations between thermodynamic functions of state and process variables remain unchanged when the system is viewed at different time scales and resolutions. Our results show that the dynamics on a fast time scale contribute an entropic term to the internal energy function u(S)(x) for the slow dynamics. Based on the conditional free energy u(S)(x), we can then treat the slow dynamics as if the fast dynamics is nonexistent. Furthermore, we show that the free energy, which characterizes the spontaneous organization in a system without detailed balance, is invariant with or without the fast dynamics: The fast dynamics is assumed to reach stationarity instantaneously on the slow time scale; it has no effect on the systems free energy. The same cannot be said for the entropy and the internal energy, both of which contain the same contribution from the fast dynamics. We also investigate the consequences of time-scale separation in connection to the concepts of quasi-stationarity and steady adiabaticity introduced in the phenomenological steady-state thermodynamics.

Distributions for negative-feedback-regulated stochastic gene expression: dimension reduction and numerical solution of the chemical master equation.

In this work we introduce a novel approach to study biochemical noise. It comprises a simplification of the master equation of complex reaction schemes (via an adiabatic approximation) and the numerical solution of the reduced master equation. The accuracy of this procedure is tested by comparing its results with analytic solutions (when available) and with Gillespie stochastic simulations. We further employ our approach to study the stochastic expression of a simple gene network, which is subject to negative feedback regulation at the transcriptional level. Special attention is paid to the influence of negative feedback on the amplitude of intrinsic noise, as well as on the relaxation rate of the system probability distribution function to the steady solution. Our results suggest the existence of an optimal feedback strength that maximizes this relaxation rate.