Model Of Lac Operon Research Articles

The establishment process of lac operon model and the analysis of several teaching problems

Gene structure and expression regulation mechanism are the research hotspots and focus of modern life sciences. The lac operon is a cluster of genes through which Escherichia coli catabolizes lactose. It was first proposed by F. Jacob and J. Monod, who were also awarded the Nobel Prize in Physiology or Medicine in 1965 for their contributions. Thereafter, the lac operon has become the classic teaching case of the gene regulation mechanism in microbiology, genetics and molecular biology, and been highly valued by teachers and students alike. Although the conclusion is easy to follow and memorize, its rich connotation and esoteric reasoning has rendered it difficult to understand, neither is it easy for teachers to fully exploit the advantages of this teaching case. Therefore it is necessary to have an in-depth understanding of the genetic structure and working principle of the lac operon, especially the scientific background and thinking process through which scientists revealed these mysteries. In this paper, the historical discovery and analysis process of the E. coli lac operon was reviewed by following their footprints, listening to their analysis of experimental results. Based on the DNA sequences, the reasons for several unusual phenomena of lac operon expression were also discussed to exemplify the teaching value of the classic cases in genetics and molecular biology.

Attractor Stability in Finite Asynchronous Biological System Models.

We present mathematical techniques for exhaustive studies of long-term dynamics of asynchronous biological system models. Specifically, we extend the notion of [Formula: see text]-equivalence developed for graph dynamical systems to support systematic analysis of all possible attractor configurations that can be generated when varying the asynchronous update order (Macauley and Mortveit in Nonlinearity 22(2):421, 2009). We extend earlier work by Veliz-Cuba and Stigler (J Comput Biol 18(6):783-794, 2011), Goles et al. (Bull Math Biol 75(6):939-966, 2013), and others by comparing long-term dynamics up to topological conjugation: rather than comparing the exact states and their transitions on attractors, we only compare the attractor structures. In general, obtaining this information is computationally intractable. Here, we adapt and apply combinatorial theory for dynamical systems from Macauley and Mortveit (Proc Am Math Soc 136(12):4157-4165, 2008. https://doi.org/10.1090/S0002-9939-09-09884-0 ; 2009; Electron J Comb 18:197, 2011a; Discret Contin Dyn Syst 4(6):1533-1541, 2011b. https://doi.org/10.3934/dcdss.2011.4.1533 ; Theor Comput Sci 504:26-37, 2013. https://doi.org/10.1016/j.tcs.2012.09.015 ; in: Isokawa T, Imai K, Matsui N, Peper F, Umeo H (eds) Cellular automata and discrete complex systems, 2014. https://doi.org/10.1007/978-3-319-18812-6_6 ) to develop computational methods that greatly reduce this computational cost. We give a detailed algorithm and apply it to(i) thelac operon model forEscherichia coli proposed by Veliz-Cuba and Stigler (2011), and(ii) the regulatory network involved in the control of the cell cycle and cell differentiation in theCaenorhabditis elegans vulva precursor cells proposed by Weinstein et al.(BMC Bioinform 16(1):1, 2015). In both cases, we uncover all possible limit cycle structures for these networks under sequential updates. Specifically, for the lac operon model, rather than examining all[Formula: see text] sequential update orders, we demonstrate that it is sufficient to consider344 representative update orders, and, more notably, that these344 representatives give rise to 4 distinct attractor structures. A similar analysis performed for the C.elegans model demonstrates that it has precisely125 distinct attractor structures. We conclude with observations on the variety and distribution of the models' attractor structures and use the results to discuss their robustness.

Stability and Hopf bifurcation analysis for a Lac operon model with nonlinear degradation rate and time delay.

In this paper, we construct a discrete time delay Lac operon model with nonlinear degradation rate for mRNA, resulting from the interaction among several identical mRNA pieces. By taking a discrete time delay as bifurcation parameter, we investigate the nonlinear dynamical behaviour arising from the model, using mathematical tools such as stability and bifurcation theory. Firstly, we discuss the existence and uniqueness of the equilibrium for this system and investigate the effect of discrete delay on its dynamical behaviour. Absence or limited delay causes the system to have a stable equilibrium, which changes into a Hopf point producing oscillations if time delay is increased. These sustained oscillation are shown to be present only if the nonlinear degradation rate for mRNA satisfies specific conditions. The direction of the Hopf bifurcation giving rise to such oscillations is also determined, via the use of the so-called multiple time scales technique. Finally, numerical simulations are shown to validate and expand the theoretical analysis. Overall, our findings suggest that the degree of nonlinearity of the model can be used as a control parameter for the stabilisation of the system.

Stability and Hopf bifurcation analysis of lac Operon model with distributed delay and nonlinear degradation rate.

We propose a simple model of lac operon that describes the expression of B-galactosidase from lac Z gene in Escherichia coli, through the interaction among several identical mRNA. Our goal is to explore the complex dynamics (i.e. the oscillation phenomenon) of this architecture mediated by this interaction. This model was theoretically and numerically investigated using distributed time delay. We considered the average delay as a bifurcation parameter and the nonlinear degradation rate as a control parameter. Sufficient conditions for local stability were gained by using the Routh-Hurwitz criterion in the case of a weak delay kernel. Then we proved that Hopf bifurcation happened and the direction of the periodic solution was determined using multiple time scale technique. Our results suggest that the interaction among several identical mRNA plays the main role in gene regulation.

Aggregation for Computing Multi-Modal Stationary Distributions in 1-D Gene Regulatory Networks.

This paper proposes aggregation-based, three-stage algorithms to overcome the numerical problems encountered in computing stationary distributions and mean first passage times for multi-modal birth-death processes of large state space sizes. The considered birth-death processes which are defined by Chemical Master Equations are used in modeling stochastic behavior of gene regulatory networks. Computing stationary probabilities for a multi-modal distribution from Chemical Master Equations is subject to have numerical problems due to the probability values running out of the representation range of the standard programming languages with the increasing size of the state space. The aggregation is shown to provide a solution to this problem by analyzing first reduced size subsystems in isolation and then considering the transitions between these subsystems. The proposed algorithms are applied to study the bimodal behavior of the lac operon of E. coli described with a one-dimensional birth-death model. Thus, the determination of the entire parameter range of bimodality for the stochastic model of lac operon is achieved.

The mechanistic-holistic divide revisited: The case of the lac operon

In this paper, I revisit the development of the repression model of genetic regulation in the lac operon to challenge a common application of a conceptual framework in the history of biology. I take Allen's (1978) account of the changes in the life sciences during the early and mid-twentieth century as an example of a common application of a framework based on the dichotomy between a mechanistic, or reductionist, approach to science and a holistic one. From this conceptual framework, Allen infers two general claims about the process of science and its goals: (1) that “mechanistic materialism” has often presented a more practical way to begin the study of complex phenomena in the life sciences, and (2) that the approach described as “holistic materialism” provides a more complete or accurate description of the natural world. The development of the lac operon model does not fit Allen's generalizations about scientific developments, and it can be used to cast some doubt on the scope of application of that conceptual framework. I argue that a better framework to interpret particular episodes in the history of molecular biology is to consider the ways in which biologists prioritize and track different aspects of the phenomena under study, rather than to focus on whether certain scientific practices are best described as developing from mechanistic to more holistic approaches. I end with some implications for the historiography of science by considering the appropriateness of different conceptual frameworks for different grains of resolution in the history of biology.

Discriminant-based bistability analysis of a TMG-induced lac operon model supported with boundedness and local stability results

This paper presents the results of a theoretical and numerical study on the analysis of bistable behavior of the most studied gene regulatory network, the lac operon, in terms of the model parameters. The boundedness of the state variables for the considered model are demonstrated, the parameter values providing the existence of the multiple equilibria and thus the bistable behavior are determined, and a local stability analysis of the equilibria is performed. The parameter region yielding the existence of multiple equilibria is determined in an algebraic way based on discriminants. The model given in the state equation form is dened by the ordinary differential equations with the rational right-hand sides constituted within Hill and Michaelis{Menten approaches based on enzyme kinetics. The presented method can also be used in the parametric studies of other gene regulatory and metabolic networks given by state equations with rational right hand sides.

Determining the bistability parameter ranges of artificially induced lac operon using the root locus method

This paper employs the root locus method to conduct a detailed investigation of the parameter regions that ensure bistability in a well-studied gene regulatory network namely, lac operon of Escherichia coli (E. coli). In contrast to previous works, the parametric bistability conditions observed in this study constitute a complete set of necessary and sufficient conditions. These conditions were derived by applying the root locus method to the polynomial equilibrium equation of the lac operon model to determine the parameter values yielding the multiple real roots necessary for bistability. The lac operon model used was defined as an ordinary differential equation system in a state equation form with a rational right hand side, and it was compatible with the Hill and Michaelis–Menten approaches of enzyme kinetics used to describe biochemical reactions that govern lactose metabolism. The developed root locus method can be used to study the steady-state behavior of any type of convergent biological system model based on mass action kinetics. This method provides a solution to the problem of analyzing gene regulatory networks under parameter uncertainties because the root locus method considers the model parameters as variable, rather than fixed. The obtained bistability ranges for the lac operon model parameters have the potential to elucidate the appearance of bistability for E. coli cells in in vivo experiments, and they could also be used to design robust hysteretic switches in synthetic biology.

State-dependent doubly weighted stochastic simulation algorithm for automatic characterization of stochastic biochemical rare events

In recent years there has been substantial growth in the development of algorithms for characterizing rare events in stochastic biochemical systems. Two such algorithms, the state-dependent weighted stochastic simulation algorithm (swSSA) and the doubly weighted SSA (dwSSA) are extensions of the weighted SSA (wSSA) by H. Kuwahara and I. Mura [J. Chem. Phys. 129, 165101 (2008)]. The swSSA substantially reduces estimator variance by implementing system state-dependent importance sampling (IS) parameters, but lacks an automatic parameter identification strategy. In contrast, the dwSSA provides for the automatic determination of state-independent IS parameters, thus it is inefficient for systems whose states vary widely in time. We present a novel modification of the dwSSA--the state-dependent doubly weighted SSA (sdwSSA)--that combines the strengths of the swSSA and the dwSSA without inheriting their weaknesses. The sdwSSA automatically computes state-dependent IS parameters via the multilevel cross-entropy method. We apply the method to three examples: a reversible isomerization process, a yeast polarization model, and a lac operon model. Our results demonstrate that the sdwSSA offers substantial improvements over previous methods in terms of both accuracy and efficiency.

Molecular Biology in the Work of Deleuze and Guattari

This article looks at Deleuze and Guattari's understanding of molecular biology, focusing particularly on their reading of two highly influential works by the eminent French molecular biologists François Jacob and Jacques Monod, La logique du vivant (The Logic of Living Systems) and Le hasard et la nécessité (Chance and Necessity). In these two works, Jacob and Monod present the significance of molecular biology in broadly reductionist terms. What is more, the lac operon model of gene regulation that they propose serves to reinforce the so-called Central Dogma of molecular biology, according to which information passes from DNA to RNA to proteins, with no reverse route. However, Deleuze and Guattari discover intensive potentials within the descriptions of molecular biology offered by both writers. It is argued that Jacob's work in particular, as it has developed in the years since the publication of La logique du vivant in 1970, has itself developed these intensive potentials.

Molecular Biology in the Work of Deleuze and Guattari

This article looks at Deleuze and Guattari's understanding of molecular biology, focusing particularly on their reading of two highly influential works by the eminent French molecular biologists François Jacob and Jacques Monod, La logique du vivant (The Logic of Living Systems) and Le hasard et la nécessité (Chance and Necessity). In these two works, Jacob and Monod present the significance of molecular biology in broadly reductionist terms. What is more, the lac operon model of gene regulation that they propose serves to reinforce the so-called Central Dogma of molecular biology, according to which information passes from DNA to RNA to proteins, with no reverse route. However, Deleuze and Guattari discover intensive potentials within the descriptions of molecular biology offered by both writers. It is argued that Jacob's work in particular, as it has developed in the years since the publication of La logique du vivant in 1970, has itself developed these intensive potentials.

Integrative modeling of gene expression and metabolism with E-CELL System

A gene-expression model for an E-CELL simulation was constructed, and the simulation was carried out. The model was integrated with a metabolism model of the self-sustaining virtual cell model which was constructed based on aMycoplasma genitalium cell. Details of the model structure and the results of the simulation are shown. AnEscherichia coli lac-operon model was also constructed by integrating and abstracting the gene-expression model. Wherever possible, experimental parameters were used to construct the model