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Register a new userOn the discrete Peyrard-Bishop model of DNA: stationary solutions and stability
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As a first step in the search of an analytical study of mechanical denaturation of DNA in terms of the sequence, we study stable, stationary solutions in the discrete, finite and homogeneous Peyrard-Bishop DNA model. We find and classify all the stationary solutions of the model, as well as analytic approximations of them, both in the continuum and in the discrete limits. Our results explain the structure of the solutions reported by Theodorakopoulos {em et al.} [Phys. Rev. Lett. {bf 93}, 258101 (2004)] and provide a way to proceed to the analysis of the generalized version of the model incorporating the genetic information.
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We discuss the effect of heterogeneity on the chaotic properties of the Peyrard-Bishop-Dauxois nonlinear model of DNA. Results are presented for the maximum Lyapunov exponent and the deviation vector distribution. Different compositions of adenine-thymine (AT) and guanine-cytosine (GC) base pairs are examined for various energies up to the melting point of the corresponding sequence. We also consider the effect of the alternation index, which measures the heterogeneity of the DNA chain through the number of alternations between different types (AT or GC) of base pairs, on the chaotic behavior of the system. Biological gene promoter sequences have been also investigated, showing no distinct behavior of the maximum Lyapunov exponent.
The zinc finger structure where a Zn2+ ion binds to 4 cysteine or histidine amino acids in a tetrahedral structure is very common motif of nucleic acid binding proteins. The corresponding interaction model is present in 3% of the genes of human genome. As a result, zinc finger has been shown to be extremely useful in various therapeutic and research capacities, as well as in biotechnology. In stable configuration, the cysteine amino acids are deprotonated and become negatively charged. This means the Zn2+ ion is overscreened by 4 cysteine charges (overcharged). It is question of whether this overcharged configuration is also stable when such negatively charged zinc finger binds to negatively charged DNA molecule. Using all atom molecular dynamics simulation up to microsecond range of an androgen receptor protein dimer, we investigate how the deprotonated state of cysteine influences its structure, dynamics, and function in binding o DNA molecules. Our results show that the deprotonated state of cysteine residues are essential for mechanical stabilization of the functional, folded conformation. Not only this state stabilizes the protein structure, it also stabilizes the protein-DNA binding complex. The differences in structural and energetic properties of the two (sequence-identical) monomers are also investigated showing the strong influence of DNA on the structure of zinc fingers upon complexation. Our result has potential impact on better molecular understanding of one of the most common classes of zinc fingers
A variety of physical, social and biological systems generate complex fluctuations with correlations across multiple time scales. In physiologic systems, these long-range correlations are altered with disease and aging. Such correlated fluctuations in living systems have been attributed to the interaction of multiple control systems; however, the mechanisms underlying this behavior remain unknown. Here, we show that a number of distinct classes of dynamical behaviors, including correlated fluctuations characterized by $1/f$-scaling of their power spectra, can emerge in networks of simple signaling units. We find that under general conditions, complex dynamics can be generated by systems fulfilling two requirements: i) a ``small-world topology and ii) the presence of noise. Our findings support two notable conclusions: first, complex physiologic-like signals can be modeled with a minimal set of components; and second, systems fulfilling conditions (i) and (ii) are robust to some degree of degradation, i.e., they will still be able to generate $1/f$-dynamics.
The spreading of bacterial populations is central to processes in agriculture, the environment, and medicine. However, existing models of spreading typically focus on cells in unconfined settings--despite the fact that many bacteria inhabit complex and crowded environments, such as soils, sediments, and biological tissues/gels, in which solid obstacles confine the cells and thereby strongly regulate population spreading. Here, we develop an extended version of the classic Keller-Segel model of bacterial spreading that incorporates the influence of confinement in promoting both cell-solid and cell-cell collisions. Numerical simulations of this extended model demonstrate how confinement fundamentally alters the dynamics and morphology of spreading bacterial populations, in good agreement with recent experimental results. In particular, with increasing confinement, we find that cell-cell collisions increasingly hinder the initial formation and the long-time propagation speed of chemotactic pulses. Moreover, also with increasing confinement, we find that cellular growth and division plays an increasingly dominant role in driving population spreading--eventually leading to a transition from chemotactic spreading to growth-driven spreading via a slower, jammed front. This work thus provides a theoretical foundation for further investigations of the influence of confinement on bacterial spreading. More broadly, these results help to provide a framework to predict and control the dynamics of bacterial populations in complex and crowded environments.
Problems of search and recognition appear over different scales in biological systems. In this review we focus on the challenges posed by interactions between proteins, in particular transcription factors, and DNA and possible mechanisms which allow for a fast and selective target location. Initially we argue that DNA-binding proteins can be classified, broadly, into three distinct classes which we illustrate using experimental data. Each class calls for a different search process and we discuss the possible application of different search mechanisms proposed over the years to each class. The main thrust of this review is a new mechanism which is based on barrier discrimination. We introduce the model and analyze in detail its consequences. It is shown that this mechanism applies to all classes of transcription factors and can lead to a fast and specific search. Moreover, it is shown that the mechanism has interesting transient features which allow for stability at the target despite rapid binding and unbinding of the transcription factor from the target.
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