Collective dynamics of molecular motors pulling on fluid membranes

The collective dynamics of $N$ weakly coupled processive molecular motors are considered theoretically. We show, using a discrete lattice model, that the velocity-force curves strongly depend on the effective dynamic interactions between motors and differ significantly from a simple mean field prediction. They become essentially independent of $N$ if it is large enough. For strongly biased motors such as kinesin this occurs if $N\gtrsim 5$. The study of a two-state model shows that the existence of internal states can induce effective interactions.Comment: 5 pages, 5 figure

Phase Transition in Two Species Zero-Range Process

We study a zero-range process with two species of interacting particles. We show that the steady state assumes a simple factorised form, provided the dynamics satisfy certain conditions, which we derive. The steady state exhibits a new mechanism of condensation transition wherein one species induces the condensation of the other. We study this mechanism for a specific choice of dynamics.Comment: 8 pages, 3 figure

Translocation of a Single Stranded DNA Through a Conformationally Changing Nanopore

We investigate the translocation of a single stranded DNA through a pore which fluctuates between two conformations, using coupled master equations. The probability density function of the first passage times (FPT) of the translocation process is calculated, displaying a triple, double or mono peaked behavior, depending on the interconversion rates between the conformations, the applied electric field, and the initial conditions. The cumulative probability function of the FPT, in a field-free environment, is shown to have two regimes, characterized by fast and slow timescales. An analytical expression for the mean first passage time of the translocation process is derived, and provides, in addition to the interconversion rates, an extensive characterization of the translocation process. Relationships to experimental observations are discussed.Comment: 8 pages, 5 figures, Biophys. J., in pres

Classes of fast and specific search mechanisms for proteins on DNA

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.Comment: 65 pages, 23 figure

The HIV-1 Rev/RRE system is required for HIV-1 5' UTR cis elements to augment encapsidation of heterologous RNA into HIV-1 viral particles

Abstract Background The process of HIV-1 genomic RNA (gRNA) encapsidation is governed by a number of viral encoded components, most notably the Gag protein and gRNA cis elements in the canonical packaging signal (ψ). Also implicated in encapsidation are cis determinants in the R, U5, and PBS (primer binding site) from the 5' untranslated region (UTR). Although conventionally associated with nuclear export of HIV-1 RNA, there is a burgeoning role for the Rev/RRE in the encapsidation process. Pleiotropic effects exhibited by these cis and trans viral components may confound the ability to examine their independent, and combined, impact on encapsidation of RNA into HIV-1 viral particles in their innate viral context. We systematically reconstructed the HIV-1 packaging system in the context of a heterologous murine leukemia virus (MLV) vector RNA to elucidate a mechanism in which the Rev/RRE system is central to achieving efficient and specific encapsidation into HIV-1 viral particles. Results We show for the first time that the Rev/RRE system can augment RNA encapsidation independent of all cis elements from the 5' UTR (R, U5, PBS, and ψ). Incorporation of all the 5' UTR cis elements did not enhance RNA encapsidation in the absence of the Rev/RRE system. In fact, we demonstrate that the Rev/RRE system is required for specific and efficient encapsidation commonly associated with the canonical packaging signal. The mechanism of Rev/RRE-mediated encapsidation is not a general phenomenon, since the combination of the Rev/RRE system and 5' UTR cis elements did not enhance encapsidation into MLV-derived viral particles. Lastly, we show that heterologous MLV RNAs conform to transduction properties commonly associated with HIV-1 viral particles, including in vivo transduction of non-dividing cells (i.e. mouse neurons); however, the cDNA forms are episomes predominantly in the 1-LTR circle form. Conclusions Premised on encapsidation of a heterologous RNA into HIV-1 viral particles, our findings define a functional HIV-1 packaging system as comprising the 5' UTR cis elements, Gag, and the Rev/RRE system, in which the Rev/RRE system is required to make the RNA amenable to the ensuing interaction between Gag and the canonical packaging signal for subsequent encapsidation

Bubble dynamics in DNA

The formation of local denaturation zones (bubbles) in double-stranded DNA is an important example for conformational changes of biological macromolecules. We study the dynamics of bubble formation in terms of a Fokker-Planck equation for the probability density to find a bubble of size n base pairs at time t, on the basis of the free energy in the Poland-Scheraga model. Characteristic bubble closing and opening times can be determined from the corresponding first passage time problem, and are sensitive to the specific parameters entering the model. A multistate unzipping model with constant rates recently applied to DNA breathing dynamics [G. Altan-Bonnet et al, Phys. Rev. Lett. 90, 138101 (2003)] emerges as a limiting case.Comment: 9 pages, 2 figure

Criterion for phase separation in one-dimensional driven systems

A general criterion for the existence of phase separation in driven one-dimensional systems is proposed. It is suggested that phase separation is related to the size dependence of the steady-state currents of domains in the system. A quantitative criterion for the existence of phase separation is conjectured using a correspondence made between driven diffusive models and zero-range processes. Several driven diffusive models are discussed in light of the conjecture

Why is the DNA Denaturation Transition First Order?

We study a model for the denaturation transition of DNA in which the molecules are considered as composed of a sequence of alternating bound segments and denaturated loops. We take into account the excluded-volume interactions between denaturated loops and the rest of the chain by exploiting recent results on scaling properties of polymer networks of arbitrary topology. The phase transition is found to be first order in d=2 dimensions and above, in agreement with experiments and at variance with previous theoretical results, in which only excluded-volume interactions within denaturated loops were taken into account. Our results agree with recent numerical simulations.Comment: Revised version. To appear in Phys. Rev. Let