抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

Recent single-molecule enzymology measurements with improved statistics have demonstrated that a single enzyme molecule exhibits large temporal fluctuations of the turnover rate constant at a broad range of time scales (from 1 ms to 100 s). The rate constant fluctuations, termed as dynamic disorder, are associated with fluctuations of the protein conformations observed on the same time scales. We discuss the unique information extractable from these experiments and the reconciliation of these observations with ensemble-averaged Michaelis−Menten equation. A theoretical model based on the generalized Langevin equation (GLE) treatment of Kramers' barrier crossing problem for chemical reactions accounts naturally for the observation of dynamic disorder and highly dispersed kinetics.

http://www.people.fas.harvard.edu/~skou/papers/AccChem.pdf?origin=publication_detail

Fluctuating enzymes: lessons from single-molecule studies.

Simple models for complex nonequilibrium fluids

Conformational dynamics of proteins can be interpreted as itinerant motions as the protein traverses from one state to another on a complex network in conformational space or, more generally, in state space. Here we present a scheme to extract a multiscale state space network (SSN) from a single-molecule time series. Analysis by this method enables us to lift degeneracy—different physical states having the same value for a measured observable—as much as possible. A state or node in the network is defined not by the value of the observable at each time but by a set of subsequences of the observable over time. The length of the subsequence can tell us the extent to which the memory of the system is able to predict the next state. As an illustration, we investigate the conformational fluctutation dynamics probed by single-molecule electron transfer (ET), detected on a photon-by-photon basis. We show that the topographical features of the SSNs depend on the time scale of observation; the longer the time scale, the simpler the underlying SSN becomes, leading to a transition of the dynamics from anomalous diffusion to normal Brownian diffusion.

https://www.pnas.org/content/pnas/105/2/536.full.pdf

Multiscale complex network of protein conformational fluctuations in single-molecule time series

The translocation dynamics of a polymer chain through a nanopore in the absence of an external driving force is analyzed by means of scaling arguments, fractional calculus, and computer simulations. The problem at hand is mapped on a one-dimensional anomalous diffusion process in terms of the reaction coordinate $s$ (i.e., the translocated number of segments at time $t$) and shown to be governed by a universal exponent $\ensuremath{\alpha}=2∕(2\ensuremath{\nu}+2\ensuremath{-}{\ensuremath{\gamma}}_{1})$, where $\ensuremath{\nu}$ is the Flory exponent and ${\ensuremath{\gamma}}_{1}$ is the surface exponent. Remarkably, it turns out that the value of $\ensuremath{\alpha}$ is nearly the same in two and three dimensions. The process is described by a fractional diffusion equation which is solved exactly in the interval $0lslN$ with appropriate boundary and initial conditions. The solution gives the probability distribution of translocation times as well as the variation with time of the statistical moments $⟨s(t)⟩$ and $⟨{s}^{2}(t)⟩\ensuremath{-}{⟨s(t)⟩}^{2}$, which provide a full description of the diffusion process. The comparison of the analytic results with data derived from extensive Monte Carlo simulations reveals very good agreement and proves that the diffusion dynamics of unbiased translocation through a nanopore is anomalous in its nature.

/pdf/polymer-translocation-through-a-nanopore-a-showcase-of-50v04d8xvw.pdf

Polymer translocation through a nanopore: A showcase of anomalous diffusion

Time-dependent fluctuations in the distance x(t) between two segments along a polymer are one measure of its overall conformational dynamics. The dynamics of x(t), modeled as the coordinate of a particle moving in a one-dimensional potential well in thermal contact with a reservoir, is treated with a generalized Langevin equation whose memory kernel K(t) can be calculated from the time-correlation function of distance fluctuations C(t)≡⟨x(0)x(t)⟩. We compute C(t) for a semiflexible continuum model of the polymer and use it to determine K(t) via the GLE. The calculations demonstrate that C(t) is well approximated by a Mittag-Leffler function and K(t) by a power-law decay on time scales of several decades. Both functions depend on a number of parameters characterizing the polymer, including chain length, degree of stiffness, and the number of intervening residues between the two segments. The calculations are compared with the recent observation of a nonexponential C(t) and a power law K(t) in the conformat...

Multiple time scale dynamics of distance fluctuations in a semiflexible polymer: A one-dimensional generalized Langevin equation treatment

The Wilemski–Fixman model of diffusion controlled-reactions [J. Chem. Phys. 58, 4009 (1973)] is combined with a generalized random walk description of chain conformations to predict the dependence of the closure time \tau on the chain length N of polymers with reactive end groups and nonlocal interactions. The nonlocal interactions are modeled by a modification to the connectivity term in the Edwards continuum representation of the polymer. The modification involves a parameter h lying between 0 and 1 that is a measure of the extent of correlation between adjacent monomers on the chain backbone. Different choices of h correspond to chain conformations of different average radial dimensions. In particular, the values 1/3, 1/2 and 3/5 provide approximations to the statistics of polymers in poor, theta and good solvents, respectively. The closure time \tau of such chains is calculated analytically for different N. In all cases, \tau is found to vary as a power law in N, Nb, with b a function of h. For the special case h = 1/3, which models collapsed polymers and globular proteins, b is about 1.6–1.7.

/pdf/dynamics-of-chain-closure-approximate-treatment-of-nonlocal-beg5d65etx.pdf

Dynamics of chain closure: Approximate treatment of nonlocal interactions

In this paper we explore the conformational properties of random A–B block copolymers with semiflexible segments in a constant force field as a model of the behavior of biopolymers under tension. The degree of semiflexibility of individual blocks, which is characterized by a persistence length l, may range from values that correspond to complete flexibility of the block to values that correspond to nearly complete rigidity. The distribution of blocks is described by a two-state Markov process that generates the statistics governing the process of living polymerization in the steady state. Force-extension curves for this model of the polymer are calculated as an average over the chains conformations (which are described by a finitely extensible Gaussian model), as well as over both quenched and annealed distributions of the sequence of A and B blocks along the chain backbone. The results are sensitive to the nature of the sequence distribution: in the annealed case, the force-extension curves are sigmoidal for essentially all values of the parameters that characterize the conformational properties of the A and B blocks and their statistical correlations, while in the quenched case, the curves exhibit plateau regions that are reminiscent of various kinds of transitions in proteins and DNA.

/pdf/semiflexible-random-a-b-block-copolymers-under-tension-1s2lxlglwh.pdf

Semiflexible random A–B block copolymers under tension

Random copolymers made up of subunits with arbritary degrees of flexibility are useful as models of biomolecules with different kinds of secondary structural motifs. We show that the mean square end-to-end distance 〈R2〉 of a two-letter A–B random heteropolymer in which the constituent polymeric subunits are represented as continuum wormlike chains and the randomness is described by the two-state Markov process introduced by Fredrickson, Milner, and Leibler [Macromolecules 25, 6341 (1992)] can be obtained in closed form. The expression for 〈R2〉 is a function of several parameters, including the number n of subunits, the fraction f of one kind of subunit, the persistence lengths lA and lB of the two subunits, and the degree of correlation λ between successive subunits. The variation of 〈R2〉 with each of these parameters is discussed.

/pdf/conformational-properties-of-randomly-flexible-15ri6cesx7.pdf

Pallavi Debnath

Papers

Multiple time scale dynamics of distance fluctuations in a semiflexible polymer: A one-dimensional generalized Langevin equation treatment

Dynamics of chain closure: Approximate treatment of nonlocal interactions

Semiflexible random A–B block copolymers under tension

Conformational properties of randomly flexible heteropolymers