Finite-size scaling of the error threshold transition in finite population

The error threshold transition in a stochastic (i.e. finite population) version of the quasispecies model of molecular evolution is studied using finite-size scaling. For the single-sharp-peak replication landscape, the deterministic model exhibits a first-order transition at $Q=Q_c=1/a$, where $Q$ is the probability of exact replication of a molecule of length $L \to \infty$, and $a$ is the selective advantage of the master string. For sufficiently large population size, $N$, we show that in the critical region the characteristic time for the vanishing of the master strings from the population is described very well by the scaling assumption \tau = N^{1/2} f_a \left [ \left (Q - Q_c) N^{1/2} \right ] , where $f_a$ is an $a$-dependent scaling function.Comment: 8 pages, 3 ps figures. submitted to J. Phys.

Statistical mechanics of RNA folding: importance of alphabet size

We construct a minimalist model of RNA secondary-structure formation and use it to study the mapping from sequence to structure. There are strong, qualitative differences between two-letter and four or six-letter alphabets. With only two kinds of bases, there are many alternate folding configurations, yielding thermodynamically stable ground-states only for a small set of structures of high designability, i.e., total number of associated sequences. In contrast, sequences made from four bases, as found in nature, or six bases have far fewer competing folding configurations, resulting in a much greater average stability of the ground state.Comment: 7 figures; uses revtex

Error threshold in finite populations

A simple analytical framework to study the molecular quasispecies evolution of finite populations is proposed, in which the population is assumed to be a random combination of the constiyuent molecules in each generation,i.e., linkage disequilibrium at the population level is neglected. In particular, for the single-sharp-peak replication landscape we investigate the dependence of the error threshold on the population size and find that the replication accuracy at threshold increases linearly with the reciprocal of the population size for sufficiently large populations. Furthermore, in the deterministic limit our formulation yields the exact steady-state of the quasispecies model, indicating then the population composition is a random combination of the molecules.Comment: 14 pages and 4 figure

Translocation of structured polynucleotides through nanopores

We investigate theoretically the translocation of structured RNA/DNA molecules through narrow pores which allow single but not double strands to pass. The unzipping of basepaired regions within the molecules presents significant kinetic barriers for the translocation process. We show that this circumstance may be exploited to determine the full basepairing pattern of polynucleotides, including RNA pseudoknots. The crucial requirement is that the translocation dynamics (i.e., the length of the translocated molecular segment) needs to be recorded as a function of time with a spatial resolution of a few nucleotides. This could be achieved, for instance, by applying a mechanical driving force for translocation and recording force-extension curves (FEC's) with a device such as an atomic force microscope or optical tweezers. Our analysis suggests that with this added spatial resolution, nanopores could be transformed into a powerful experimental tool to study the folding of nucleic acids.Comment: 9 pages, 5 figure

RNA secondary structure formation: a solvable model of heteropolymer folding

The statistical mechanics of heteropolymer structure formation is studied in the context of RNA secondary structures. A designed RNA sequence biased energetically towards a particular native structure (a hairpin) is used to study the transition between the native and molten phase of the RNA as a function of temperature. The transition is driven by a competition between the energy gained from the polymer's overlap with the native structure and the entropic gain of forming random contacts. A simplified Go-like model is proposed and solved exactly. The predicted critical behavior is verified via exact numerical enumeration of a large ensemble of similarly designed sequences.Comment: 4 pages including 2 figure

Field theory for a reaction-diffusion model of quasispecies dynamics

RNA viruses are known to replicate with extremely high mutation rates. These rates are actually close to the so-called error threshold. This threshold is in fact a critical point beyond which genetic information is lost through a second-order phase transition, which has been dubbed the ``error catastrophe.'' Here we explore this phenomenon using a field theory approximation to the spatially extended Swetina-Schuster quasispecies model [J. Swetina and P. Schuster, Biophys. Chem. {\bf 16}, 329 (1982)], a single-sharp-peak landscape. In analogy with standard absorbing-state phase transitions, we develop a reaction-diffusion model whose discrete rules mimic the Swetina-Schuster model. The field theory representation of the reaction-diffusion system is constructed. The proposed field theory belongs to the same universality class than a conserved reaction-diffusion model previously proposed [F. van Wijland {\em et al.}, Physica A {\bf 251}, 179 (1998)]. From the field theory, we obtain the full set of exponents that characterize the critical behavior at the error threshold. Our results present the error catastrophe from a new point of view and suggest that spatial degrees of freedom can modify several mean field predictions previously considered, leading to the definition of characteristic exponents that could be experimentally measurable.Comment: 13 page

The Vienna RNA Websuite

The Vienna RNA Websuite is a comprehensive collection of tools for folding, design and analysis of RNA sequences. It provides a web interface to the most commonly used programs of the Vienna RNA package. Among them, we find folding of single and aligned sequences, prediction of RNA–RNA interactions, and design of sequences with a given structure. Additionally, we provide analysis of folding landscapes using the barriers program and structural RNA alignments using LocARNA. The web server together with software packages for download is freely accessible at http://rna.tbi.univie.ac.at/

Statistical mechanics of RNA folding: a lattice approach

We propose a lattice model for RNA based on a self-interacting two-tolerant trail. Self-avoidance and elements of tertiary structure are taken into account. We investigate a simple version of the model in which the native state of RNA consists of just one hairpin. Using exact arguments and Monte Carlo simulations we determine the phase diagram for this case. We show that the denaturation transition is first order and can either occur directly or through an intermediate molten phase.Comment: 8 pages, 9 figure

Statistical mechanics of secondary structures formed by random RNA sequences

The formation of secondary structures by a random RNA sequence is studied as a model system for the sequence-structure problem omnipresent in biopolymers. Several toy energy models are introduced to allow detailed analytical and numerical studies. First, a two-replica calculation is performed. By mapping the two-replica problem to the denaturation of a single homogeneous RNA in 6-dimensional embedding space, we show that sequence disorder is perturbatively irrelevant, i.e., an RNA molecule with weak sequence disorder is in a molten phase where many secondary structures with comparable total energy coexist. A numerical study of various models at high temperature reproduces behaviors characteristic of the molten phase. On the other hand, a scaling argument based on the extremal statistics of rare regions can be constructed to show that the low temperature phase is unstable to sequence disorder. We performed a detailed numerical study of the low temperature phase using the droplet theory as a guide, and characterized the statistics of large-scale, low-energy excitations of the secondary structures from the ground state structure. We find the excitation energy to grow very slowly (i.e., logarithmically) with the length scale of the excitation, suggesting the existence of a marginal glass phase. The transition between the low temperature glass phase and the high temperature molten phase is also characterized numerically. It is revealed by a change in the coefficient of the logarithmic excitation energy, from being disorder dominated to entropy dominated.Comment: 24 pages, 16 figure

Charting the future of cancer health disparities research: A position statement from the American Association for Cancer Research, the American Cancer Society, the American Society of Clinical Oncology, and the National Cancer Institute

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138314/1/caac21404_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138314/2/caac21404.pd