Anderson Localization, Non-linearity and Stable Genetic Diversity

In many models of genotypic evolution, the vector of genotype populations satisfies a system of linear ordinary differential equations. This system of equations models a competition between differential replication rates (fitness) and mutation. Mutation operates as a generalized diffusion process on genotype space. In the large time asymptotics, the replication term tends to produce a single dominant quasispecies, unless the mutation rate is too high, in which case the populations of different genotypes becomes de-localized. We introduce a more macroscopic picture of genotypic evolution wherein a random replication term in the linear model displays features analogous to Anderson localization. When coupled with non-linearities that limit the population of any given genotype, we obtain a model whose large time asymptotics display stable genotypic diversityComment: 25 pages, 8 Figure

Guest charges in an electrolyte: renormalized charge, long- and short-distance behavior of the electric potential and density profile

We complement a recent exact study by L. Samaj on the properties of a guest charge $Q$ immersed in a two-dimensional electrolyte with charges $+1/-1$. In particular, we are interested in the behavior of the density profiles and electric potential created by the charge and the electrolyte, and in the determination of the renormalized charge which is obtained from the long-distance asymptotics of the electric potential. In Samaj's previous work, exact results for arbitrary coulombic coupling $\beta$ were obtained for a system where all the charges are points, provided $\beta Q<2$ and $\beta < 2$. Here, we first focus on the mean field situation which we believe describes correctly the limit $\beta\to 0$ but $\beta Q$ large. In this limit we can study the case when the guest charge is a hard disk and its charge is above the collapse value $\beta Q>2$. We compare our results for the renormalized charge with the exact predictions and we test on a solid ground some conjectures of the previous study. Our study shows that the exact formulas obtained by Samaj for the renormalized charge are not valid for $\beta Q>2$, contrary to a hypothesis put forward by Samaj. We also determine the short-distance asymptotics of the density profiles of the coions and counterions near the guest charge, for arbitrary coulombic coupling. We show that the coion density profile exhibit a change of behavior if the guest charge becomes large enough ($\beta Q\geq 2-\beta$). This is interpreted as a first step of the counterion condensation (for large coulombic coupling), the second step taking place at the usual Manning--Oosawa threshold $\beta Q=2$

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

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

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

Accuracy of PECARN, CATCH, and CHALICE head injury decision rules in children: a prospective cohort study

© 2017 Elsevier Ltd Background Clinical decision rules can help to determine the need for CT imaging in children with head injuries. We aimed to validate three clinical decision rules (PECARN, CATCH, and CHALICE) in a large sample of children. Methods In this prospective observational study, we included children and adolescents (age

Red Queen Coevolution on Fitness Landscapes

Species do not merely evolve, they also coevolve with other organisms. Coevolution is a major force driving interacting species to continuously evolve ex- ploring their fitness landscapes. Coevolution involves the coupling of species fit- ness landscapes, linking species genetic changes with their inter-specific ecological interactions. Here we first introduce the Red Queen hypothesis of evolution com- menting on some theoretical aspects and empirical evidences. As an introduction to the fitness landscape concept, we review key issues on evolution on simple and rugged fitness landscapes. Then we present key modeling examples of coevolution on different fitness landscapes at different scales, from RNA viruses to complex ecosystems and macroevolution.Comment: 40 pages, 12 figures. To appear in "Recent Advances in the Theory and Application of Fitness Landscapes" (H. Richter and A. Engelbrecht, eds.). Springer Series in Emergence, Complexity, and Computation, 201

Stable stem enabled Shannon entropies distinguish non-coding RNAs from random backgrounds

<p>Abstract</p> <p>Background</p> <p>The computational identification of RNAs in genomic sequences requires the identification of signals of RNA sequences. Shannon base pairing entropy is an indicator for RNA secondary structure fold certainty in detection of structural, non-coding RNAs (ncRNAs). Under the Boltzmann ensemble of secondary structures, the probability of a base pair is estimated from its frequency across all the alternative equilibrium structures. However, such an entropy has yet to deliver the desired performance for distinguishing ncRNAs from random sequences. Developing novel methods to improve the entropy measure performance may result in more effective ncRNA gene finding based on structure detection.</p> <p>Results</p> <p>This paper shows that the measuring performance of base pairing entropy can be significantly improved with a constrained secondary structure ensemble in which only canonical base pairs are assumed to occur in energetically stable stems in a fold. This constraint actually reduces the space of the secondary structure and may lower the probabilities of base pairs unfavorable to the native fold. Indeed, base pairing entropies computed with this constrained model demonstrate substantially narrowed gaps of Z-scores between ncRNAs, as well as drastic increases in the Z-score for all 13 tested ncRNA sets, compared to shuffled sequences.</p> <p>Conclusions</p> <p>These results suggest the viability of developing effective structure-based ncRNA gene finding methods by investigating secondary structure ensembles of ncRNAs.</p

Analysis of conserved microRNAs in floral tissues of sexual and apomictic Boechera species

<p>Abstract</p> <p>Background</p> <p>Apomixis or asexual seed formation represents a potentially important agronomic trait whose introduction into crop plants could be an effective way to fix and perpetuate a desirable genotype through successive seed generations. However, the gene regulatory pathways underlying apomixis remain unknown. In particular, the potential function of microRNAs, which are known to play crucial roles in many aspects of plant growth and development, remains to be determined with regards to the switch from sexual to apomictic reproduction.</p> <p>Results</p> <p>Using bioinformatics and microarray validation procedures, 51 miRNA families conserved among angiosperms were identified in <it>Boechera</it>. Microarray assay confirmed 15 of the miRNA families that were identified by bioinformatics techniques. 30 cDNA sequences representing 26 miRNAs could fold back into stable pre-miRNAs. 19 of these pre-miRNAs had miRNAs with <it>Boechera</it>-specific nucleotide substitutions (NSs). Analysis of the Gibbs free energy (ΔG) of these pre-miRNA stem-loops with NSs showed that the <it>Boechera</it>-specific miRNA NSs significantly (p ≤ 0.05) enhance the stability of stem-loops. Furthermore, six transcription factors, the Squamosa promoter binding protein like SPL6, SPL11 and SPL15, Myb domain protein 120 (MYB120), RELATED TO AP2.7 DNA binding (RAP2.7, TOE1 RAP2.7) and TCP family transcription factor 10 (TCP10) were found to be expressed in sexual or apomictic ovules. However, only SPL11 showed differential expression with significant (p ≤ 0.05) up-regulation at the megaspore mother cell (MMC) stage of ovule development in apomictic genotypes.</p> <p>Conclusions</p> <p>This study constitutes the first extensive insight into the conservation and expression of microRNAs in <it>Boechera </it>sexual and apomictic species. The miR156/157 target squamosa promoter binding protein-like 11 (SPL11) was found differentially expressed with significant (p ≤ 0.05) up-regulation at the MMC stage of ovule development in apomictic genotypes. The results also demonstrate that nucleotide changes in mature miRNAs significantly (p ≤ 0.05) enhance the thermodynamic stability of pre-miRNA stem-loops.</p

Hybridization thermodynamics of NimbleGen Microarrays

Background While microarrays are the predominant method for gene expression profiling, probe signal variation is still an area of active research. Probe signal is sequence dependent and affected by probe-target binding strength and the competing formation of probe-probe dimers and secondary structures in probes and targets. Results We demonstrate the benefits of an improved model for microarray hybridization and assess the relative contributions of the probe-target binding strength and the different competing structures. Remarkably, specific and unspecific hybridization were apparently driven by different energetic contributions: For unspecific hybridization, the melting temperature Tm was the best predictor of signal variation. For specific hybridization, however, the effective interaction energy that fully considered competing structures was twice as powerful a predictor of probe signal variation. We show that this was largely due to the effects of secondary structures in the probe and target molecules. The predictive power of the strength of these intramolecular structures was already comparable to that of the melting temperature or the free energy of the probe-target duplex. Conclusions This analysis illustrates the importance of considering both the effects of probe-target binding strength and the different competing structures. For specific hybridization, the secondary structures of probe and target molecules turn out to be at least as important as the probe-target binding strength for an understanding of the observed microarray signal intensities. Besides their relevance for the design of new arrays, our results demonstrate the value of improving thermodynamic models for the read-out and interpretation of microarray signals