Quantification of the differences between quenched and annealed averaging for RNA secondary structures

The analytical study of disordered system is usually difficult due to the necessity to perform a quenched average over the disorder. Thus, one may resort to the easier annealed ensemble as an approximation to the quenched system. In the study of RNA secondary structures, we explicitly quantify the deviation of this approximation from the quenched ensemble by looking at the correlations between neighboring bases. This quantified deviation then allows us to propose a constrained annealed ensemble which predicts physical quantities much closer to the results of the quenched ensemble without becoming technically intractable.Comment: 9 pages, 14 figures, submitted to Phys. Rev.

Plant Genome Size Influences Stress Tolerance of Invasive and Native Plants via Plasticity

Plant genome size influences the functional relationships between cellular and whole‐plant physiology, but we know little about its importance to plant tolerance of environmental stressors and how it contributes to range limits and invasion success. We used native and invasive lineages of a wetland plant to provide the first experimental test of the Large Genome Constraint Hypothesis (LGCH)—that plants with large genomes are less tolerant of environmental stress and less plastic under stress gradients than plants with small genomes. We predicted that populations with larger genomes would have a lower tolerance and less plasticity to a stress gradient than populations with smaller genomes. In replicated experiments in northern and southern climates in the United States, we subjected plants from 35 populations varying in genome size and lineage to two salinity treatments. We measured traits associated with growth, physiology, nutrition, defense, and plasticity. Using AICc model selection, we found all plant traits, except stomatal conductance, were influenced by environmental stressors and genome size. Increasing salinity was stressful to plants and affected most plant traits. Notably, biomass in the high‐salinity treatment was 3.0 and 4.9 times lower for the invasive and native lineages, respectively. Plants in the warmer southern greenhouse had higher biomass, stomate density, stomatal conductance, leaf toughness, and lower aboveground percentage of N and total phenolics than in the northern greenhouse. Moreover, responses to the salinity gradient were generally much stronger in the southern than northern greenhouse. Aboveground biomass increased significantly with genome size for the invasive lineage (43% across genome sizes) but not for the native. For 8 of 20 lineage trait comparisons, greenhouse location × genome size interaction was also significant. Interestingly, the slope of the relationship between genome size and trait means was in the opposite direction for some traits between the gardens providing mixed support for LGCH. Finally, for 30% of the comparisons, plasticity was significantly related to genome size—for some plant traits, the relationship was positive, and in others, it was negative. Overall, we found mixed support for LGCH and for the first time found that genome size is associated with plasticity, a trait widely regarded as important to invasion success

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

Counting, generating and sampling tree alignments

Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical sets of matches between identical pairs of trees. This ambiguity is uninformative, and detrimental to any probabilistic analysis.In this work, we consider tree alignments up to equivalence. Our first result is a precise asymptotic enumeration of tree alignments, obtained from a context-free grammar by mean of basic analytic combinatorics. Our second result focuses on alignments between two given ordered trees $S$ and $T$. By refining our grammar to align specific trees, we obtain a decomposition scheme for the space of alignments, and use it to design an efficient dynamic programming algorithm for sampling alignments under the Gibbs-Boltzmann probability distribution. This generalizes existing tree alignment algorithms, and opens the door for a probabilistic analysis of the space of suboptimal RNA secondary structures alignments.Comment: ALCOB - 3rd International Conference on Algorithms for Computational Biology - 2016, Jun 2016, Trujillo, Spain. 201

Evolution Equation of Phenotype Distribution: General Formulation and Application to Error Catastrophe

An equation describing the evolution of phenotypic distribution is derived using methods developed in statistical physics. The equation is solved by using the singular perturbation method, and assuming that the number of bases in the genetic sequence is large. Applying the equation to the mutation-selection model by Eigen provides the critical mutation rate for the error catastrophe. Phenotypic fluctuation of clones (individuals sharing the same gene) is introduced into this evolution equation. With this formalism, it is found that the critical mutation rate is sometimes increased by the phenotypic fluctuations, i.e., noise can enhance robustness of a fitted state to mutation. Our formalism is systematic and general, while approximations to derive more tractable evolution equations are also discussed.Comment: 22 pages, 2 figure

Modeling long-range memory with stationary Markovian processes

In this paper we give explicit examples of power-law correlated stationary Markovian processes y(t) where the stationary pdf shows tails which are gaussian or exponential. These processes are obtained by simply performing a coordinate transformation of a specific power-law correlated additive process x(t), already known in the literature, whose pdf shows power-law tails 1/x^a. We give analytical and numerical evidence that although the new processes (i) are Markovian and (ii) have gaussian or exponential tails their autocorrelation function still shows a power-law decay =1/T^b where b grows with a with a law which is compatible with b=a/2-c, where c is a numerical constant. When a<2(1+c) the process y(t), although Markovian, is long-range correlated. Our results help in clarifying that even in the context of Markovian processes long-range dependencies are not necessarily associated to the occurrence of extreme events. Moreover, our results can be relevant in the modeling of complex systems with long memory. In fact, we provide simple processes associated to Langevin equations thus showing that long-memory effects can be modeled in the context of continuous time stationary Markovian processes.Comment: 5 figure

Neuropsychological outcomes following paediatric temporal lobe surgery for epilepsies: Evidence from a systematic review

Objective: The systematic review aimed to assess the neuropsychological outcomes of temporal lobe resections for epilepsy in children. Additional objectives included determining whether earlier age at surgery leads to better neuropsychological outcomes; the relationships between and predictors of these outcomes. Methods: Using advanced search terms, a systematic review of electronic databases was conducted, comprising MEDLINE, Embase, PsycINFO, Global Health, Web of Science and CINAHL. Included studies reported on outcome following neurosurgical treatment for epilepsy. Specifically, studies were included if they reported neuropsychological outcomes and were concerned only with temporal lobe resection. Results: 73 studies met inclusion criteria. For reported neuropsychological outcomes, the majority of participants remained stable after surgery; some declined and some improved. There was some evidence for increased material-specific memory deficits after temporal lobe surgery based on resection side, and more positive cognitive outcome for those with lower pre-surgical ability level. Significance: Retrieved evidence highlights the need for improvements to quality of methodology and reporting. Appropriately designed prospective multicentre trials should be conducted with adequate follow-up for long-term outcomes to be measured. Core outcome measures should be agreed between centres. This would permit higher quality evidence so that clinicians, young people and their families may make better informed decisions about whether or not to proceed with surgery and likely post-operative profile

Rank Statistics in Biological Evolution

We present a statistical analysis of biological evolution processes. Specifically, we study the stochastic replication-mutation-death model where the population of a species may grow or shrink by birth or death, respectively, and additionally, mutations lead to the creation of new species. We rank the various species by the chronological order by which they originate. The average population N_k of the kth species decays algebraically with rank, N_k ~ M^{mu} k^{-mu}, where M is the average total population. The characteristic exponent mu=(alpha-gamma)/(alpha+beta-gamma)$ depends on alpha, beta, and gamma, the replication, mutation, and death rates. Furthermore, the average population P_k of all descendants of the kth species has a universal algebraic behavior, P_k ~ M/k.Comment: 4 pages, 3 figure