SIS epidemics with household structure: the self-consistent field method

We consider a stochastic SIS infection model for a population partitioned into m households assuming random mixing. We solve the model in the limit m→∞ by using the self-consistent field method of statistical physics. We derive a number of explicit results, and give numerical illustrations. We then do numerical simulations of the model for finite m and without random mixing. We find in many of these cases that the self-consistent field method is a very good approximation.     

Population dynamics in a spin-glass model of chemical evolution

Summary We introduce a simple model describing the evolution of a population of information-carrying macromolecules. We discuss the asymptotic dependence of the variability of the population on different parameters, representing the severity or the fluctuations of the environment. We show the existence of a transition separating a neutralist evolutionary regime from a trapped one. We investigate the dependence of the evolutionary behavior of the population on the correlation properties of the fitness landscape.     

Dielectric relaxation in proteins: the computational perspective

In photoexcitation and electron transfer, a new dipole or charge is introduced, and the structure is adjusted. This adjustment represents dielectric relaxation, which is the focus of this review. We concentrate on a few selected topics. We discuss linear response theory, as a unifying framework and a tool to describe non-equilibrium states. We review recent, molecular dynamics simulation studies that illustrate the calculation of dynamic and thermodynamic properties, such as Stokes shifts or reorganization free energies. We then turn to the macroscopic, continuum electrostatic view. We recall the physical definition of a dielectric constant and revisit the decomposition of the free energy into a reorganization and a static term. We review some illustrative continuum studies and discuss some difficulties that can arise with the continuum approach. In conclusion, we consider recent developments that will increase the accuracy and broaden the scope of all these methods.     

Spatial and spatio-temporal patterns in a cell-haptotaxis model

We investigate a cell-haptotaxis model for the generation of spatial and spatio-temporal patterns in one dimension. We analyse the steady state problem for specific boundary conditions and show the existence of spatially hetero-geneous steady states. A linear analysis shows that stability is lost through a Hopf bifurcation. We carry out a nonlinear multi-time scale perturbation procedure to study the evolution of the resulting spatio-temporal patterns. We also analyse the model in a parameter domain wherein it exhibits a singular dispersion relation.     

Role of Small Oligomers on the Amyloidogenic Aggregation Free-Energy Landscape

We combine atomic-force-microscopy particle-size-distribution measurements with earlier measurements on 1-anilino-8-naphthalene sulfonate, thioflavin T, and dynamic light scattering to develop a quantitative kinetic model for the aggregation of β-lactoglobulin into amyloid. We directly compare our simulations to the population distributions provided by dynamic light scattering and atomic force microscopy. We combine species in the simulation according to structural type for comparison with fluorescence fingerprint results. The kinetic model of amyloidogenesis leads to an aggregation free-energy landscape. We define the roles of and propose a classification scheme for different oligomeric species based on their location in the aggregation free-energy landscape. We relate the different types of oligomers to the amyloid cascade hypothesis and the toxic oligomer hypothesis for amyloid-related diseases. We discuss existing kinetic mechanisms in terms of the different types of oligomers. We provide a possible resolution to the toxic oligomer-amyloid coincidence.     

An evolutionary strategy for all-atom folding of the 60-amino-acid bacterial ribosomal protein l20

We have investigated an evolutionary algorithm for de novo all-atom folding of the bacterial ribosomal protein L20. We report results of two simulations that converge to near-native conformations of this 60-amino-acid, four-helix protein. We observe a steady increase of "native content" in both simulated ensembles and a large number of near-native conformations in their final populations. We argue that these structures represent a significant fraction of the low-energy metastable conformations, which characterize the folding funnel of this protein. These data validate our all-atom free-energy force field PFF01 for tertiary structure prediction of a previously inaccessible structural family of proteins. We also compare folding simulations of the evolutionary algorithm with the basin-hopping technique for the Trp-cage protein. We find that the evolutionary algorithm generates a dynamic memory in the simulated population, which leads to faster overall convergence.     

Extraordinary Transmission Characteristics of Subwavelength Nanoholes with Rectangular Lattice

We investigate the extraordinary optical transmission (EOT) properties of nanohole arrays with a rectangular lattice for label-free refractive index sensing applications. We show that the deviation within the periodicities along the two axes at the nanohole plane leads to more advantageous spectral quality of EOT signal compared to the conventional square lattice geometries. We introduce a way to further improve the sensitivity of the aperture system by carefully choosing the periodicities. We introduce nanohole arrays with a rectangular lattice supporting EOT signals with larger figure-of-merit values as well as enabling much stronger light transmission. We also model a nanohole system covered with a thin dielectric layer, mimicking biomolecules captured on the gold surface, in order to show its biosensing capability. We also show that certain deviation amounts between periodicities create spectral splitting within the EOT signal leading to larger spectral shifts in the presence of a thin dielectric film.     

A model for the origin and properties of flicker-induced geometric phosphenes

We present a model for flicker phosphenes, the spontaneous appearance of geometric patterns in the visual field when a subject is exposed to diffuse flickering light. We suggest that the phenomenon results from interaction of cortical lateral inhibition with resonant periodic stimuli. We find that the best temporal frequency for eliciting phosphenes is a multiple of intrinsic (damped) oscillatory rhythms in the cortex. We show how both the quantitative and qualitative aspects of the patterns change with frequency of stimulation and provide an explanation for these differences. We use Floquet theory combined with the theory of pattern formation to derive the parameter regimes where the phosphenes occur. We use symmetric bifurcation theory to show why low frequency flicker should produce hexagonal patterns while high frequency produces pinwheels, targets, and spirals.     

Extinction times and size of the surviving species in a two-species competition process

We investigate a stochastic model for the competition between two species. Based on percentiles of the maximum number of individuals in the ecosystem, we present an approximating model for which the extinction time can be thought of as a phase-type random variable. We determine formulae for the probabilities of extinction and the moments of the extinction time. We discuss the use of several quasi-stationary assumptions. We include a comparative study between existing asymptotic results, results obtained from a simulation of the process, and our solution.     

A Hierarchical Bayesian Design for Phase I Trials of Novel Combinations of Cancer Therapeutic Agents

Summary We propose a hierarchical model for the probability of dose‐limiting toxicity (DLT) for combinations of doses of two therapeutic agents. We apply this model to an adaptive Bayesian trial algorithm whose goal is to identify combinations with DLT rates close to a prespecified target rate. We describe methods for generating prior distributions for the parameters in our model from a basic set of information elicited from clinical investigators. We survey the performance of our algorithm in a series of simulations of a hypothetical trial that examines combinations of four doses of two agents. We also compare the performance of our approach to two existing methods and assess the sensitivity of our approach to the chosen prior distribution.     

Anesthesia in the mouse using a combination of ketamine and promazine

An anesthetic combination of ketamine and promazine was tested in 25 male and 25 female mice of each of two strains. The mean induction time was 5 minutes for the C57BL/6We mouse and 8 minutes for the DBA/2We mouse. No sex differences were observed. The mean duration time was 45 minutes for the C57BL/6We male, 53 minutes for the C57BL/TWe female, 29 minutes for the DBA/2We male, and 35 minutes for the DBA/2We female. The mean recovery time was 39 minutes for the C57BL/6We male, 38 minutes for the C57BL/6We female, 21 minutes for the DBA/2We male, and 24 minutes for the DBA/2We female. The drug combination provided effective anesthesia for these strains of the laboratory mouse for a period of 30--50 minutes after a single intramuscular injection.     

Gene mapping via the ancestral recombination graph

We present a multilocus gene mapping method based on linkage disequilibrium, which uses the ancestral recombination graph to model the history of sequences that may harbor an influential variant. We describe the construction of a recurrence equation used to make inferences about the location of a trait-influencing mutation. We demonstrate how a Monte Carlo algorithm combined with a local importance sampling scheme can be used for mapping. We explain how to simulate the timing of events in the coalescent in the presence of recombination and mutation, which accomodates variable population size. We provide an example to illustrate the use of the method, which can be easily extended to more general situations. Although the method is computationally intensive and variation in the likelihood profiles can occur, the method offers a great deal of promise.     

The Quasispecies for the Wright–Fisher Model

We consider the classical Wright–Fisher model of population genetics. We prove the existence of an error threshold for the mutation probability per nucleotide, below which a quasispecies is formed. We show a new phenomenon, specific to a finite population model, namely the existence of a population threshold: to ensure the stability of the quasispecies, the population size has to be at least of the same order as the genome length. We derive an explicit formula describing the quasispecies.     

Estimating the number of founder lineages from haplotypes of closely linked SNPs

We consider an isolated population founded by a small number of individuals randomly chosen from a source population of known genetic composition at a known time in the past. We develop a Monte-Carlo maximum-likelihood method for estimating the number of founding individuals from the haplotype frequencies at several SNP (single nucleotide polymorphism) loci in a sample. We assume the isolated population was founded recently enough that that mutation can be ignored and that haplotype frequencies in the source population have not changed. We apply the method to simulated data and show that it is unbiased. With a reasonable number of individuals sampled, it is possible to estimate the number of founders within a factor of 2. We show that the performance of the method is not degraded substantially if the frequencies of the rare haplotypes in the source are not known precisely and if there is some recombination. We illustrate the use of our method by applying it to a previously published data set from a recently founded population of wolves (Canis lupus) in Scandinavia.     

Statistical alignment of retropseudogenes and their functional paralogs

We describe a model for the sequence evolution of a processed pseudogene and its paralog from a common protein-coding ancestor. The model accounts for substitutions, insertions, and deletions and combines nucleotide- and codon-level mutation models. We give a dynamic programming method for calculating the likelihood of homology between two sequences in the model and describe the accompanying alignment algorithm. We also describe how ancestral codons can be computed when the same gene produced multiple pseudogene homologs. We apply our methods to the evolution of human cytochrome c.     

Cranial morphological variation of Dromiciops gliroides (Microbiotheria) along its geographical distribution in south-central Chile: A three-dimensional analysis

We analyzed the variation in cranial morphology of the marsupial Dromiciops gliroides along its distribution in south-central Chile. We evaluated whether the cranial morphological variation is congruent with the phylogeographic structure previously observed in this species. We built three-dimensional models of 69 crania on which we digitized 30 landmarks. We used standard geometric morphometric methods to extract and analyze the shape and size components of the crania. Our data showed a subtle but consistent cranial size and shape variation along the studied distributional range, suggesting a geographic variation pattern rather than a phylogeographic structuring. Indeed, our multivariate analyses recovered a subtle morphological differentiation between island and mainland populations, contrary to what is suggested by a former phylogeographic study. We detected that either the cranial size variation, as well as the insularity and the latitude could be important factors underlying the cranial shape changes. We suggest that an interplay of historical and contemporary processes could be shaping the morphological pattern observed in this marsupial.     

Online clustering algorithms

We introduce a set of clustering algorithms whose performance function is such that the algorithms overcome one of the weaknesses of K-means, its sensitivity to initial conditions which leads it to converge to a local optimum rather than the global optimum. We derive online learning algorithms and illustrate their convergence to optimal solutions which K-means fails to find. We then extend the algorithm by underpinning it with a latent space which enables a topology preserving mapping to be found. We show visualisation results on some standard data sets.     

Phylogenetic trait conservation in the partner choice of a group of ectomycorrhizal trees

Ecological interactions are frequently conserved across evolutionary time. In the case of mutualisms, these conserved interactions may play a large role in structuring mutualist communities. We hypothesized that phylogenetic trait conservation could play a key role in determining patterns of association in the ectomycorrhizal symbiosis, a globally important trophic mutualism. We used the association between members of the pantropical plant tribe Pisonieae and its fungal mutualist partners as a model system to test the prediction that Pisonieae‐associating ectomycorrhizal fungi will be more closely related than expected by chance, reflecting a conserved trait. We tested this prediction using previously published and newly generated sequences in a Bayesian framework incorporating phylogenetic uncertainty. We report that phylogenetic trait conservation does exist in this association. We generated a five‐marker phylogeny of members of the Pisonieae and used this phylogeny in a Bayesian relaxed molecular clock analysis. We established that the most recent common ancestors of Pisonieae species and Pisonieae‐associating fungi sharing phylogenetic conservation of their patterns of ectomycorrhizal association occurred no more recently than 14.2 Ma. We therefore suggest that phylogenetic trait conservation in the Pisonieae ectomycorrhizal mutualism association represents an inherited syndrome which has existed for at least 14 Myr.