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.     

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.     

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.     

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.     

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.     

Four-state models and regulation of contraction of smooth muscle. I. Physical considerations, stability, and solutions.

Cyclic four-state models are frequently used in biology to represent a variety of molecular behaviors. A common experimental strategy to test such models is to follow the behavior of the real system after some of the rate constants are changed in a stepwise manner. We analyze the mathematical behavior of a simple example of such a model applicable to the regulation of contraction of smooth muscle, but our results apply in general to any linear, cyclic four-state model. We discuss detailed balance and requirements for linearity. We find that the only way to have sustained oscillations is for the rate constants of the model to be themselves oscillatory. We state conditions for decaying oscillations and find that in models that do not follow strictly first-order kinetics and do not satisfy detailed balance, these conditions can hold. We show analytically that the response of any state to step changes in the rate constants is the sum of three weighted exponentials plus a constant term, the steady-state value. We provide explicit expressions for the time dependence of all state variables. We discuss a simple way to use these results to obtain numerical solutions in cases where the rate constants change in an arbitrary way.     

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.     

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.     

Tail posterior probability for inference in pairwise and multiclass gene expression data

We consider the problem of identifying differentially expressed genes in microarray data in a Bayesian framework with a noninformative prior distribution on the parameter quantifying differential expression. We introduce a new rule, tail posterior probability, based on the posterior distribution of the standardized difference, to identify genes differentially expressed between two conditions, and we derive a frequentist estimator of the false discovery rate associated with this rule. We compare it to other Bayesian rules in the considered settings. We show how the tail posterior probability can be extended to testing a compound null hypothesis against a class of specific alternatives in multiclass data.     

microRNA-34a is tumor suppressive in brain tumors and glioma stem cells

We recently found that microRNA-34a (miR-34a) is downregulated in human glioma tumors as compared to normal brain, and that miR-34a levels in mutant-p53 gliomas were lower than in wildtype-p53 tumors. We showed that miR-34a expression in glioma and medulloblastoma cells inhibits cell proliferation, G1/S cell cycle progression, cell survival, cell migration and cell invasion, but that miR-34a expression in human astrocytes does not affect cell survival and cell cycle. We uncovered the oncogenes c-Met, Notch-1 and Notch-2 as direct targets of miR-34a that are inhibited by miR-34a transfection. We found that c-Met levels in human glioma specimens inversely correlate with miR-34a levels. We showed that c-Met and Notch partially mediate the inhibitory effects of miR-34a on cell proliferation and cell death. We also found that mir-34a expression inhibits in vivo glioma xenograft growth. We concluded that miR-34a is a potential tumor suppressor in brain tumors that acts by targeting multiple oncogenes. In this extra view, we briefly review and discuss the implications of these findings and present new data on the effects of miR-34a in glioma stem cells. The new data show that miR-34a expression inhibits various malignancy endpoints in glioma stem cells. Importantly, they also show for the first time that miR-34a expression induces glioma stem cell differentiation. Altogether, the data suggest that miR-34a is a tumor suppressor and a potential potent therapeutic agent that acts by targeting multiple oncogenic pathways in brain tumors and by inducing the differentiation of cancer stem cells.     

Coexistence and emergent neutrality generate synchrony among competitors in fluctuating environments

Many competitive communities exhibit a puzzling amount of species diversity. In this study, we model a community of symmetric competitors in a fluctuating environment. We use biologically realistic temperature-dependent growth curves with a widely hypothesized trade-off between maximum growth and nice breadth to control the shapes of the curves of different species. We perform three analyses of the community dynamics to investigate the role of environmental fluctuations in community composition and species diversity. We initiate communities with equal abundances of all species and randomize the temperature fluctuations so that there is no correlation between species responses, only noise. We initiate single populations and allow other species to randomly invade the community. We also knock out extant species one by one from an established community and allow them to reinvade after the remaining species have adjusted. We find that competitors with sufficiently different temperature niches coexist via temporal niche differentiation. We also find long-term persistence of species that are very similar to a dominant competitor. This creates communities with species clumped along a temperature niche axis, with stable coexistence between groups and near neutrality within groups. The near neutrality results in interspecific synchrony within the groups, providing an explanation for the maintenance of high diversity in competitive communities where synchrony is commonly observed.     

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.     

The joint allele-frequency spectrum in closely related species

We develop the theory for computing the joint frequency spectra of alleles in two closely related species. We allow for arbitrary population growth in both species after they had a common ancestor. We focus on the case in which a single chromosome is sequenced from one of the species. We use classical diffusion theory to show that, if the ancestral species was at equilibrium under mutation and drift and a chromosome from one of the descendant species carries the derived allele, the frequency spectrum in the other species is uniform, independently of the demographic history of both species. We also predict the expected densities of segregating and fixed sites when the chromosome from the other species carries the ancestral allele. We compare the predictions of our model with the site-frequency spectra of SNPs in the four HapMap populations of humans when the nucleotide present in the Neanderthal DNA sequence is ancestral or derived, using the chimp genome as the outgroup.     

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.     

Effective detection of remote homologues by searching in sequence dataset of a protein domain fold

Profile matching methods are commonly used in searches in protein sequence databases to detect evolutionary relationships. We describe here a sensitive protocol, which detects remote similarities by searching in a specialized database of sequences belonging to a fold. We have assessed this protocol by exploring the relationships we detect among sequences known to belong to specific folds. We find that searches within sequences adopting a fold are more effective in detecting remote similarities and evolutionary connections than searches in a database of all sequences. We also discuss the implications of using this strategy to link sequence and structure space.     

Kinetics of lipid-membrane binding and conformational change of L-BABP

We designed an experimental approach to differentiate the kinetics of protein binding to a lipid membrane from the kinetics of the associated conformational change in the protein. We measured the fluorescence intensity of the single Trp6 in chicken liver bile acid-binding protein (L-BABP) as a function of time after mixing the protein with lipid membranes. We mixed the protein with pure lipid membranes, with lipid membranes in the presence of a soluble quencher, and with lipid membranes containing a fluorescence quencher attached to the lipid polar head group. We fitted simultaneously the experimental curves to a three-state kinetic model. We conclude that in a first step, the binding of L-BABP to the interfacial region of the anionic lipid polar head groups occurred simultaneously with a conformational change to the partly unfolded state. In a second slower step, Trp6 buried within the polar head group region, releasing contacts with the aqueous phase.     

Effect of the rate of phytoplankton growth on the spaced-time dynamics of plankton communities in an homogeneous environment

We use a conceptual mathematical reaction-diffusion model to investigate the mechanisms of spatial structure formation and complex temporal dynamics of plankton in a heterogeneous environment. We take into account basic trophic interactions, namely, "prey-predator" interactions between phytoplankton, zooplankton, and fish in upper layers of natural waters. We consider plankton as a passive contaminant in turbulent waters. We show that plankton structure formation can result from the difference in phytoplankton growth rate in neighboring habitats. Phytoplankton and zooplankton biomass is shown to undergo both regular and chaotic oscillations. The fish predation rate substantially affects the spatial and temporal dynamics of plankton in a heterogeneous environment.     

Rapid tilt-series acquisition for electron cryotomography

Using a new Titan Krios stage equipped with a single-axis holder, we developed two methods to accelerate the collection of tilt-series. We demonstrate a continuous-tilting method that can record a tilt-series in seconds, but with loss of details finer than ～4?nm. We also demonstrate a fast-incremental method that can record a tilt-series several-fold faster than current methods and with similar resolution. We characterize the utility of both methods in real biological electron cryotomography workflows. We identify opportunities for further improvements in hardware and software and speculate on the impact such advances could have on structural biology.     

Emergence of morphological order in the network formation of Physarum polycephalum

Emergence in a system appears through the interaction of its components, giving rise to higher order or complexity in the system. We tested for the presence of emergent properties in a biological system using the simplest biological entity of a unicellular organism; the plasmodium of Physarum polycephalum, a giant unicellular amoeboid organism that forms a network-like tubular structure connecting its food sources. We let two plasmodium networks within a single cell interact with each other, and observed how the intracellular interaction affected the morphologenesis of the plasmodium networks. We found that the two networks developed homologous morphology. We further discuss the presence of autonomous and emergent properties in homologous network formation.