Multi-patch deterministic and stochastic models for wildlife diseases

Spatial heterogeneity and host demography have a direct impact on the persistence or extinction of a disease. Natural or human-made landscape features such as forests, rivers, roads, and crops are important to the persistence of wildlife diseases. Rabies, hantaviruses, and plague are just a few examples of wildlife diseases where spatial patterns of infection have been observed. We formulate multi-patch deterministic and stochastic epidemic models and use these models to investigate problems related to disease persistence and extinction. We show in some special cases that a unique disease-free equilibrium exists. In these cases, a basic reproduction number ?₀ can be computed and shown to be bounded below and above by the minimum and maximum patch reproduction numbers ? _j , j=1, …, n. The basic reproduction number has a simple form when there is no movement or when all patches are identical or when the movement rate approaches infinity. Numerical examples of the deterministic and stochastic models illustrate the disease dynamics for different movement rates between three patches.     

Cargo properties play a critical role in myosin Va-driven cargo transport along actin filaments

High-resolution experiments revealed that a single myosin-Va motor can transport micron-sized cargo on actin filaments in a stepwise manner. However, intracellular cargo transport is mediated through the dense actin meshwork by a team of myosin Va motors. The mechanism of how motors interact mechanically to bring about efficient cargo transport is still poorly understood. This study describes a stochastic model where a quantitative understanding of the collective behaviors of myosin Va motors is developed based on cargo stiffness. To understand how cargo properties affect the overall cargo transport, we have designed a model in which two myosin Va motors were coupled by wormlike chain tethers with persistence length ranging from 10 to 80 nm and contour length from 100 to 200 nm, and predicted distributions of velocity, run length, and tether force. Our analysis showed that these parameters are sensitive to both the contour and persistence length of cargo. While the velocity of two couple motors is decreased compared to a single motor (from 531 ± 251 nm/s to as low as 318 ± 287 nm/s), the run length (716 ± 563 nm for a single motor) decreased for short, rigid tethers (to as low as 377 ± 187 μm) and increased for long, flexible tethers (to as high as 1.74 ± 1.50 μm). The sensitivity of processive properties to tether rigidity (persistence length) was greatest for short tethers, which caused the motors to exhibit close, yet anti-cooperative coordination. Motors coupled by longer tethers stepped more independently regardless of tether rigidity. Therefore, the properties of the cargo or linkage must play an essential role in motor-motor communication and cargo transport.     

Study of the Geometry and Folding Pattern of Leaves of Mimosa pudica

Many structural and functional properties possessed by plants have great potentials to stimulate new concepts and inno-vative ideas in the field of biomimetic engineering. The key inputs from biology can be used for creation of efficient and op-timized structures. The study of the geometry and folding pattern of leaves of Mimosa pudica,referred as Sensitive Plant,reveals some of the peculiar characteristics during folding and unfolding. When the leaf is touched,it quickly folds its leaflets and pinnae and droops downward at the petiole attachment. With the help of experiments on simulation model,the variations in angle of leaflets and degree of compaction after folding are investigated.     

A superposition free method for protein conformational ensemble analyses and local clustering based on a differential geometry representation of backbone

Here a differential geometry (DG) representation of protein backbone is explored on the analyses of protein conformational ensembles. The protein backbone is described by curvature, κ, and torsion, τ, values per residue and we propose 1) a new dissimilarity and protein flexibility measurement and 2) a local conformational clustering method. The methods were applied to Ubiquitin and c-Myb-KIX protein conformational ensembles and results show that κ\τ metric space allows to properly judge protein flexibility by avoiding the superposition problem. The d_max measurement presents equally good or superior results when compared to RMSF, especially for the intrinsically unstructured protein. The clustering method is unique as it relates protein global to local dynamics by providing a global clustering solutions per residue. The methods proposed can be especially useful to the analyses of highly flexible proteins. The software written for the analyses presented here is available at https://github.com/AMarinhoSN/FleXgeo for academic usage only.     

Bayesian Semiparametric Frailty Selection in Multivariate Event Time Data

Biomedical studies often collect multivariate event time data from multiple clusters (either subjects or groups) within each of which event times for individuals are correlated and the correlation may vary in different classes. In such survival analyses, heterogeneity among clusters for shared and specific classes can be accommodated by incorporating parametric frailty terms into the model. In this article, we propose a Bayesian approach to relax the parametric distribution assumption for shared and specific‐class frailties by using a Dirichlet process prior while also allowing for the uncertainty of heterogeneity for different classes. Multiple cluster‐specific frailty selections rely on variable selection‐type mixture priors by applying mixtures of point masses at zero and inverse gamma distributions to the variance of log frailties. This selection allows frailties with zero variance to effectively drop out of the model. A reparameterization of log‐frailty terms is performed to reduce the potential bias of fixed effects due to variation of the random distribution and dependence among the parameters resulting in easy interpretation and faster Markov chain Monte Carlo convergence. Simulated data examples and an application to a lung cancer clinical trial are used for illustration.     

Minimizing model fitting objectives that contain spurious local minima by bootstrap restarting

Objective functions that arise when fitting nonlinear models often contain local minima that are of little significance except for their propensity to trap minimization algorithms. The standard methods for attempting to deal with this problem treat the objective function as fixed and employ stochastic minimization approaches in the hope of randomly jumping out of local minima. This article suggests a simple trick for performing such minimizations that can be employed in conjunction with most conventional nonstochastic fitting methods. The trick is to stochastically perturb the objective function by bootstrapping the data to be fit. Each bootstrap objective shares the large-scale structure of the original objective but has different small-scale structure. Minimizations of bootstrap objective functions are alternated with minimizations of the original objective function starting from the parameter values with which minimization of the previous bootstrap objective terminated. An example is presented, fitting a nonlinear population dynamic model to population dynamic data and including a comparison of the suggested method with simulated annealing. Convergence diagnostics are discussed.     

A stochastic modeling of early HIV-1 population dynamics

In a recent paper, Tuckwell and Le Corfec [J. Theor. Biol. 195 (1998) 450-463] applied the multi-dimensional diffusion process to model early human immunodeficiency virus type-1 (HIV-1) population dynamics. The purpose of this paper is to assess certain features and consequences of their model in the context of Tan and Wu's stochastic approach [Math. Biosci. 147 (1998) 173-205].