Stochastic von Bertalanffy models, with applications to fish recruitment

We consider three individual-based models describing growth in stochastic environments. Stochastic differential equations (SDEs) with identical von Bertalanffy deterministic parts are formulated, with a stochastic term which decreases, remains constant, or increases with organism size, respectively. Probability density functions for hitting times are evaluated in the context of fish growth and mortality. Solving the hitting time problem analytically or numerically shows that stochasticity can have a large positive impact on fish recruitment probability. It is also demonstrated that the observed mean growth rate of surviving individuals always exceeds the mean population growth rate, which itself exceeds the growth rate of the equivalent deterministic model. The consequences of these results in more general biological situations are discussed.     

Sustained oscillations via coherence resonance in SIR

Sustained oscillations in a stochastic SIR model are studied using a new multiple scale analysis. It captures the interaction of the deterministic and stochastic elements together with the separation of time scales inherent in the appearance of these dynamics. The nearly regular fluctuations in the infected and susceptible populations are described via an explicit construction of a stochastic amplitude equation. The agreement between the power spectral densities of the full model and the approximation verifies that coherence resonance is driving the behavior. The validity criteria for this asymptotic approximation give explicit expressions for the parameter ranges in which one expects to observe this phenomenon.     

Extracellular noise-induced stochastic synchronization in heterogeneous quorum sensing network

Quorum sensing is a bacterial mechanism used to synchronize the coordinated response of a microbial population. Because quorum sensing in Gram-negative bacteria depends on release and detection of a diffusible signaling molecule (autoinducer) among a multicellular group, it is considered a simple form of cell-cell communication for the purposes of mathematical analysis. Stochastic equation systems have provided a common approach to model biochemical or biophysical processes. Recently, the effect of noise to synchronize a specific homogeneous quorum sensing network was successfully modeled using a stochastic equation system with fixed parameters. The question remains of how to model quorum sensing networks in a general setting. To address this question, we first set a stochastic equation system as a general model for a heterogeneous quorum sensing network. Then, using two relevant biophysical characteristics of Gram-negative bacteria (the permeability of the cell membrane to the autoinducer and the symmetry of autoinducer diffusion) we construct the solution of the stochastic equation system at an abstract level. The solution indicates that stable synchronization of a quorum sensing network is robustly induced by an environment with a heterogenous distribution of extracellular and intracellular noise. The synchronization is independent of the initial state of the system and is solely the result of the connectivity of the cell network established through the effects of extracellular noise.     

Robusticity and sexual dimorphism in the postcranium of modern hunter-gatherers from Australia

Throughout much of prehistory, humans practiced a hunting and gathering subsistence strategy. Elevated postcranial robusticity and sexually dimorphic mobility patterns are presumed consequences of this strategy, in which males are attributed greater robusticity and mobility than females. Much of the basis for these trends originates from populations where skeletal correlates of activity patterns are known (e.g., cross-sectional geometric properties of long bones), but in which activity patterns are inferred using evidence such as archaeological records (e.g., Pleistocene Europe). Australian hunter-gatherers provide an opportunity to critically assess these ideas since ethnographic documentation of their activity patterns is available. We address the following questions: do skeletal indicators of Australian hunter-gatherers express elevated postcranial robusticity and sexually dimorphic mobility relative to populations from similar latitudes, and do ethnographic accounts support these findings. Using computed tomography, cross-sectional images were obtained from 149 skeletal elements including humeri, radii, ulnae, femora, and tibiae. Cross-sectional geometric properties were calculated from image data and standardized for body size. Australian hunter-gatherers often have reduced robusticity at femoral and humeral midshafts relative to forager (Khoi-San), agricultural/industrialized (Zulu), and industrialized (African American) groups. Australian hunter-gatherers display more sexual dimorphism in upper limb robusticity than lower limb robusticity. Attributing specific behavioral causes to upper limb sexual dimorphism is premature, although ethnographic accounts support sex-specific differences in tool use. Virtually absent sexual dimorphism in lower limb robusticity is consistent with ethnographic accounts of equivalently high mobility among females and males. Thus, elevated postcranial robusticity and sexually dimorphic mobility do not always characterize hunter-gatherers.     

Bayesian inference for stochastic epidemic models with time-inhomogeneous removal rates

Stochastic compartmental models of the SEIR type are often used to make inferences on epidemic processes from partially observed data in which only removal times are available. For many epidemics, the assumption of constant removal rates is not plausible. We develop methods for models in which these rates are a time-dependent step function. A reversible jump MCMC algorithm is described that permits Bayesian inferences to be made on model parameters, particularly those associated with the step function. The method is applied to two datasets on outbreaks of smallpox and a respiratory disease. The analyses highlight the importance of allowing for time dependence by contrasting the predictive distributions for the removal times and comparing them with the observed data.      

Stochastic simulation of daily air temperature and precipitation from monthly normals in North America north of Mexico

A simple, stochastic daily temperature and precipitation generator (TEMPGEN) was developed to generate inputs for the study of the effects of climate change on models driven by daily weather information when climate data are available as monthly summaries. The model uses as input only 11 sets of monthly normal statistics from individual weather stations. It needs no calibration, and was parameterized and validated for use in Canada and the continental United States. Monthly normals needed are: mean and standard deviation of daily minimum and maximum temperature, first and second order autoregressive terms for daily deviations of minimum and maximum temperatures from their daily means, correlation of deviations of daily minimum and maximum temperatures, total precipitation, and the interannual variance of total precipitation. The statistical properties and distributions of daily temperature and precipitation data produced by this generator compared quite favorably with observations from 708 stations throughout North America (north of Mexico). The algorithm generates realistic seasonal patterns, variability and extremes of temperature, precipitation, frost-free periods and hot spells. However, it predicts less accurately the daily probability of precipitation, extreme precipitation events and the duration of extreme droughts.     

Detection of pockets on protein surfaces using small and large probe spheres to find putative ligand binding sites

One of the simplest ways to predict ligand binding sites is to identify pocket-shaped regions on the protein surface. Many programs have already been proposed to identify these pocket regions. Examination of their algorithms revealed that a pocket intrinsically has two arbitrary properties, "size" and "depth". We proposed a new definition for pockets using two explicit adjustable parameters that correspond to these two arbitrary properties. A pocket region is defined as a space into which a small probe can enter, but a large probe cannot. The radii of small and large probe spheres are the two parameters that correspond to the "size" and "depth" of the pockets, respectively. These values can be adjusted individual putative ligand molecule. To determine the optimal value of the large probe spheres radius, we generated pockets for thousands of protein structures in the database, using several size of large probe spheres, examined the correspondence of these pockets with known binding site positions. A new measure of shallowness, a minimum inaccessible radius, R(inaccess), indicated that binding sites of coenzymes are very deep, while those for adenine/guanine mononucleotide have only medium shallowness and those for short peptides and oligosaccharides are shallow. The optimal radius of large probe spheres was 3-4 A for the coenzymes, 4 A for adenine/guanine mononucleotides, and 5 A or more for peptides/oligosaccharides. Comparison of our program with two other popular pocket-finding programs showed that our program had a higher performance of detecting binding pockets, although it required more computational time.     

van der Waals forces influencing adhesion of cells

Adhesion molecules, often thought to be acting by a ‘lock and key’ mechanism, have been thought to control the adhesion of cells. While there is no doubt that a coating of adhesion molecules such as fibronectin on a surface affects cell adhesion, this paper aims to show that such surface contamination is only one factor in the equation. Starting from the baseline idea that van der Waals force is a ubiquitous attraction between all molecules, and thereby must contribute to cell adhesion, it is clear that effects from geometry, elasticity and surface molecules must all add on to the basic cell attractive force. These effects of geometry, elasticity and surface molecules are analysed. The adhesion force measured between macroscopic polymer spheres was found to be strongest when the surfaces were absolutely smooth and clean, with no projecting protruberances. Values of the measured surface energy were then about 35 mJ m⁻², as expected for van der Waals attractions between the non-polar molecules. Surface projections such as abrasion roughness or dust reduced the molecular adhesion substantially. Water cut the measured surface energy to 3.4 mJ m⁻². Surface active molecules lowered the adhesion still further to less than 0.3 mJ m⁻². These observations do not support the lock and key concept.