Cooperativity in two-state protein folding kinetics

We present a solvable model that predicts the folding kinetics of two-state proteins from their native structures. The model is based on conditional chain entropies. It assumes that folding processes are dominated by small-loop closure events that can be inferred from native structures. For CI2, the src SH3 domain, TNfn3, and protein L, the model reproduces two-state kinetics, and it predicts well the average Phi-values for secondary structures. The barrier to folding is the formation of predominantly local structures such as helices and hairpins, which are needed to bring nonlocal pairs of amino acids into contact.     

Spite and the scale of competition

In recent years there has been a large body of theoretical work examining how local competition can reduce and even remove selection for altruism between relatives. However, it is less well appreciated that local competition favours selection for spite, the relatively neglected ugly sister of altruism. Here, we use extensions of social evolution theory that were formulated to deal with the consequences for altruism of competition between social partners, to illustrate several points on the evolution of spite. Specifically, we show that: (i) the conditions for the evolution of spite are less restrictive than previously assumed; (ii) previous models which have demonstrated selection for spite often implicitly assumed local competition; (iii) the scale of competition must be allowed for when distinguishing different forms of spite (Hamiltonian vs. Wilsonian); (iv) local competition can enhance the spread of spiteful greenbeards; and (v) the theory makes testable predictions for how the extent of spite should vary dependent upon population structure and average relatedness.     

Electrostatic interactions in a peptide--RNA complex

Parallel experimental measurements and theoretical calculations have been used to investigate the energetics of electrostatic interactions in the complex formed between a 22 residue, alpha-helical peptide from the N protein of phage lambda and its cognate 19 nucleotide box B RNA hairpin. Salt-dependent free energies were measured for both peptide folding from coil to helix and peptide binding to RNA, and from these the salt-dependence of binding pre-folded, helical peptide to RNA was determined ( partial differential (DeltaG degrees (dock))/ partial differential log[KCl]=5.98(+/-0.21)kcal/mol). (A folding transition taking place in the RNA hairpin loop was shown to have a negligible dependence on salt concentration.) The non-linear Poisson-Boltzmann equation was used to calculate the same salt dependence of the binding free energy as 5.87(+/-0.22)kcal/mol, in excellent agreement with the measured value. Close agreement between experimental measurements and calculations was also obtained for two variant peptides in which either a basic or acidic residue was replaced with an uncharged residue, and for an RNA variant with a deletion of a single loop nucleotide. The calculations suggest that the strength of electrostatic interactions between a peptide residue and RNA varies considerably with environment, but that all 12 positive and negative N peptide charges contribute significantly to the electrostatic free energy of RNA binding, even at distances up to 11A from backbone phosphate groups. Calculations also show that the net release of ions that accompanies complex formation originates from rearrangements of both peptide and RNA ion atmospheres, and includes accumulation of ions in some regions of the complex as well as displacement of cations and anions from the ion atmospheres of the RNA and peptide, respectively.     

Power-law versus exponential distributions of animal group sizes

There has been some confusion concerning the animal group size: an exponential distribution was deduced by maximizing the entropy; lognormal distributions were practically used; as power-law decay with exponent 3/2 was proposed in physical analogy to aerosol condensation. Here I show that the animal group-size distribution follows a power-law decay with exponent 1, and is truncated at a cut-off size which is the expected size of the groups an arbitrary individual engages in. An elementary model of animal aggregation based on binary splitting and coalescing on contingent encounter is presented. The model predicted size distribution holds for various data from pelagic fishes and mammalian herbivores in the wild.     

A study of prey-predator relations for mammals

In this paper, we present a prey-predator nonlinear model for mammals, consisting of large- and small-size prey species with group defence, in a partially protected habitat. If the prey size is small, then it is more prone to the predator at higher densities. Conversely, large prey size at higher densities tend to develop group defence. Therefore, the predator will be attracted towards that area where prey are less in number. A new physical constant has been introduced into the radiation-type condition on that part of the boundary where interaction between prey and predator takes place. This constant allows us to efficiently model group defence capabilities of the herds and its numerical values have to be determined for different pairs of prey-predator species from field observations. A way of measuring the constants involved in the model is suggested. Numerical results are provided and thoroughly discussed for a habitat of circular shape. The obtained results show that in the region away from the protected area, the density of large-size prey species is higher than that of small-size prey species, a fact that is in accordance with observations.     

An exactly solvable model of population dynamics with density-dependent migrations and the Allee effect

We consider a single-species model of population dynamics allowing for migrations and the Allee effect. Two types of migration are taken into account: one caused by environmental factors (e.g., a passive transport with the wind or water current) and the other associated with biological mechanisms. While the first type is apparently density-independent, the speed of migration in the second one can depend on the population density. Mathematically, this model consists of a non-linear partial differential equation of advection-diffusion-reaction type. Using an appropriate change of variables, we obtain an exact solution of the equation describing propagation of travelling population fronts. We show that, depending on parameter values and thus on the relative intensity of density-dependent and density-independent factors, the direction of the propagation can be different thus describing either species invasion or species retreat.     

Effect of channel geometry on the electrostatic potential in acetylcholine channels

We study the effect of channel geometry on the potential barrier encountered by ions as they permeate the acetylcholine receptor channel. Among the various channel geometries which have been used to represent the acetylcholine receptor channel include the cylinder and the toroidal catenary. The main reasons for those choices appear to be the facilitation of separation of the Poisson equation, rather than biological considerations. We consider a novel and realistic acetylcholine channel geometry, and calculate the electrostatic potential profiles within it, and compare our results with results from other channel geometries.     

A mathematical model of quorum sensing in a growing bacterial biofilm

In a process called quorum sensing, bacteria monitor their population density via extracellular signaling molecules and modulate gene expression accordingly. This paper describes a one-dimensional model of a growing Pseudomonas aeruginosa biofilm. Quorum sensing has been included in the model by the addition of equations describing the production, degradation, and diffusion of acyl-homoserine lactones in the biofilm. In order for quorum sensing to initiate near the substratum, in accordance with experimental observations, model results suggest that cells in oxygen-deficient regions of the biofilm must still be synthesizing the signal compound. This result highlights the importance of careful study of the relationship between metabolic activity of the bacterium and signal synthesis. Received 11 March 2002/ Accepted in revised form 01 August 2002     

Methods and method evaluation for mycotoxins

Mycotoxins are metabolites of molds frequently found on and in agricultural commodities, food and feeds. Owing to their demonstrated acute, sub-acute and, in some cases, chronic toxicity, an effort has been made, worldwide, to control human and animal exposure to these toxic chemicals. This effort depends upon the availability of validated analytical methods for their detection and quantitation. This paper outlines the methodology available, and the procedures used to validate, i.e. evaluate, these methods based on the use of interlaboratory collaborative studies and the application of the HORRAT.