A numeric study of the noise-induced tremor in a mathematical model of the stretch reflex

A mathematical model of the stretch reflex for the cat soleus muscle is presented. The time-delay differential equations of the model are solved using the fourth-order Runge-Kutta algorithm, introducing a Gaussian-noise term to simulate the environmental noise. The muscle response dynamics are then studied under various levels of average muscle activation. Finally, the feasibility of explaining the so-called physiological tremor from the properties of the stretch reflex mechanisms is discussed by comparing our results with reported experimental evidence.     

A new topological method to measure protein structure similarity

A method for the quantitative evaluation of structural similarity between protein pairs is developed that makes use of a Delaunay-based topological mapping. The result of the mapping is a three-dimensional array which is representative of the global structural topology and whose elements can be used to construe an integral scoring scheme. This scoring scheme was tested for its dependence on the protein length difference in a pairwise comparison, its ability to provide a reasonable means for structural similarity comparison within a family of structural neighbors of similar length, and its sensitivity to the differences in protein conformation. It is shown that such a topological evaluation of similarity is capable of providing insight into these points of interest. Protein structure comparison using the method is computationally efficient and the topological scores, although providing different information about protein similarity, correlate well with the distance root-mean-square deviation values calculated by rigid-body structural alignment.     

Three-dimensional structure of the inclusion complex between phloridzin and beta-cyclodextrin

The inclusion of phloridzin into beta-cyclodextrin was studied as a model of molecular recognition in membranes. Effects on 1H NMR spectra and NOE correlational peaks between phloridzin and beta-cyclodextrin were observed in the complex. Strong NOEs were observed between hydrogens of a phenol group in phloridzin and beta-cyclodextrin. The three-dimensional structure of the inclusion complex between phloridzin and beta-cyclodextrin was simulated with distance constraints estimated by the intensity of NOE peaks using the DADAS90 programs. Two inclusion possibilities were suggested-the large rim of beta-cyclodextrin as an entrance of the inclusion and the small rim of beta-cyclodextrin as the entrance. In both cases, the phenol group of phloridzin was included in the hydrophobic space of beta-cyclodextrin.     

Metapopulation dynamics with quasi-local competition

Stepping-stone models for the ecological dynamics of metapopulations are often used to address general questions about the effects of spatial structure on the nature and complexity of population fluctuations. Such models describe an ensemble of local and spatially isolated habitat patches that are connected through dispersal. Reproduction and hence the dynamics in a given local population depend on the density of that local population, and a fraction of every local population disperses to neighboring patches. In such models, interesting dynamic phenomena, e.g. the persistence of locally unstable predator-prey interactions, are only observed if the local dynamics in an isolated patch exhibit non-equilibrium behavior. Therefore, the scope of these models is limited. Here we extend these models by making the biologically plausible assumption that reproductive success in a given local habitat not only depends on the density of the local population living in that habitat, but also on the densities of neighboring local populations. This would occur if competition for resources occurs between neighboring populations, e.g. due to foraging in neighboring habitats. With this assumption of quasi-local competition the dynamics of the model change completely. The main difference is that even if the dynamics of the local populations have a stable equilibrium in isolation, the spatially uniform equilibrium in which all local populations are at their carrying capacity becomes unstable if the strength of quasi-local competition reaches a critical level, which can be calculated analytically. In this case the metapopulation reaches a new stable state, which is, however, not spatially uniform anymore and instead results in an irregular spatial pattern of local population abundance. For large metapopulations, a huge number of different, spatially non-uniform equilibrium states coexist as attractors of the metapopulation dynamics, so that the final state of the system depends critically on the initial conditions. The existence of a large number of attractors has important consequences when environmental noise is introduced into the model. Then the metapopulation performs a random walk in the space of all attractors. This leads to large and complicated population fluctuations whose power spectrum obeys a red-shifted power law. Our theory reiterates the potential importance of spatial structure for ecological processes and proposes new mechanisms for the emergence of non-uniform spatial patterns of abundance and for the persistence of complicated temporal population fluctuations.     

Metapopulation theory for fragmented landscapes

We review recent developments in spatially realistic metapopulation theory, which leads to quantitative models of the dynamics of species inhabiting highly fragmented landscapes. Our emphasis is in stochastic patch occupancy models, which describe the presence or absence of the focal species in habitat patches. We discuss a number of ecologically important quantities that can be derived from the full stochastic models and their deterministic approximations, with a particular aim of characterizing the respective roles of the structure of the landscape and the properties of the species. These quantities include the threshold condition for persistence, the contributions that individual habitat patches make to metapopulation dynamics and persistence, the time to metapopulation extinction, and the effective size of a metapopulation living in a heterogeneous patch network.     

Distributed torsion angle grid search in high dimensions: A systematic approach to NMR structure determination

Two complementary approaches for systematic search in torsion angle space are described for the generation of all conformations of polypeptides which satisfy experimental NMR restraints, hard-sphere van der Waals radii, and rigid covalent geometry. The first procedure is based on a recursive, tree search algorithm for the examination of linear chains of torsion angles, and uses a novel treatment to propagate the search results to neighboring regions so that the structural consequences of the restraints are fully realized. The second procedure is based on a binary combination of torsion vector spaces for connected submolecules, and produces intermediate results in Cartesian space for a more robust restraint analysis. Restraints for NMR applications include bounds on torsion angles and internuclear distances, including relational and degenerate restraints involving equivalent and nonstereoassigned protons. To illustrate these methods, conformation search results are given for the tetrapeptide APGA restrained to an idealized -turn conformation, an alanine octapeptide restrained to a right-handed helical conformation, and the structured region of the peptide SYPFDV.     

The stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays and reaction–diffusion terms

The global asymptotic stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays and reaction–diffusion terms is investigated. Under some suitable assumptions and using Lyapunov–Krasovskii functional method, we apply the linear matrix inequality technique to propose some new sufficient conditions for the global asymptotic stability of the addressed model in the stochastic sense. The mixed time delays comprise both the time-varying and continuously distributed delays. The effectiveness of the theoretical result is illustrated by a numerical example.     

On the lack of specificity of proteins and its consequences for a theory of biological organization

It is now widely recognized that gene expression and cellular processes include a probabilistic component. However, this does not essentially modify the theory of genetic programming. This stochastic aspect, which is called noise, is usually conceived as a margin of fluctuation in the way the genetic program functions and the latter remains understood as a specific mechanism guided by genetic information. In contrast, recent data show that proteins do not possess a high level of specificity. They can interact with numerous molecular partners. As a consequence molecular interactions are not simply “noisy”. Because they are subject to large combinatorial interaction possibilities, they are also intrinsically stochastic and must be sorted out by the cell structure. This contradicts the genetic programming theory which is based on the idea that protein interactions are directed by their stereospecificity and genetic information. Taking into account the lack of protein specificity leads to a new theory. Natural selection acts not only in evolution but also in ontogenesis by sorting stochastic molecular interactions. In this frame, the making up of an organism, instead of being a simple bottom-top process in which information flows from genes to phenotypes, is both a bottom-top and top-bottom process. Genes provide proteins, but their stochastic interactions are sorted by selective constraints arising from the cell and multi-cellular structures, which are themselves subject to the action of natural selection.     

Articular to diaphyseal proportions of human and great ape metatarsals

This study proposes a new way to use metatarsals to identify locomotor behavior of fossil hominins. Metatarsal head articular dimensions and diaphyseal strength in a sample of chimpanzees, gorillas, orangutans, and humans (n = 76) are used to explore the relationships of these parameters with different locomotor modes. Results show that ratios between metatarsal head articular proportions and diaphyseal strength of the hallucal and fifth metatarsal discriminate among extant great apes and humans based on their different locomotor modes. In particular, the hallucal and fifth metatarsal characteristics of humans are functionally related to the different ranges of motion and load patterns during stance phase in the forefoot of humans in bipedal locomotion. This method may be applicable to isolated fossil hominin metatarsals to provide new information relevant to debates regarding the evolution of human bipedal locomotion. The second to fourth metatarsals are not useful in distinguishing among hominoids. Further studies should concentrate on measuring other important qualitative and quantitative differences in the shape of the metatarsal head of hominoids that are not reflected in simple geometric reconstructions of the articulation, and gathering more forefoot kinematic data on great apes to better understand differences in range of motion and loading patterns of the metatarsals. Am J Phys Anthropol 143:198–207, 2010. © 2010 Wiley‐Liss, Inc.