A model for hydranth regeneration inTubularia

Pigment distribution presages hydranth regeneration in the marine hydroidTubularia. We suggest that such a distribution could result from a reaction-diffusion system. A model system based on a practical reaction scheme is studied and spatial structures found which closely resemble this pigment distribution. Finite-amplitude spatial structures in reaction-diffusion systems are considered. Whereas in one spatial dimension the final structures are normally very similar to the transient patterns which emerge from a linear analysis, it is shown that in more than one dimension this is not necessarily the case. The reasons for this are discussed.     

Interconversion of replication and recombination structures: implications for terminal repeats and concatemers

Replication and recombination structures can be interconverted by branch-migration. Using this simple concept a novel mechanism is proposed for generating concatemers through an initial single-strand DNA invasion into a duplex. Only DNAs with terminal repeats can form concatemers, and Herpes Simplex Virus DNA replication is considered in detail. The model is more parsimonious than other models such as Watson's for concatemer formation.     

Geometric cooperativity and anticooperativity of three-body interactions in native proteins

Characterizing multibody interactions of hydrophobic, polar, and ionizable residues in protein is important for understanding the stability of protein structures. We introduce a geometric model for quantifying 3-body interactions in native proteins. With this model, empirical propensity values for many types of 3-body interactions can be reliably estimated from a database of native protein structures, despite the overwhelming presence of pairwise contacts. In addition, we define a nonadditive coefficient that characterizes cooperativity and anticooperativity of residue interactions in native proteins by measuring the deviation of 3-body interactions from 3 independent pairwise interactions. It compares the 3-body propensity value from what would be expected if only pairwise interactions were considered, and highlights the distinction of propensity and cooperativity of 3-body interaction. Based on the geometric model, and what can be inferred from statistical analysis of such a model, we find that hydrophobic interactions and hydrogen-bonding interactions make nonadditive contributions to protein stability, but the nonadditive nature depends on whether such interactions are located in the protein interior or on the protein surface. When located in the interior, many hydrophobic interactions such as those involving alkyl residues are anticooperative. Salt-bridge and regular hydrogen-bonding interactions, such as those involving ionizable residues and polar residues, are cooperative. When located on the protein surface, these salt-bridge and regular hydrogen-bonding interactions are anticooperative, and hydrophobic interactions involving alkyl residues become cooperative. We show with examples that incorporating 3-body interactions improves discrimination of protein native structures against decoy conformations. In addition, analysis of cooperative 3-body interaction may reveal spatial motifs that can suggest specific protein functions.     

Probabilistic pathway representation of cognitive information

We present for mental processes the program of mathematical mapping which has been successfully realized for physical processes. We emphasize that our project is not about mathematical simulation of the brain's functioning as a complex physical system, i.e., mapping of physical and chemical processes in the brain on mathematical spaces. The project is about mapping of purely mental processes on mathematical spaces. We present various arguments--philosophic, mathematical, information, and neurophysiological--in favor of the p-adic model of mental space. p-adic spaces have structures of hierarchic trees and in our model such a tree hierarchy is considered as an image of neuronal hierarchy. Hierarchic neural pathways are considered as fundamental units of information processing. As neural pathways can go through the whole body, the mental space is produced by the whole neural system. Finally, we develop the probabilistic neural pathway model in that mental states are represented by probability distributions on mental space.     

Unbalanced Repeated Measures with Random Coefficients

In a random coefficient repeated measures model, the regression coefficients relating the observations to some underlying variable, such as time, are themselves taken to be random distributed over experimental units. In this paper, a general approach to repeated measures analysis is extended to this wider model. In the model three specific error structures for the random regression coefficients have been studied, viz, the random coefficients variance matrix is considered to be (i) diagonal, (ii) proportional to the identity matrix and (iii) completely general. An example will be analyzed to illustrate the procedure.     

Modelling and detecting deep brain activity with MEG and EEG

We introduce an anatomical and electrophysiological model of deep brain structures dedicated to magnetoencephalography (MEG) and electroencephalography (EEG) source imaging. So far, most imaging inverse models considered that MEG/EEG surface signals were predominantly produced by cortical, hence superficial, neural currents. Here we question whether crucial deep brain structures such as the basal ganglia and the hippocampus may also contribute to distant, scalp MEG and EEG measurements. We first design a realistic anatomical and electrophysiological model of these structures and subsequently run Monte-Carlo experiments to evaluate the respective sensitivity of the MEG and EEG to signals from deeper origins. Results indicate that MEG/EEG may indeed localize these deeper generators, which is confirmed here from experimental MEG data reporting on the modulation of alpha (10–12 Hz) brain waves.     

Theoretical structure of the polar regions of the tropocollagen molecule

The theoretical conformations of poly (Gly-Ala-Glu) have been studied. This peptide was chosen as a model for the glycine led triads of the polar regions in collagen. The most favorable conformations are found to be based on the extended and folded forms of the 2₇ helix (2_7a and 2_7b). It is suggested that triple-strand structures of folded 2₇ helices exist in the polar collagen regions, and a structural model is presented which is in accord with recent ultrastructural deformation studies. It is a necessary condition for this structure that glycine occur in the lead of the peptide triads. In regions of the collagen molecule where the primary sequence does not contain triads (e.g., in the telopeptide region), random structures based on energy minimization of peptide neighbors are considered briefly. It seems likely that such regions contain an admixture of left-hand α, polyproline II, and 2₇ helix structures.     

A combinatorial toolbox for protein sequence design and landscape analysis in the grand canonical model.

In modern biology, one of the most important research problems is to understand how protein sequences fold into their native 3D structures. To investigate this problem at a high level, one wishes to analyze the protein landscapes, i.e., the structures of the space of all protein sequences and their native 3D structures. Perhaps the most basic computational problem at this level is to take a target 3D structure as input and design a fittest protein sequence with respect to one or more fitness functions of the target 3D structure. We develop a toolbox of combinatorial techniques for protein landscape analysis in the Grand Canonical model of Sun, Brem, Chan, and Dill. The toolbox is based on linear programming, network flow, and a linear-size representation of all minimum cuts of a network. It not only substantially expands the network flow technique for protein sequence design in Kleinberg's seminal work but also is applicable to a considerably broader collection of computational problems than those considered by Kleinberg. We have used this toolbox to obtain a number of efficient algorithms and hardness results. We have further used the algorithms to analyze 3D structures drawn from the Protein Data Bank and have discovered some novel relationships between such native 3D structures and the Grand Canonical model.     

A case study in the design of flexible assembly systems

The design of production systems is generally based on economic considerations, which are related to certain technical criteria, such as capacity, availability, and reliability. To realize a cost-effective design, these technical and economic criteria should be considered in their mutual coherence during the conceptual design process. This paper focuses on a productivity model, which is related to this subject. This model allows an opinion to be formed about the technical and economic performance of conceptual robotic assembly cells, during the process of design. First, the system design process is discussed in brief, after which the productivity variables are presented. An illustration of the model is used to assess the technical and economic behavior of alternative system structures for the assembly of a power plug assortment.     

ATTRACTIVE STRUCTURES AND THE STABILITY OF HERMAPHRODITIC SEX EXPRESSION IN FLOWERING PLANTS

Plant attributes serving both male and female sex functions are thought to favor hermaphroditic breeding systems over systems where sex expression is separated between individuals. Morphological features used by plants to attract biotic pollinators can be considered in this light, because such “attractive” structures are prerequisite for both pollen donation and receipt. A model involving allocation of a limiting resource between attractive structures benefiting both sex functions, structures benefiting male function only, and structures benefiting female function only, is constructed and analyzed using the evolutionary stable strategy (ESS) approach. Contrary to expectation, conditions resulting in large allocation to attractive structures tend to destabilize hermaphroditism, although the effect is slight. Substantial asymmetry in the benefits accruing to male and female fertility for a given investment in pollinator attraction produces more pronounced effects, reducing the parameter space in which hermaphroditism is expected. Results of this model are used to assess the importance of “accelerating gain” curves previously suggested for the evolution of dioecy in flowering plants. Accelerating gains associated with fruit production and dispersal represent female function only, and can be sufficient to initiate evolution toward dioecy. Accelerating gains associated with pollinator attraction may contribute to the evolution of separate sexes only if male function benefits from increased investment in attractive structures at a disproportionate rate compared to female function. Even in this instance, though, hermaphroditism may be evolutionarily stable.     

Mechanochemical model of microtubule structure and self-assembly kinetics

Microtubule self-assembly is largely governed by the chemical kinetics and thermodynamics of tubulin-tubulin interactions. An important aspect of microtubule assembly is that hydrolysis of the beta-tubulin-associated GTP promotes protofilament curling. Protofilament curling presumably drives the transition from tip structures associated with growth (sheetlike projections and blunt ends) to those associated with shortening (rams' horns and frayed ends), and transitions between these structures have been proposed to be important for growth-shortening transitions. However, previous models for microtubule dynamic instability have not considered such structures or mechanics explicitly. Here we present a three-dimensional model that explicitly incorporates mechanical stress and strain within the microtubule lattice. First, we found that the model recapitulates three-dimensional tip structures and rates of assembly and disassembly for microtubules grown under standard conditions, and we propose that taxol may stabilize microtubule growth by reducing flexural rigidity. Second, in contrast to recent suggestions, it was determined that sheetlike tips are more likely to undergo catastrophe than blunt tips. Third, partial uncapping of the tubulin-GTP cap provides a possible mechanism for microtubule pause events. Finally, simulations of the binding and structural effects of XMAP215 produced the experimentally observed growth and shortening rates, and tip structure.     

The foldability landscape of model proteins

Molecular evolution may be considered as a walk in a multidimensional fitness landscape, where the fitness at each point is associated with features such as the function, stability, and survivability of these molecules. We present a simple model for the evolution of protein sequences on a landscape with a precisely defined fitness function. We use simple lattice models to represent protein structures, with the ability of a protein sequence to fold into the structure with lowest energy, quantified as the foldability, representing the fitness of the sequence. The foldability of the sequence is characterized based on the spin glass model of protein folding. We consider evolution as a walk in this foldability landscape and study the nature of the landscape and the resulting dynamics. Selective pressure is explicitly included in this model in the form of a minimum foldability requirement. We find that different native structures are not evenly distributed in interaction space, with similar structures and structures with similar optimal foldabilities clustered together. Evolving proteins marginally fulfill the selective criteria of foldability. As the selective pressure is increased, evolutionary trajectories become increasingly confined to “neutral networks,” where the sequence and the interactions can be significantly changed while a constant structure is maintained. © 1997 John Wiley & Sons, Inc. Biopoly 42: 427–438, 1997     

How are model protein structures distributed in sequence space?

The figure-to-structure maps for all uniquely folding sequences of short hydrophobic polar (HP) model proteins on a square lattice is analyzed to investigate aspects considered relevant to evolution. By ranking structures by their frequencies, few very frequent and many rare structures are found. The distribution can be empirically described by a generalized Zipf's law. All structures are relatively compact, yet the most compact ones are rare. Most sequences falling to the same structure belong to "neutral nets." These graphs in sequence space are connected by point mutations and centered around prototype sequences, which tolerate the largest number (up to 55%) of neutral mutations. Profiles have been derived from these homologous sequences. Frequent structures conserve hydrophobic cores only while rare ones are sensitive to surface mutations as well. Shape space covering, i.e., the ability to transform any structure into most others with few point mutations, is very unlikely. It is concluded that many characteristic features of the sequence-to-structure map of real proteins, such as the dominance of few folds, can be explained by the simple HP model. In analogy to protein families, nets are dense and well separated in sequence space. Potential implications in better understanding the evolution of proteins and applications to improving database searches are discussed.     

Rate of passive conduction in lattice structures]

A mathematical model of passive conduction in syncitial symmetric structures is considered. Explicit formulae of the dependence of a decrease of stationary solution and of electrotonic conduction velocity are obtained.     

A model of myoglobin self-organization

The self-organization of helical regions of myoglobin into a compact tertiary structure is considered on the basis of the hypothesis on the step-wise mechanism of self-organization of protein molecules. It is assumed that the self-organization begins with the formation of “ centers of crystallization ” and proceeds with the growth of one such center or by a sequential collapse of two or more grown centers.Different pathways of self-organization of myoglobin are considered; the most favourable structures corresponding to the greatest number of dehydrated bulky hydroptiobic groups and to all the strongly hydrophilic groups exposed to water are selected at every stage of the given pathway and the others are neglected. One of the two most favourable structures obtained in such a way coincides in rough resolution with the native tertiary structure of protein.     

A simple genetic algorithm for the optimization of multidomain protein homology models driven by NMR residual dipolar coupling and small angle <Emphasis Type="Italic">X</Emphasis>-ray scattering data

Most proteins comprise several domains and/or participate in functional complexes. Owing to ongoing structural genomic projects, it is likely that it will soon be possible to predict, with reasonable accuracy, the conserved regions of most structural domains. Under these circumstances, it will be important to have methods, based on simple-to-acquire experimental data, that allow to build and refine structures of multi-domain proteins or of protein complexes from homology models of the individual domains/proteins. It has been recently shown that small angle X-ray scattering (SAXS) and NMR residual dipolar coupling (RDC) data can be combined to determine the architecture of such objects when the X-ray structures of the domains are known and can be considered as rigid objects. We developed a simple genetic algorithm to achieve the same goal, but by using homology models of the domains considered as deformable objects. We applied it to two model systems, an S1KH bi-domain of the NusA protein and the γS-crystallin protein. Despite its simplicity our algorithm is able to generate good solutions when driven by SAXS and RDC data.     

Less can be more: RNA-adapters may enhance coding capacity of replicators

It is still not clear how prebiotic replicators evolved towards the complexity found in present day organisms. Within the most realistic scenario for prebiotic evolution, known as the RNA world hypothesis, such complexity has arisen from replicators consisting solely of RNA. Within contemporary life, remarkably many RNAs are involved in modifying other RNAs. In hindsight, such RNA-RNA modification might have helped in alleviating the limits of complexity posed by the information threshold for RNA-only replicators. Here we study the possible role of such self-modification in early evolution, by modeling the evolution of protocells as evolving replicators, which have the opportunity to incorporate these mechanisms as a molecular tool. Evolution is studied towards a set of 25 arbitrary 'functional' structures, while avoiding all other (misfolded) structures, which are considered to be toxic and increase the death-rate of a protocell. The modeled protocells contain a genotype of different RNA-sequences while their phenotype is the ensemble of secondary structures they can potentially produce from these RNA-sequences. One of the secondary structures explicitly codes for a simple sequence-modification tool. This 'RNA-adapter' can block certain positions on other RNA-sequences through antisense base-pairing. The altered sequence can produce an alternative secondary structure, which may or may not be functional. We show that the modifying potential of interacting RNA-sequences enables these protocells to evolve high fitness under high mutation rates. Moreover, our model shows that because of toxicity of misfolded molecules, redundant coding impedes the evolution of self-modification machinery, in effect restraining the evolvability of coding structures. Hence, high mutation rates can actually promote the evolution of complex coding structures by reducing redundant coding. Protocells can successfully use RNA-adapters to modify their genotype-phenotype mapping in order to enhance the coding capacity of their genome and fit more information on smaller sized genomes.     

The many faces of actin: matching assembly factors with cellular structures

Actin filaments are major components of at least 15 distinct structures in metazoan cells. These filaments assemble from a common pool of actin monomers, but do so at different times and places, and in response to different stimuli. All of these structures require actin-filament assembly factors. To date, many assembly factors have been identified, including Arp2/3 complex, multiple formin isoforms and spire. Now, a major task is to figure out which factors assemble which actin-based structures. Here, we focus on structures at the plasma membrane, including both sheet-like protrusive structures (such as lamellipodia and ruffles) and finger-like protrusions (such as filopodia and microvilli). Insights gained from studies of adherens junctions and the immunological synapse are also considered.     

Molecular modeling study of cyclic pentapeptide CXCR4 antagonists: new insight into CXCR4-FC131 interactions

CXCR4 is a G-protein coupled receptor that is associated with many diseases such as breast cancer metastasis, HIV infection, leukemic disease and rheumatoid arthritis, and is thus considered an attractive drug target. Previously, we identified a cyclic pentapeptide, FC131, that is a potent antagonist for CXCR4. In this study, we constructed a three dimensional model of the CXCR4-FC131 complex. To investigate the backbone flexibility of FC131, we performed molecular dynamics simulations of FC131 based on the NMR structure of FC131, and obtained snapshot structures from the trajectories which were used to model the docking pose of FC131 into CXCR4. Our final model of the CXCR4-FC131 complex is partially different from the X-ray crystal structure of CXCR4-CVX15 and suggests water-mediated interactions. Nevertheless, this docking pose is consistent with the experimental data. We believe our model will aid in the discovery and development of small-molecule antagonists for CXCR4.     

The intervertebral ossicles of the Insectivora

The anatomical and systematic distribution of intervertebral ossicles is reviewed for insecti-voran forms known to manifest such structures and for some additional forms. The anatomy, morphology and functional significance of these ossicles is considered and the conclusion is reached that such formations constitute a mechanical device designed to stabilize the vertebral column in certain specialized insectivoran forms.