Species packing in nonsmooth competition models

Despite the potential for competition to generate equilibrium coexistence of infinitely tightly packed species along a trait axis, prior work has shown that the classical expectation of system-specific limits to the similarity of stably coexisting species is sound. A key reason is that known instances of continuous coexistence are fragile, requiring fine-tuning of parameters: A small alteration of the parameters leads back to the classical limiting similarity predictions. Here we present, but then cast aside, a new theoretical challenge to the expectation of limiting similarity. Robust continuous coexistence can arise if competition between species is modeled as a nonsmooth function of their differences—specifically, if the competition kernel (differential response of species’ growth rates to changes in the density of other species along the trait axis) has a nondifferentiable sharp peak at zero trait difference. We will say that these kernels possess a “kink.” The difference in predicted behavior stems from the fact that smooth kernels do not change to a first-order approximation around their maxima, creating strong competitive interactions between similar species. “Kinked” kernels, on the other hand, decrease linearly even for small species differences, reducing interspecific competition compared with intraspecific competition for arbitrarily small species differences. We investigate what mechanisms would lead to kinked kernels in the first place. It turns out that discontinuities in resource utilization generate them. We argue that such sudden jumps in the utilization of resources are unrealistic, and therefore, one should expect kernels to be smooth in reality.     

Ideal architecture of residue packing and its observation in protein structures.

A simple model of sphere packing has been investigated as an ideal model for long-range interactions for the packing of non-bonded residues in protein structures. By superposing all residues, the geometry of packing around a central residue is investigated. It is found that all residues conform almost perfectly to this lattice model for sphere packing when a radius of 6.5 A is used to define non-bonded (virtual) interacting residues. Side-chain positions with respect to sequential backbone segments are relatively regular as well. This lattice can readily be used in conformation simulations to reduce the conformational space.     

Novel method for the rapid evaluation of packing in protein structures

There has been considerable effort to predict the structure of proteins from their amino acid sequences. A major problem in all prediction efforts has been that, short of a direct comparison with crystallographic co-ordinates, it is often difficult to evaluate the merit of a model, or "proposed" protein structure. Here, we present a method for evaluating proposed protein structures that does not require a structural model of complete atomic detail. Our method evaluates residue-residue packing density using a simplified model of the polypeptide chain where amino acids are represented as one, two (histidine, tyrosine and phenylalanine), or three (tryptophan) spheres. This method also gives a measure of the appropriateness of residue-residue contacts, thus giving a measure of the amino acid distribution throughout the protein. Amino acid packing and amino acid distribution, as evaluated by this technique, are consistent with the accuracy of model-built structures. We have been able to select the best structures from a set of combinatorially generated models using this method, and we anticipate that it will be useful as a general tool for model-building.     

Gap junction structures. VI. Variation and conservation in connexon conformation and packing.

Correlation of structural changes in isolated gap junctions with the mechanism of channel gating is complicated by the effects of isolation procedures and the lack of a direct functional assay. The effect of variations in the isolation procedure are examined by comparison of the structures of gap junctions isolated by different protocols. X-ray diffraction data from over two hundren specimens are compared to provide a basis for identification of invariant aspects of the connexon structure and variable properties related either to functional switching or experimental modifications. We discuss the relationship between subunit tilt, lattice symmetry and packing, and membrane curvature and demonstrate that membrane curvature may be a natural consequence of the structure of the connexons and the patterns of interactions between them.     

Calculation of helix packing angles in protein structures

Software is presented for the calculation of packing angles and geometry of helical secondary structure elements in protein structures. AVAILABILITY: C language source code and documentation is available from http://www.bioinformatics.leeds.ac.uk.     

Discovery of local packing motifs in protein structures

We present a language for describing structural patterns of residues in protein structures and a method for the discovery of such patterns that recur in a set of protein structures. The patterns impose restrictions on the spatial position of each residue, their order along the amino acid chain, and which amino acids are allowed in each position. Unlike other methods for comparing sets of protein structures, our method is not based on the use of pairwise structure comparisons which is often time consuming and can produce inconsistent results. Instead, the method simultaneously takes into account information from all structures in the search for conserved structure patterns which are potential structure motifs. The method is based on describing the spatial neighborhoods of each residue in each structure as a string and applying a sequence pattern discovery method to find patterns common to subsets of these strings. Finally it is checked whether the similarities between the neighborhood strings correspond to spatially similar substructures. We apply the method to analyze sets of very disparate proteins from the four different protein families: serine proteases, cuprodoxins, cysteine proteinases, and ferredoxins. The motifs found by the method correspond well to the site and motif information given in the annotation of these proteins in PDB, Swiss-Prot, and PROSITE. Furthermore, the motifs are confirmed by using the motif data to constrain the structural alignment of the proteins obtained with the program SAP. This gave the best superposition/alignment of the proteins given the motif assignment.     

Liquid-crystalline, phage-like packing of encapsidated DNA in herpes simplex virus.

The organization of DNA within the HSV-1 capsid has been determined by cryoelectron microscopy and image reconstruction. Purified C-capsids, which are fully packaged, were compared with A-capsids, which are empty. Unlike A-capsids, C-capsids show fine striations and punctate arrays with a spacing of approximately 2.6 nm. The packaged DNA forms a uniformly dense ball, extending radially as far as the inner surface of the icosahedral (T = 16) capsid shell, whose structure is essentially identical in A-capsids and C-capsids. Thus we find no evidence for the inner T = 4 shell previously reported by Schrag et al. to be present in C-capsids. Encapsidated HSV-1 DNA closely resembles that previously visualized in bacteriophages T4 and lambda, thus supporting the idea of a close parallelism between the respective assembly pathways of a major family of animal viruses (the herpesviruses) and a major family of bacterial viruses.     

Hidden Markov models that use predicted secondary structures for fold recognition.

There are many proteins that share the same fold but have no clear sequence similarity. To predict the structure of these proteins, so called "protein fold recognition methods" have been developed. During the last few years, improvements of protein fold recognition methods have been achieved through the use of predicted secondary structures (Rice and Eisenberg, J Mol Biol 1997;267:1026-1038), as well as by using multiple sequence alignments in the form of hidden Markov models (HMM) (Karplus et al., Proteins Suppl 1997;1:134-139). To test the performance of different fold recognition methods, we have developed a rigorous benchmark where representatives for all proteins of known structure are matched against each other. Using this benchmark, we have compared the performance of automatically-created hidden Markov models with standard-sequence-search methods. Further, we combine the use of predicted secondary structures and multiple sequence alignments into a combined method that performs better than methods that do not use this combination of information. Using only single sequences, the correct fold of a protein was detected for 10% of the test cases in our benchmark. Including multiple sequence information increased this number to 16%, and when predicted secondary structure information was included as well, the fold was correctly identified in 20% of the cases. Moreover, if the correct secondary structure was used, 27% of the proteins could be correctly matched to a fold. For comparison, blast2, fasta, and ssearch identifies the fold correctly in 13-17% of the cases. Thus, standard pairwise sequence search methods perform almost as well as hidden Markov models in our benchmark. This is probably because the automatically-created multiple sequence alignments used in this study do not contain enough diversity and because the current generation of hidden Markov models do not perform very well when built from a few sequences.     

DNA associations: packing calculations in A-, B-, and Z-DNA structures.

A detailed theoretical study has been carried out to examine the modes of DNA-DNA interactions on the basis of hard-sphere contact criteria. Two helices of identical structure and length are oriented side-by-side and their relative positions are controlled by translations along and rotations about specific axes. Short atomic contacts between pairs of atoms in the structures are assessed and contact-free configurations are compiled. The computed contact-free arrangements of A, B, and Z double helices are found to be remarkably similar to the packing motifs observed in DNA crystals and stretched fibers. Equally interesting in the study are the broad ranges of sterically acceptable arrangements that preserve the overall packing morphology of neighboring duplexes: Among the most notable morphological features in the helical complexes are extended "super" major and minor grooves which might facilitate the wrapping and packaging of DNA chains in supramolecular assemblies. The hard-sphere computations, however, are insufficient for quantitative interpretation of the packing of DNA helices in the solid state. The results are, nevertheless, a useful starting point for energy based studies as well as relevant to the analysis of long-range interactions in DNA supercoils and cruciforms.     

Steric packing and molecular geometry. I. Simulation on tetrahedral structures of weak covalent bonding

In the first attempt, the molecular geometries of more than 50 tetrahedral structures of f-block and group IVB transition metal organometallic compounds were simulated based on the uniform packing principle. The results are in good agreement with those obtained by X-ray diffraction. It thus provides clear evidence that steric packing plays the dominant role in structures of weak crystal field stabilization energy (CFSE).     

ODE models for oncolytic virus dynamics

Replicating oncolytic viruses are able to infect and lyse cancer cells and spread through the tumor, while leaving normal cells largely unharmed. This makes them potentially useful in cancer therapy, and a variety of viruses have shown promising results in clinical trials. Nevertheless, consistent success remains elusive and the correlates of success have been the subject of investigation, both from an experimental and a mathematical point of view. Mathematical modeling of oncolytic virus therapy is often limited by the fact that the predicted dynamics depend strongly on particular mathematical terms in the model, the nature of which remains uncertain. We aim to address this issue in the context of ODE modeling, by formulating a general computational framework that is independent of particular mathematical expressions. By analyzing this framework, we find some new insights into the conditions for successful virus therapy. We find that depending on our assumptions about the virus spread, there can be two distinct types of dynamics. In models of the first type (the “fast spread” models), we predict that the viruses can eliminate the tumor if the viral replication rate is sufficiently high. The second type of models is characterized by a suboptimal spread (the “slow spread” models). For such models, the simulated treatment may fail, even for very high viral replication rates. Our methodology can be used to study the dynamics of many biological systems, and thus has implications beyond the study of virus therapy of cancers.     

Water-soluble beta-sheet models which self-assemble into fibrillar structures.

Self-assembly of beta-sheet domains resulting in the formation of pathogenic, fibrillar protein aggregates (amyloids) is a characteristic feature of various medical disorders. These include neurodegenerative diseases, such as Alzheimer's, Huntington's, and Creutzfeldt-Jacob's. A significant problem in studying such aggregation processes is the poor solubility of these beta-sheet complexes. The present work describes water-soluble de novo beta-sheet peptides which self-assemble into fibrillar structures. The model peptides enable studies of the relationship between beta-sheet stability and association behavior. The peptides [DPKGDPKG-(VT)n-GKGDPKPD-NH2, n = 3-8] are composed of a central beta-sheet-forming domain (VT-sequence), and N- and C-terminal nonstructured octapeptide sequences which promote water solubility. Conformational analyses by circular dichroism and Fourier transform infrared spectroscopy indicate the influence of peptide length, D-amino acid substitution, and concentration on the ability of the peptides to form stable beta-sheet structures. The association behavior investigated by analytical ultracentrifugation and dynamic light scattering was found to correlate strongly with the stability of a beta-sheet conformation. Model peptides with n >/= 6 form stable, water-soluble beta-sheet complexes with molecular masses of more than 2000 kDa, which are organized in fibrillar structures. The fibrils examined by Congo Red staining and electron microscopy show some similarities with naturally occurring amyloid fibrils.     

Identification of structures for ion channel kinetic models

Markov models of ion channel dynamics have evolved as experimental advances have improved our understanding of channel function. Past studies have examined limited sets of various topologies for Markov models of channel dynamics. We present a systematic method for identification of all possible Markov model topologies using experimental data for two types of native voltage-gated ion channel currents: mouse atrial sodium currents and human left ventricular fast transient outward potassium currents. Successful models identified with this approach have certain characteristics in common, suggesting that aspects of the model topology are determined by the experimental data. Incorporating these channel models into cell and tissue simulations to assess model performance within protocols that were not used for training provided validation and further narrowing of the number of acceptable models. The success of this approach suggests a channel model creation pipeline may be feasible where the structure of the model is not specified a priori.     

Molecular dynamics simulations of papilloma virus E2 DNA sequences: dynamical models for oligonucleotide structures in solution

The specificity of papilloma virus E2 protein-DNA binding depends critically upon the sequence of a region of the DNA not in direct contact with the protein, and represents one of the simplest known examples of indirect readout. A detailed characterization of this system in solution is important to the further investigation hypothesis of a structural code for DNA recognition by regulatory proteins. In the crystalline state, the E2 DNA oligonucleotide sequence, d(ACCGAATTCGGT), exhibits three different structural forms. We report herein studies of the structure of E2 DNA in solution based on a series of molecular dynamics (MD) simulations including counterions and water, utilizing both the canonical and various crystallographic structures as initial points of departure. All MDs converged on a single dynamical structure of d(ACCGAATTCGGT) in solution. The predicted structure is in close accord with two of the three crystal structures, and indicates that a significant kink in the double helix at the central ApT step in the other crystal molecule may be a packing effect. The dynamical fine structure was analyzed on the basis of helicoidal parameters. The calculated curvature in the sequence was found to originate primarily from YPR steps in the regions flanking the central AATT tract. In order to study the role of structural adaptation of the DNA in the binding process, a subsequent simulation on the 16-mer cognate sequence d(CAACCGAATTCGGTTG) was initiated from the crystallographic coordinates of the bound DNA in the crystal structure of the protein DNA complex. MD simulations starting with the protein-bound form relaxed rapidly back to the dynamical structure predicted from the previous simulations on the uncomplexed DNA. The MD results show that the bound form E2 DNA is a dynamically unstable structure in the absence of protein, and arises as a consequence of both structural changes intrinsic to the sequence and induced by the interaction with protein.     

Chromatin-like structures in polyoma virus and simian virus 10 lytic cycle.

Nucleoprotein complexes containing viral DNA and cellular histones were extracted from nuclei of permissive cells infected with polyoma virus or simian virus 40 (SV40) and examined by electron microscopy. Polyoma and SV40 nucleoprotein complexes are almost identical. They appear as relaxed circular molecules consisting of 20 to 21 globular particles interconnected by thin filaments. Their contour length in 0.02 M salt is 2.7 times shorter than that of viral DNA form I obtained after dissociation of the proteins in 1 M NaCl. The nucleosomes have an average diameter of 12.5 nm. Each nucleosome contains 175 to 205 DNA base pairs condensed fivefold in length. The nucleosomes are regularly spaced on the circular molecule. The internucleosomal filaments are made of naked DNA, and each filament contains about 55 base pairs. The partial sensitivity of the nucleoprotein complex to cleavage by EcoR1 endonuclease suggests that the nucleosomes are not formed at specific sites on the viral genome. Faster sedimenting nucleoprotein complexes containing replicative intermediates were studied. Isopycnic centrifugation in metrizamide gradients in the absence of aldehyde fixation showed that these molecules conserved the same DNA-to-protein ratio as the form I DNA-containing complexes.     

Toward a robust model of packing and scale-up for chromatographic beds. 2. Flow packing

We developed and evaluated a model for predicting the flow packing of nonrigid chromatographic resins. The model is based on elasticity theory and accounts for resin rigidity and column diameter. When a modulus determined from a standard mechanical compression (consolidation) test is used, the model captures the primary phenomena of the scale-up process. However, moduli determined from flow-packing experiments improve the accuracy of the predictions and show that the apparent rigidity of chromatographic resins is lower for flow packing than for mechanical compression. Using a modulus from flow-packing experiments provided quantitative scale-up predictions of flow packing carried out in columns with diameters between 200 and 450 mm at different locations and by different operators.