Contact interactions method: a new algorithm for protein folding simulations.

Computer simulations of simple exact lattice models are an aid in the study of protein folding process; they have sometimes resulted in predictions experimentally proved. The contact interactions (CI) method is here proposed as a new algorithm for the conformational search in the low-energy regions of protein chains modeled as copolymers of hydrophobic and polar monomers configured as self-avoiding walks on square or cubic lattices. It may be regarded as an extension of the standard Monte Carlo method improved by the concept of cooperativity deriving from nonlocal contact interactions. A major difference with respect to other algorithms is that criteria for the acceptance of new conformations generated during the simulations are not based on the energy of the entire molecule, but cooling factors associated with each residue define regions of the model protein with higher or lower mobility. Nine sequences of length ranging from 20 to 64 residues were used on the square lattice and 15 sequences of length ranging from 46 to 136 residues were used on the cubic lattice. The CI algorithm proved very efficient both in two and three dimensions, and allowed us to localize energy minima not localized by other searching algorithms described in the literature. Use of this algorithm is not limited to the conformational search, because it allows the exploration of thermodynamic and kinetic behavior of model protein chains.     

Accurate general method for lattice approximation of three-dimensional structure of a chain molecule

An algorithm based on dynamic programming gives the lattice models having the minimal RMS deviations from the actual folds of protein (RNA, etc.) chains for a given lattice and a given orientation of the macromolecule relative to the lattice. The algorithm is applicable for 3-D lattices of any kind. The accuracy of the lattice approximation increases when the distance between neighbor chain links is not rigidly fixed. Special repulsive potentials facilitate generation of self-avoiding lattice chains. The results of model building show the efficiency and precisionof this proposed general method when compared with others. © 1995 Wiley-Liss, Inc.     

Lattices for ab initio protein structure prediction

In the study of the protein folding problem with ab initio methods, the protein backbone can be built on some periodic lattices. Any vertex of these lattices can be occupied by a "ball," which can represent the mass center of an amino acid in a simplified coarse-grained model of the protein. The backbone, at a coarse-grained level, can be constituted of a No Reverse Self Avoiding Walk, which cannot intersect itself and cannot go back on itself. There is still much debate between those who use lattices to simplify the study of the protein folding problem and those preferring to work by using an off-lattice approach. Lattices can help to identify the protein tertiary structure in a computational less-expensive way, than off-lattice approaches that have to consider a potentially infinite number of possible structures. However, the use of a lattice, constituted of insufficiently accurate direction vectors, constrains the predictive ability of the model. The aim of this study is to perform a systematic screening of 7 known classic and 11 newly proposed lattices in terms of predictive power. The crystal structures of 42 different proteins (14 mainly alpha helical, 14 mainly beta sheet and 14 mixed structure proteins) were compared to the most accurate simulated models for each lattice. This strategy defines a scale of fitness for all the analyzed lattices and demonstrates that an increase in the coordination number and in the degrees of freedom is necessary but not sufficient to reach the best result. Instead, the introduction of a good set of direction vectors, as developed and tested in this study, strongly increases the lattice performance.     

The Role of Membrane-Mediated Interactions in the Assembly and Architecture of Chemoreceptor Lattices

In vivo fluorescence microscopy and electron cryo-tomography have revealed that chemoreceptors self-assemble into extended honeycomb lattices of chemoreceptor trimers with a well-defined relative orientation of trimers. The signaling response of the observed chemoreceptor lattices is remarkable for its extreme sensitivity, which relies crucially on cooperative interactions among chemoreceptor trimers. In common with other membrane proteins, chemoreceptor trimers are expected to deform the surrounding lipid bilayer, inducing membrane-mediated anisotropic interactions between neighboring trimers. Here we introduce a biophysical model of bilayer-chemoreceptor interactions, which allows us to quantify the role of membrane-mediated interactions in the assembly and architecture of chemoreceptor lattices. We find that, even in the absence of direct protein-protein interactions, membrane-mediated interactions can yield assembly of chemoreceptor lattices at very dilute trimer concentrations. The model correctly predicts the observed honeycomb architecture of chemoreceptor lattices as well as the observed relative orientation of chemoreceptor trimers, suggests a series of “gateway” states for chemoreceptor lattice assembly, and provides a simple mechanism for the localization of large chemoreceptor lattices to the cell poles. Our model of bilayer-chemoreceptor interactions also helps to explain the observed dependence of chemotactic signaling on lipid bilayer properties. Finally, we consider the possibility that membrane-mediated interactions might contribute to cooperativity among neighboring chemoreceptor trimers.     

A Novel Mathematical Model Describing Adaptive Cellular Drug Metabolism and Toxicity in the Chemoimmune System

Cells cope with the threat of xenobiotic stress by activating a complex molecular network that recognizes and eliminates chemically diverse toxic compounds. This “chemoimmune system” consists of cellular Phase I and Phase II metabolic enzymes, Phase 0 and Phase III ATP Binding Cassette (ABC) membrane transporters, and nuclear receptors regulating these components. In order to provide a systems biology characterization of the chemoimmune network, we designed a reaction kinetic model based on differential equations describing Phase 0–III participants and regulatory elements, and characterized cellular fitness to evaluate toxicity. In spite of the simplifications, the model recapitulates changes associated with acquired drug resistance and allows toxicity predictions under variable protein expression and xenobiotic exposure conditions. Our simulations suggest that multidrug ABC transporters at Phase 0 significantly facilitate the defense function of successive network members by lowering intracellular drug concentrations. The model was extended with a novel toxicity framework which opened the possibility of performing in silico cytotoxicity assays. The alterations of the in silico cytotoxicity curves show good agreement with in vitro cell killing experiments. The behavior of the simplified kinetic model suggests that it can serve as a basis for more complex models to efficiently predict xenobiotic and drug metabolism for human medical applications.     

Co-operative response of chemically excitable membrane III. Three-state model

The general three-state model is formulated first, which is the direct extension of the unified two-state model previously formulated (Kijima & Kijima, 1978). In this model, each protomer in a symmetrically interacting system (oligomers or lattices) can take three states, S, R and Q, where S and R states are the same as in the two-state model and Q state is another state either corresponding to a different open-state of ionophore from R open-state or corresponding to another closed state of ionophore. The model has no restriction on the value of Hill coefficient at the midpoint of the dose-response curves in contrast to two-state models. It is applied on GABA sensitive inhibitory synapse of crayfish muscle to account for anomalous behaviour of the membrane in I^? solution.The simplified versions of the above general three-state model are also formulated (simplified three-state model), in which it is assumed that R and Q state are equivalent in regard to the nearest neighbor interaction. By this assumption, R and Q state are collectively treated as state A and mathematical formula obtained on Ising model are applicable on this model. This model is applied on the insect sugar receptor which was shown to be incompatible with the two-state models (Kijima & Kijima, 1980). Further simplification of the above simplified model results in two convenient models: three-state KNF model and three-state MWC model, which have minimum parameters but sufficient to account for most experiments. They give plausible physico-chemical base on the “classical model” in which the existence of both inactive and active ligand-receptor complex is assumed.     

Interstitial contacts in an RNA-dependent RNA polymerase lattice

Catalytic activities can be facilitated by ordered enzymatic arrays that co-localize and orient enzymes and their substrates. The purified RNA-dependent RNA polymerase from poliovirus self-assembles to form two-dimensional lattices, possibly facilitating the assembly of viral RNA replication complexes on the cytoplasmic face of intracellular membranes. Creation of a two-dimensional lattice requires at least two different molecular contacts between polymerase molecules. One set of polymerase contacts, between the “thumb” domain of one polymerase and the back of the “palm” domain of another, has been previously defined. To identify the second interface needed for lattice formation and to test its function in viral RNA synthesis, we used a hybrid approach of electron microscopic and biochemical evaluation of both wild-type and mutant viral polymerases to evaluate computationally generated models of this second interface. A unique solution satisfied all constraints and predicted a two-dimensional structure formed from antiparallel arrays of polymerase fibers that use contacts from the flexible amino-terminal region of the protein. Enzymes that contained mutations in this newly defined interface did not form lattices and altered the structure of wild-type lattices. When reconstructed into virus, mutations that disrupt lattice assembly exhibited growth defects, synthetic lethality or both, supporting the function of the oligomeric lattice in infected cells. Understanding the structure of polymerase lattices within the multimeric RNA-dependent RNA polymerase complex should facilitate antiviral drug design and provide a precedent for other positive-strand RNA viruses.     

Three-dimensional structure of the M-MuLV CA protein on a lipid monolayer: a general model for retroviral capsid assembly

Although retroviruses from different genera form morphologically distinct capsids, we have proposed that all of these structures are composed of similar hexameric arrays of capsid (CA) protein subunits and that their distinct morphologies reflect different distributions of pentameric declinations that allow the structures to close. Consistent with this model, CA proteins from both HIV-1 and Rous sarcoma virus (RSV) form similar hexagonal lattices. However, recent structural studies have suggested that the Moloney murine leukemia virus (M-MuLV) CA protein may assemble differently. We now report an independent three-dimensional reconstruction of two-dimensional crystals of M-MuLV CA. This new reconstruction reveals a hexameric lattice that is similar to those formed by HIV-1 and RSV CA, supporting a generalized model for retroviral capsid assembly.     

16S rRNA Phylogenetic Investigation of the Candidate Division “Korarchaeota”

The environmental distribution and phylogeny of “Korarchaeota,” a proposed ancient archaeal division, was investigated by using the 16S rRNA gene framework. Korarchaeota-specific primers were designed based on previously published sequences and used to screen a variety of environments. Korarchaeota 16S rRNA genes were amplified exclusively from high temperature Yellowstone National Park hot springs and a 9°N East Pacific Rise deep-sea hydrothermal vent. Phylogenetic analyses of these and all available sequences suggest that Korarchaeota exhibit a high level of endemicity.     

Assessing site-interdependent phylogenetic models of sequence evolution

In recent works, methods have been proposed for applying phylogenetic models that allow for a general interdependence between the amino acid positions of a protein. As of yet, such models have focused on site interdependencies resulting from sequence-structure compatibility constraints, using simplified structural representations in combination with a set of statistical potentials. This structural compatibility criterion is meant as a proxy for sequence fitness, and the methods developed thus far can incorporate different site-interdependent fitness proxies based on other measurements. However, no methods have been proposed for comparing and evaluating the adequacy of alternative fitness proxies in this context, or for more general comparisons with canonical models of protein evolution. In the present work, we apply Bayesian methods of model selection-based on numerical calculations of marginal likelihoods and posterior predictive checks-to evaluate models encompassing the site-interdependent framework. Our application of these methods indicates that considering site-interdependencies, as done here, leads to an improved model fit for all data sets studied. Yet, we find that the use of pairwise contact potentials alone does not suitably account for across-site rate heterogeneity or amino acid exchange propensities; for such complexities, site-independent treatments are still called for. The most favored models combine the use of statistical potentials with a suitably rich site-independent model. Altogether, the methodology employed here should allow for a more rigorous and systematic exploration of different ways of modeling explicit structural constraints, or any other site-interdependent criterion, while best exploiting the richness of previously proposed models.     

NERDSS: A Nonequilibrium Simulator for Multibody Self-Assembly at the Cellular Scale

Currently, a significant barrier to building predictive models of cellular self-assembly processes is that molecular models cannot capture minutes-long dynamics that couple distinct components with active processes, whereas reaction-diffusion models cannot capture structures of molecular assembly. Here, we introduce the nonequilibrium reaction-diffusion self-assembly simulator (NERDSS), which addresses this spatiotemporal resolution gap. NERDSS integrates efficient reaction-diffusion algorithms into generalized software that operates on user-defined molecules through diffusion, binding and orientation, unbinding, chemical transformations, and spatial localization. By connecting the fast processes of binding with the slow timescales of large-scale assembly, NERDSS integrates molecular resolution with reversible formation of ordered, multisubunit complexes. NERDSS encodes models using rule-based formatting languages to facilitate model portability, usability, and reproducibility. Applying NERDSS to steps in clathrin-mediated endocytosis, we design multicomponent systems that can form lattices in solution or on the membrane, and we predict how stochastic but localized dephosphorylation of membrane lipids can drive lattice disassembly. The NERDSS simulations reveal the spatial constraints on lattice growth and the role of membrane localization and cooperativity in nucleating assembly. By modeling viral lattice assembly and recapitulating oscillations in protein expression levels for a circadian clock model, we illustrate the adaptability of NERDSS. NERDSS simulates user-defined assembly models that were previously inaccessible to existing software tools, with broad applications to predicting self-assembly in vivo and designing high-yield assemblies in vitro.     

Evolutionary Sequence Modeling for Discovery of Peptide Hormones

There are currently a large number of “orphan” G-protein-coupled receptors (GPCRs) whose endogenous ligands (peptide hormones) are unknown. Identification of these peptide hormones is a difficult and important problem. We describe a computational framework that models spatial structure along the genomic sequence simultaneously with the temporal evolutionary path structure across species and show how such models can be used to discover new functional molecules, in particular peptide hormones, via cross-genomic sequence comparisons. The computational framework incorporates a priori high-level knowledge of structural and evolutionary constraints into a hierarchical grammar of evolutionary probabilistic models. This computational method was used for identifying novel prohormones and the processed peptide sites by producing sequence alignments across many species at the functional-element level. Experimental results with an initial implementation of the algorithm were used to identify potential prohormones by comparing the human and non-human proteins in the Swiss-Prot database of known annotated proteins. In this proof of concept, we identified 45 out of 54 prohormones with only 44 false positives. The comparison of known and hypothetical human and mouse proteins resulted in the identification of a novel putative prohormone with at least four potential neuropeptides. Finally, in order to validate the computational methodology, we present the basic molecular biological characterization of the novel putative peptide hormone, including its identification and regional localization in the brain. This species comparison, HMM-based computational approach succeeded in identifying a previously undiscovered neuropeptide from whole genome protein sequences. This novel putative peptide hormone is found in discreet brain regions as well as other organs. The success of this approach will have a great impact on our understanding of GPCRs and associated pathways and help to identify new targets for drug development.     

Evidence for Existence of “Mesotogas,” Members of the Order Thermotogales Adapted to Low-Temperature Environments

All cultivated isolates of the bacterial order Thermotogales are either thermophiles or hyperthermophiles, but Thermotogales 16S rRNA gene sequences have been detected in many mesophilic anaerobic and microaerophilic environments, particularly within communities involved in the remediation of pollutants. Here we provide metagenomic evidence for the existence of Thermotogales lineages, which we informally call “mesotoga,” that are adapted to growth at lower temperatures. Two fosmid clones containing mesotoga DNA, originating from a low-temperature enrichment culture that degrades a polychlorinated biphenyl congener, were sequenced. Phylogenetic analysis clearly puts this bacterial lineage within the Thermotogales order, with the rRNA gene trees and 21 of 58 open reading frames strongly supporting this relationship. An analysis of protein sequence composition showed that mesotoga proteins are adapted to function at lower temperatures than are their identifiable homologs from thermophilic and hyperthermophilic members of the order Thermotogales, supporting the notion that this bacterium lives and grows optimally at lower temperatures. The phylogenetic analysis suggests that the mesotoga lineage from which our fosmids derive has used both the acquisition of genes from its neighbors and the modification of existing thermophilic sequences to adapt to a mesophilic lifestyle.     

ULTRASTRUCTURE OF THE Z LINE OF SKELETAL MUSCLE FIBERS

A new model of Z-line structure in skeletal muscle is proposed. Unlike previous models it is capable of explaining the two apparently inconsistent lattice arrangements seen in thin sections, i.e., the "basket weave" lattice and the smaller lattice recently reported in the literature. The model is based on four looping helical strands derived from the I filaments within the Z line. Each of these four strands form hairpin-shaped loops within the Z line and then join with an adjacent I filament in the same sarcomere. The two apparently different lattices represent a common structure viewed at slightly different levels of section.     

Ultrastructural basis of airway smooth muscle contraction

The sliding filament theory of contraction that was developed for striated muscle is generally believed to be also applicable to smooth muscle. However, the well-organized myofilament lattice (i.e., the sarcomeric structure) found in striated muscle has never been clearly delineated in smooth muscle. There is evidence that the myofilament lattice in some smooth muscles, such as airway smooth muscle, is malleable; it can be reshaped to fit a large range of cell dimensions while the maximal overlap between the contractile filaments is maintained. In this review, some early models of the structurally static contractile apparatus of smooth muscle are described. The focus of the review, however, is on the recent findings supporting a model of structurally dynamic contractile apparatus and cytoskeleton for airway smooth muscle. A list of unanswered questions regarding smooth muscle ultrastructure is also proposed in this review, in the hope that it will provide some guidance for future research.     

Pattern formation in discrete cell lattices

In recent years, models for lattices of discrete cells have been attracting increased attention due to their greater flexibility to represent signalling and contact-dependent cell-cell interaction than conventional reaction-diffusion models. Using the almost forgotten method of Othmer and Scriven (1971) to calculate eigenvalues and eigenvectors for the Jacobian of the homogeneous state, a Turing-like linear stability analysis is carried out for diffusion-driven (DD) and signalling-driven (SD) discrete models. The method is a generalisation of the original method of Turing (1952). For two-species models it is found that there are profound differences between the two types of model when the size of the lattice increases. For DD models, the homogeneous state is typically either always stable, always unstable, or becomes unstable when the lattice gets suffficiently large. For SD models, the homogeneous state is typically unstable independent of lattice size, and stable only in a minor part of parameter space. Thus, SD models seem in general more pattern-prone than DD models. The conjecture that the linear analysis predicts the final pattern is investigated for a DD system with Thomas internal dynamics. Commonly the final pattern resembles the pattern of the initial perturbation of the homogeneous state, but this is by no means a general feature. When applied to a recent model for Delta-Notch lateral inhibition, linear analysis must be supplemented by various non-linear techniques to get a deeper insight into the patterning mechanisms. The overall conclusion is that a linear Turing analysis may be useful for predicting pattern, but when it comes to explaining patterns, non-linear analysis cannot be ignored. Received: 1 March 2000 / Revised version: 23 April 2000 / Published online: 12 October 2001     

Positive and negative design in stability and thermal adaptation of natural proteins

The aim of this work is to elucidate how physical principles of protein design are reflected in natural sequences that evolved in response to the thermal conditions of the environment. Using an exactly solvable lattice model, we design sequences with selected thermal properties. Compositional analysis of designed model sequences and natural proteomes reveals a specific trend in amino acid compositions in response to the requirement of stability at elevated environmental temperature: the increase of fractions of hydrophobic and charged amino acid residues at the expense of polar ones. We show that this “from both ends of the hydrophobicity scale” trend is due to positive (to stabilize the native state) and negative (to destabilize misfolded states) components of protein design. Negative design strengthens specific repulsive non-native interactions that appear in misfolded structures. A pressure to preserve specific repulsive interactions in non-native conformations may result in correlated mutations between amino acids that are far apart in the native state but may be in contact in misfolded conformations. Such correlated mutations are indeed found in TIM barrel and other proteins.     

Origin-Dependent Inverted-Repeat Amplification: Tests of a Model for Inverted DNA Amplification

DNA replication errors are a major driver of evolution—from single nucleotide polymorphisms to large-scale copy number variations (CNVs). Here we test a specific replication-based model to explain the generation of interstitial, inverted triplications. While no genetic information is lost, the novel inversion junctions and increased copy number of the included sequences create the potential for adaptive phenotypes. The model—Origin-Dependent Inverted-Repeat Amplification (ODIRA)—proposes that a replication error at pre-existing short, interrupted, inverted repeats in genomic sequences generates an extrachromosomal, inverted dimeric, autonomously replicating intermediate; subsequent genomic integration of the dimer yields this class of CNV without loss of distal chromosomal sequences. We used a combination of in vitro and in vivo approaches to test the feasibility of the proposed replication error and its downstream consequences on chromosome structure in the yeast Saccharomyces cerevisiae. We show that the proposed replication error—the ligation of leading and lagging nascent strands to create “closed” forks—can occur in vitro at short, interrupted inverted repeats. The removal of molecules with two closed forks results in a hairpin-capped linear duplex that we show replicates in vivo to create an inverted, dimeric plasmid that subsequently integrates into the genome by homologous recombination, creating an inverted triplication. While other models have been proposed to explain inverted triplications and their derivatives, our model can also explain the generation of human, de novo, inverted amplicons that have a 2:1 mixture of sequences from both homologues of a single parent—a feature readily explained by a plasmid intermediate that arises from one homologue and integrates into the other homologue prior to meiosis. Our tests of key features of ODIRA lend support to this mechanism and suggest further avenues of enquiry to unravel the origins of interstitial, inverted CNVs pivotal in human health and evolution.