Modeling of halorhodopsin and rhodopsin based on bacteriorhodopsin

Bacteriorhodopsin (BR), halorhodopsin (HR), and rhodopsin (Rh) all belong to the class of seven-helix membrane proteins. For BR, a structural model at atomic resolution is available; for HR, diffraction data are available only down to a resolution of 6 Å in the membrane plane, and for Rh, down to 9 Å. BR and HR are closely related proteins with a sequence homology of 34%, while Rh does not share any sequence homology with BR. An atomic model for HR is derived that is based on sequence alignment and the atomic model for BR and is improved by molecular dynamics simulations. The model structure obtained accounts well for the experimentally observed difference between HR and BR in the projection map, where HR exhibits a higher density in the region between helices D and E. The reason for this difference lies partially in the different side chains and partially in slightly different helix tilts. The scattering amplitudes and phases of the model structure are calculated and agree with the experimental data down to a resolution of about 8 Å. If the helix positions are adopted from the projection map for HR and used as input in the model, this number improves to 7 Å. Analogously, an atomic model for Rh is derived based on the atomic model for BR and subjected to molecular dynamics simulations. Optimal agreement with the experimental projection map for Rh is obtained when the entire model structure is rotated slightly about two axes in the membrane plane. The agreement with the experimental projection map is not as satisfactory as for HR, but the results indicate that even for a nonhomologous, but structurally related, protein such as Rh, an acceptable model structure can be derived from the structure of BR. © 1996 Wiley-Liss, Inc.     

Maximum Likelihood based comparison of the specific growth rates for P. aeruginosa and four mutator strains

The specific growth rate for P. aeruginosa and four mutator strains mutT, mutY, mutM and mutY–mutM is estimated by a suggested Maximum Likelihood, ML, method which takes the autocorrelation of the observation into account. For each bacteria strain, six wells of optical density, OD, measurements are used for parameter estimation. The data is log-transformed such that a linear model can be applied. The transformation changes the variance structure, and hence an OD-dependent variance is implemented in the model. The autocorrelation in the data is demonstrated, and a correlation model with an exponentially decaying function of the time between observations is suggested. A model with a full covariance structure containing OD-dependent variance and an autocorrelation structure is compared to a model with variance only and with no variance or correlation implemented. It is shown that the model that best describes data is a model taking into account the full covariance structure. An inference study is made in order to determine whether the growth rate of the five bacteria strains is the same. After applying a likelihood-ratio test to models with a full covariance structure, it is concluded that the specific growth rate is the same for all bacteria strains. This study highlights the importance of carrying out an explorative examination of residuals in order to make a correct parametrization of a model including the covariance structure. The ML method is shown to be a strong tool as it enables estimation of covariance parameters along with the other model parameters and it makes way for strong statistical tools for inference studies.     

A model for the three-dimensional structure of glucagon

A literature search on the structural aspects of glucagon in dilute aqueous solution has been undertaken. We have found that a compact, well-defined structure must exist and propose a model for that structure. In doing so, care was taken to distinguish between the raw data themselves and the interpretations drawn from them, and to bring about a model consistent with as much of the data as possible. The model building was performed on Corey-Pauling-Koltun (CPK) space-filling models using secondary structure prediction rules, experimental data such as fluorescence quenching, circular dichroism, NMR and high resolution dark field electron microscopy, and was guided by a hierarchy of intramolecular interactions which places hydrophobic bonding first and hydrogen bonding second. This last criterion places a strict requirement on the model-building to maximize contacts among complementary hydrophobic surfaces; this means that no empty spaces are allowed inside the folded molecule. The resultant model is consistent with all the relevant data. Furthermore, as demanded by any structure building exercise, the model suggests structure-function relationships. One of the predictions drawn from the structure—the binding of guanosine-5′-triphosphate (GTP)—has been confirmed by a preliminary experiment (reported elsewhere). Another aspect of the structure suggests a subtle mechanism for allostery.     

Two-H-Bonded and One-H-Bonded Structure Alternations in Collagen

Abstract

This paper concerns the conformational variability of collagen as related to the concrete tripeptides (GXY)_n constituting its primary structure. The previously elaborated model (V.G. Tumanyan, N.G. Esipova, Biophysics 28, 1021–1025, 1983) with two nets of hydrogen bonds is useful for tripeptides where X is an amino acid. If X is an imino acid, the common one-bonded Rich & Crick model is valid. In this work, compound sequences including tripeptides of different types are considered. Molecular mechanics is used to assess the conformations of the junction regions when a structure with two nets of hydrogen bonds precedes the structure with one net, and vice versa. Thus, all types of sequences typical for natural collagen are covered. It is shown that the combined model representing an alternation of the two-H-bonded model and the one-H-bonded Rich & Crick model is satisfactory stere-ochemically, and provides more favorable energy in comparison with the continuous one-H-bonded model. Besides, a more favorable hydration of the molecule occurs in this case. Some conclusions are made about interchain and intrachain ionic bonds. Thus, it is deduced for the concrete fibrillar protein how a one-dimensional structure determines three-dimensional structure. The macromolecular structure thus suggested is in accord with the experimental data on hydrogen exchange.     

LIGNUM: A Tree Model Based on Simple Structural Units

The model LIGNUM treats a tree as a collection of a large numberof simple units which correspond to the organs of the tree.The model describes the three dimensional structure of the treecrown and defines the growth in terms of the metabolism takingplace in these units. The activities of physiological processescan be explicitly related to the tree structures in which theyare taking place. The time step is 1 year. The crown of the model tree consists of tree segments, branchingpoints and buds. Each pair of tree segments is separated bya branching point. The buds produce new tree segments, branchingpoints and buds. The tree segments contain wood, bark and foliage.A model tree consisting of simple elements translates convenientlyto a list structure: the computer program implementing LIGNUMtreats the tree as a collection of lists. The annual growth of the tree is driven by available photosyntheticproducts after respiration losses are accounted for. The photosyntheticrate of foliage depends on the amount of light. The amount ofphotosynthates allocated to the growth of new tree segmentsis controlled by the light conditions and the amount of foliageon the mother tree segment. In principle, the biomass relationshipsof the tree parts follow the pipe model hypothesis. The orientationof new tree segments results from the application of constantbranching angles. LIGNUM has been parametrized for young Scotspine (Pinus sylvestrisL.) trees. However, the model is generic;with a change of parameter values and minor modifications itcan be applied to other species as well. Growth model; object-oriented modelling; tree architecture; branching structure; Pinus sylvestrisL.; developmental morphology and physiology; photosynthesis; respiration     

Two-H-bonded and one-H-bonded structure alternations in collagen

This paper concerns the conformational variability of collagen as related to the concrete tripeptides (GXY)n constituting its primary structure. The previously elaborated model (V.G.Tumanyan, N.G.Esipova, Biophysics 28, 1021-1025, 1983) with two nets of hydrogen bonds is useful for tripeptides where X is an amino acid. If X is an imino acid, the common one-bonded Rich & Crick model is valid. In this work, compound sequences including tripeptides of different types are considered. Molecular mechanics is used to assess the conformations of the junction regions when a structure with two nets of hydrogen bonds precedes the structure with one net, and vice versa. Thus, all types of sequences typical for natural collagen are covered. It is shown that the combined model representing an alternation of the two-H-bonded model and the one-H-bonded Rich & Crick model is satisfactory stereochemically, and provides more favorable energy in comparison with the continuous one-H-bonded model. Besides, a more favorable hydration of the molecule occures in this case. Some conclusions are made about interchain and intrachain ionic bonds. Thus, it is deduced for the concrete fibrillar protein how a one-dimensional structure determines three-dimensional structure. The macromolecular structure thus suggested is in accord with the experimental data on hydrogen exchange.     

Contact prediction for beta and alpha‐beta proteins using integer linear optimization and its impact on the first principles 3D structure prediction method ASTRO‐FOLD

An integer linear optimization model is presented to predict residue contacts in β, α + β, and α/β proteins. The total energy of a protein is expressed as sum of a C^α? C^α distance dependent contact energy contribution and a hydrophobic contribution. The model selects contact that assign lowest energy to the protein structure as satisfying a set of constraints that are included to enforce certain physically observed topological information. A new method based on hydrophobicity is proposed to find the β‐sheet alignments. These β‐sheet alignments are used as constraints for contacts between residues of β‐sheets. This model was tested on three independent protein test sets and CASP8 test proteins consisting of β, α + β, α/β proteins and it was found to perform very well. The average accuracy of the predictions (separated by at least six residues) was ～61%. The average true positive and false positive distances were also calculated for each of the test sets and they are 7.58 Å and 15.88 Å, respectively. Residue contact prediction can be directly used to facilitate the protein tertiary structure prediction. This proposed residue contact prediction model is incorporated into the first principles protein tertiary structure prediction approach, ASTRO‐FOLD. The effectiveness of the contact prediction model was further demonstrated by the improvement in the quality of the protein structure ensemble generated using the predicted residue contacts for a test set of 10 proteins. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

THE STRUCTURE OF GRANA IN FLOWERING PLANTS

A model of granum structure, consisting of multiple helical frets wound around each cylindrical granum, is proposed as a representation of granum structure for flowering plants in general. This model was originally formulated for grana in the mesophyll plastids of Zea mays and was subsequently extended to grana of Phaseolus vulgaris by additional studies. The model is now shown to be applicable also to grana in the plastids of Cannabis sativa, Elodea canadensis, Nicotiana rustica, Pisum sativum, and Spinacia oleracea. This sample of seven angiosperms includes genera commonly studied by other workers in their ultrastructural investigations of plastid structure.     

A structural model for the chromophore-binding domain of ovine rhodopsin

A putative model for the structure of the relatively independent carboxyl-terminal domain of (rhod)opsin has been developed by use of a combination of several secondary structure prediction methods. The validity of this approach was confirmed by comparing the secondary structure for bacteriorhodopsin as predicted by these methods with its known low resolution structure. The resulting predicted structure agreed well with the experimental data. The model obtained for opsin incorporates two transmembrane α-helical rods linked by an intradiscal loop. Each of the helical sections is interrupted by a short irregular region. One of these includes the lysyl residue to which the chromophore 11-cis retinal is attached. The second non-regular segment, almost opposite the first, contains a cysteinyl and a tryptophanyl residue which may be involved in protein—chromophore interaction. The proposed structure of this whole domain could prove instructive in the elucidation of the primary events of visual transduction.     

A discrete,stochastic model of colonial phytoplankton population size structure: Development and application to in situ imaging-in-flow cytometer observations of Dinobryon

The scientific community lacks models for the dynamic changes in population size structure that occur in colonial phytoplankton. This is surprising, as size is a key trait affecting many aspects of phytoplankton ecology, and colonial forms are very common. We aim to fill this gap with a new discrete, stochastic model of dynamic changes in phytoplankton colonies' population size structure. We use the colonial phytoplankton Dinobryon as a proof-of-concept organism. The model includes four stochastic functions—division, stomatocyst production, colony breakage, and colony loss—to determine Dinobryon population size structure and populations counts. Although the functions presented here are tailored to Dinobryon, the model is readily adaptable to represent other colonial taxa. We demonstrate how fitting our model to in situ observations of colony population size structure can provide a powerful approach to explore colony size dynamics. Here, we have (1) collected high-frequency in situ observations of Dinobryon in Lac (Lake) Montjoie (Quebec, Canada) in 2013 with a moored Imaging FlowCytobot (IFCB) and (2) fit the model to those observations with a genetic algorithm solver that extracts parameter estimates for each of the four stochastic functions. As an example of the power of this model-data integration, we also highlight ecological insights into Dinobryon colony size and stomatocyst production. The Dinobryon population was enriched in larger, flagellate-rich colonies near bloom initiation and shifted to smaller and emptier colonies toward bloom decline.     

Assembly of protein structure from sparse experimental data: An efficient Monte Carlo model

A new, efficient method for the assembly of protein tertiary structure from known, loosely encoded secondary structure restraints and sparse information about exact side chain contacts is proposed and evaluated. The method is based on a new, very simple method for the reduced modeling of protein structure and dynamics, where the protein is described as a lattice chain connecting side chain centers of mass rather than Cαs. The model has implicit built-in multibody correlations that simulate short- and long-range packing preferences, hydrogen bonding cooperativity and a mean force potential describing hydrophobic interactions. Due to the simplicity of the protein representation and definition of the model force field, the Monte Carlo algorithm is at least an order of magnitude faster than previously published Monte Carlo algorithms for structure assembly. In contrast to existing algorithms, the new method requires a smaller number of tertiary restraints for successful fold assembly; on average, one for every seven residues as compared to one for every four residues. For example, for smaller proteins such as the B domain of protein G, the resulting structures have a coordinate root mean square deviation (cRMSD), which is about 3 Å from the experimental structure; for myoglobin, structures whose backbone cRMSD is 4.3 Å are produced, and for a 247-residue TIM barrel, the cRMSD of the resulting folds is about 6 Å. As would be expected, increasing the number of tertiary restraints improves the accuracy of the assembled structures. The reliability and robustness of the new method should enable its routine application in model building protocols based on various (very sparse) experimentally derived structural restraints. Proteins 32:475–494, 1998. © 1998 Wiley-Liss, Inc.     

Homology modelling of a sensor histidine kinase from Aeromonas hydrophila

Aeromonas hydrophila has been implicated in extra-intestinal infection and diarrhoea in humans. Targetting unique effectors of bacterial pathogens is considered a powerful strategy for drug design against bacterial variations to drug resistance. The two-component bacterial system involving sensor histidine kinase (SHK) and its response regulators is considered a lucrative target for drug design. This is the first report describing a three-dimensional (3D) structure for SHK of A. hydrophila. The model was constructed by homology modelling using the X-ray structure of PleD—a response regulator—in conjunction with cdiGMP (PDB code 1W25) and HemAT sensor domain (PDB code 1OR4)—a globin coupled sensor. A combination of homology modelling methodology and molecular dynamics (MD) simulations was applied to obtain a reasonable structure to understand the dynamic behaviour of SHK. Homology modelling was performed using MODELLER9v2 software. The structure was relaxed to eliminate bad atomic contacts. The final model obtained by molecular mechanics and dynamics methods was assessed using PROCHECK and VERIFY 3D graph, which confirmed that the final refined model is reliable. Until complete biochemical and structural data of SHK are determined by experimental means, this model can serve as a valuable reference for characterising the protein and could be explored for drug targetting by design of suitable inhibitors.     

Generation of a third-order folded structure for chromatin

A model for the initiation of the diffuse-condensed transition of chromatin induced by a change in the conformation of lysine-rich histones is proposed. Three levels of folded structures are discussed. The first-order folded structure refers to the structure of the repeat unit of chromatin, which is called the nucleosome. The nucleosome contains a nuclease resistant region in which 140 base pairs of DNA are wrapped around the surface of a histone aggregated of two copies each of the histones H2A, H2B, H3 and H4. This DNA-histone aggregate is called a core particle. The nuclease accessible region of the nucleosome is approximately 60 base pairs of DNA which link the core particle, hence the terminology “linker DNA.” The lysine-rich histones, (Hl, H5), which are more loosely bound than the core histones, are associated with the linker DNA. The second-order folded structure refers to the conformation of a polynucleosome. Based on neutron scattering and quasielastic light scattering studies the second-order folded structure is assumed to be an extended helix in solution with 5–7 nucleosome units per turn. The third-order folded structure is defined as that structure resulting from the first stage in the condensation process induced by a conformational change in the lysine-rich histones. Generation of the third-order folded structure in the proposed model is effected by an increased affinity of the lysine-rich histones for super-helical DNA in the core particles in adjacent turns of the second-order folded structure. Since the lysine-rich histones preferentially bind to A-T rich regions in DNA, the distribution of these regions would determine the third-order folded structure. The net effect of a non-random distribution of A-T rich regions as in the proposed model is the generation of a helix for the third-order folded structure. The assumption of a non-random distribution of A-T rich regions is indirectly supported by proflavine binding studies reported herein and by the existence of repetitive and non-repetitive DNA regions inferred from renaturation studies. One consequence of the proposed mechanism is that the majority of the A-T rich regions are in the interior of the third-order folded structure. Promoter sites of high A-T content would then be inaccessible to polymerases. The proposed model also suggests a role for spacer DNA in the genome. Higher order folded structures must also be present in the final state of condensed chromatin since the three orders of folded structures considered in this communication accounts for only 2% of that required in the diffuse-condensed transition.     

The inverse niche model for food webs with parasites

Although parasites represent an important component of ecosystems, few field and theoretical studies have addressed the structure of parasites in food webs. We evaluate the structure of parasitic links in an extensive salt marsh food web, with a new model distinguishing parasitic links from non-parasitic links among free-living species. The proposed model is an extension of the niche model for food web structure, motivated by the potential role of size (and related metabolic rates) in structuring food webs. The proposed extension captures several properties observed in the data, including patterns of clustering and nestedness, better than does a random model. By relaxing specific assumptions, we demonstrate that two essential elements of the proposed model are the similarity of a parasite’s hosts and the increasing degree of parasite specialization, along a one-dimensional niche axis. Thus, inverting one of the basic rules of the original model, the one determining consumers’ generality appears critical. Our results support the role of size as one of the organizing principles underlying niche space and food web topology. They also strengthen the evidence for the non-random structure of parasitic links in food webs and open the door to addressing questions concerning the consequences and origins of this structure.     

Molecular modeling of the three-dimensional structure of GLP-1R and its interactions with several agonists

Glucagon-like peptide-1 receptor (GLP-1R) is a promising molecular target for developing drugs treating type 2 diabetes. We have predicted the complete three-dimensional structure of GLP-1R and the binding modes of several GLP-1R agonists, including GLP-1, Boc5, and Cpd1, through a combination of homology modeling, molecular docking, and long-time molecular dynamics simulation on a lipid bilayer. Our model can reasonably interpret the results of a number of mutation experiments regarding GLP-1R as well as the successful modification to GLP-1 by Liraglutide. Our model is also validated by a recently revealed crystal structure of the extracellular domain of GLP-1R. An activation mechanism of GLP-1R agonists is proposed based on the principal component analysis and normal mode analysis on our predicted GLP-1R structure. Before the complete structure of GLP-1R is determined through experimental means, our model may serve as a valuable reference for characterizing the interactions between GLP-1R and its agonists. Figure Comparison of our predicted model of rGLP-1R (left) with the recently revealed crystal structure of hGLP-1R (right)     

Modeling of G-Protein Coupled Receptors with Bacteriorhodopsin as a Template. A Novel Approach Based on Interaction Energy Differences

Abstract

The structure of bacteriorhodopsin was used as a template to generate a model for G-protein coupled receptors. However, these receptors and the template are not related by sequence homology. Therefore a pragmatic and reproducible approach was developed to achieve an energetically favourable accommodation of receptor sequences to the backbone structure of bacteriorhodopsin. Improved interaction energy differences are used in a two step procedure analogous to a hypothetical folding mechanism for integral membrane proteins. The resulting model is in good agreement with existing data from structure-function studies.     

Stability patterns and trophic structure in a Delaware Bay plankton community.

Using qualitative loop analysis we have extended our examination of a Delaware Bay plankton community to include an investigation of the roles played by the various entities (population, guild or nutrient) in the community. In an entity removal exercise, we used stability relationships as a probe into community structure. Six types of stability change are possible as a result of entity removal from the system: stable to stable (s-->s); stable to unstable (s-->u); stable to disconnected (s-->d); unstable to stable (u-->s); unstable to unstable (u-->u); unstable to disconnected (u-->d). Using these changes as an investigative tool, we found that in order to account for the stability-instability patterns, it was necessary to construct a refined trophic structure model. The observed connections between the entities in the larger model could be grouped into two different types of stability substructures: a simple pattern and a more complex branching pattern. These patterns map easily onto the refined trophic structure model. Using stability analysis it is also possible to model community structure in ways other than the traditional trophic approach. Patterns of system necessity and relative contribution to stability are observed. These patterns match the refined trophic structure model derived previously. The roles that the various entities play in the overall community were followed over an annual cycle. Entities were seen to change their roles as a function of time and status within a subgroup. These results show that stability determinations have the potential to be used as a valuable tool in community analysis.