Knowledge-based versus experimentally acquired distance and angle constraints for NMR structure refinement

Nuclear Overhauser effects (NOE) distance constraints and torsion angle constraints are major conformational constraints for nuclear magnetic resonance (NMR) structure refinement. In particular, the number of NOE constraints has been considered as an important determinant for the quality of NMR structures. Of course, the availability of torsion angle constraints is also critical for the formation of correct local conformations. In our recent work, we have shown how a set of knowledge-based short-range distance constraints can also be utilized for NMR structure refinement, as a complementary set of conformational constraints to the NOE and torsion angle constraints. In this paper, we show the results from a series of structure refinement experiments by using different types of conformational constraints--NOE, torsion angle, or knowledge-based constraints--or their combinations, and make a quantitative assessment on how the experimentally acquired constraints contribute to the quality of structural models and whether or not they can be combined with or substituted by the knowledge-based constraints. We have carried out the experiments on a small set of NMR structures. Our preliminary calculations have revealed that the torsion angle constraints contribute substantially to the quality of the structures, but require to be combined with the NOE constraints to be fully effective. The knowledge-based constraints can be functionally as crucial as the torsion angle constraints, although they are statistical constraints after all and are not meant to be able to replace the latter.     

Kinetic constraints for formation of steady states in biochemical networks

The constraint-based analysis has emerged as a useful tool for analysis of biochemical networks. This work introduces the concept of kinetic constraints. It is shown that maximal reaction rates are appropriate constraints only for isolated enzymatic reactions. For biochemical networks, it is revealed that constraints for formation of a steady state require specific relationships between maximal reaction rates of all enzymes. The constraints for a branched network are significantly different from those for a cyclic network. Moreover, the constraints do not require Michaelis-Menten constants for most enzymes, and they only require the constants for the enzymes at the branching or cyclic point. Reversibility of reactions at system boundary or branching point may significantly impact on kinetic constraints. When enzymes are regulated, regulations may impose severe kinetic constraints for the formation of steady states. As the complexity of a network increases, kinetic constraints become more severe. In addition, it is demonstrated that kinetic constraints for networks with co-regulation can be analyzed using the approach. In general, co-regulation enhances the constraints and therefore larger fluctuations in fluxes can be accommodated in the networks with co-regulation. As a first example of the application, we derive the kinetic constraints for an actual network that describes sucrose accumulation in the sugar cane culm, and confirm their validity using numerical simulations.     

Identifying constraints that govern cell behavior: a key to converting conceptual to computational models in biology?

Cells must abide by a number of constraints. The environmental constrains of cellular behavior and physicochemical limitations affect cellular processes. To regulate and adapt their functions, cells impose constraints on themselves. Enumerating, understanding, and applying these constraints leads to a constraints-based modeling formalism that has been helpful in converting conceptual models to computational models in biology. The continued success of the constraints-based approach depends upon identification and incorporation of new constraints to more accurately define cellular capabilities. This review considers constraints in terms of environmental, physicochemical, and self-imposed regulatory and evolutionary constraints with the purpose of refining current constraints-based models of cell phenotype.     

Constraining null models with environmental gradients: a new method for evaluating the effects of environmental factors and geometric constraints on geographic diversity patterns

The relative effects of climate and geometric constraints on geographic diversity patterns have long been controversial. We developed a new method to assess the role of geometric constraints in shaping altitudinal richness patterns. We showed how plant species richness on four mountains in southwest China are shaped by geometric constraints and environmental gradients together. Contrary to previous studies, our results suggested that: 1) small‐ and large‐ranged species richness were largely controlled by the same environmental gradients, and differed mainly in the effect of geometric constraints. 2) The contribution of geometric constraints (in addition to environmental gradients) to explaining species richness was greater when species richness peaked at low altitudes than at mid‐altitudes, suggesting that geometric constraints may be very important when richness peaks are far away from mid‐domains. 3) Relating species richness directly to environmental factors (the most widely used method in biodiversity studies) may be misleading when geometric constraints may be affecting the richness pattern, because this method may overestimate the effect of environmental factors by failing to distinguish the confounding effect of geometric constraints. Instead, the effect of environmental factors can be evaluated with an underlying gradient derived from small‐ranged species. 4) The geometric constraints effect cannot be fully evaluated by pure geometric constraints models, and is better evaluated with range‐based models constrained with environmental gradients. 5) If the generality of our findings is supported for other taxa on other gradients, then many previous studies on the effects of climate and of geometric constraints on geographic diversity patterns may need to be re‐visited.     

Modularity and reliability in the organization of organisms

An organism persists only if it satisfies internal and external constraints. Within the organism networks of processes meet the constraints. In such networks a principle of matching often obtains: the pattern of coupling among processes matches the correlation among constraints. That is, a module—a cluster of coupled processes—meets a constraint. Dissociable modules meet dissociàble constraints. A hierarchy of modules meets a hierarchy of constraints. We have inquired whether such matching is predicted by an optimality criterion in a simple example. We find that in an ensemble of networks with unreliable processes, the networks that meet the constraints with highest reliability obey the principle of matching. The difference in reliability between modular and nonmodular networks that meet the same constraints is a function of the probability of success per process. Our results suggest that this difference is maximal at a probability of success that increases monotonically with the number of processes in the network.     

Microsatellite Behavior with Range Constraints: Parameter Estimation and Improved Distances for Use in Phylogenetic Reconstruction

A symmetric stepwise mutation model with reflecting boundaries is employed to evaluate microsatellite evolution under range constraints. Methods of estimating range constraints and mutation rates under the assumptions of the model are developed. Least squares procedures are employed to improve molecular distance estimation for use in phylogenetic reconstruction in the case where range constraints and mutation rates vary across loci. The bias and accuracy of these methods are evaluated using computer simulations, and they are compared to previously existing methods which do not assume range constraints. Range constraints are seen to have a substantial impact on phylogenetic conclusions based on molecular distances, particularly for more divergent taxa. Results indicate that if range constraints are in effect, the methods developed here should be used in both the preliminary planning and final analysis of phylogenetic studies employing microsatellites. It is also seen that in order to make accurate phylogenetic inferences under range constraints, a larger number of loci are required than in their absence.     

Is sociality driven by the costs of dispersal or the benefits of philopatry? A role for kin-discrimination mechanisms

The role of ecological constraints in promoting sociality is currently much debated. Using a direct-fitness approach, we show this role to depend on the kin-discrimination mechanisms underlying social interactions. Altruism cannot evolve under spatially based discrimination, unless ecological constraints prevent complete dispersal. Increasing constraints enhances both the proportion of philopatric (and thereby altruistic) individuals and the level of altruistic investments conceded in pairwise interactions. Familiarity-based discrimination, by contrast, allows philopatry and altruism to evolve at significant levels even in the absence of ecological constraints. Increasing constraints further enhances the proportion of philopatric (and thereby altruistic) individuals but not the level of altruism conceded. Ecological constraints are thus more likely to affect social evolution in species in which restricted cognitive abilities, large group size, and/or limited period of associative learning force investments to be made on the basis of spatial cues.     

Topological constraints are major determinants of tRNA tertiary structure and dynamics and provide basis for tertiary folding cooperativity

Recent studies have shown that basic steric and connectivity constraints encoded at the secondary structure level are key determinants of 3D structure and dynamics in simple two-way RNA junctions. However, the role of these topological constraints in higher order RNA junctions remains poorly understood. Here, we use a specialized coarse-grained molecular dynamics model to directly probe the thermodynamic contributions of topological constraints in defining the 3D architecture and dynamics of transfer RNA (tRNA). Topological constraints alone restrict tRNA''s allowed conformational space by over an order of magnitude and strongly discriminate against formation of non-native tertiary contacts, providing a sequence independent source of folding specificity. Topological constraints also give rise to long-range correlations between the relative orientation of tRNA''s helices, which in turn provides a mechanism for encoding thermodynamic cooperativity between distinct tertiary interactions. These aspects of topological constraints make it such that only several tertiary interactions are needed to confine tRNA to its native global structure and specify functionally important 3D dynamics. We further show that topological constraints are conserved across tRNA''s different naturally occurring secondary structures. Taken together, our results emphasize the central role of secondary-structure-encoded topological constraints in defining RNA 3D structure, dynamics and folding.     

Topological constraints: using RNA secondary structure to model 3D conformation, folding pathways, and dynamic adaptation

Accompanying recent advances in determining RNA secondary structure is the growing appreciation for the importance of relatively simple topological constraints, encoded at the secondary structure level, in defining the overall architecture, folding pathways, and dynamic adaptability of RNA. A new view is emerging in which tertiary interactions do not define RNA 3D structure, but rather, help select specific conformers from an already narrow, topologically pre-defined conformational distribution. Studies are providing fundamental insights into the nature of these topological constraints, how they are encoded by the RNA secondary structure, and how they interplay with other interactions, breathing new meaning to RNA secondary structure. New approaches have been developed that take advantage of topological constraints in determining RNA backbone conformation based on secondary structure, and a limited set of other, easily accessible constraints. Topological constraints are also providing a much-needed framework for rationalizing and describing RNA dynamics and structural adaptation. Finally, studies suggest that topological constraints may play important roles in steering RNA folding pathways. Here, we review recent advances in our understanding of topological constraints encoded by the RNA secondary structure.     

A novel method for predicting and using distance constraints of high accuracy for refining protein structure prediction

The principal bottleneck in protein structure prediction is the refinement of models from lower accuracies to the resolution observed by experiment. We developed a novel constraints‐based refinement method that identifies a high number of accurate input constraints from initial models and rebuilds them using restrained torsion angle dynamics (rTAD). We previously created a Bayesian statistics‐based residue‐specific all‐atom probability discriminatory function (RAPDF) to discriminate native‐like models by measuring the probability of accuracy for atom type distances within a given model. Here, we exploit RAPDF to score (i.e., filter) constraints from initial predictions that may or may not be close to a native‐like state, obtain consensus of top scoring constraints amongst five initial models, and compile sets with no redundant residue pair constraints. We find that this method consistently produces a large and highly accurate set of distance constraints from which to build refinement models. We further optimize the balance between accuracy and coverage of constraints by producing multiple structure sets using different constraint distance cutoffs, and note that the cutoff governs spatially near versus distant effects in model generation. This complete procedure of deriving distance constraints for rTAD simulations improves the quality of initial predictions significantly in all cases evaluated by us. Our procedure represents a significant step in solving the protein structure prediction and refinement problem, by enabling the use of consensus constraints, RAPDF, and rTAD for protein structure modeling and refinement. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Resource-allocation constraint governs structure and function of microbial communities in metabolic modeling

Predictive modeling tools for assessing microbial communities are important for realizing transformative capabilities of microbiomes in agriculture, ecology, and medicine. Constraint-based community-scale metabolic modeling is unique in its potential for making mechanistic predictions regarding both the structure and function of microbial communities. However, accessing this potential requires an understanding of key physicochemical constraints, which are typically considered on a per-species basis. What is needed is a means of incorporating global constraints relevant to microbial ecology into community models. Resource-allocation constraint, which describes how limited resources should be distributed to different cellular processes, sets limits on the efficiency of metabolic and ecological processes. In this study, we investigate the implications of resource-allocation constraints in community-scale metabolic modeling through a simple mechanism-agnostic implementation of resource-allocation constraints directly at the flux level. By systematically performing single-, two-, and multi-species growth simulations, we show that resource-allocation constraints are indispensable for predicting the structure and function of microbial communities. Our findings call for a scalable workflow for implementing a mechanistic version of resource-allocation constraints to ultimately harness the full potential of community-scale metabolic modeling tools.     

Simulated annealing with restrained molecular dynamics using a flexible restraint potential: theory and evaluation with simulated NMR constraints.

A new functional representation of NMR-derived distance constraints, the flexible restraint potential, has been implemented in the program CONGEN (Bruccoleri RE, Karplus M, 1987, Biopolymers 26:137-168) for molecular structure generation. In addition, flat-bottomed restraint potentials for representing dihedral angle and vicinal scalar coupling constraints have been introduced into CONGEN. An effective simulated annealing (SA) protocol that combines both weight annealing and temperature annealing is described. Calculations have been performed using ideal simulated NMR constraints, in order to evaluate the use of restrained molecular dynamics (MD) with these target functions as implemented in CONGEN. In this benchmark study, internuclear distance, dihedral angle, and vicinal coupling constant constraints were calculated from the energy-minimized X-ray crystal structure of the 46-amino acid polypeptide crambin (ICRN). Three-dimensional structures of crambin that satisfy these simulated NMR constraints were generated using restrained MD and SA. Polypeptide structures with extended backbone and side-chain conformations were used as starting conformations. Dynamical annealing calculations using extended starting conformations and assignments of initial velocities taken randomly from a Maxwellian distribution were found to adequately sample the conformational space consistent with the constraints. These calculations also show that loosened internuclear constraints can allow molecules to overcome local minima in the search for a global minimum with respect to both the NMR-derived constraints and conformational energy. This protocol and the modified version of the CONGEN program described here are shown to be reliable and robust, and are applicable generally for protein structure determination by dynamical simulated annealing using NMR data.     

Constraints and selection: insights from microsporogenesis in Asparagales

Developmental constraints have been proposed to interfere with natural selection in limiting the available set of potential adaptations. Whereas this concept has long been debated on theoretical grounds, it has been investigated empirically only in a few studies. In this article, we evaluate the importance of developmental constraints during microsporogenesis (male meiosis in plants), with an emphasis on phylogenetic patterns in Asparagales. Different developmental constraints were tested by character reshuffling or by simulated distributions. Among the different characteristics of microsporogenesis, only cell wall formation appeared as constrained. We show that constraints may also result from biases in the correlated occurrence of developmental steps (e.g., lack of successive cytokinesis when wall formation is centripetal). We document such biases and their potential outcomes, notably the establishment of intermediate stages, which allow development to bypass such constraints. These insights are discussed with regard to potential selection on pollen morphology.     

Ab initio prediction of thermodynamically feasible reaction directions from biochemical network stoichiometry

Analysis of the stoichiometric structure of metabolic networks provides insights into the relationships between structure, function, and regulation of metabolic systems. Based on knowledge of only reaction stoichiometry, certain aspects of network functionality and robustness can be predicted. Current theories focus on breaking a metabolic network down into non-decomposable pathways able to operate in steady state. The physics underlying these theories is based on mass balance and the laws of thermodynamics. However, due to the inherent nonlinearity of the thermodynamic constraints on metabolic fluxes, computational analysis of large-scale biochemical systems can be expensive. In this study, it is shown how the feasible reaction directions may be determined by either computing the allowable ranges under the mass-balance and thermodynamic constraints or by analyzing the stoichiometric structure of the network. The computed reaction directions translate into a set of linear constraints necessary for thermodynamic feasibility. This set of necessary linear constraints is shown to be sufficient to guarantee feasibility in certain cases, thus translating the nonlinear thermodynamic constraints to linear. We show that for a reaction network of 44 internal reactions representing energy metabolism, the computed linear inequality constraints represent necessary and sufficient conditions for thermodynamic feasibility.     

Protein threading with profiles and distance constraints using clique based algorithms

With the advent of experimental technologies like chemical cross-linking, it has become possible to obtain distances between specific residues of a newly sequenced protein. These types of experiments usually are less time consuming than X-ray crystallography or NMR. Consequently, it is highly desired to develop a method that incorporates this distance information to improve the performance of protein threading methods. However, protein threading with profiles in which constraints on distances between residues are given is known to be NP-hard. By using the notion of a maximum edge-weight clique finding algorithm, we introduce a more efficient method called FTHREAD for profile threading with distance constraints that is 18 times faster than its predecessor CLIQUETHREAD. Moreover, we also present a novel practical algorithm NTHREAD for profile threading with Non-strict constraints. The overall performance of FTHREAD on a data set shows that although our algorithm uses a simple threading function, our algorithm performs equally well as some of the existing methods. Particularly, when there are some unsatisfied constraints, NTHREAD (Non-strict constraints threading algorithm) performs better than threading with FTHREAD (Strict constraints threading algorithm). We have also analyzed the effects of using a number of distance constraints. This algorithm helps the enhancement of alignment quality between the query sequence and template structure, once the corresponding template structure is determined for the target sequence.     

Paramagnetism-based versus classical constraints: An analysis of the solution structure of Ca Ln calbindin D9k

The relative importance of paramagnetism-based constraints (i.e. pseudocontact shifts, residual dipolar couplings and nuclear relaxation enhancements) with respect to classical constraints in solution structure determinations of paramagnetic metalloproteins has been addressed. The protein selected for the study is a calcium binding protein, calbindin D9k, in which one of the two calcium ions is substituted with cerium(III). From 1823 NOEs, 191 dihedral angles, 15 hydrogen bonds, 769 pseudocontact shifts, 64 orientational constraints, 26 longitudinal relaxation rates, plus 969 pseudocontact shifts from other lanthanides, a final family with backbone r.m.s.d. from the average of 0.25 A was obtained. Then, several families of structures were generated either by removing subsets of paramagnetism-based constraints or by removing increasing numbers of NOEs. The results show the relative importance of the various paramagnetism-based constraints and their good complementarity with the diamagnetic ones. Although a resolved structure cannot be obtained with paramagnetism-based constraints only, it is shown that a reasonably well resolved backbone fold can be safely obtained by retaining as few as 29 randomly chosen long-range NOEs using the standard version of the program PSEUDYANA.     

Integrating thermodynamic and enzymatic constraints into genome-scale metabolic models

Stoichiometric genome-scale metabolic network models (GEMs) have been widely used to predict metabolic phenotypes. In addition to stoichiometric ratios, other constraints such as enzyme availability and thermodynamic feasibility can also limit the phenotype solution space. Extended GEM models considering either enzymatic or thermodynamic constraints have been shown to improve prediction accuracy. In this paper, we propose a novel method that integrates both enzymatic and thermodynamic constraints in a single Pyomo modeling framework (ETGEMs). We applied this method to construct the EcoETM (E. coli metabolic model with enzymatic and thermodynamic constraints). Using this model, we calculated the optimal pathways for cellular growth and the production of 22 metabolites. When comparing the results with those of iML1515 and models with one of the two constraints, we observed that many thermodynamically unfavorable and/or high enzyme cost pathways were excluded from EcoETM. For example, the synthesis pathway of carbamoyl-phosphate (Cbp) from iML1515 is both thermodynamically unfavorable and enzymatically costly. After introducing the new constraints, the production pathways and yields of several Cbp-derived products (e.g. L-arginine, orotate) calculated using EcoETM were more realistic. The results of this study demonstrate the great application potential of metabolic models with multiple constraints for pathway analysis and phenotype prediction.     

多约束代谢网络模型的研究进展

基于约束的基因组尺度代谢网络模型(genome-scale metabolic models,GEMs)分析已被广泛应用于代谢表型的预测.而实际细胞中代谢速率除计量学约束外,还受到酶资源可用性和反应热力学可行性等其他因素影响,在GEMs中整合酶资源约束或者热力学约束构建多约束代谢网络模型可以进一步缩小优化解空间,提升细...     

Towards quantification of vocal imitation in the zebra finch

The transition from an amorphous subsong into mature song requires a series of vocal changes. By tracing song elements during development, we have shown that the imitation trajectory to the target could not be predicted based on monotonic progression of vocal changes, indicating an internal component that imposes constraints on song development. Here we further examine the nature of constraints on song imitation in the zebra finch. We first present techniques for identifying and tracing distinctive vocal changes, and then we examine how sequences of vocal change are expressed and coordinated. Examples suggest two types of constraints on song imitation, based on the nature of the temporal context. Developmentally diachronic constraints are imposed by sequential dependencies between vocal changes as a function of developmental time, whereas developmentally synchronic constraints are given by the acoustic context of notes within the song. Finally, we show that the tendency of birds to copy certain sounds in the song model before others might be related to such constraints. We suggest that documenting the full range of distinctive vocal changes and the coordination of their expression would be useful for testing mechanisms of vocal imitation.