Macromolecular structural elucidation with solid-state NMR-derived orientational constraints

Summary The complete structure determination of a polypeptide in a lipid bilayer environment is demonstrated built solely upon orientational constraints derived from solid-state NMR observations. Such constraints are obtained from isotopically labeled samples uniformly aligned with respect to the B₀ field. Each observation constrains the molecular frame with respect to B₀ and the bilayer normal, which are arranged to be parallel. These constraints are not only very precise (a few tenths of a degree), but also very accurate. This is clearly demonstrated as the back bone structure is assembled sequentially and the i to i+6 hydrogen bonds in this structure of the gramicidin channel are shown on average to be within 0.5 Å of ideal geometry. Similarly, the side chains are assembled independently and in a radial direction from the backbone. The lack of considerable atomic overlap between side chains also demonstrates the accuracy of the constraints. Through this complete structure, solid-state NMR is demonstrated as an approach for determining three-dimensional macromolecular structure.     

Model quality assessment using distance constraints from alignments

Given a set of alternative models for a specific protein sequence, the model quality assessment (MQA) problem asks for an assignment of scores to each model in the set. A good MQA program assigns these scores such that they correlate well with real quality of the models, ideally scoring best that model which is closest to the true structure. In this article, we present a new approach for addressing the MQA problem. It is based on distance constraints extracted from alignments to templates of known structure, and is implemented in the Undertaker program for protein structure prediction. One novel feature is that we extract noncontact constraints as well as contact constraints. We describe how the distance constraint extraction is done and we show how they can be used to address the MQA problem. We have compared our method on CASP7 targets and the results show that our method is at least comparable with the best MQA methods that were assessed at CASP7. We also propose a new evaluation measure, Kendall's τ, that is more interpretable than conventional measures used for evaluating MQA methods (Pearson's r and Spearman's ρ). We show clear examples where Kendall's τ agrees much more with our intuition of a correct MQA, and we therefore propose that Kendall's τ be used for future CASP MQA assessments. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Excitability constraints on voltage-gated sodium channels

We study how functional constraints bound and shape evolution through an analysis of mammalian voltage-gated sodium channels. The primary function of sodium channels is to allow the propagation of action potentials. Since Hodgkin and Huxley, mathematical models have suggested that sodium channel properties need to be tightly constrained for an action potential to propagate. There are nine mammalian genes encoding voltage-gated sodium channels, many of which are more than approximately 90% identical by sequence. This sequence similarity presumably corresponds to similarity of function, consistent with the idea that these properties must be tightly constrained. However, the multiplicity of genes encoding sodium channels raises the question: why are there so many? We demonstrate that the simplest theoretical constraints bounding sodium channel diversity--the requirements of membrane excitability and the uniqueness of the resting potential--act directly on constraining sodium channel properties. We compare the predicted constraints with functional data on mammalian sodium channel properties collected from the literature, including 172 different sets of measurements from 40 publications, wild-type and mutant, under a variety of conditions. The data from all channel types, including mutants, obeys the excitability constraint; on the other hand, channels expressed in muscle tend to obey the constraint of a unique resting potential, while channels expressed in neuronal tissue do not. The excitability properties alone distinguish the nine sodium channels into four different groups that are consistent with phylogenetic analysis. Our calculations suggest interpretations for the functional differences between these groups.     

Suppression of Escherichia coli dnaA46 mutations by integration of plasmid R100.1. derivatives: constraints imposed by the replication terminus.

We have studies the phenotypic suppression of a dnaA46 mutation by plasmid integration at preselected chromosomal sites after introducing homologous sequences (Mu prophages) onto both the chromosomes and the suppressive plasmid. The plasmids used were all derived from plasmid R100.1. We found that the conditions required to get viable suppressive integration varied as the plasmid integration site moved from the origin to the terminus of chromosome replication. Two constraints were observed. Both appeared to be linked to the new characteristics acquired by chromosome replication from the integrated plasmid. One constraint was that strains with integrative suppression near the terminus terC were viable only in minimal medium. The rich medium sensitivity of these strains was correlated with a loss of regulation of initiation. The other constraint was a requirement for a specific orientation in certain regions of the chromosome. The two branches defined by normally initiated replication, between oriC and terC, were also symmetrical with respect to these plasmid orientation constraints. In studying the possible reasons for a plasmid orientation constraint, we found that, of the two forks initiated in bidirectional replication from the integrated plasmid, one was capable of moving across the terC region with a higher movability than the other.     

A global analysis of NMR distance constraints from the PDB

Information obtained from Nuclear Magnetic Resonance (NMR) experiments is encoded as a set of constraint lists when calculating three-dimensional structures for a protein. With the amount of constraint data from the world wide Protein Data Bank (wwPDB) that is now available, it is possible to do a global, large-scale analysis using only information from the constraints, without taking the coordinate information into account. This article describes such an analysis of distance constraints from NOE data based on a set of 1834 NMR PDB entries containing 1909 protein chains. In order to best represent the quality and extent of the data that is currently deposited at the wwPDB, only the original data as deposited by the authors was used, and no attempt was made to ‘clean up’ and further interpret this information. Because the constraint lists provide a single set of data, and not an ensemble of structural solutions, they are easier to analyse and provide a reduced form of structural information that is relevant for NMR analysis only. The online resource resulting from this analysis () makes it possible to check, for example, how often a particular contact occurs when assigning NOESY spectra, or to find out whether a particular sequence fragment is likely to be difficult to assign. In this respect it formalises information that scientists with experience in spectrum analysis are aware of but cannot necessarily quantify. The analysis described here illustrates the importance of depositing constraints (and all other possible NMR derived information) along with the structure coordinates, as this type of information can greatly assist the NMR community.     

An easy way to include weak alignment constraints into NMR structure calculations

We have recently shown that an energy penalty for the incorporation of residual tensorial constraints into molecular structure calculations can be formulated without the explicit knowledge of the Saupe orientation tensor (Moltke and Grzesiek, J. Biomol. NMR, 1999, 15, 77–82). Here we report the implementation of such an algorithm into the program X-PLOR. The new algorithm is easy to use and has good convergence properties. The algorithm is used for the structure refinement of the HIV-1 Nef protein using 252 dipolar coupling restraints. The approach is compared to the conventional penalty function with explicit knowledge of the orientation tensor's amplitude and rhombicity. No significant differences are found with respect to speed, Ramachandran core quality or coordinate precision.     

The structure of an integral membrane peptide: a deuterium NMR study of gramicidin.

Solid state deuterium NMR was employed on oriented multilamellar dispersions consisting of 1,2-dilauryl-sn-glycero-3-phosphatidylcholine and deuterium (2H) exchange-labeled gramicidin D, at a lipid to protein molar ratio (L/P) of 15:1, in order to study the dynamic structure of the channel conformation of gramicidin in a liquid crystalline phase. The corresponding spectra were used to discriminate between several structural models for the channel structure of gramicidin (based on the left- and right-handed beta 6.3 LD helix) and other models based on a structure obtained from high resolution NMR. The oriented spectrum is complicated by the fact that many of the doublets, corresponding to the 20 exchangeable sites, partially overlap. Furthermore, the asymmetry parameter, eta, of the electric field gradient tensor of the amide deuterons is large (approximately 0.2) and many of the amide groups are involved in hydrogen bonding, which is known to affect the quadrupole coupling constant. In order to account for these complications in simulating the spectra in the fast motional regime, an ab initio program called Gaussian 90 was employed, which permitted us to calculate, by quantum mechanical means, the complete electric field gradient tensor for each residue in gramicidin (using two structural models). Our results indicated that the left-handed helical models were inconsistent with our observed spectra, whereas a model based on the high-resolution structure derived by Arseniev and coworkers, but relaxed by a simple energy minimization procedure, was consistent with our observed spectra. The molecular order parameter was then estimated from the motional narrowing assuming the relaxed (right-handed) Arseniev structure. Our resultant order parameter of SZZ = 0.91 translates into an rms angle of 14 degrees, formed by the helix axis and the local bilayer normal. The strong resemblance between our spectra (and also those reported for gramicidin in 1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine (DPPC) multilayers) and the spectra of the same peptide incorporated in a lyotropic nematic phase, suggests that the lyotropic nematic phase simulates the local environment of the lipid bilayer.     

The ontogenetic complexity of developmental constraints

Developmental constraint is a theoretically important construct bridging ontogenetic and evolutionary studies. We propose a new operationalization of this notion that exploits the unusually rich measurement structure of landmark data. We represent landmark configurations by their partial warps, a basis for morphospace that represents a set of localized features of form. A finding of developmental constraint arises from the interplay between age-varying means and age-specific variances in these subspaces of morphospace. Examination of variances and means in 16 ventral skull landmarks in the cotton rat S. fulviventer at ages 1, 10, 20, and 30 days yielded three types of developmental constraint: canalization (constraint to relatively constant form age by age); chreods (reduction of variance orthogonal to the mean trajectory over ages); and opposition (reduction of age-specific variance along the mean trajectory over ages). While canalization and chreodic constraints have been noted previously, the oppositional type of constraint appears novel. Only one of our characters, relative length and orientation of the incisive foramen, appears to be canalized. Although skull growth becomes increasingly integrated through ontogeny, our characters display a remarkable spatiotemporal complexity in patterns of variance reduction. The specific assortment of constraints observed may be related to the precociality of Sigmodon. We suggest that Waddington's diagrammatic presentation of the “epigenetic landscape” may be misleading in quantitative studies of developmental regulation.     

Gramicidin cation channel: an experimental determination of the right-handed helix sense and verification of beta-type hydrogen bonding

Due to the difficulty of obtaining protein/lipid cocrystals for diffraction studies, structural research on intrinsic membrane proteins and polypeptides has been largely restricted to indirect experimental techniques. Hence, many fundamental questions associated with peptide/lipid systems remain unanswered. In particular, the handedness of the gramicidin A transmembrane ion channel incorporated into lipid bilayers has been an open question for nearly two decades. In this study, solid-state 15N NMR spectroscopy is employed to probe directly the secondary structure of the polypeptide backbone. Recent determinations of the 15N chemical shift anisotropy tensor with respect to the molecular frame enable the quantitative evaluation of the 15N chemical shift resonances obtained from oriented dimyristoylphosphatidylcholine (DMPC) bilayer samples containing specific site 15N labeled gramicidin. This direct structural approach verifies the beta-sheet hydrogen-bonding pattern proposed by Urry [Urry, D. W. (1971) Proc. Natl. Acad. Sci. U.S.A. 68, 672-676] and determines that in our DMPC bilayer preparations the gramicidin channel is right-handed. Additional structural information is provided by the 15N chemical shift data in the form of orientational constraints on the C alpha-C alpha axis orientation of individual peptides relative to the helix axis. The significance of these solid-state NMR results lies in the direct determination of the helix sense and the verification of the beta-type hydrogen bonding, in the development of the solid-state NMR methods for obtaining such information, and in emphasizing the importance of having direct structural data at atomic resolution.     

Relationship between protein structure and geometrical constraints.

We evaluate to what extent the structure of proteins can be deduced from incomplete knowledge of disulfide bridges, surface assignments, secondary structure assignments, and additional distance constraints. A cost function taking such constraints into account was used to obtain protein structures using a simple minimization algorithm. For small proteins, the approximate structure could be obtained using one additional distance constraint for each amino acid in the protein. We also studied the effect of using predicted secondary structure and surface assignments. The constraints used in this approach typically may be obtained from low-resolution experimental data. When using a cost function based on distances, half of the resulting structures will be mirrored, because the resulting structure and its mirror image will have the same cost. The secondary structure assignments were therefore divided into chirality constraints and distance constraints. Here we report that the problem of mirrored structures, in some cases, can be solved by using a chirality term in the cost function.     

The importance of energetic versus pelvic constraints on reproductive allocation by the eastern fence lizard (Sceloporus undulatus)

In ectothermic species, females often produce larger eggs in colder environments. Models based on energetic constraints suggest that this pattern is an adaptation to compensate for the slower growth of offspring in the cold. Yet, females in cold environments also tend to be larger than females in warm environments. Consequently, thermal clines in egg size could be caused by pelvic constraints, which stem from the inability of large eggs to pass through a small pelvic aperture. Models based on energetic constraints and models based on pelvic constraints predict similar relationships between maternal size and egg size. However, pelvic constraints should produce these relationships both within and among populations, whereas energetic constraints would not necessarily do so. If pelvic constraints are important, we might also expect small females to compensate by producing eggs that are relatively rich in lipids (i.e. high energy density). The present study aimed to assess whether energetic or pelvic constraints generate geographical variation in egg size of the lizard Sceloporus undulatus . Pelvic width is very highly correlated with body length in S. undulatus , making maternal size a suitable measure of pelvic constraint. Although maternal size and egg mass (dry and wet) covaried among populations, these variables were generally not related within populations. Energetic density of eggs tended to increase with decreasing egg mass (dry and wet), but this relationship was strongest in populations where no relationship between maternal size and egg mass was observed. Our results do not support the pelvic constraint model and thus indicate energetic constraints play a greater role in generating geographical variation in egg size.  © 2007 The Linnean Society of London, Biological Journal of the Linnean Society , 2007, 91 , 513–521.     

基于酶约束的代谢网络模型研究进展及其应用

基因组尺度代谢网络模型已经成功地应用于指导代谢工程改造,但由于传统通量平衡分析法仅考虑化学计量学和反应方向约束,模拟得到的是理论最优结果,对一些现象如代谢溢流、底物层级利用等无法准确描述。近年来人们通过在代谢网络模型中引入新的蛋白量、热力学等约束发展了新的约束优化计算方法,可以更准确真实地模拟细胞在不同条件下的代谢行为。文中主要对近年来提出的多种酶约束模型进行评述,对酶约束引入的基本思路、酶约束的数学方程表示及优化目标设定、引入酶约束后对代谢通量计算结果的影响及酶约束模型在代谢工程菌种改造中的应用等进行了全面深入的介绍,并提出了已有各种方法存在的主要问题,展望了相关方法的未来发展方向。通过引入新的约束,代谢网络模型能够更精确模拟和预测细胞在环境和基因扰动下的代谢行为,为代谢工程菌种改造提供更准确可靠的指导。     

Phenotypic plasticity and optimal timing of metamorphosis under uncertain time constraints

Life-history theory suggests that optimal timing of metamorphosis should depend on growth conditions and time constraints under which individuals develop. Current models cannot make reliable predictions for species in ephemeral habitats where individuals often face an increasing mortality risk over time because these models assume time-invariant mortality rates (i.e., daily mortality rates remain constant) and fixed seasons. We examined the plasticity of growth, development, and body mass at metamorphosis in tadpoles of the tree-hole breeding frog Phrynobatrachus guineensis in relation to an unpredictable time constraint in the field and in controlled experiments along a fixed density and food gradient. Mean mass and age at metamorphosis of sibships were positively correlated with per capita food level. Based on our results, we developed a simple model of the optimal timing of metamorphosis under time-dependent mortality rates showing that development rates are not only adjusted to growth conditions but also to time-variant mortality rates. The increasing mortality rate represents a time constraint that favors a reduced larval period, but because it is based on probabilities of survival it allows a trade-off between development time and mass. We extend this model to different types of time constraints and show that it can predict the range of documented reaction norms. Differences between species in␣the correlation of age and mass at metamorphosis may have evolved due to differences in their time-variant mortality rates.     

13C solid-state NMR of gramicidin A in a lipid membrane.

The natural-abundance 13C NMR spectrum of gramicidin A in a lipid membrane was acquired under magic-angle spinning conditions. With fast sample spinning (15 kHz) at approximately 65 degrees C the peaks from several of the aliphatic, beta-, alpha-, aromatic, and carbonyl carbons in the peptide could be resolved. The resolution in the 13C spectrum was superior that observed with 1H NMR under similar conditions. The 13C linewidths were in the range 30-100 Hz, except for the alpha- and beta-carbons, the widths of which were approximately 350 Hz. The beta-sheet-like local structure of gramicidin A was observed as an upfield shift of the gramicidin alpha and carbonyl resonances. Under slow sample spinning (500 Hz), the intensity of the spinning sidebands from 13C in the backbone carbonyls was used to determine the residual chemical shift tensor. As expected, the elements of the residual chemical shift tensor were consistent with the single-stranded, right-handed beta6.3 helix structure proposed for gramicidin A in lipid membranes.     

Analysis of affected sib pairs, with covariates--with and without constraints

Covariate models have previously been developed as an extension to affected-sib-pair methods in which the covariate effects are jointly estimated with the degree of excess allele sharing. These models can estimate the differences in sib-pair allele sharing that are associated with measurable environment or genes. When there are no covariates, the pattern of identical-by-descent allele sharing in affected sib pairs is expected to fall within a small triangular region of the potential parameter space, under most genetic models. By restriction of the estimated allele sharing to this triangle, improved power is obtained in tests for genetic linkage. When the affected-sib-pair model is generalized to allow for covariates that affect allele sharing, however, new constraints and new methods for the application of constraints are required. Three generalized constraint methods are proposed and evaluated by use of simulated data. The results compare the power of the different methods, with and without covariates, for a single-gene model with age-dependent onset and for quantitative and qualitative gene-environment and gene-gene interaction models. Covariates can improve the power to detect linkage and can be particularly valuable when there are qualitative gene-environment interactions. In most situations, the best strategy is to assume that there is no dominance variance and to obtain constrained estimates for covariate models under this assumption.     

Genotype networks shed light on evolutionary constraints

An evolutionary constraint is a bias or limitation in phenotypic variation that a biological system produces. One can distinguish physicochemical, selective, genetic and developmental causes of such constraints. Here, I discuss these causes in three classes of system that bring forth many phenotypic traits and evolutionary innovations: regulatory circuits, macromolecules and metabolic networks. In these systems, genotypes with the same phenotype form large genotype networks that extend throughout a vast genotype space. Such genotype networks can help unify different causes of evolutionary constraints. They can show that these causes ultimately emerge from the process of development; that is, how phenotypes form from genotypes. Furthermore, they can explain important consequences of constraints, such as punctuated stasis and canalization.     

Improving fold recognition of protein threading by experimental distance constraints

We present a comprehensive analysis of methods for improving the fold recognition rate of the threading approach to protein structure prediction by the utilization of few additional distance constraints. The distance constraints between protein residues may be obtained by experiments such as mass spectrometry or NMR spectroscopy. We applied a post-filtering step with new scoring functions incorporating measures of constraint satisfaction to ranking lists of 123D threading alignments. The detailed analysis of the results on a small representative benchmark set show that the fold recognition rate can be improved significantly by up to 30% from about 54%-65% to 77%-84%, approaching the maximal attainable performance of 90% estimated by structural superposition alignments. This gain in performance adds about 10% to the recognition rate already achieved in our previous study with cross-link constraints only. Additional recent results on a larger benchmark set involving a confidence function for threading predictions also indicate notable improvements by our combined approach, which should be particularly valuable for rapid structure determination and validation of protein models.     

Solution structure of [d(GTATATAC)]2 via restrained molecular dynamics simulations with nuclear magnetic resonance constraints derived from relaxation matrix analysis of two-dimensional nuclear Overhauser effect experiments

Two-dimensional nuclear Overhauser effect (2D NOE) spectra have been used as the experimental basis for determining the solution structure of the duplex [d(GTATATAC)]2 employing restrained molecular dynamics (rMD) simulations. The MARDIGRAS algorithm has been employed to construct a set of 233 interproton distance constraints via iterative complete relaxation matrix analysis utilizing the peak intensities from the 2D NOE spectra obtained for different mixing times and model structures. The upper and lower bounds for each of the constraints, defining size of a flat-well potential function term used in the rMD simulations, were conservatively chosen as the largest or smallest value calculated by MARDIGRAS. Three different starting models were utilized in several rMD calculations: energy-minimized A-DNA, B-DNA, and a structure containing wrinkled D-DNA in the interior. Considerable effort was made to define the appropriate force constants to be employed with the NOE terms in the AMBER force field, using as criteria the average constraints deviation, the constraints violation energy and the total energy. Of the 233 constraints, one was generated indirectly, but proved to be crucial in defining the structure: the cross-strand A5-H2 A5-H2 distance. As those two protons resonate isochronously for the self-complementary duplex, the distance cannot be determined directly. However, the general pattern of 2D NOE peak intensities, spin-lattice relaxation time (T1) values, and 31P nuclear magnetic resonance spectra lead to use of the A3-H2 A7-H2 distance for A5-H2 A5-H2 as well. Five rMD runs, with different random number seeds, were made for each of the three starting structures with the full distance constraint set. The average structure from all 15 runs and the five-structure averages from each starting structure were all quite similar. Two rMD runs for each starting structure were made with the A5-H2 A5-H2 constraint missing. The average of these six rMD runs revealed differences in structure, compared to that with the full set of constraints, primarily for the middle two base-pairs involving the missing cross-strand constraint but global deviations also were found. Conformational analysis of the resulting structures revealed that the inner four to six base-pairs differed in structure from the termini. Furthermore, an alternating structure was suggested with features alternating for the A-T and T-A steps.     

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.     

Sport science for salmon and other species: ecological consequences of metabolic power constraints

For metabolically demanding behaviours, power supply (ATP resynthesis per unit time) is an important constraint on performance. Yet ecology as a discipline lacks a framework to account for these power constraints. We developed such a framework (borrowing concepts from sports science) and applied it to the upriver migration of anadromous fish. Our models demonstrate how metabolic power constraints alters optimal migratory behaviour; in response to strong counter flows, fish minimise cost of transport by alternating between rapid, anaerobically fuelled swimming and holding to restore spent fuels. Models ignoring power constraints underestimated the effect of elevated water temperature on migration speed and costs (by up to 60%). These differences were primarily due to a temperature‐mediated reduction in aerobic scope that impairs the ability of fish to rapidly migrate through warm waters. Our framework provides a mechanistic link between temperature‐induced reductions in aerobic scope and their ecological consequences for individuals, populations and communities.