Diffusion-Collision Model for the Folding Kinetics of the λ-Repressor Operator-Binding Domain

Abstract

The operator-binding domain of the λ-repressor contains five α-helices and an extended N-terminal arm in the crystal structure determined by Pabo and Lewis reported in Nature 298, 443,1982 (1). The four helices form a “box” enclosing a hydrophobic core, with the fifth helix interacting with the equivalent helix in a dimer. With a small number of well-defined secondary structure elements (microdomains), the repressor is well suited for an analysis of its folding pathways and kinetics by use of the diffusion-collision model. In this paper, the basic elements of the model appropriate to a several microdomain protein are formulated and applied to a set of folding pathways consistent with the crystal structure of the operator- binding domain. The overall kinetics, as well as the time-dependence of intermediate states are determined as a function of the microdomain stability parameter.     

Role of conformational heterogeneity in domain swapping and adapter function of the Cks proteins

Cks proteins are adapter molecules that coordinate the assembly of multiprotein complexes. They share the ability to domain swap by exchanging a beta-strand, beta4. Here we use NMR spectroscopy and molecular dynamics simulations to investigate the dynamic properties of human Cks1 and its response on assembly with components of the SCF(Skp2) ubiquitin ligation machinery. In the NMR experiment with the free form of Cks1, a subset of residues displayed elevated R2 values and the cross-peaks of neighboring residues were missing from the spectrum, indicating a substantial conformational exchange contribution on the microsecond to millisecond time scale. Strikingly the region of greatest conformational variability was the beta4-strand that domain swaps to form the dimer. Binding of the ligand common to all Cks proteins, Cdk2, suppressed the conformational heterogeneity. This response was specific to Cdk2 binding; in contrast, binding of Skp2, a ligand unique to human Cks1, did not alter the dynamic behavior. Short time (<5 ns) molecular dynamics simulations indicate that residues of Cks1 that form the binding site for phosphorylated ligands are considerably more flexible in the free form of Cks1 than they are in the Cdk2-Cks1 complex. A cooperative interaction between Cdk2 and Cks1 is suggested, which reduces the configurational entropy of Cks1 and therefore facilitates phosphoprotein binding. Indications of an unusual dynamic behavior of strand beta4 in the free form of Cks1 were obtained from longer time scale (50 ns) dynamics simulations. A spontaneous reversible unzipping of hydrogen bonds between beta4 and beta2 was observed, suggesting an early intermediate structure for unfolding and/or domain swapping. We propose that the dynamic properties of the beta-sheet and its modification upon ligand binding underlie the domain swapping ability and the adapter function of Cks proteins.     

Solvent mobility and the protein 'glass' transition

Proteins and other biomolecules undergo a dynamic transition near 200 K to a glass-like solid state with small atomic fluctuations. This dynamic transition can inhibit biological function. To provide a deeper understanding of the relative importance of solvent mobility and the intrinsic protein energy surface in the transition, a novel molecular dynamics simulation procedure with the protein and solvent at different temperatures has been used. Solvent mobility is shown to be the dominant factor in determining the atomic fluctuations above 180 K, although intrinsic protein effects become important at lower temperatures. The simulations thus complement experimental studies by demonstrating the essential role of solvent in controlling functionally important protein fluctuations.     

A homolog of mammalian antizyme is present in fission yeast Schizosaccharomyces pombe but not detected in budding yeast Saccharomyces cerevisiae

MOTIVATION: The antizymes (AZ) are proteins that regulate cellular polyamine pools in metazoa. To search for remote homologs in single-celled eukaryotes, we used computer software based on hidden Markov models. The most divergent homolog detected was that of the fission yeast Schizosaccharomyces pombe. Sequence identities between S.POMBE: AZ and known AZs are as low as 18-22% in the most conserved C-terminal regions. The authenticity of the S.POMBE: AZ is validated by the presence of a conserved nucleotide sequence that, in metazoa, promotes a +1 programmed ribosomal frameshift required for AZ expression. However, no homolog was detected in the completed genome of the budding yeast Saccharomyces cerevisiae. Procedural details and supplementary information can be found at http://itsa.ucsf.edu/ approximately czhu/AZ.     

Calibrating E-values for hidden Markov models using reverse-sequence null models

MOTIVATION: Hidden Markov models (HMMs) calculate the probability that a sequence was generated by a given model. Log-odds scoring provides a context for evaluating this probability, by considering it in relation to a null hypothesis. We have found that using a reverse-sequence null model effectively removes biases owing to sequence length and composition and reduces the number of false positives in a database search. Any scoring system is an arbitrary measure of the quality of database matches. Significance estimates of scores are essential, because they eliminate model- and method-dependent scaling factors, and because they quantify the importance of each match. Accurate computation of the significance of reverse-sequence null model scores presents a problem, because the scores do not fit the extreme-value (Gumbel) distribution commonly used to estimate HMM scores' significance. RESULTS: To get a better estimate of the significance of reverse-sequence null model scores, we derive a theoretical distribution based on the assumption of a Gumbel distribution for raw HMM scores and compare estimates based on this and other distribution families. We derive estimation methods for the parameters of the distributions based on maximum likelihood and on moment matching (least-squares fit for Student's t-distribution). We evaluate the modeled distributions of scores, based on how well they fit the tail of the observed distribution for data not used in the fitting and on the effects of the improved E-values on our HMM-based fold-recognition methods. The theoretical distribution provides some improvement in fitting the tail and in providing fewer false positives in the fold-recognition test. An ad hoc distribution based on assuming a stretched exponential tail does an even better job. The use of Student's t to model the distribution fits well in the middle of the distribution, but provides too heavy a tail. The moment-matching methods fit the tails better than maximum-likelihood methods. AVAILABILITY: Information on obtaining the SAM program suite (free for academic use), as well as a server interface, is available at http://www.soe.ucsc.edu/research/compbio/sam.html and the open-source random sequence generator with varying compositional biases is available at http://www.soe.ucsc.edu/research/compbio/gen_sequence     

Glycogen phosphorylase inhibitors: a free energy perturbation analysis of glucopyranose spirohydantoin analogues

GP catalyzes the phosphorylation of glycogen to Glc-1-P. Because of its fundamental role in the metabolism of glycogen, GP has been the target for a systematic structure-assisted design of inhibitory compounds, which could be of value in the therapeutic treatment of type 2 diabetes mellitus. The most potent catalytic-site inhibitor of GP identified to date is spirohydantoin of glucopyranose (hydan). In this work, we employ MD free energy simulations to calculate the relative binding affinities for GP of hydan and two spirohydantoin analogues, methyl-hydan and n-hydan, in which a hydrogen atom is replaced by a methyl- or amino group, respectively. The results are compared with the experimental relative affinities of these ligands, estimated by kinetic measurements of the ligand inhibition constants. The calculated binding affinity for methyl-hydan (relative to hydan) is 3.75 +/- 1.4 kcal/mol, in excellent agreement with the experimental value (3.6 +/- 0.2 kcal/mol). For n-hydan, the calculated value is 1.0 +/- 1.1 kcal/mol, somewhat smaller than the experimental result (2.3 +/- 0.1 kcal/mol). A free energy decomposition analysis shows that hydan makes optimum interactions with protein residues and specific water molecules in the catalytic site. In the other two ligands, structural perturbations of the active site by the additional methyl- or amino group reduce the corresponding binding affinities. The computed binding free energies are sensitive to the preference of a specific water molecule for two well-defined positions in the catalytic site. The behavior of this water is analyzed in detail, and the free energy profile for the translocation of the water between the two positions is evaluated. The results provide insights into the role of water molecules in modulating ligand binding affinities. A comparison of the interactions between a set of ligands and their surrounding groups in X-ray structures is often used in the interpretation of binding free energy differences and in guiding the design of new ligands. For the systems in this work, such an approach fails to estimate the order of relative binding strengths, in contrast to the rigorous free energy treatment.     

SPrCY: comparison of structural predictions in the Saccharomyces cerevisiae genome

SUMMARY: SPrCY is a web-accessible database which provides comparison of structure prediction results for the Saccharomyces cerevisiae genome. This web service offers the ability to search, analyze and compare the yeast structural predictions from sequence-only (Superfamily, PDBAA BLAST and Pfam) and sequence-structure-based (SAM-T02, 3D-PSSM, mGenTHREADER) methods. AVAILABILITY: The service is freely available via web at http://agave.wustl.edu/yeast/     

Why protein R-factors are so large: a self-consistent analysis

The R-factor and R-free are commonly used to measure the quality of protein models obtained in X-ray crystallography. Well-refined protein structures usually have R-factors in the range of 20-25%, whereas intrinsic errors in the experimental data are usually around 5%. We use molecular dynamics simulations to perform a self-consistent analysis by which we determine the major factors contributing to large values of protein R-factors. The analysis shows that significant R-factor values can arise from the use of isotropic B-factors to model anisotropic protein motions and from coordinate errors. Even in the absence of coordinate errors, the use of isotropic B-factors can cause the R-factors to be around 10%; for coordinate errors smaller than 0.2 A, the two errors types make similar contributions. The inaccuracy of the energy function used and multistate protein dynamics are unlikely to make significant contributions to the large R-factors.