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Identifying biologically active compound classes using phenotypic screening data and sampling statistics.

Scoring the activity of compounds in phenotypic high-throughput assays presents a unique challenge because of the limited resolution and inherent measurement error of these assays. Techniques that leverage the structural similarity of compounds within an assay can be used to improve the hit-recovery rate from screening data. A technique is presented that uses clustering and sampling statistics to predict likely compound activity by scoring entire structural classes. A set of phenotypic assays performed against a commercially available compound library was used as a test set. Using the class-scoring technique, the resultant activity prediction scores were more reproducible than individual assay measurements, and class scoring recovered known active compounds more efficiently than individual assay measurements because class scoring had fewer false positives. Known biologically active compounds were recovered 87% of the time using class scores, suggesting a low false-negative rate that compared well to individual assay measurements. In addition, many weak and potentially novel classes of active compounds, overlooked by individual assay measurements, were suggested.

Actins↗

Differences in nocturnal basal and rhythmic prolactin secretion in untreated compared to treated HIV-infected men are associated with CD4+ T-lymphocytes.

The existence of decreased hypothalamic dopaminergic tone in HIV-infected men has been suggested. In a cross-sectional study, we determined 12 h nocturnal basal and pulsatile prolactin (PRL) release levels (by blood sampling every 10 min) and their correlation with CD4+ T cells in seven volunteer HIV-negative, healthy men (group 1), and 21 normoprolactinemic, euthyroid, HIV-infected men divided into 3 groups (each group = 7): (i) group 2, asymptomatic HIV-infected stage A1 men, untreated; (ii) group 3, AIDS stage C3 without active opportunistic infections, untreated; and (iii) group 4, previously stage C3 after at least 6 months of successful highly active antiretroviral therapy. Serum PRL was measured by radioimmunoanalysis and the results were analysed by waveform-independent deconvolution analysis. CD4+ T lymphocytes were measured by flow cytometry and viral load by a nucleic acid sequence-based amplification assay. No differences were detected in the first two groups. In the third group, however, 100% of prolactin secretion was found to be pulsatile with a shorter secretory burst duration (P = 0.04), and a greater circulating half-life and pulse amplitude (P < or = 0.04). Group 4 had the greatest basal prolactin secretion (P < or = 0.04), and a shorter secretory burst duration (P = 0.04 vs group 2), circulating half-life (P = 0.01 vs group 3) and intersecretory burst interval (P = 0.06 vs group 1). PRL approximate entropy was similar among all groups. Linear correlations existed between CD4+ T cell counts and PRL secretory burst half duration (r = 0.62, P = 0.002) and amplitude (r = -0.63, P = 0.001), and in circulating serum half-life (r = - 0.61, P = 0.002) in HIV-infected groups. Viral load showed no correlations. It is suggested that differential changes in nocturnal prolactin secretion among HIV-infected men occurred while maintaining the normal coordinate feedback and/or feedforward control within the lactotropic axis. These changes may represent an adaptative mechanism to sustain, by different means, the maximal physiologic PRL production to stimulate the highest cellular immune response and/or reconstitution in attempting to survive.

Adult↗

The effect of single-nucleotide polymorphism marker selection on patterns of haplotype blocks and haplotype frequency estimates.

The definition of haplotype blocks of single-nucleotide polymorphisms (SNPs) has been proposed so that the haplotypes can be used as markers in association studies and to efficiently describe human genetic variation. The International Haplotype Map (HapMap) project to construct a comprehensive catalog of haplotypic variation in humans is underway. However, a number of factors have already been shown to influence the definition of blocks, including the population studied and the sample SNP density. Here, we examine the effect that marker selection has on the definition of blocks and the pattern of haplotypes by using comparable but complementary SNP sets and a number of block definition methods in various genomic regions and populations that were provided by the Encyclopedia of DNA Elements (ENCODE) project. We find that the chosen SNP set has a profound effect on the block-covered sequence and block borders, even at high marker densities. Our results question the very concept of discrete haplotype blocks and the possibility of generalizing block findings from the HapMap project. We comparatively apply the block-free tagging-SNP approach and discuss both the haplotype approach and the tagging-SNP approach as means to efficiently catalog genetic variation.

Algorithms↗

Interacting damage models mapped onto Ising and percolation models.

We introduce a class of damage models on regular lattices with isotropic interactions between the broken cells of the lattice. Quasi-static fiber bundles are an example. The interactions are assumed to be weak, in the sense that the stress perturbation from a broken cell is much smaller than the mean stress in the system. The system starts intact with a surface-energy threshold required to break any cell sampled from an uncorrelated quenched-disorder distribution. The evolution of this heterogeneous system is ruled by Griffith's principle which states that a cell breaks when the release in potential (elastic) energy in the system exceeds the surface-energy barrier necessary to break the cell. By direct integration over all possible realizations of the quenched disorder, we obtain the probability distribution of each damage configuration at any level of the imposed external deformation. We demonstrate an isomorphism between the distributions so obtained and standard generalized Ising models, in which the coupling constants and effective temperature in the Ising model are functions of the nature of the quenched-disorder distribution and the extent of accumulated damage. In particular, we show that damage models with global load sharing are isomorphic to standard percolation theory and that damage models with a local load sharing rule are isomorphic to the standard Ising model, and draw consequences thereof for the universality class and behavior of the autocorrelation length of the breakdown transitions corresponding to these models. We also treat damage models having more general power-law interactions, and classify the breakdown process as a function of the power-law interaction exponent. Last, we also show that the probability distribution over configurations is a maximum of Shannon's entropy under some specific constraints related to the energetic balance of the fracture process, which firmly relates this type of quenched-disorder based damage model to standard statistical mechanics.

Journal Article↗

Alterations in cortisol secretory dynamics in adolescent girls with anorexia nervosa and effects on bone metabolism.

Anorexia nervosa (AN) is associated with low bone density in adolescents and adults. Hypercortisolemia has been reported in adults with this disorder and has been hypothesized to be a factor in bone loss. However, the secretory dynamics of cortisol in adolescents with AN and the contribution of alterations in cortisol secretion to bone metabolism in AN have not been examined. We examined the dynamics of cortisol secretion by Cluster and deconvolutional analysis in 23 girls with AN and 21 healthy adolescents of comparable age and maturity. Cortisol sampling was performed every 30 min for 12 h overnight. Twenty-four-hour urinary free cortisol (UFC) and creatinine (cr) were obtained for all subjects. The surface area (SA) of the subjects was calculated. Markers of bone turnover (type 1 procollagen, osteocalcin, and N-telopeptide) were examined. Subjects with AN were prospectively followed over 1 yr, and those who recovered weight (defined as a 10% increase in body mass index) were again studied. On Cluster analysis, girls with AN had significantly higher mean cortisol (8.6 +/- 2.0 vs. 5.9 +/- 1.1 microg/dl; P < 0.0001), nadir cortisol (5.5 +/- 2.3 vs. 3.4 +/- 1.2 microg/dl; P = 0.0008), valley mean cortisol (7.0 +/- 2.7 vs. 4.7 +/- 1.5 microg/dl; P = 0.001), peak amplitude (12.6 +/- 4.4 vs. 7.8 +/- 3.0 microg/dl; P = 0.0004), peak area (652 +/- 501 vs. 340 +/- 238 microg/dl; P = 0.02), and total area under the curve (6112 +/- 1467 vs. 4117 +/- 802 microg/dl; P < 0.0001) than healthy adolescents. On deconvolutional analysis, the frequency of nocturnal secretory bursts (7.0 +/- 1.2 vs. 5.8 +/- 1.3 /12 h; P = 0.001), total nocturnal pulsatile cortisol secretion (69.3 +/- 14.7 vs. 53.9 +/- 11.1 microg/dl; P = 0.0003), and total cortisol secretion (89.6 +/- 18.8 vs. 71.2 +/- 17.6 microg/dl; P = 0.002) were significantly higher in girls with AN than in healthy controls. Cortisol half-life trended higher in girls with AN. However, basal cortisol secretion and approximate entropy did not differ between the groups. UFC/cr and UFC/cr.SA were significantly higher in girls with AN than in controls [0.050 +/- 0.028 vs. 0.036 +/- 0.017 (P = 0.04) and 0.035 +/- 0.020 vs. 0.023 +/- 0.012 (P = 0.03)]. Six of 23 girls with AN had UFC/cr.SA values that were more than 2 sd above those in healthy controls. An inverse correlation was noted between measures of cortisol concentration as well as pulsatile secretion and measures of nutritional status (body mass index, fat mass, leptin, insulin, and IGF-I). An oral glucose load suppressed cortisol levels in healthy adolescents, but not in AN patients. Weight recovery was associated with a significant decrease in the number of secretory bursts. In girls with AN, strong inverse correlations were noted between levels of cortisol (mean, nadir, and total area under the curve) and levels of markers of bone formation (C-terminal propeptide of type 1 procollagen and osteocalcin). Conversely, in healthy controls, cortisol values did not predict levels of markers of bone turnover. Adolescent girls with AN have significantly higher serum cortisol concentrations and UFC/cr.SA values than healthy adolescents. This increased cortisol concentration is a function of increased frequency of secretory bursts, resulting in increased pulsatile secretion. Hypercortisolemia appears to be a direct consequence of undernutrition and is associated with a decrease in markers of bone formation. Therefore, high cortisol values in AN may contribute to the low bone density observed in adolescents with this disorder by decreasing bone formation.

Adolescent↗

Incorporating protein conformational flexibility into the calculation of pH-dependent protein properties.

A method for combining calculations of residue pKa's with changes in the position of polar hydrogens has been developed. The Boltzmann distributions of proton positions in hydroxyls and neutral titratable residues are found in the same Monte Carlo sampling procedure that determines the amino acid ionization states at each pH. Electrostatic, Lennard-Jones potentials, and torsion angle energies are considered at each proton position. Many acidic and basic residues are found to have significant electrostatic interactions with either a water- or hydroxyl-containing side chain. Protonation state changes are coupled to reorientation of the neighboring hydroxyl dipoles, resulting in smaller free energy differences between neutral and ionized residues than when the protein is held rigid. Multiconformation pH titration gives better agreement with the experimental pKa's for triclinic hen egg lysozyme than conventional rigid protein calculations. The hydroxyl motion significantly increases the protein dielectric response, making it sensitive to the composition of the local protein structure. More than one conformer per residue is often found at a given pH, providing information about the distribution of low-energy lysozyme structures.

Entropy↗

Towards accurate ab initio QM/MM calculations of free-energy profiles of enzymatic reactions.

Reliable studies of enzymatic reactions by combined quantum mechanical/molecular mechanics (QM/MM) approaches, with an ab initio description of the quantum region, presents a major challenge to computational chemists. The main problem is the need for a large amount of computer time to evaluate the QM energy, which in turn makes it extremely challenging to perform proper configurational sampling. This work presents major progress toward the evaluation of ab initio QM/MM free-energy surfaces and activation free energies of reactions in enzymes and in solutions. This is done by exploiting our previous idea of using the empirical valence bond (EVB) method as a reference potential and then using the linear response approximation (LRA) approach to evaluate the free energies of transfer from the EVB to the QM/MM surfaces in the reactant and product state. However, the new crucial step involves the use of a constraint at the transition state that fixes the system at a given value of the reaction coordinate and allows us to use the LRA at the transition state. The advance offered by the present approach is particularly significant because it evaluates the free energy associated with both the substrate and the solvent motions. This evaluation appeared to be a relatively simple task once one uses a classical reference potential. The main problem has been using the reference potential for the evaluation of the free-energy contributions associated with the solute motions where the difference between the reference EVB potential and the QM/MM potential can be large. The present refinement finally allows us to overcome the problems with the solute fluctuations and therefore to obtain, for the first time, a free-energy barrier that reflects the solute entropy properly. Thus, we present a way to evaluate the complete QM/MM activation free energy with an equal footing treatment of the solute and the solvent. This provides a general consistent and effective strategy for evaluating the QM/MM activation free energies in proteins and in solution. Our advance allows one to explore consistently various mechanistic and catalytic proposals while using ab initio (ai) QM/MM approaches.

Computer Simulation↗

Impact of pulsatility on the ensemble orderliness (approximate entropy) of neurohormone secretion.

Regular patterns of neurohormone secretion are driven by underlying pulsatile and subordinate (feedback sensitive) dynamics. Measures of time-series orderliness, e.g., the approximate entropy (ApEn) statistic (Pincus SM. Proc Natl Acad Sci 88: 2297-2301, 1991), vividly discriminate pathological and physiological patterns of hormone release. To investigate how specific pulsatility features impact regularity estimates, we have examined the sensitivity of the ApEn metric to systematic variations in the frequency, amplitude, and half-life of simulated neurohormone pulse trains (Veldhuis JD, Carlson ML, and Johnson ML. Proc Natl Acad Sci 84: 7686-7690, 1987) and compared the impact of a high vs. low baseline luteinizing hormone (LH) pattern regularity state mimicking the normal female luteal phase and the young male, respectively. Shortening the interpulse interval length elevated ApEn in both pulsatility models, thereby signifying greater ensemble series irregularity. The frequency sensitivity of ApEn was robust to several complementary renditions of ApEn and to variations in experimental uncertainty, basal (nonpulsatile) LH secretion, and secretory burst amplitude. ApEn rose with increasing hormone half-life, especially in the face of low baseline variability emulated by midluteal LH secretion profiles. High variability of secretory burst amplitude, pulse duration, or interpeak intervals increased ApEn in the more orderly femalelike construct; in the highly irregular malelike LH pulse model, these variability changes had little effect on ApEn. In summary, the ensemble regularity statistic, ApEn, quantifies unequal pattern orderliness in neurohormone pulse trains with minimal dependence on mean pulse amplitude, interpulse baseline, or (subthreshold) sample uncertainty. Thus ApEn monitors changing secretory event frequency and interpulse variability with sensitivity to starting pattern regularity, providing a mechanistic linkage between model evolution and statistical change.

Female↗

Computer simulation of the free energy of peptides with the local states method: analogues of gonadotropin releasing hormone in the random coil and stable states.

The Helmholtz free energy F (rather than the energy) is the correct criterion for stability; therefore, calculation of F is important for peptides and proteins that can populate a large number of metastable states. The local states (LS) method proposed by H. Meirovitch [(1977) Chemical Physics Letters, Vol. 45, p. 389] enables one to obtain upper and lower bounds of the conformational free energy, FB (b,l) and FA (b,l), respectively, from molecular dynamics (MD) or Monte Carlo samples. The correlation parameter b is the number of consecutive dihedral or valence angles along the chain that are taken into account explicitly. The continuum angles are approximated by a discretization parameter l; the larger are b and l, the better the approximations; while FA can be estimated efficiently, it is more difficult to estimate FB. The method is further developed here by applying it to MD trajectories of a relatively large molecule (188 atoms), the potent "Asp4-Dpr10" antagonist [cyclo(4/10)-(Ac-delta 3Pro1-D-pFPhe2-D-Trp3-Asp4-Tyr5-D-Nal6-Leu7-Arg8 -Pro9- Dpr10-NH2)] of gonadotropin releasing hormone (GnRH). The molecule was simulated in vacuo at T = 300 K in two conformational states, previously investigated [J. Rizo et al. Journal of the American Chemical Society, (1992) Vol. 114, p. 2860], which differ by the orientation of the N-terminal tail, above (tail up, TU) and below (tail down, TD) the cyclic heptapeptide ring. As in previous applications of the LS method, we have found the following: (1) While FA is a crude approximation for the correct F, results for the difference, delta FA = FA (TD)-FA (TU) converge rapidly to 5.6 (1) kcal/mole as the approximation is improved (i.e., as b and l are increased), which suggests that this is the correct value for delta F; therefore TD is more stable than TU. (The corresponding difference in entropy, T delta SA = 1.3(2) kcal/mole, is equal to the value obtained by the harmonic approximation.) (2) The lowest approximation, which has the minimal number of local states, i.e., based on b = 0 (no correlations) and l = 1 (the angle values are distributed homogeneously), also leads to the correct value of delta F, within the error bars. This is important since the lowest approximation can be applied even to large proteins. (3) The method enables one to define the entropy of a part of the molecule and thus to measure the flexibility of this part.(ABSTRACT TRUNCATED AT 400 WORDS)

Amino Acid Sequence↗

Application of ab initio molecular dynamics for a priori elucidation of the mechanism in unimolecular decomposition: the case of 5-nitro-2,4-dihydro-3H-1,2,4-triazol-3-one (NTO).

We have tested a new and general approach for the theoretical study of unimolecular decomposition. By combining the power of the ab initio molecular dynamics (MD) and ab initio molecular orbital (MO) methods, our approach requires no prior experimental knowledge or intuitive assumptions about the decomposition. Instead, the reaction channels are first sampled theoretically by simulating a molecule at high temperature in a number of trajectories, using the density functional theory (DFT) based ab initio MD method with a planewave basis set and pseudopotentials. Each type of these channels is then further examined by well-established ab initio MO method to locate the energy barrier and transition structure and to verify the ab initio MD results. The power of such an approach is demonstrated in a case study for the complicated unimolecular thermal decomposition of NTO (5-nitro-2,4-dihydro-3H-1,2,4-triazol-3-one), with several interesting new features uncovered. The C-NO2 homolysis is indeed the dominant channel at high temperature, while the departing NO2 could capture a H atom from the NTO ring to form HONO, by either a concerted bond breaking mechanism or by a bimolecular reaction between the NO2 group and the triazol ring. At lower temperature, the dissociation channels initiated by hydrogen migrations should be activated first. The channel with hydrogen migration followed by ring opening and then by HONO loss has an energy barrier of 38.0 kcal/mol at the rate-determining step, being the lowest among all the investigated dissociation paths and much lower than previously thought. The energy barrier for nitro-nitrite rearrangement is lower than that for the C-NO2 homolysis but makes only a minor contribution due to the entropy factor. And the NTO ring could rupture in the two C-N bonds connected to the carbonyl carbon, and the energy barriers for such processes are only 2-4 kcal/mol higher than that for the C-NO2 homolysis.

Journal Article↗

Thermodynamics of native protein/foreign surface interactions. IV. Calorimetric and microelectrophoretic study of human fibrinogen sorption onto glass and LTI-carbon.

1. According to a working hypothesis put forward in the previous papers of this series2-4, the initial phases of native blood/foreign surface interactions have been considered within the framework of a physicochemical model of contact activation at the molecular level. The salient features of this hypothesis are: a) the arrival and adsorption of native plasma proteins on a contact surface overwhelmingly precedes that of the cellular blood components; b) the interaction energy that arises between a particular foreign surface and native plasma proteins settling on it, is a characteristic quantity depending upon the effective surface molecular structure as well as the nature of the proteins; c) the "intensity" of native protein/foreign surface interactions can be treated in terms of thermodynamic quantities since these energy terms are independent of the type of forces acting between protein and surface; and d) depending upon the degree to which the adsorption of a native protein is thermodynamically favored by enthalpy and/or entropy factors, the interaction energy can be utilized to induce conformational changes of varying degree in the sorbed protein. 2. Using glass and low temperature isotropic (LTI) carbon adsorbents, i.e., a known procoagulant and a relevant biomaterial, respectively, the adsorption properties and the potential surface-induced conformational changes of high-purity native human fibrinogen (clottability greater than or equal to 92%) were studied, at 25 degrees C, by 3 independent methods. In all of the experiments performed, a) both adsorbents were employed in the form of particles less than or equal to 1.0 mu representing specific surface areas of 9.85 M2/Gm and 27.7 (nominal) M2/Gm for the glass and LTI-carbon powders, respectively, and b) the fibrinogen was absorbed from a standaridized buffer (pH = 7.2, ionic strength 0.05) using the same fixed surface area/protein solution volume ratio with a given adsorbent. 3. The 25 degrees C adsorption isotherms of fibrinogen obtained for both the glass and LTI-carbon powder adsorbents are not amenable to Langmuir type analysis but indicate multilayer sorption with a possible change in binding mechanism after the completion of the first sorbed monolayer. The adsorptivities attained at first monolayer coverage were slightly greater on glass (approximately 0.76 mug/cm2) than on LTI-carbon (approximately 0.52 mug/cm2). 4. Using a custom-built, thermistorized, isothermal-jacketed microcalorimeter routinely capable of resolving temperature changes of 0.00001 degrees C in 100 ml of aqueous sample volume, the "intensity" of interaction between fibrinogen and each of the microparticulate adsorbents was studied by the direct measurement of the net overall enthalpy changes, hI(SLP)25 arising as a result of protein adsorption. From these values, the net heat of protein sorption has been determined...

Adsorption↗

Folding very short peptides using molecular dynamics.

Peptides often have conformational preferences. We simulated 133 peptide 8-mer fragments from six different proteins, sampled by replica-exchange molecular dynamics using Amber7 with a GB/SA (generalized-Born/solvent-accessible electrostatic approximation to water) implicit solvent. We found that 85 of the peptides have no preferred structure, while 48 of them converge to a preferred structure. In 85% of the converged cases (41 peptides), the structures found by the simulations bear some resemblance to their native structures, based on a coarse-grained backbone description. In particular, all seven of the beta hairpins in the native structures contain a fragment in the turn that is highly structured. In the eight cases where the bioinformatics-based I-sites library picks out native-like structures, the present simulations are largely in agreement. Such physics-based modeling may be useful for identifying early nuclei in folding kinetics and for assisting in protein-structure prediction methods that utilize the assembly of peptide fragments.

Biophysical Phenomena↗

Thermodynamics of stacking and of self-association of the dinucleoside monophosphate m2(6)A-U from proton NMR chemical shifts: differential concentration temperature profile method.

Chemical shifts of base and sugar protons of the modified ribodinucleoside monophosphate N6-dimethyladenylyl(3'-5')uridine (m2(6)A-U) were measured at 100, 360 and 400 MHz in aqueous solution. Seven different samples were used with concentrations ranging from 0.28 mM to 32.7 mM. The temperature was varied from -5 degrees C to 105 degrees C. An internal temperature calibration was used. The effects of intermolecular self-association and of intramolecular stacking on the chemical shifts were quantitatively separated by means of a new approach: differential concentration/temperature profiles (DCTP). Several computational models were tested and the analysis allowed deeper insight into the behaviour of m2(6)A-U at the molecular level. The simple two-state approach for both self-association and stacking already afforded a significant improvement over models in which the association is entirely neglected. A computer least-squares analysis of the chemical shift behaviour of each individual proton yielded thermodynamic parameters for self-association and stacking. However, the two-state model did not suffice to reproduce accurately all of the observations. A satisfactory fit required two additional assumptions: (a) the aromatic protons experience different association shifts in stacked and in unstacked molecules: (b) a temperature-dependent conformational equilibrium exists between sets of unstacked microstates. The stacked state is taken to represent a single conformational species. The implementation of this extended model in the least-squares optimization allowed the reproduction of over one thousand chemical shift observations within experimental error. Thermodynamic equilibrium parameters deduced for intramolecular stacking are: delta H degrees x = -28.8 kJ mol-1, delta S degrees x = -93 J mol-1 K-1. These numbers agree well with those obtained earlier by us from circular dichroism spectra. The equilibrium enthalpy and entropy values deduced for the association process are: delta H degrees A = -35 kJ mol-1 and delta S degrees A = -95 J mol-1 K-1.

Adenosine Monophosphate↗

The proficiency of a thermophilic chorismate mutase enzyme is solely through an entropic advantage in the enzyme reaction.

A study of the Thermus thermophilus chorismate mutase (TtCM) is described by using quantum mechanics (self-consistent-charge density-functional tight binding)/molecular mechanics, umbrella sampling, and the weighted histogram analysis method. The computed free energies of activation for the reactions in water and TtCM are comparable to the experimental values. The free energies for formation of near attack conformer have been determined to be 8.06 and 0.05 kcal/mol in water and TtCM, respectively. The near attack conformer stabilization contributes approximately 90% to the proficiency of the enzymatic reaction compared with the reaction in water. The transition state (TS) structures and partial atom charges are much the same in the enzymatic and water reactions. The difference in the electrostatic interactions of Arg-89 with O13 in the enzyme-substrate complex and enzyme-TS complex provides the latter with but 0.55 kcal/mol of 1.92 kcal/mol total TS stabilization. Differences in electrostatic interactions between components at the active site in the enzyme-substrate complex and enzyme-TS complex are barely significant, such that TS stabilization is of minor importance and the enzymatic catalysis is through an entropic advantage.

Binding Sites↗

Statistical mechanics of protein folding, unfolding and fluctuation.

Conformational fluctuations of globular proteins in the native state and the processes of folding and unfolding are studied from the statistical mechanical point of view. 1) It is pointed out that the formation of the native specific conformation of a globular protein is not a result of random sampling of minimum energy conformations. This fact provides a motivation for the study of the processes of folding, or the paths of folding, of proteins. The processes of folding and unfolding are shown to be statistical mechanical in nature. 2) The conformational (folding and unfolding) transitions in globular proteins are compared with the helix-coil transitions in polypeptides. The gradedness of the latter transition is shown to be due to the fact that the phenomenon is of an essentially one-dimensional system. The former transition is characterized ideally by the fact that it is of the all-or-none type. 3) A lattice model of proteins is introduced. "A protein molecule" is defined as a chain of noninteresting units of a given length on a two-dimensional square lattice. The copolymeric character of protein molecules is incorporated into the model by specificities of interunit interactions. 4) This model proved powerful for studying the statistical mechanical characterization of protein denaturation and fluctuations. The specificities of interunit interactions were shown to be the primary factors responsible for the all-or-none type transition from native to denatured states of globular proteins. 5) The model is studied by the Monte Carlo method of Metropolis et al., which simulates a kinetic process approximately. The method is shown to be a promising tool in finding the native conformation of proteins from their amino acid sequence. 6) A new theoretical method is developed to study phenomenologically the processes of protein folding and unfolding and the conformational fluctuations in the native state. An important role is played by a quantity S(H): the entropy of a protein molecule in solution in the conformational states with a given value of enthalpy H. Qualitative character of the S-H curve, such as whether it is convex or concave determines characteristics of the conformational transition in a globular protein such as whether or not it is of the all-or-none type. 7) The concept of an ideal process of protein folding and unfolding is introduced and defined by three statements. The S-H curve is calculated for this ideal process. The curve is shown to be concave, indicating that the transition is of the all-or-none type. This conclusion is drawn essentially from the globularity and specificity of the native conformational of proteins. 8) Residual structures in the denatured state and conformational fluctuations in the native state are discussed. In order to discuss the latter, an independent fluctuating site model is introduced, in which it is assumed that there are several independent fluctuating sites, each localized in some part of the protein molecule...

Computers↗

Molecular dynamics - potential of mean force calculations as a tool for understanding ion permeation and selectivity in narrow channels.

Ion channels catalyze the permeation of charged molecules across cell membranes and are essential for many vital physiological functions, including nerve and muscle activity. To understand better the mechanisms underlying ion conduction and valence selectivity of narrow ion channels, we have employed free energy techniques to calculate the potential of mean force (PMF) for ion movement through the prototypical gramicidin A channel. Employing modern all-atom molecular dynamics (MD) force fields with umbrella sampling methods that incorporate one hundred 1-2 ns trajectories, we find that it is possible to achieve semi-quantitative agreement with experimental binding and conductance measurements. We also examine the sensitivity of the MD-PMF results to the choice of MD force field and compare PMFs for potassium, calcium and chloride ions to explore the basis for the valence selectivity of this narrow and uncharged ion channel. A large central barrier is observed for both anions and divalent ions, consistent with lack of experimental conductance. Neither anion or divalent cation is seen to be stabilized inside the channel relative to the bulk electrolyte and each leads to large disruptions to the protein and membrane structure when held deep inside the channel. Weak binding of calcium ions outside the channel corresponds to a free energy well that is too shallow to demonstrate channel blocking. Our findings emphasize the success of the MD-PMF approach and the sensitivity of ion energetics to the choice of biomolecular force field.

Barium↗

Modeling protein-small molecule interactions: structure and thermodynamics of noble gases binding in a cavity in mutant phage T4 lysozyme L99A.

The complexes of phage T4 lysozyme L99A with noble gases have been studied by molecular dynamics simulation. In a long simulation of the complex with one Xe atom, the structure was found to undergo global conformation change involving a reversible opening and closing of the entrance to the substrate-binding site, during which the conformations of the N and C-terminal domains varied little. The distributions of Xe positions sampled in dynamics simulations were refined in terms of anisotropic Gaussian distributions via least-squares minimization of the difference between Fourier transforms. In addition, molecular transformation simulations have been applied in order to calculate the binding free energies of Xe, Kr and Ar relative to a standard state at a pressure of 1 bar. A single bound Xe is found to assume an equilibrium distribution over three adjacent preferred sites, while in a two-Xe complex, the two Xe atoms preferentially occupy two of these. The positions of the three sites agree closely with the positions of bound Xe determined in the refined crystal structure of a complex formed at a pressure of 8 bar Xe, and the calculated affinities agree well with the observed partial occupancies. At a pressure of 8 bar, a mixture of one-Xe and two-Xe complexes is present, and similarly for complexes with Kr and Ar, with single occupancy relatively more prevalent with Kr and Ar. (Binding of a third Xe atom is found to be quite unfavorable.) A comparison with simulation results for the binding of benzene to the same site leads to the conclusion that binding of Xe within cavities in proteins is common because of several favorable factors: (1) Xe has a large atomic polarizability; (2) Xe can be applied at a relatively high pressure, i.e. high chemical potential; (3) an unfavorable entropic term related to the need to orient the ligand in the binding site is absent. Finally, it is found that the model's binding energy of a water molecule in the cavity is insufficient to overcome the unfavorable binding entropy.

Amino Acid Substitution↗

The folding mechanism of a beta-sheet: the WW domain.

The folding thermodynamics and kinetics of the Pin WW domain, a three-stranded antiparallel beta-sheet, have been characterized extensively. Folding and activation free energies were determined as a function of temperature for 16 mutants, which sample all strands and turns of the molecule. The mutational phi value (Phi(m)) diagram is a smooth function of sequence, indicating a prevalence of local interactions in the transition state (TS). At 37 degrees C, the diagram has a single pronounced maximum at turn 1: the rate-limiting step during folding is the formation of loop 1. In contrast, key residues for thermodynamic stability are located in the strand hydrophobic clusters, indicating that factors contributing to protein stability and folding kinetics are not correlated. The location of the TS along the entropic reaction coordinate Phi(T), obtained by temperature-tuning the kinetics, reveals that sufficiently destabilizing mutants in loop 2 or in the Leu7-Trp11-Tyr24-Pro37 hydrophobic cluster can cause a switch to a late TS. Phi(m) analysis is usually applied "perturbatively" (methyl truncation), but with Phi(T) to quantitatively assess TS shifts along a reaction coordinate, more severe mutations can be used to probe regions of the free energy surface beyond the TS.

Amino Acid Sequence↗