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PubMed2006

A free energy principle for the brain.

By formulating Helmholtz's ideas about perception, in terms of modern-day theories, one arrives at a model of perceptual inference and learning that can explain a remarkable range of neurobiological facts: using constructs from statistical physics, the problems of inferring the causes of sensory input and learning the causal structure of their generation can be resolved using exactly the same principles. Furthermore, inference and learning can proceed in a biologically plausible fashion. The ensuing scheme rests on Empirical Bayes and hierarchical models of how sensory input is caused. The use of hierarchical models enables the brain to construct prior expectations in a dynamic and context-sensitive fashion. This scheme provides a principled way to understand many aspects of cortical organisation and responses. In this paper, we show these perceptual processes are just one aspect of emergent behaviours of systems that conform to a free energy principle. The free energy considered here measures the difference between the probability distribution of environmental quantities that act on the system and an arbitrary distribution encoded by its configuration. The system can minimise free energy by changing its configuration to affect the way it samples the environment or change the distribution it encodes. These changes correspond to action and perception respectively and lead to an adaptive exchange with the environment that is characteristic of biological systems. This treatment assumes that the system's state and structure encode an implicit and probabilistic model of the environment. We will look at the models entailed by the brain and how minimisation of its free energy can explain its dynamics and structure.

Afferent Pathways↗

PubMed1998

Graded testosterone infusions distinguish gonadotropin negative-feedback responsiveness in Asian and white men--a Clinical Research Center study.

Recently, multicenter clinical trials to determine male contraceptive efficacy disclosed that testosterone-induced suppression of spermatogenesis to azoospermia occurred in about 90% of Asian but only 60-70% of white men. To test whether there are ethnic differences in the sensitivity of gonadotropin secretion to suppression by testosterone, we administered constant infusions of testosterone at 0, 7, 14, and 28 mg/1.7 m2 x 24 h i.v. for 48 h to 9 Asian and 8 white normal male volunteers (22-42 yr old). During the last 8 h of each infusion dose, 10-min frequent blood sampling was carried out for later LH and FSH measurements by sensitive fluoroimmunoassays. Analyses of LH secretory pulses showed that LH pulse width, height, area, and total area under the curve (LH concentration vs. time) were significantly more suppressed in Asians than in whites during the lowest infusion dose of testosterone. With increasing testosterone dose, the suppression of pulsatile LH secretion was not different in the two ethnic groups. In contrast to pulsatile LH secretion, the responsiveness of pulsatile FSH secretion to exogenous testosterone infusion was not different between the two ethnic groups. At baseline, Asian men had a significantly higher mean number of FSH pulses and mean incremental pulse heights than did white men. Serum inhibin B levels were not distinguishable in the two ethnic groups, but the FSH profiles were quantifiably more irregular (higher approximate entropy) in the Asian volunteers. Our data suggest that, compared with white men, Asian men respond earlier and with more marked suppression of pulsatile LH secretion to ramped testosterone infusions. The elevated basal serum FSH concentrations (and more irregular FSH release pattern) observed in Asian men may suggest a small relative decrease in spermatogenic reserve and/or gonadal negative feedback. Whether these differences contribute to the observed differences in suppression of spermatogenesis in Asians vs. non-Asians in male contraceptive studies is not yet known.

Adult↗

PubMed1999

Evaluation of LH secretory dynamics during the rat proestrous LH surge.

The preovulatory luteinizing hormone (LH) surge results from the integration of complex interactions among gonadal steroids and hypothalamic and pituitary hormones. To evaluate changes in LH secretory dynamics that occur during the rat LH surge, we have 1) obtained frequently sampled serum LH concentration time series, 2) used both waveform-dependent and waveform-independent convolution analyses, and 3) independently assessed proestrous LH half-life and basal non-gonadotropin-releasing hormone (GnRH)-dependent LH secretion during the LH surge. Waveform-independent pulse analysis revealed a 24-fold increase in the maximal pulsatile LH secretory rate attained during late proestrus compared with early proestrus. A 15-fold increase was quantified for the mean LH secretory rate. In complementary analyses, we applied a measured LH half-life of 17 +/- 2.7 min and a median basal LH secretion rate of 0.0046 microgram. l-1. min-1 for convolution analysis, revealing a 16-fold increase in the mass of LH released/burst and more than sixfold rise in the amplitude of the secretory peaks. Evaluation of the approximate entropy of the LH surge profiles was performed, showing an increase in the orderliness of the LH release process during the surge. We conclude that both quantitative (mass/burst) and qualitative (approximate entropy) features of LH release are regulated during the proestrous LH surge.

Animals↗

PubMed2000

The short-term and long-term reproducibility of spectral turbulence and late potential variables of the signal-averaged ECG in a population sample of healthy subjects and the impact of gender, age, and noise.

Previous methods for frequency domain analysis of the signal-averaged ECG (SAECG) have had low reproducibility. The reproducibility of time domain late potential analysis and spectral turbulence analysis was evaluated with 2 immediately consecutive SAECG recordings in 121 randomly selected subjects without heart disease (short-term) and also in 47 subjects after 1 month (long-term). A test was late potential positive if 2 or more of 3 variables were outside the reference limits and spectral turbulence positive if the score was 3 or 4. The short-term reproducibility was high for the filtered QRS duration (FQRSD), root mean square amplitude of the last 40 ms (RMS40) and high frequency low amplitude signals less than 40 microV (HFLAS40) of the time domain and total QRS duration (TQRSD), power spectral density of the last 40 ms and the late potential duration of time domain analogous analyses. The Spearman rank order correlation coefficients were 0.89, 0.88, and 0.84 and 0.97, 0.91 and 0.97, respectively. The reproducibility of the spectral score variables varied, and the correlation for the low slice correlation ratio was 0.71, spectral entropy 0.61, interslice correlation mean 0.58, and interslice correlation SD 0.28. A diagnostic inconsistency between 2 tests occurred in 0 (0%) subjects in late potential analysis if FQRSD was required for positivity, and in 7 (6%) otherwise, and in 9 (7%) of spectral turbulence analysis. If the spectral variable mean peaks per slice, with a correlation of 0.89, replaced interslice correlation SD in the spectral score, diagnostic inconsistency occurred in 0 (0%) subjects. The reproducibility seemed higher in women and in younger people but significantly only for interslice correlation subjects mean and HFLAS40. The long-term reproducibility did not differ significantly from short-term for any variable. In conclusion, the reproducibility was high in all time domain and time domain analogous variables. It varied among the spectral turbulence score variables and was very low for interslice correlation SD. The reproducibility of the spectral score improved substantially if this variable was replaced by mean peaks per slice.

Adult↗

PubMed1993

Investigation of conformational equilibrium of polypeptides by internal coordinate stochastic dynamics. Met5-enkephalin.

The equilibrium population of different conformational states of a polypeptide can in principle be obtained by a very long molecular dynamics simulation. The method of internal coordinate molecular dynamics earlier developed in this laboratory (A.K. Mazur and R.A. Abagyan J. Biomol. Struct. Dyn. 6,833 (1989)) allows one to use time steps much larger than usual for computing molecular trajectories. It is shown here that the sampling of the conformational space can be additionally enhanced by adding a random component to the set of forces applied to atoms. We describe the algorithms by which the random force is introduced and also a special method which excludes the fast rotation of polar hydrogens from equations of motion but keeps them movable. As a result the task stated in the title becomes realistic. Internal coordinate stochastic dynamics is applied for scanning the conformational space of the pentapeptide Met5-enkephalin which is a common test example widely used in theoretical studies. A large number of conformational transitions is observed during the 20 ns simulation starting from the global energy minimum thus allowing us to arrive at a nearly Boltzmann distribution of populations of conformational states. A few states are found which are distinguished by high apparent configurational entropy which turn out to correspond well to experimentally observed conformations of enkephalins.

Enkephalin, Methionine↗

PubMed2002

Physical stability of amorphous pharmaceuticals: Importance of configurational thermodynamic quantities and molecular mobility.

This work relates the thermodynamic quantities (Gc, Hc, and Sc) and the molecular mobility values (1/tau) of five structurally diverse amorphous compounds to their crystallization behavior. The model compounds included: ritonavir, ABT-229, fenofibrate, sucrose, and acetaminophen. Modulated temperature DSC was used to measure the heat capacities as a function of temperature for the amorphous and crystalline phases of each compound. Knowledge of the heat capacities and fusion data allowed calculation of the configurational thermodynamic quantities and the Kauzmann temperatures (T(K)) using established relationships. The molecular relaxation time constants (tau) were then calculated from the Vogel-Tammann-Fulcher representation of the Adam-Gibbs model. Amorphous samples were heated at 1 K/min and a reduced crystallization temperature, defined as (Tc - Tg)/(Tm-Tg), was used to compare crystallization tendencies. Crystallization was observed for all compounds except ritonavir. The configurational free energy values (Gc) show that thermodynamic driving forces for crystallization follow the order: ritonavir > acetaminophen approximately fenofibrate > sucrose > ABT-229. The entropic barrier to crystallization, which is inversely related to the probability that the molecules are in the proper orientation, followed the order: ritonavir > fenofibrate > ABT-229 > acetaminophen approximately sucrose. Molecular mobility values, which are proportional to molecular collision rates, followed the order: acetaminophen > fenofibrate > sucrose > ABT-229 approximately ritonavir. Crystallization studies under nonisothermal conditions revealed that compounds with the highest entropic barriers and lowest mobilities were most difficult to crystallize, regardless of the thermodynamic driving forces. This investigation demonstrates the importance of both configurational entropy and molecular mobility to understanding the physical stability of amorphous pharmaceuticals.

Algorithms↗

PubMed1996

Predicting axillary lymph node metastases in breast carcinoma patients.

Routine axillary dissection is primarily used as a means of assessing prognosis to establish appropriate treatment plans for patients with primary breast carcinoma. However, axillary dissection offers no therapeutic benefit to node negative patients and patients may incur unnecessary morbidity, including mild to severe impairment of arm motion and lymphedema, as a result. This paper outlines a method of evaluating the probability of harbouring lymph node metastases at the time of initial surgery by assessment of tumour based parameters, in order to provide an objective basis for further selection of patients for treatment or investigation. The novel aspect of this study is the use of Maximum Entropy Estimation (MEE) to construct probabilistic models of the relationship between the risk factors and the outcome. Two hundred and seventeen patients with invasive breast carcinoma were studied. Surgical treatment included axillary clearance in all cases, so that the pathologic status of the nodes was known. Tumour size was found to be significantly correlated (P < 0.001) to the axillary lymph node status in the multivariate anlaysis with age (P = 0.089) and vascular invasion (P = 0.08) marginally correlated. Using the multivariate model constructed, 38 patients were predicted to have risk of nodal metastases lower than 20%, of these only 4 (10%) patients had lymph node metastases. A comparison with the Multivariate Logistic Regression (MLR) was carried out. It was found that the predictive quality of the MEE model was better than that of the MLR model. In view of the small sample size, further verification of this model is required in assessing its practical application to a larger population.

Axilla↗

PubMed1990

Reverse turns in blocked dipeptides are intrinsically unstable in water.

We have carried out molecular dynamics simulations to study the conformational equilibria of two blocked dipeptides, Ac-Ala-Ala-NHMe and trans-Ac-Pro-Ala-NHMe, in water (Ac, amino-terminal blocking group COCH3; NHMe, carboxy-terminal blocking group NHCH3). Using specialized sampling techniques we computed free-energy surfaces as functions of a conformation co-ordinate that corresponds to hydrogen-bonded reverse turns at small values and to extended conformations at large values. The free-energy difference between hydrogen-bonded reverse turn conformations and extended conformations, determined from the equilibrium constants for reverse turn unfolding, is approximately -5 kcal/mole for Ac-Ala-Ala-NHMe, and -10 kcal/mole for Ac-Pro-Ala-NHMe. These results demonstrate that reverse turns in blocked dipeptides are intrinsically unstable in water. That is, in the absence of strongly stabilizing sequence-specific inter-residue interactions involving side-chains and/or charged terminal groups, the extended conformations of small peptides are highly favored in solution. By thermodynamically decomposing the free-energy differences, we found that the peptide-water entropy is the primary reason for the exceptional stability of the extended conformations of both peptides, and that the differences between the two peptides are primarily due to differences in the peptide-water interactions. In addition, we assessed the "proline effect" on the conformational equilibria by comparing the differences in configurational entropies between the reverse turn and extended conformations of the two peptides. As expected, the extended conformation of the Pro-Ala peptide is destabilized by reduced configurational entropy, but the effect is negligible in the blocked dipeptides. Finally, we compared our results with the results of several other experimental studies to identify some of the specific interactions that may be responsible for stabilizing reverse turns in small peptides in solution.

Amino Acid Sequence↗

PubMed2004

Unfolded state of polyalanine is a segmented polyproline II helix.

Definition of the unfolded state of proteins is essential for understanding their stability and folding on biological timescales. Here, we find that under near physiological conditions the configurational ensemble of the unfolded state of the simplest protein structure, polyalanine alpha-helix, cannot be described by the commonly used Flory random coil model, in which configurational probabilities are derived from conformational preferences of individual residues. We utilize novel effectively ergodic sampling algorithms in the presence of explicit aqueous solvation, and observe water-mediated formation of polyproline II helical (P(II)) structure in the natively unfolded state of polyalanine, and its facilitation of alpha-helix formation in longer peptides. The segmented P(II) helical coil preorganizes the unfolded state ensemble for folding pathway entry by reducing the conformational space available to the diffusive search. Thus, as much as half of the folding search in polyalanine is accomplished by preorganization of the unfolded state.

Computer Simulation↗

PubMed2005

Adsorption of cationic polyacrylamide onto sepiolite.

The adsorption of PAM onto sepiolite from aqueous solutions has been investigated systematically as a function of some parameters such as calcination temperature of sepiolite, pH, ionic strength and temperature. The adsorption of cationic polyacrylamide (PAM) increases with pH from 5.50 to 11.00, temperature from 25 to 55 degrees C and ionic strength from 0 to 0.1molL(-1). The sepiolite sample calcined at 200 degrees C has a higher adsorption capacity than the other calcined samples. Adsorption isotherms of PAM onto sepiolite have been determined and correlated with common isotherm equations such as Langmuir and Freundlich isotherm models. The Langmuir isotherm model appeared to fit the isotherm data better than the Freundlich isotherm model. The physical properties of this adsorbent are consistent with the parameters obtained from the isotherm equations. The zeta potentials of sepiolite suspensions have been measured in aqueous solutions of NaCl and different PAM concentrations and pH. From the experimental results: (i) pH strongly alters the zeta potential of sepiolite, (ii) sepiolite has an isoelectric point at about pH 6.6 in water and about pH 8 in 250mgL(-1) PAM concentration, (iii) PAM changes the interface charge from negative to positive for sepiolite. Effect of temperature on adsorption has been quantified by calculating various thermodynamic parameters such as Gibbs free energy, enthalpy and entropy. The dimensionless separation factor (R(L)) has shown that sepiolite can be used for adsorption of PAM from aqueous solutions.

Acrylic Resins↗

PubMed2006

Motion correction properties of the shells k-space trajectory.

The feasibility of a k-space trajectory that samples data on a set of 3D shells is demonstrated with phantom and volunteer experiments. Details of an interleaved multi-shot, helical spiral pulse sequence and a gridding reconstruction algorithm that uses Voronoi diagrams are provided. The motion-correction properties of the shells k-space trajectory are described. It is shown that when used in conjunction with three point markers, k-space data acquired with the shells trajectory provide a generalization of the RINGLET method, allowing for correction of arbitrary rigid-body motion with six degrees of freedom. Use of dedicated navigator echoes or redundant acquisitions of k-space data are not required. Retrospective motion correction is demonstrated with controlled phantom experiments and with seven healthy human volunteers. The motion correction is shown to improve the images, both qualitatively and quantitatively with a metric calculated from image entropy. Advantages and challenges of the shells trajectory are discussed, with particular attention to acquisition efficiency.

Algorithms↗

PubMed1996

The orderliness of the growth hormone (GH) release process and the mean mass of GH secreted per burst are highly conserved in individual men on successive days.

Endocrine glands signal their remote target tissues via physiologically pulsatile release of regulatory molecules. A cardinal assumption of most pathophysiological experiments is that discrete attributes of pulsatile hormone secretion are stable over successive untreated observation intervals; i.e. repeated measurements show serial within-subject reproducibility. To test this hypothesis in the GH axis, we sampled blood every 10 min for 48 h in 14 healthy men (age range, 29-77 yr; body mass index, 21-51 kg/m2). The 2 consecutive 24-h serum profiles were subjected to ultrasensitive GH chemiluminescence assay (sensitivity, 0.002 micrograms/L) with a new dose-dependent variance model to estimate within-assay precision. We then applied deconvolution analysis to estimate the number, mass, amplitude, and duration of underlying GH secretory bursts as well as simultaneously calculate the apparent GH half-life and any concurrent basal hormone secretion. Test-retest consistency was assessed by the Pearson correlation coefficient, and differences were determined by paired nonparametric (Wilcoxon) testing. Comparing successive 24-h profiles, no significant differences existed in any of the foregoing secretion or half-life measures or in a novel estimate of the relative disorderliness of hormone release, namely approximate entropy. Correlation was minimal for secretory burst amplitude and half-duration. In contrast, the calculated mean mass of GH secreted per burst was highly conserved across sessions within subjects, with an r value of 0.932 (P < 10(-6). This correlation equaled or exceeded that of mean and integrated serum GH concentrations on consecutive days (r = 0.920; P = 0.00003). The calculated daily GH production rate was also strongly reproduced (r = 0.784; P = 0.0009). Moreover, the within-subject GH half-life and GH secretory burst frequency estimates were well correlated on successive days (P = 0.034-0.004; r = 0.568-0.711). Approximate entropy values were consistent at r = 0.837 (P = 0.0019). In addition, basal GH secretion rates correlated at r = 0.622 (P = 0.0176). We conclude that homeostatic control mechanisms within the GH-insulin-like growth factor I axis strongly preserve the day to day mean mass of GH secreted per burst and the serial orderliness of the GH release process in individual healthy men across a wide span of ages and body compositions.

Adult↗

PubMed2005

Removal of dyes from aqueous solution using fly ash and red mud.

Fly ash and red mud have been employed as adsorbents for the removal of a typical basic dye, methylene blue, from aqueous solution. Heat treatment and chemical treatment have also been applied to the as-received fly ash and red mud samples. It is found that fly ash generally shows higher adsorption capacity than red mud. The raw fly ash and red mud show adsorption capacity at 1.4 x 10(-5) and 7.8 x 10(-6) mol/g, respectively. Heat treatment reduces the adsorption capacity for both fly ash and red mud but acid treatment by HNO(3) induces a different effect on fly ash and red mud. Nitric acid treatment results in an increase in adsorption capacity of fly ash (2.4 x 10(-5) mol/g) while it decreases the adsorption capacity for red mud (3.2 x 10(-6) mol/g). The adsorption data have been analysed using Langmuir, Freundlich and Redlich-Peterson isotherms. The results indicate that the Redlich-Peterson model provides the best correlation of the experimental data. Isotherms have also been used to obtain the thermodynamic parameters such as free energy, enthalpy and entropy of adsorption. For fly ash and red mud, adsorption of methylene blue is endothermic reaction with DeltaH(0) at 76.1 and 10.8 kJ/mol, respectively.

Adsorption↗

PubMed2005

Changes in cardiovascular autonomic regulation among elderly subjects: follow-up of sixteen years.

BACKGROUND: Previous cross-sectional studies have suggested that cardiac autonomic regulation, measured as heart rate (HR) variability, is altered upon ageing, and that altered HR variability may predict mortality. However, there are no longitudinal follow-up reports of the changes of HR dynamics in elderly subjects. AIM & METHOD: This study was designed to examine the longitudinal changes in the spectral, fractal, and complexity measures of HR variability in a random sample of 41 elderly subjects (mean age 69+/-4 years), who underwent repeated 24-hour Holter recordings at the baseline and after 16 years' follow-up. Several cardiovascular risk factors were determined at the baseline. RESULTS: A time-domain index, standard deviation of N-N intervals (SDNN) (142+/-34 msec versus 133+/-50 msec, not significant (NS)), and the high frequency spectral component of HR variability (219+/-222 msec(2)versus 268+/-287 msec(2), NS) did not change during the follow-up. The low frequency power (LF) of HR variability decreased from 678+/-654 msec(2) to 436+/-651 msec(2) (P<0.01). Among the fractal HR variability indexes, the power-law slope (ss) (-1.31+/-0.20 versus -1.47+/-0.21, P<0.001) and the short-term fractal exponent a1 (1.16+/-0.19 versus 1.06+/-0.18, P<0.01) decreased significantly. Approximate entropy remained unchanged. CONCLUSIONS: The magnitude of total HR variability and the respiratory vagal modulation of HR do not change over time in the elderly. However, the spectral and fractal characteristics of HR behavior still undergo alterations upon ageing.

Aged↗

PubMed2006

Enthalpies of DNA melting in the presence of osmolytes.

The melting of DNA in the presence of osmolytes has been studied with the intention of obtaining information about how base pair stability is affected by changes in solution conditions. In previous investigations, the melting enthalpies were assumed to be constant as osmolalities change, but no systematic evaluation of whether this condition is true has been offered. This paper presents calorimetric data on the melting of two synthetic DNA samples in the presence of a number of common osmolytes. Poly(dAdT)*poly(dTdA) and poly(dGdC)*poly(dCdG) melting have been examined by differential scanning calorimetry in solutions containing ethylene glycol, glycerol, sucrose, urea, betaine, PEG 200 and PEG 1450 at increasing osmolalities. The results show small, but significant changes in the enthalpy of melting of the two polynucleotides that are different, depending on the structure of the cosolvent. The polyols, ethylene glycol, glycerol, PEG 200 and also urea all show decreases in melting enthalpy, while betaine and sucrose display increases with increasing concentration of cosolvent. The large stabilizing PEG 1450 shows no change within the experimental errors. Using concepts relating to preferential interactions of the cosolvents with the DNA base pairs, it is possible to interpret some of the observed changes in the thermodynamic properties of melting. The results indicate that there is strong entropy-enthalpy compensation upon melting base pairs, but entropy increases dominate to cause the decreases in stability with increased cosolvent concentration. Excess hydration parameters are evaluated and their magnitudes discussed in terms of changes in cosolvent interactions with the DNA base pairs.

Base Composition↗

PubMed2005

Adsorption of polyvinylimidazole onto kaolinite.

The adsorption of polyvinylimidazole (PVI) onto kaolinite from aqueous solutions has been investigated systematically as a function of parameters such as calcination temperature of kaolinite, pH, ionic strength, and temperature. According to the experimental results, the adsorption of PVI increases with pH from 8.50 to 11.50, temperature from 25 to 55 degrees C, and ionic strength from 0 to 0.1 mol L(-1). The kaolinite sample calcined at 600 degrees C has a maximum adsorption capacity. Adsorption isotherms of PVI onto kaolinite have been determined and correlated with common isotherm equations such as Langmuir and Freundlich isotherm models. The Langmuir isotherm model appeared to fit the isotherm data better than the Freundlich isotherm model. The physical properties of this adsorbent are consistent with the parameters obtained from the isotherm equations. Furthermore, the zeta potentials of kaolinite suspensions have been measured in aqueous solutions of different PVI concentrations and pH. From the experimental results, (i) pH strongly alters the zeta potential of kaolinite; (ii) kaolinite has an isoelectric point at about pH 2.35 in water and about pH 8.75 in 249.9 ppm PVI concentration; (iii) PVI changes the interface charge from negative to positive for kaolinite. The study of temperature effect has been quantified by calculating various thermodynamic parameters such as Gibbs free energy, enthalpy, and entropy changes. The dimensionless separation factor (RL) has shown that kaolinite can be used for adsorption of PVI from aqueous solutions.

Journal Article↗

PubMed2005

Overcoming entropic barrier with coupled sampling at dual resolutions.

An enhanced sampling method is proposed for ab initio protein folding simulations. The new method couples a high-resolution model for accuracy and a low-resolution model for efficiency. It aims to overcome the entropic barrier found in the exponentially large protein conformational space when a high-resolution model, such as an all-atom molecular mechanics force field, is used. The proposed method is designed to satisfy the detailed balance condition so that the Boltzmann distribution can be generated in all sampling trajectories in both high and low resolutions. The method was tested on model analytical energy functions and ab initio folding simulations of a beta-hairpin peptide. It was found to be more efficient than replica-exchange method that is used as its building block. Analysis with the analytical energy functions shows that the number of energy calculations required to find global minima and to converge mean potential energies is much fewer with the new method. Ergodic measure shows that the new method explores the conformational space more rapidly. We also studied imperfect low-resolution energy models and found that the introduction of errors in low-resolution models does decrease its sampling efficiency. However, a reasonable increase in efficiency is still observed when the global minima of the low-resolution models are in the vicinity of the global minimum basin of the high-resolution model. Finally, our ab initio folding simulation of the tested peptide shows that the new method is able to fold the peptide in a very short simulation time. The structural distribution generated by the new method at the equilibrium portion of the trajectory resembles that in the equilibrium simulation starting from the crystal structure.

Algorithms↗

PubMed2003

Critical assessment of side-chain conformational space sampling procedures designed for quantifying the effect of side-chain environment.

We introduce a family of procedures designed to sample side-chain conformational space at particular locations in protein structures. These procedures (CRSP) use intensive cycles of random assignment of side-chain conformations followed by minimization to determine all the conformations that a group of side-chains can adopt simultaneously. First, we consider a procedure evolving in the dihedral space (dCRSP). Our results suggest that it can accurately map low-energy conformations adopted by clusters of side-chains of a protein. dCRSP is relatively insensitive to various important parameters, and it is sufficiently accurate to capture efficiently the constraint induced by the environment on the conformations a particular side-chain can adopt. Our results show that dCRSP, compared with molecular dynamics (MD), can overcome the problem of the limited set of conformations reached in a reasonable amount of simulations. Next, we introduce procedures (vCRSP) in which valence angles are relaxed, and we assess how efficiently they quantify the conformational entropy of side-chains in the protein native state. For simple peptides, entropies obtained with vCRSP are fully compatible with those obtained with a Monte Carlo procedure. For side-chains in a protein environment, however, vCRSP appears of limited use. Finally, we consider a two-step procedure that combines dCRSP and vCRSP. Our tests suggest that it is able to overcome the limitations of vCRSP. We also note that dCRSP provides a reasonable initial approximation. This family of procedures offers promise in quantifying the contribution of conformational entropy to the energetics of protein structures.

Algorithms↗