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PubMed1985

Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters.

Two-dimensional spatial linear filters are constrained by general uncertainty relations that limit their attainable information resolution for orientation, spatial frequency, and two-dimensional (2D) spatial position. The theoretical lower limit for the joint entropy, or uncertainty, of these variables is achieved by an optimal 2D filter family whose spatial weighting functions are generated by exponentiated bivariate second-order polynomials with complex coefficients, the elliptic generalization of the one-dimensional elementary functions proposed in Gabor's famous theory of communication [J. Inst. Electr. Eng. 93, 429 (1946)]. The set includes filters with various orientation bandwidths, spatial-frequency bandwidths, and spatial dimensions, favoring the extraction of various kinds of information from an image. Each such filter occupies an irreducible quantal volume (corresponding to an independent datum) in a four-dimensional information hyperspace whose axes are interpretable as 2D visual space, orientation, and spatial frequency, and thus such a filter set could subserve an optimally efficient sampling of these variables. Evidence is presented that the 2D receptive-field profiles of simple cells in mammalian visual cortex are well described by members of this optimal 2D filter family, and thus such visual neurons could be said to optimize the general uncertainty relations for joint 2D-spatial-2D-spectral information resolution. The variety of their receptive-field dimensions and orientation and spatial-frequency bandwidths, and the correlations among these, reveal several underlying constraints, particularly in width/length aspect ratio and principal axis organization, suggesting a polar division of labor in occupying the quantal volumes of information hyperspace.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗

PubMed2001

Direct electrochemical characterization of hyperthermophilic Thermococcus celer metalloenzymes involved in hydrogen production from pyruvate.

The reduction potentials of the metalloproteins pyruvate ferredoxin oxidoreductase (POR), ferredoxin, and hydrogenase isolated from hyperthermophilic Thermococcus celer (Topt = 88 degrees C) were determined as a function of temperature from 10 to 85 degrees C. Square-wave voltammetry experiments were carried out on 15 microL samples directly at an unmodified "edge-polished" pyrolytic graphite electrode using MgCl2 as an electrode promoter. POR exhibited two voltammetric waves with peaks at -280 and -403 mV at room temperature, indicating multiple redox centers, and a single wave at -420 mV at 85 degrees C. These waves displayed different temperature-dependent peak positions and peak heights, indicating that these redox centers have different thermodynamic and kinetic properties. Ferredoxin displayed a single linear temperature-dependent voltammetric wave at -280 mV at room temperature and -327 mV at 85 degrees C. Hydrogenase displayed a single biphasic temperature-dependent voltammetric wave at -197 mV at room temperature and -211 mV at 85 degrees C. Thermodynamic parameters associated with electron transfer, namely standard enthalpies and entropies for the redox centers in the various proteins, are reported.

Electrochemistry↗

PubMed1995

The thermal unfolding of hevein, a small disulfide-rich protein.

Differential scanning calorimetry was used to study the thermal unfolding of hevein, a 43-residue disulfide-rich protein whose three-dimensional structure has been determined by X-ray diffraction. In the range pH 2.0-3.7 this process was approximately 75% reversible as judged by repeated scans on the same sample. The ratios of van'tr Hoff to calorimetric enthalpies were considerably larger than one, suggesting that intermolecular cooperation is involved in the unfolding of this protein. Alternatively, it is possible that the partial irreversibility of this process may cause distortions of the endotherm that affect the calculation of the van't Hoff enthalpy. Experimental changes in heat capacity and enthalpy were compared with those calculated from polar and nonpolar surface areas buried in the native state. It was found that when the unfolded state is represented as an extended chain without disulfide cross-links, experimental and calculated parameters agree well. However, if the unfolded protein is modeled with the presence of disulfide bridges, the agreement between the two sets of parameters is lost. The entropy change/residue at 112 degrees C is considerably smaller than the average value for globular proteins, thus suggesting that, as expected, disulfide bonds strongly influence the entropy of the unfolded state of this protein.

Antimicrobial Cationic Peptides↗

PubMed2002

Polyproline II structure in a sequence of seven alanine residues.

A sequence of seven alanine residues-too short to form an alpha-helix and whose side chains do not interact with each other-is a particularly simple model for testing the common description of denatured proteins as structureless random coils. The (3)J(HN alpha) coupling constants of individual alanine residues have been measured from 2 to 56 degrees C by using isotopically labeled samples. The results display a thermal transition between different backbone conformations, which is confirmed by CD spectra. The NMR results suggest that polyproline II is the dominant conformation at 2 degrees C and the content of beta strand is increased by approximately 10% at 55 degrees C relative to that at 2 degrees C. The polyproline II conformation is consistent with recent studies of short alanine peptides, including structure prediction by ab initio quantum mechanics and solution structures for both a blocked alanine dipeptide and an alanine tripeptide. CD and other optical spectroscopies have found structure in longer "random coil" peptides and have implicated polyproline II, which is a major backbone conformation in residues within loop regions of protein structures. Our result suggests that the backbone conformational entropy in alanine peptides is considerably smaller than estimated by the random coil model. New thermodynamic data confirm this suggestion: the entropy loss on alanine helix formation is only 2.2 entropy units per residue.

Alanine↗

PubMed2002

Compliant design of artificial graft: compliance determination by new digital X-ray imaging system-based method.

The development of an artificial graft requires formulation of biomechanical design criteria. The compliance of artifical grafts, based on the intraluminal pressure-internal diameter (Pi-Di) relationship, was measured by a novel method using a digital X-ray imaging system coupled with an edge detection algorithm and a pressure transducer. The Pi-Di values were obtained from digital angiographic images under continuous inflation of a canine femoral artery anastomosed with an expanded poly(tetrafluoroethylene) (ePTFE) vascular graft as a model vessel with a pressurized contrast medium. The Di at Pi using an NIH Image software specially programmed for the entropy filter method, which enables the detection of the edge of the vessel phantoms of the images, was determined. The Pi-Di relationships showed a "J-shape" curve for the artery, a steeper line with a very low pressure-dependent distensibility for the ePTFE graft, and an intermediate curve for the anastomosis protion. The two indices for the vessel compliance, the stiffness parameter (beta value) and the diameter compliance (Cd), both of which were calculated from the Pi-Di relationships, were 10.6 and 6.8%/mmHg x 10(-2) for the artery, 164 and 0.51%/mmHg x 10(-2) for the ePTFE, and 14.4 and 5.5%/mmHg x 10(-2) for the anastomosis portion, respectively. This method can measure compliance at any portions of the sampling vessel in a single experiment on a real-time basis with very high accuracy, compared with conventional methods, and even in cases of intimal thickening and/or connective tissues-adhered vessels, and may serve to provide information on compliant design criteria of artificial and tissue-engineered graft.

Algorithms↗

PubMed2001

Secretory process regularity monitors neuroendocrine feedback and feedforward signaling strength in humans.

The present experiments examine the neuroregulatory hypothesis that the degree of sample-by-sample regularity of hormone output by an interlinked hypothalamopituitary target-organ system monitors the strength of feedback and/or feedforward signaling. To test this postulate and assess its generality, we implemented a total of nine thematically complementary perturbation experiments. In particular, we altered feedback or feedforward signaling selectively in two distinct neuroendocrine systems; namely, the growth hormone (GH) insulin-like growth factor type I (IGF-I) and the luteinizing hormone-testosterone axes. Four experimental paradigms comprised preferential reduction vs. enhancement of IGF-I or testosterone feedback signal strength; and, conversely, five others entailed selective attenuation vs. augmentation of GH-releasing hormone and gonadotropin-releasing hormone feedforward signal intensity. In these independent interventions, quantitation of subordinate (nonpulsatile) secretory pattern reproducibility via the approximate entropy statistic unmasked salient changes (P values typically <10(-3)) in the conditional regularity of serial hormone output with high consistency (96-100%). In particular, approximate entropy quantified degradation of secretory subpattern orderliness under either muted feedback restraint or heightened feedforward drive. Assuming valid interpretation of the biological constraints imposed, these experimental observations coincide with earlier reductionist mathematical predictions, wherein increased irregularity of coupled parameter output mirrors attenuated feedback and/or augmented feedforward coupling within an integrative system.

Fasting↗

PubMed2001

Altered neuroregulation of GH secretion in viscerally obese premenopausal women.

We used deconvolution analysis of 24-h plasma GH concentration profiles (10- min sampling intervals) to appraise GH secretion rates and elimination kinetics in obese (body mass index, approximately 34 kg/m2) premenopausal women with large visceral fat area (LVFA; n = 8) vs. small visceral fat area (SVFA; n = 8) as determined by magnetic resonance imaging. The subjects were matched for body mass index, body fat percentage, and age. The impact of the loss of 50% of prestudy weight excess induced by caloric restriction was assessed as well. The results were compared with those obtained in normal weight control women (n = 8). LVFA subjects manifested markedly (4-fold) reduced mean plasma GH levels, which was brought about by jointly diminished basal and pulsatile GH secretion. Moreover, visceral obesity was associated with loss of regularity of GH release, as established by the approximate entropy statistic. In contrast, SVFA subjects produced normal daily amounts of GH and exhibited mean 24-h plasma GH concentrations that were similar to those in normal weight controls. GH half-life and distribution volume were not different among the study groups. Importantly, weight loss did not affect the daily GH secretion rate in LVFA women, so that their mean plasma GH concentration remained considerably reduced (approximately 50%) compared with controls (despite the loss of approximately 40% of visceral fat). Normal GH kinetics in SVFA women were not significantly influenced by weight reduction. Thus, GH neuroregulation appears to be particularly altered in obese women with a tendency to store fat in their visceral adipose depot. Because weight loss did not reverse GH secretion rate in viscerally obese women, we speculate that relative hyposomatotropism is a primary feature of these women, which could be involved in their tendency to preferentially store excess fat in visceral adipose tissue.

Adipose Tissue↗

PubMed2006

Low-dimensional, free-energy landscapes of protein-folding reactions by nonlinear dimensionality reduction.

The definition of reaction coordinates for the characterization of a protein-folding reaction has long been a controversial issue, even for the "simple" case in which one single free-energy barrier separates the folded and unfolded ensemble. We propose a general approach to this problem to obtain a few collective coordinates by using nonlinear dimensionality reduction. We validate the usefulness of this method by characterizing the folding landscape associated with a coarse-grained protein model of src homology 3 as sampled by molecular dynamics simulations. The folding free-energy landscape projected on the few relevant coordinates emerging from the dimensionality reduction can correctly identify the transition-state ensemble of the reaction. The first embedding dimension efficiently captures the evolution of the folding process along the main folding route. These results clearly show that the proposed method can efficiently find a low-dimensional representation of a complex process such as protein folding.

Algorithms↗

PubMed2003

Theoretical calculation and experimental study on the third-order nonlinearity parameter C/A for organic liquids and biological fluids.

In the present paper we deal with calculating and measuring the third-order nonlinearity parameter C/A for organic liquids and biological fluids. For the organic liquids, the second-order derivative of sound speed with respect to pressure at constant entropy is discussed in terms of thermodynamic parameters, and a formula for calculating C/A is established. Calculated results of C/A for various organic liquids demonstrate that omitting the second-order derivative of sound speed with respect to sound pressure in an isentropic process, could overestimate the value of C/A about 20%-30%. For measuring C/A, the finite-amplitude insert substitution technique is employed. A theoretical description of the sound pressure amplitude for the third-order harmonics is obtained using the perturbation method, in which the sound pressure amplitude of the third-order harmonics is shown approximately as a parabolic function of the propagation distance in the medium. By measuring and comparing the sound pressure amplitudes of the third-order harmonics when inserting a test sample, the reference liquid, and a comparative liquid, respectively, the value of C/A for the sample liquid is determined with reference to known C/A values of reference and comparative liquids. An experimental setup is developed, and the measured values of C/A for the organic liquids agree with the predicted ones calculated by the thermodynamic methods. Furthermore, the finite-amplitude method is extended to measure the C/A parameter for biological fluids, and the measured values of C/A for several biological fluids are also presented.

Body Fluids↗

PubMed2006

Folding kinetics of a lattice protein via a forward flux sampling approach.

We implement a forward flux sampling approach [R. J. Allen et al., J. Chem. Phys. 124, 194111 (2006)] for calculating transition rate constants and for sampling paths of protein folding events. The algorithm generates trajectories for the transition between the unfolded and folded states as chains of partially connected paths, which can be used to obtain the transition-state ensemble and the properties that characterize these intermediates. We apply this approach to Monte Carlo simulations of a model lattice protein in open space and in confined spaces of varying dimensions. We study the effect of confinement on both protein thermodynamic stability and folding kinetics; the former by mapping free-energy landscapes and the latter by the determination of rate constants and mechanistic details of the folding pathway. Our results show that, for the range of temperatures where the native state is stable, confinement of a protein destabilizes the unfolded state by reducing its entropy, resulting in increased thermodynamic stability of the folded state. Relative to the folding in open space, we find that the kinetics can be accelerated at temperatures above the temperature at which the unconfined protein folds fastest and that the rate constant increases with the number of constrained dimensions. By examining the statistical properties of the transition-state ensemble, we detect signs of a classical nucleation folding mechanism for a core of native contacts formed at an early stage of the process. This nucleus acts as folding foci and is composed of those residues that have higher probability to form native contacts in the transition-state intermediates, which can vary depending on the confinement conditions of the system.

Computer Simulation↗

PubMed1982

Microcalorimetric study of the interaction of human and bovine serum albumins with tryptophan and tryptophan analogs.

The thermodynamic parameters for the protein-ligand binding have been obtained by microcalorimetry on three albumin samples (fatty acid free human serum albumin (I), fraction V human serum albumin (II), and fraction V bovine serum albumin (III)) bound with l-tryptophan (A) and three-ring tryptophan analogs (B and B*). The percentage, mu, of binding molecules (equivalent to the number of sites) is found to be 1.0 for I and 0.65 for II (in good agreement with dialysis results on the same systems) and 1.0 for III. The large negative delta H(bind) (-27.2 to -33.2 kJ . mol-1) constitutes the main contribution to delta G(bind) (-23.0 to -31.2 kJ . mol-1). The better binding of I-III towards B and B* compared with A is due to delta S(bind) being less negative. This is interpreted as a lesser loss of entropy for the three-ring ligands than for the normal tryptophan when they are bound. Data obtained on the proteins (heat of dilution; Huggins' constant, k') correlate well with mu or Qmax. This indicates that these physicochemical data could be used to characterize and compare rapidly some albumins of different sources. The unexpected finding that the parameters of I and III are nearer to each other than they are from II is discussed.

Animals↗

PubMed2006

On the calculation of absolute free energies from molecular-dynamics or Monte Carlo data.

We propose a method for calculating absolute free energies from Monte Carlo or molecular-dynamics data. The method is based on the identity that expresses the partition function Q as a Boltzmann average: 1Q=w(p,x)exp[betaH(p,x)], where w(p,x) is an arbitrary weight function such that its integral over the phase space is equal to 1. In practice, to minimize statistical errors the weight function is chosen such that the regions of the phase space where sampling statistics are poor are excluded from the average. The "ideal" weight function would be the equilibrium phase-space density exp[-betaH(p,x)]Q itself. We consider two methods for constructing the weight function based on different estimates of the equilibrium phase-space density from simulation data. In the first method, it is chosen to be a Gaussian function, whose parameters are obtained from the covariance matrix of the atomic coordinates. In the second, a clustering algorithm is used to attempt partitioning the data into clusters corresponding to different basins of attraction visited by the system. The weight function is then constructed as a superposition of Gaussians calculated for each cluster separately. We show that these strategies can be used to improve upon previous methods of estimating absolute entropies from covariance matrices.

Algorithms↗

PubMed2003

Interpolation artifacts in multimodality image registration based on maximization of mutual information.

Mutual information (MI) is an increasingly popular match metric for multimodality image registration. However, its value is affected by interpolation, which may limit registration accuracy. The purpose of this study was to characterize the artifacts from eight interpolators and to investigate efficient strategies to overcome these artifacts. The interpolators were: 1) nearest neighbor; 2) linear; 3) cubic Catmull-Rom; 4) Hamming-windowed sinc; 5) partial volume; 6) NN with jittered sampling (JIT); 7) NN with histogram blurring (BLUR); and 8) NN with JIT and BLUR. The impact of interpolation on MI was evaluated in two dimensions over different translational and rotational misregistration. Interpolation caused spurious fluctuations in MI whenever the voxel grids had coinciding periodicities and were nearly aligned. The artifacts did not lessen by using intensity interpolators with wider support (e.g., cubic Catmull-Rom, Hamming-windowed sinc). PV could lead to either arch artifacts or inverted-arch artifacts, depending on the relative voxel sizes. Several strategies reduced artifacts and improved registration robustness: JIT, BLUR, avoiding an extreme number of intensity bins, and resampling the images in a rotated orientation with different relative voxel sizes (e.g., pi/3). These findings also apply to related methods, including normalized MI, joint entropy, and Hill's third moment.

Algorithms↗

PubMed2002

Thoroughly sampling sequence space: large-scale protein design of structural ensembles.

Modeling the inherent flexibility of the protein backbone as part of computational protein design is necessary to capture the behavior of real proteins and is a prerequisite for the accurate exploration of protein sequence space. We present the results of a broad exploration of sequence space, with backbone flexibility, through a novel approach: large-scale protein design to structural ensembles. A distributed computing architecture has allowed us to generate hundreds of thousands of diverse sequences for a set of 253 naturally occurring proteins, allowing exciting insights into the nature of protein sequence space. Designing to a structural ensemble produces a much greater diversity of sequences than previous studies have reported, and homology searches using profiles derived from the designed sequences against the Protein Data Bank show that the relevance and quality of the sequences is not diminished. The designed sequences have greater overall diversity than corresponding natural sequence alignments, and no direct correlations are seen between the diversity of natural sequence alignments and the diversity of the corresponding designed sequences. For structures in the same fold, the sequence entropies of the designed sequences cluster together tightly. This tight clustering of sequence entropies within a fold and the separation of sequence entropy distributions for different folds suggest that the diversity of designed sequences is primarily determined by a structure's overall fold, and that the designability principle postulated from studies of simple models holds in real proteins. This has important implications for experimental protein design and engineering, as well as providing insight into protein evolution.

Amino Acid Sequence↗

PubMed2001

Determinants and interindividual variation of R-R interval dynamics in healthy middle-aged subjects.

Determinants and intersubject variations of fractal and complexity measures of R-R interval variability were studied in a random population of 200 healthy middle-aged women (age 51 +/- 6 yr) and 189 men (age 50 +/- 6 yr) during controlled conditions in the supine and sitting positions. The short-term fractal exponent (alpha(1)) was lower in women than men in both the supine (1.18 +/- 0.20 vs. 1.12 +/- 0.17, P < 0.01) and sitting position (P < 0.001). Approximate entropy (ApEn), a measure of complexity, was higher in women in the sitting position (1.16 +/- 0.17 vs. 1.07 +/- 0.19, P < 0.001), but no gender-related differences were observed in ApEn in the supine position. Fractal and complexity measures were not related to any other demographic, laboratory, or lifestyle factors. Intersubject variations in a fractal measure, alpha(1) (e.g., 1.15 +/- 0.20 in the supine position, z value 1.24, not significant), and in a complexity measure, ApEn (e.g., 1.14 +/- 0.18 in the supine position, z value 1.44, not significant), were generally smaller and more normally distributed than the variations in the traditional measures of heart rate variability (e.g., standard deviation of R-R intervals 49 +/- 21 ms in the supine position, z value 2.53, P < 0.001). These results in a large random population sample show that healthy subjects express relatively little interindividual variation in the fractal and complexity measures of heart rate behavior and, unlike the traditional measures of heart rate variability, they are not related to lifestyle, metabolic, or demographic variables. However, subtle gender-related differences are also present in fractal and complexity measures of heart rate behavior.

Adult↗

PubMed2005

Biased sampling of nonequilibrium trajectories: can fast switching simulations outperform conventional free energy calculation methods?

We have investigated the maximum computational efficiency of reversible work calculations that change control parameters in a finite amount of time. Because relevant nonequilibrium averages are slow to converge, a bias on the sampling of trajectories can be beneficial. Such a bias, however, can also be employed in conventional methods for computing reversible work, such as thermodynamic integration or umbrella sampling. We present numerical results for a simple one-dimensional model and for a Widom insertion in a soft sphere liquid, indicating that, with an appropriately chosen bias, conventional methods are in fact more efficient. We describe an analogy between nonequilibrium dynamics and mappings between equilibrium ensembles, which suggests that the practical inferiority of fast switching is quite general. Finally, we discuss the relevance of adiabatic invariants in slowly driven Hamiltonian systems for the application of Jarzynski's theorem.

Chemistry, Physical↗

PubMed2006

Site-specific experiments on folding/unfolding of Jun coiled coils: thermodynamic and kinetic parameters from spin inversion transfer nuclear magnetic resonance at leucine-18.

The 32-residue leucine zipper subsequence, called here Jun-lz, associates in benign media to form a parallel two-stranded coiled coil. Studies are reported of its thermal unfolding/folding transition by circular dichroism (CD) on samples of natural isotopic abundance and by both equilibrium and spin inversion transfer (SIT) nuclear magnetic resonance (NMR) on samples labeled at the leucine-18 alpha-carbon with 99% 13C. The data cover a wide range of temperature and concentration, and show that Jun-lz unfolds below room temperature, being far less stable than some other leucine zippers such as GCN4. 13C-NMR shows two well-separated resonances. We ascribe the upfield one to 13C spins on unfolded single chains and the downfield one to 13C spins on coiled-coil dimers. Their relative intensities provide a measure of the unfolding equilibrium constant. In SIT NMR, the recovery of the equilibrium magnetization after one resonance is inverted is modulated in part by the unfolding and folding rate constants, which are accessible from the data. Global Bayesian analysis of the equilibrium and SIT NMR data provide values for the standard enthalpy, entropy, and heat capacity of unfolding, and show the latter to be unusually large. The CD results are compatible with the NMR findings. Global Bayesian analysis of the SIT NMR data yields the corresponding activation parameters for unfolding and folding. The results show that both reaction directions are activated processes. Activation for unfolding is entropy driven, enthalpy opposed. Activation for folding is strongly enthalpy opposed and somewhat entropy opposed, falsifying the idea that the barrier for folding is solely due to a purely entropic search for properly registered partners. The activation heat capacity is much larger for folding, so almost the entire overall change is due to the folding direction. This latter finding, if it applies to GCN4 leucine zippers, clears up an extant apparent disagreement between folding rate constants for GCN4 as determined by chevron analysis and NMR in differing temperature regimes.

Carbon Isotopes↗

PubMed2004

The increase in denaturation temperature following cross-linking of collagen is caused by dehydration of the fibres.

Differential scanning calorimetry (DSC) was used to study the thermal stability of native and synthetically cross-linked rat-tail tendon at different levels of hydration, and the results compared with native rat-tail tendon. Three cross-linking agents of different length between functional groups were used: malondialdehyde (MDA), glutaraldehyde and hexamethylene diisocyanate (HMDC). Each yielded the same linear relation between the reciprocal of the denaturation temperature in Kelvin, T(max), and the water volume fraction, epsilon (1/T(max)=0.000731epsilon+0.002451) up to a critical hydration level, the volume fraction of water in the fully hydrated fibre. Thereafter, water was in excess, T(max) was constant and the fibre remained unchanged, no matter how much excess water was added. This T(max) value and the corresponding intrafibrillar volume fraction of water were as follows: 84.1 degrees C and 0.48 for glutaraldehyde treated fibres, 74.1 degrees C and 0.59 for HMDC treated fibres, 69.3 degrees C and 0.64 for MDA treated fibres, and 65.1 degrees C and 0.69 for untreated native fibres. Borohydride reduction of the native enzymic aldimines did not increase the denaturation temperature of the fibres. As all samples yielded the same temperature at the same hydration, the temperature could not be affected by the nature of the cross-link other than through its effect on hydration. Cross-linking therefore caused dehydration of the fibres by drawing the collagen molecules closer together and it was the reduced hydration that caused the increased temperature stability. The cross-linking studied here only reduced the quantity of water between the molecules and did not affect the water in intimate contact with, or bound to, the molecule itself. The enthalpy of denaturation was therefore unaffected by cross-linking. Thus, the "polymer-in-a-box" mechanism of stabilization, previously proposed to explain the effect of dehydration on the thermal properties of native tendon, explained the new data also. In this mechanism, the configurational entropy of the unfolding molecule is reduced by its confinement in the fibre lattice, which shrinks on cross-linking.

Animals↗