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PubMed1996

On the origin of the cooperativity of protein folding: implications from model simulations.

There is considerable experimental evidence that the cooperativity of protein folding resides in the transition from the molten globule to the native state. The objective of this study is to examine whether simplified models can reproduce this cooperativity and if so, to identify its origin. In particular, the thermodynamics of the conformational transition of a previously designed sequence (A. Kolinski, W. Galazka, and J. Skolnick, J. Chem. Phys. 103: 10286-10297, 1995), which adopts a very stable Greek-key beta-barrel fold has been investigated using the entropy Monte Carlo sampling (ESMC) technique of Hao and Scheraga (M.-H. Hao and H.A. Scheraga, J. Phys. Chem. 98: 9882-9883, 1994). Here, in addition to the original potential, which includes one body and pair interactions between side chains, the force field has been supplemented by two types of multi-body potentials describing side chain interactions. These potentials facilitate the protein-like pattern of side chain packing and consequently increase the cooperativity of the folding process. Those models that include an explicit cooperative side chain packing term exhibit a well-defined all-or-none transition from a denatured, random coil state to a high-density, well-defined, nativelike low-energy state. By contrast, models lacking such a term exhibit a conformational transition that is essentially continuous. Finally, an examination of the conformations at the free-energy barrier between the native and denatured states reveals that they contain a substantial amount of native-state secondary structure, about 50% of the native contacts, and have an average root mean square radius of gyration that is about 15% larger than native.

Amino Acids↗

PubMed1998

Reduced disorderliness of growth hormone release in biochemically inactive acromegaly after pituitary surgery.

The episodicity of 24 h GH release was studied in 18 patients with active acromegaly, 12 patients 7-10 days after pituitary surgery, 14 patients long after operation (3-17 years), and 21 healthy gender- and age-matched control subjects, using a recently introduced scale- and model-independent regularity statistic, approximate entropy (ApEn). Blood samples were taken at 10-min intervals for 24 h, and plasma GH concentrations were measured by immunofluorometric assay (detection limit 11.5 ng/l). For this study we selected operated patients who were biochemically in remission, defined by normal circulating IGF-I and insulin-like growth factor-binding protein-3 (IGFBP-3) concentrations, normal glucose-suppressed plasma GH concentration (<0.38 microg/l), and the normalization of the paradoxical rise of GH to TRH or GnRH. In patients with active acromegaly ApEn was 1.23+/-0.04, with no overlap with the control subjects (P = 1.2 x 10[-16]), who had an ApEn of 0.40+/-0.04. ApEn in patients shortly after surgery was 0.71+/-0.09 (P < 0.001 vs controls), and long after surgery 0.56+/-0.05 (P < 0.011 vs controls). ApEn values in treated and untreated patients correlated significantly with the plasma concentration of IGF-I (r=0.531) and IGFBP-3 (r=0.598), and the log-transformed 24h GH secretion rate (r=0.749). Shortly after surgery only one-third of the patients had a normal ApEn value, whereas long after surgery about 70% of the patients had a normal ApEn value. Although ApEn eventually normalized in about 70% of the operated patients, the cause of the persistence of abnormal GH release in the remainder of the subjects is not known, and might reflect permanent hypothalamic-pituitary dysfunction or a very early recurrence of the somatotroph adenoma.

Acromegaly↗

PubMed2003

Multiple-quantum magic-angle spinning spectroscopy using nonlinear sampling.

NMR spectroscopy is a relatively insensitive technique and many biomolecular applications operate near the limits of sensitivity and resolution. A particularly challenging example is detection of the quadrupolar nucleus 17O, due to its low natural abundance, large quadrupole couplings, and low gyromagnetic ratio. Yet the chemical shift of 17O spans almost 1000 ppm in organic molecules and it serves as a potentially unique reporter of hydrogen bonding in peptides, nucleic acids, and water, and as a valuable complement to 13C and 15N NMR. Recent developments including the multiple-quantum magic-angle spinning (MQMAS) experiment have enabled the detection of 17O in biological solids, but very long data acquisitions are required to achieve sufficient sensitivity and resolution. Here, we perform nonlinear sampling in the indirect dimension of MQMAS experiments to substantially reduce the total acquisition time and improve sensitivity and resolution. Nonlinear sampling prevents the use of the discrete Fourier transform; instead, we employ maximum entropy (MaxEnt) reconstruction. Nonlinearly sampled MQMAS spectra are shown to provide high resolution and sensitivity in several systems, including lithium sulfate monohydrate (LiSO(4)-H(2)17O) and L-asparagine monohydrate (H(2)17O). The combination of nonlinear sampling and MaxEnt reconstruction promises to make the application of 17O MQMAS practical in a wider range of biological systems.

Anisotropy↗

PubMed2001

Discriminating the relation between relations: the role of entropy in abstract conceptualization by baboons (Papio papio) and humans (Homo sapiens).

Two baboons (Papio papio) successfully learned relational matching-to-sample: They picked the choice display that involved the same relation among 16 pictures (same or different) as the sample display, although the sample display shared no pictures with the choice displays. The baboons generalized relational matching behavior to sample displays created from novel pictures. Further experiments varying the number of sample pictures and the mixture of same and different sample pictures suggested that entropy plays a key role in the baboons' conceptual behavior. Two humans (Homo sapiens) were similarly trained and tested; their behavior was both similar to and different from the baboons' behavior. The results suggest that animals other than humans and chimpanzees can discriminate the relation between relations. They further suggest that entropy detection may underlie same-different conceptualization, but that additional processes may participate in human conceptualization.

Animals↗

PubMed1994

Improved resolution in triple-resonance spectra by nonlinear sampling in the constant-time domain.

Nonlinear sampling along the constant-time dimension is applied to the constant-time HNCO spectrum of the dimerization domain of Gal4. Nonlinear sampling was used for the nitrogen dimension, while the carbon and proton dimensions were sampled linearly. A conventional ct-HNCO spectrum is compared with a nonlinearly sampled spectrum, where the gain in experiment time obtained from nonlinear sampling is used to increase the resolution in the carbonyl dimension. Nonlinearly sampled data are processed by maximum entropy reconstruction. It is shown that the nonlinearly sampled spectrum has a higher resolution, although it was recorded in less time. The constant intensity of the signal in the constant-time dimension allows for a variety of sampling schedules. A schedule of randomly distributed sampling points yields the best results. This general method can be used to significantly increase the quality of heteronuclear constant-time spectra.

Algorithms↗

PubMed1996

A comparison of adaptive and nonadaptive filters for reduction of power line interference in the ECG.

We have investigated the relative performance of an adaptive and nonadaptive 60-Hz notch filter applied to an ECG signal. We evaluated the performance of the two implementations with respect to adaptation rate (or transient response time), signal distortion, and implementation complexity. We also investigated the relative effect of adaptive and nonadaptive 60-Hz filtering on ECG data compression. With a 360 Hz sample rate and an adaptation time of approximately 0.3 s for a 1 mV 60-Hz signal, the adaptive implementation is less complex and introduces less noise, particularly in the ST-segment, into a typical ECG signal. When applied to ECG signals, prior to data compression by average beat subtraction and residual differencing, the residual signal resulting from the adaptively filtered signal had an average entropy 0.37 bits per sample (bps) lower than the unfiltered signal. The nonadaptive 60-Hz filter produced an average entropy decrease of 0.08 bps relative to the unfiltered ECG.

Algorithms↗

PubMed1994

Protein side-chain conformational entropy derived from fusion data--comparison with other empirical scales.

The loss of conformational entropy of protein side-chains is a major effect in the energetics of folding. The simplest approach is to enumerate the number of freely rotatable bonds. Recently, two scales of side-chain conformational entropy have been proposed based on the definition of entropy as the Boltzmann sampling over all accessible states (S = -R sigma p(i)lnp(i), where p(i) is the probability of being in a rotameric state). In one scale, derived only for aliphatic and aromatic side-chains, the values of p(i) were obtained from Monte Carlo simulations. In the other scale, the observed frequencies of different rotameric states in a database of protein crystal structures yielded an estimate for p(i). Here an empirical estimation of the fusion entropy of the side-chains is used to derive a third scale. The fusion entropy is obtained as a sum of empirically derived contributions from component hydrocarbon and functional groups. There is a good agreement between the fusion scale and the other two scales. This suggests that the magnitude of conformational entropy is being correctly established.

Computer Simulation↗

PubMed1993

Empirical scale of side-chain conformational entropy in protein folding.

A major effect in the energetics of protein folding is the loss of conformational entropy of the side-chains. The definition of entropy as the Boltzmann sampling over all states (S = -R sigma p(i) ln p(i)) requires evaluation of the probability (p(i)) of the system being in rotameric state i. The principle of this paper is to obtain an estimate of p(i) from the observed distribution of exposed side-chain rotamers in 50 non-homologous protein crystal structures. However because of limited data we show that for all side-chains except Asn, Asp and Glu the side-chain distribution is independent of burial and accordingly all data were pooled in the calculation of p(i). For Asn, Asp and Glu side-chains with relative accessibility > 60% were used. The scale includes effects due to the symmetry of side-chains such as Phe and the free rotation of side-chain amide, carboxyl and hydroxyl groups. An empirical scale for the loss of side-chain conformational entropy during protein folding is thereby obtained. Values of the change in free energy due to entropy (-T delta S) on burying a side-chain range from 0 for Ala, Gly and Pro to +2.1 kcal/mol for Gln (T = 300 K). We explore the consistency of a simple model for protein folding that includes side-chain entropy, main-chain entropy, hydrophobicity and hydrogen bonding. The stability of site-directed mutations is discussed in terms of conformational entropy.

Models, Chemical↗

PubMed1999

Quantitative tools for comparing animal communication systems: information theory applied to bottlenose dolphin whistle repertoires.

Comparative analysis of nonhuman animal communication systems and their complexity, particularly in comparison to human language, has been generally hampered by both a lack of sufficiently extensive data sets and appropriate analytic tools. Information theory measures provide an important quantitative tool for examining and comparing communication systems across species. In this paper we use the original application of information theory, that of statistical examination of a communication system's structure and organization. As an example of the utility of information theory to the analysis of animal communication systems, we applied a series of information theory statistics to a statistically categorized set of bottlenose dolphin Tursiops truncatus, whistle vocalizations. First, we use the first-order entropic relation in a Zipf-type diagram (Zipf 1949 Human Behavior and the Principle of Least Effort) to illustrate the application of temporal statistics as comparative indicators of repertoire complexity, and as possible predictive indicators of acquisition/learning in animal vocal repertoires. Second, we illustrate the need for more extensive temporal data sets when examining the higher entropic orders, indicative of higher levels of internal informational structure, of such vocalizations, which could begin to allow the statistical reconstruction of repertoire organization. Third, we propose using 'communication capacity' as a measure of the degree of temporal structure and complexity of statistical correlation, represented by the values of entropic order, as an objective tool for interspecies comparison of communication complexity. In doing so, we introduce a new comparative measure, the slope of Shannon entropies, and illustrate how it potentially can be used to compare the organizational complexity of vocal repertoires across a diversity of species. Finally, we illustrate the nature and predictive application of these higher-order entropies using a preliminary sample of dolphin whistle vocalizations. The purpose of this preliminary report is to re-examine the original application of information theory to the field of animal communication, illustrate its potential utility as a comparative tool for examining the internal informational structure of animal vocal repertoires and their development, and discuss its relationship to behavioural ecology and evolutionary theory. Copyright 1999 The Association for the Study of Animal Behaviour.

Journal Article↗

PubMed2001

The relationship between 24-hour growth hormone secretion and insulin-like growth factor I in patients with successfully treated acromegaly: impact of surgery or radiotherapy.

In patients with treated acromegaly, improved survival is associated with serum GH concentrations below 2 microgram/L (5 mU/L). A principal aim of therapy in acromegaly is to achieve a GH level less than 2 microgram/L, as such levels are thought to be "safe." However, such GH levels do not always equate with normalization of plasma insulin-like growth factor I (IGF-I), although epidemiological data linking survival or morbidity to IGF-I levels are at present lacking. The aims of this study were 1) to further define the nature of GH release in those acromegalic patients who achieve mean GH concentrations below 2 microgram/L post therapy, 2) to examine the effect of different therapeutic interventions on the 24-h GH profile (surgery alone or radiotherapy), and 3) to determine the relationship between the various characteristics of the 24-h GH profile and IGF-I production in acromegalic subjects who have achieved GH below 2 microgram/L. Spontaneous 24-h GH secretion was measured using both a conventional immunoradiometric assay (limit of detection, 0.4 microgram/L) and an ultrasensitive assay (limit of detection, 0.002 microgram/L). The GH data have been analyzed by several methods: 1) the pulse detection algorithm Cluster, 2) a distribution method for detection of peak [the observed concentration 95%, i.e. the threshold at or below which GH concentrations are assessed to be 95% of the time, as calculated by probability analysis (OC 95%)] and trough (OC, 5%) GH activity, 3) deconvolution analysis, and 4) approximate entropy analysis. GH was sampled every 20 min for 24 h, along with basal IGF-I and IGF-binding protein-3, in 21 treated acromegalic patients with a mean GH below 2 microgram/L [ACR; 9 women and 12 men; median age (range), 49 (31-76) yr] and 16 healthy controls [C; 6 women and 10 men; age, 50 (30-75) yr]. Mean 24-h serum GH concentrations were [median (range)]: ACR, 1.1 (0.04-1.5) microgram/L; C, 0.4 (0.02-3.3) microgram/L (P = 0.28). GH pulse frequency was: ACR, 11 (1-14)/24 h; C, 10 (8-18)/24 h (P = 0.41). In the GH profiles the mean heights of the GH peaks were: ACR, 1.2 (0.05-2.8) microgram/L; C, 0.8 (0.02-5.1) microgram/L (P = 0.91), and the mean GH valley nadirs were: ACR, 0.65 (0.03-1.1) microgram/L; C, 0.09 (0.01-1.8) microgram/L (P < 0.02). The OC 95% was: ACR, 1.0 (0.04-3.8) microgram/L; C, 1.0 (0.02-10) microgram/L (P = 0.65), and the OC 5% was: ACR, 0.09 (0.01-0.6) microgram/L; C, 0.01 (0.001-0.4) microgram/L (P < 0.001). The median IGF-I was: ACR, 227 (100-853) microgram/L; C, 156 (89-342) microgram/L (P < 0.005). Approximate entrophy values were: ACR, 1.06 (0.35-1.45); and C, 0.57 (0.27-1.19); P < 0.05. In the acromegaly group a significant positive correlation was found between IGF-I and the calculated GH secretory burst amplitude in the radiotherapy subset (r = 0.85; P < 0.0005) as well as between IGF-I and both the mean GH valley nadir (r = 0.60; P < 0.004) and the trough (OC 5%) GH activity for the acromegalic patients as a whole (r = 0.55; P < 0.02). We conclude that in treated acromegaly (GH, <2 microgram/L), 1) IGF-I (by approximately 50%) and basal GH secretion (by 5-fold) remain significantly elevated compared with control values despite similar mean 24-h GH concentrations; 2) the calculated GH secretory pulse amplitude, mean GH valley nadir, and OC 5% correlate positively with IGF-I; 3) the greater mean GH valley nadir and OC 5% in acromegalic patients compared with controls may account for the raised IGF-I; and 4) radiotherapy is unlikely to normalize the GH secretory pattern, which underlies the persisting elevated IGF-I levels.

Acromegaly↗

PubMed1998

Sex differences in circulating human leptin pulse amplitude: clinical implications.

Leptin, a product of fat cells, provides a signal of nutritional status to the central nervous system. Leptin concentrations have ultradian and diurnal fluctuations. We conducted this study to assess sex differences in the levels of organization of frequently sampled leptin concentrations in healthy, normal weight women and men. Leptin levels were sampled every 7 min for 24 h in 14 healthy, normal weight individuals (6 women and 8 men). The 14 leptin time series containing a total of 2898 leptin measurements were assessed by 1) algorithms that characterize statistically significant pulsatility, 2) Spectral (Fourier) analysis, 3) analysis of time intervals and variability, and 4) approximate entropy. We found that frequently sampled plasma leptin concentrations have a 24-h profile that is numerically more than twice as high in women as in men, and leptin pulse amplitude is likewise more than twice as high in women. However, healthy men and women have nearly identical concentration-independent and frequency-related 24-h and ultradian patterns. Leptin concentrations have nonrandom fluctuations over 24 h, independent of their absolute value and underlying 24-h periodicity, that are similar in men and women. Ultradian periodicities detected by Fourier time series have similar values in men and women. The strongest distinction between the sexes in the level of organization of leptin concentration is not at the level of pulse organization or oscillation frequency, but, rather, in the mass or amount of leptin released (or removed) per unit time, indicating that women might be more resistant to the effects of leptin than men. Because leptin is clinically relevant to the regulation of body weight, future studies should examine whether the relative leptin resistance exhibited by women might contribute to their increased susceptibility to disorders whose pathophysiology involves dysregulation of food intake and body weight.

Adult↗

PubMed2000

Electroencephalogram approximate entropy correctly classifies the occurrence of burst suppression pattern as increasing anesthetic drug effect.

BACKGROUND: Approximate entropy, a measure of signal complexity and regularity, quantifies electroencephalogram changes during anesthesia. With increasing doses of anesthetics, burst-suppression patterns occur. Because of the high-frequency bursts, spectrally based parameters such as median electroencephalogram frequency and spectral edge frequency 95 do not decrease, incorrectly suggesting lightening of anesthesia. The authors investigated whether the approximate entropy algorithm correctly classifies the occurrence of burst suppression as deepening of anesthesia. METHODS: Eleven female patients scheduled for elective major surgery were studied. After propofol induction, anesthesia was maintained with isoflurane only. Before surgery, the end-tidal isoflurane concentration was varied between 0.6 and 1.3 minimum alveolar concentration. The raw electroencephalogram was continuously recorded and sampled at 128 Hz. Approximate entropy, electroencephalogram median frequency, spectral edge frequency 95, burst-suppression ratio, and burst-compensated spectral edge frequency 95 were calculated offline from 8-s epochs. The relation between burst-suppression ratio and approximate entropy, electroencephalogram median frequency, spectral edge frequency 95, and burst-compensated spectral edge frequency 95 was analyzed using Pearson correlation coefficient. RESULTS: Higher isoflurane concentrations were associated with higher burst-suppression ratios. Electroencephalogram median frequency (r = 0.34) and spectral edge frequency 95 (r = 0.29) increased, approximate entropy (r = -0.94) and burst-compensated spectral edge frequency 95 (r = -0.88) decreased with increasing burst-suppression ratio. CONCLUSION: Electroencephalogram approximate entropy, but not electroencephalogram median frequency or spectral edge frequency 95 without burst compensation, correctly classifies the occurrence of burst-suppression pattern as increasing anesthetic drug effect.

Adult↗

PubMed1998

Reproducibility and efficiency testing of two sampling methods for image analysis in cytology.

OBJECTIVE: Quantitative nuclear DNA analyses and nuclear morphometry have become a widely used tool in pathology. Nevertheless, studies done by different observers utilizing the same methods very often have shown different results. One of the reasons could be that different sampling methods were used. In this study two selection methods for image analyses (the consecutive selection method and the random selection method) were tested for reproducibility and efficiency. STUDY DESIGN: Using an interactive imaging analysis system, 10 cases (5 breast adenocarcinomas, 3 prostatic cancers, 1 sarcoma, 2 prostatic hyperplasias) were measured twice by using each sampling method. Median nuclear area and entropy (i.e., a statistical descriptor of DNA histograms) were the parameters calculated. RESULTS: The results showed that using the consecutive selection method, the number of individual nuclei in a cytologic sample that should be measured to obtain reproducible results was 150 for nuclear area and 110 for entropy. The corresponding figures using random systematic selection method were 80 for assessment of nuclear area and 100 for assessment of entropy. CONCLUSION: Both methods showed high reproducibility and a good correlation with each other. The mathematical idea of "plateau values," which was used to estimate the number of measurements needed, was considered a good contribution to increasing the efficiency of both methods.

Breast Neoplasms↗

PubMed2003

Entropy evaluation using the kinetic method: is it feasible?

The kinetic method is one of the most widely used experimental techniques for the measurement of thermochemical parameters by mass spectrometry. Recently it has been realized that it can also be used to determine reaction entropies, but the validity of this approach has not been established. This Perspective evaluates kinetic method plots in cases where there is a significant entropy difference between the competing fragmentation channels (i.e. between sample and reference compounds in the dissociating cluster ion). The concept underlying this study is to calculate mass spectra theoretically, based on known thermochemical parameters and as a function of experimental conditions. This can be done accurately using the RRKM-based MassKinetics software. The resulting mass spectra are then interpreted by the kinetic method, yielding DeltaH and DeltaS values. These values are, in turn, compared with the true values used to generate the calculated mass spectra. The results show that the reaction entropy difference between sample and reference has a very large influence on kinetic method plots. This should always be considered when studying energy-dependent mass spectra (using metastable ions or low- or high-energy collision-induced dissociation (CID)), even if only DeltaH is to be determined. Kinetic method plots are not strictly linear and this becomes a serious issue in the case of small molecules showing a large entropy effect. In such cases, results obtained at a low degree of excitation are more accurate. Energy and entropy effects can be evaluated in a relatively straightforward manner: first, the apparent Gibbs energy (DeltaG(app)) and effective temperature (T(eff)) are determined from kinetic method plots (intercept and slope, respectively), obtained from experiments using various degrees of excitation. Second, the resulting DeltaG(app) is plotted against T(eff), the slope yielding DeltaS while the intercept (extrapolation to zero temperature) yields DeltaH. This data evaluation yields more accurate results than alternative methods used in the literature. The resulting DeltaH values are fairly accurate, with errors, in most cases, <4 kJ mol(-1). On the other hand, DeltaS is systematically underestimated by 20-40%. Empirically scaling DeltaS values determined by the kinetic method by 1.35 results in a DeltaS value within 20% (or 10 J mol(-1) K(-1)) of the theoretical value.

Journal Article↗

PubMed2002

Effect of angular momentum on equilibrium properties of a self-gravitating system.

The microcanonical properties of a two-dimensional system of N classical particles interacting via a smoothed Newtonian potential, as a function of the total energy E and the total angular momentum L, are discussed. The two first moments of the distribution of the linear momentum of a given particle at a fixed position show that (a) on average the system rotates like a solid body and (b) the velocity dispersion is a function of the distance from the center. In order to estimate suitable observables, a numerical method based on an importance sampling algorithm is presented. The entropy surface S shows a negative specific heat capacity region at fixed L for all L. Observables probing the average mass distribution are used to understand the link between thermostatistical properties and the spatial distribution of particles. In order to define a phase in a nonextensive system, we introduce a more general observable than that proposed by Gross and Votyakov [Eur. Phys. J. B 15, 115 (2000)]. This observable is the sign of the largest eigenvalue of the Hessian matrix of the entropy surface. If it is negative then the system is in a pure (single) phase; if it is positive then the system undergoes a first order phase transition. At large E the gravitational system is in a homogeneous gas phase. At low E there are several collapse phases. At L=0 there is a single-cluster phase and for L not equal 0 there are several phases with two clusters. The relative size of the clusters depends on L. All these pure phases are separated by a first order phase transition region. Signals of critical behavior emerge at several points of the parameter space (E,L). We also show that a huge loss of information appears if we treat the system as a function of the intensive parameters. Besides the known nonequivalence at first order phase transitions, the pure phases with two clusters of different sizes are not accessible to the canonical ensemble. Moreover, for a particular choice of intensive parameters introduced in this paper, there exist in the microcanonical ensemble some values of those intensive parameters for which the corresponding canonical ensemble does not exist, i.e., the partition sum diverges.

Journal Article↗

PubMed1989

Adolescent psychic entropy: a response to unacknowledged fears.

The purpose of this study was to explore the feasibility of measuring psychic entropy in adolescents and to note the predictability of two variables--gender and grade. The subjects were 22 male and female junior and senior high school Caucasians in a central Kentucky church youth choir. They were given the 20-item Psychic Entropy Measure for Adolescents, which is a list of 20 negatively presented statements rated on a five-point scale. The five highest scoring items specifically reflect the phenomenon of psychic entropy. The findings suggest that unacknowledged adolescent fears may be developmental. The limited sample demonstrated that a revised instrument of the Psychic Entropy Measure for Adolescents could be an effective instrument in therapy.

Adaptation, Psychological↗

PubMed2002

[Effects of sampling parameter variation on the complexity analysis of EEG].

The algorithmic complexity and the approximate entropy of EEG were calculated and analyzed with different data points, different sample frequencies and different sample time duration. The results showed that under fixed sample frequency, the longer the data was, the more stable the complexity values were. With fixed sample time duration or fixed data point, lower sample frequency would be better both for EEG distinguishing and for computing time saving.

Algorithms↗

PubMed1988

Double-stranded structure for hyaluronic acid in ethanol-aqueous solution as revealed by circular dichroism of oligomers.

The sigmoidal nature of circular dichroism (CD) changes for hyaluronic acid solutions as a function of solvent composition or temperature is studied as a function of chain length by using oligomers. We find a chain length effect with approximately nine disaccharides required for the structural transition as a function of organic solvent, which proves that the transition is cooperative with large transition enthalpy and entropy. The transition also depends on sample concentration as expected for strand association, and this was investigated in detail for oligomers 12 and 16 disaccharides long. Indeed, it was possible to prevent completely the transition in mixed solvent with sufficient dilution of these oligomers, which demonstrates strand association. The CD data in mixed solvent as a function of oligomer concentration were fit with various models for association of two and more strands. Simplex methods were used to investigate the vector space of unknowns for the models, and two-strand models were shown to consistently give a better fit. A cooperative two-strand zipper model which allows relative sliding of the chains had the smallest fitting error and produced the following thermodynamic parameters (in terms of a duplex of disaccharide units) for the ordered structure in an aqueous solution containing 45% v/v ethanol, 12.5 mM NaH2PO4, and 7.5 mM H3PO4: enthalpy of growth, -1.0 +/- 0.3 kcal mol-1; entropy of growth, -2.3 +/- 1.3 eu mol-1; enthalpy of initiation, -20 +/- 3 kcal mol-1; entropy of initiation, -71 +/- 15 eu mol-1. The results are consistent with a double-stranded and helical structure for hyaluronic acid in solutions of reduced dielectric constant.

Carbohydrate Conformation↗