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PubMed1991

Biophysical models of protein denaturation. II. Effects of denaturants and of pH.

In order to broaden the scope and increase the utility of differential scanning calorimetry, a theoretical model of calorimetric thermograms is presently proposed which facilitates their biophysical interpretation and accounts explicitly for their modifications induced by denaturing agents and/or pH. The model rests mainly on statistical-physical considerations, the denaturation-linked increase of the number of binding sites for denaturants (including H+) serving as the conceptual basis for thermogram modelling. Denaturants were envisioned as contributing indirectly to thermal denaturation by forming complexes preferentially with unfolded protein molecules, shifting thus the equilibrium towards the denatured phase. After postulating the probability of complex formation, mean numbers of the relevant molecular species were computed by ensemble averaging. Finally, an eight-parameter expression has been derived defining protein heat capacity as a function of both temperature and denaturant concentration (or pH), each of the eight parameters having a distinct biophysical meaning. The model has been tested by applying it to the prediction of the pH-dependence of thermograms. Four proteins have been considered (lysozyme, myoglobin, apomyoglobin, and ribonuclease A), each represented by a series of three to four published thermograms recorded under different pH conditions. Model equations, fitted simultaneously to all thermograms in a pH series, reproduced correctly experimental tracings. Parameter values obtained as best-fit requirements (particularly those representing the number of binding sites unmasked by denaturation and the free energy of ion binding) were in close agreement with empirical, mainly potentiometric, data from literature. The empirically established pH-independence of the total enthalpy of denaturation, the phenomenon of cold denaturation, the pH-dependence of the Gibbs free energy of denaturation, of the melting temperature and of the temperature of cold denaturation, were all correctly predicted by the model. Combined effects of multiple denaturants, including the effects of pH in the presence of denaturants other than protons, are also predictable by the model.

Calorimetry↗

PubMed1989

Tooth eruption: the phase transition theory on biological formation of an orderly structure.

The mechanism of the formation of an orderly structure from random elements in organ development was clarified by studying the maturation of the dental arch in the human mandible. First, an application of methods established in statistical physics to a system of organ development was made possible, and then, the mathematical procedures for quantitative study of the structure and development of the dental arch were established in relation to radiographic data. The experimental results demonstrate that a parallel arrangement of the longitudinal axes of the lateral teeth is formed co-operatively in the dental arch. As formulation of the results to mathematical relations, the regulatory process was expressed by a non-linear Langevin equation of order parameter denoting an angle between longitudinal axes of the individual teeth. It follows that the orderly structure evolves with a change in thermodynamic potential; that is, the establishment of order in a phase transition. We propose the concept that organ differentiation is a phase transition in a dissipative system, with the decrease of gene activity substituted for temperature.

Adolescent↗

PubMed1998

Cooperative charge fluctuations by migrating protons in globular proteins.

A review of the hydrogen bonded network on the protein surface shows the presence of a charged complex system with parallel and competitive interactions, including ionizable side-chains, migrating protons, bound water and nearby backbone peptides. This system displays cooperative effects of dynamical nature, reviewed for lysozyme as a case. By increasing the water coverage of the protein powder, the bound water cluster exhibits a percolative transition, detectable by the onset of large water-assisted displacements of migrating protons, with a parallel emergence of protein mobility and biological function. By lowering the temperature, migrating protons exhibit a glassy dielectric relaxation in the low frequency range, pointing to a frustration by competing interactions similar to that observed in spin glasses and fragile glass forming liquids. The observation of these dissipative processes implies the occurrence of spontaneous charge fluctuations. A simplified model of the protein surface, where conformational and ionizable side-chain fluctuations are averaged out, is used to discuss the statistical physics of these cooperative effects. Some biological implications of this dynamical cooperativity for enzymatic activity are briefly suggested at the end.

Enzymes↗

PubMed1998

The 'Janus' nature of proteins: systems at the verge of the microscopic and macroscopic world.

Direct measurement of the heat capacity of proteins by microcalorimetry has had a decisive impact on understanding the behaviour of these biopolymers. Statistical mechanics allow a straightforward calculation and prediction of the enthalpy and heat capacity curves from the partition function. We show that these predictions can differ from the more intuitive models used so far for the description of the thermodynamic behaviour of proteins if the transition involves a stoichiometry other than 1:1. Furthermore, we delineate that the characteristics of protein unfolding are governed by the fluctuations associated with the small size of these molecules. Therefore it may be necessary to modify the picture of the unfolding of small proteins in the light of statistical physics, while for very large proteins the current view may be maintained as a useful limiting approximation.

Journal Article↗

PubMedDate not supplied

Parametric scaling from species to growth-form diversity: an interesting analogy with multifractal functions.

We propose a measure of divergence from species to life-form diversity aimed at summarizing the ecological similarity among different plant communities without losing information on traditional taxonomic diversity. First, species and life-form relative abundances within a given plant community are determined. Next, using Rényi's generalized entropy, the diversity profiles of the analyzed community are computed both from species and life-form relative abundances. Finally, the speed of decrease from species to life-form diversity is obtained by combining the outcome of both profiles. Interestingly, the proposed measure shows some formal analogies with multifractal functions developed in statistical physics for the analysis of spatial patterns. As an application for demonstration, a small data set from a plant community sampled in the archaeological site of Paestum (southern Italy) is used.

Fractals↗

PubMed2001

Using time- and size-resolved particulate data to quantify indoor penetration and deposition behavior.

Because people spend approximately 85-90% of their time indoors, it is widely recognized that a significant portion of total personal exposures to ambient particles occurs in indoor environments. Although penetration efficiencies and deposition rates regulate indoor exposures to ambient particles, few data exist on the levels or variability of these infiltration parameters, in particular for time- and size-resolved data. To investigate ambient particle infiltration, a comprehensive particle characterization study was conducted in nine nonsmoking homes in the metropolitan Boston area. Continuous indoor and outdoor PM2.5 and size distribution measurements were made in each of the study homes over weeklong periods. Data for nighttime, nonsource periods were used to quantify infiltration factors for PM2.5 as well as for 17 discrete particle size intervals between 0.02 and 10 microns. Infiltration factors for PM2.5 exhibited large intra- and interhome variability, which was attributed to seasonal effects and home dynamics. As expected, minimum infiltration factors were observed for ultrafine and coarse particles. A physical-statistical model was used to estimate size-specific penetration efficiencies and deposition rates for these study homes. Our data show that the penetration efficiency depends on particle size as well as home characteristics. These results provide new insight on the protective role of the building shell in reducing indoor exposures to ambient particles, especially for tighter (e.g., winterized) homes and for particles with diameters greater than 1 micron.

Air Movements↗

PubMed2003

Chiral conflict. The effect of temperature on the helical sense of a polymer controlled by the competition between structurally different enantiomers: from dilute solution to the lyotropic liquid crystal state.

Helical polymers appended with paired structurally different enantiomers, which have opposing helical sense preferences, yield a new kind of relationship between optical activity and temperature, and also reveal unusual details of the nature of chiral interactions. Consistent with a statistical physical theory developed for these experiments, the proportion of the competing chiral groups, determined by synthesis, fixes the compensation temperature at which the helical senses are equally populated. The lyotropic liquid crystal state formed by these polymers yields therefore a nematic state at any chosen temperature over a very wide range, with a cholesteric state arising with tightening pitch as temperature deviates from this point. Far from the nematic temperature, the pitch reaches the nanometer scale and therefore the reflection of visible light. Before crossing zero at the nematic temperature, the optical activity becomes so large that it may be observed with the unaided eye through crossed polarizers.

Biopolymers↗

PubMed2001

Exploring complex networks.

The study of networks pervades all of science, from neurobiology to statistical physics. The most basic issues are structural: how does one characterize the wiring diagram of a food web or the Internet or the metabolic network of the bacterium Escherichia coli? Are there any unifying principles underlying their topology? From the perspective of nonlinear dynamics, we would also like to understand how an enormous network of interacting dynamical systems-be they neurons, power stations or lasers-will behave collectively, given their individual dynamics and coupling architecture. Researchers are only now beginning to unravel the structure and dynamics of complex networks.

Models, Theoretical↗

PubMed2005

Rigorous location of phase transitions in hard optimization problems.

It is widely believed that for many optimization problems, no algorithm is substantially more efficient than exhaustive search. This means that finding optimal solutions for many practical problems is completely beyond any current or projected computational capacity. To understand the origin of this extreme 'hardness', computer scientists, mathematicians and physicists have been investigating for two decades a connection between computational complexity and phase transitions in random instances of constraint satisfaction problems. Here we present a mathematically rigorous method for locating such phase transitions. Our method works by analysing the distribution of distances between pairs of solutions as constraints are added. By identifying critical behaviour in the evolution of this distribution, we can pinpoint the threshold location for a number of problems, including the two most-studied ones: random k-SAT and random graph colouring. Our results prove that the heuristic predictions of statistical physics in this context are essentially correct. Moreover, we establish that random instances of constraint satisfaction problems have solutions well beyond the reach of any analysed algorithm.

Journal Article↗

PubMed2005

An organic thyristor.

Thyristors are a class of nonlinear electronic device that exhibit bistable resistance--that is, they can be switched between two different conductance states. Thyristors are widely used as inverters (direct to alternating current converters) and for the smooth control of power in a variety of applications such as motors and refrigerators. Materials and structures that exhibit nonlinear resistance of this sort are not only useful for practical applications: they also provide systems for exploring fundamental aspects of solid-state and statistical physics. Here we report the discovery of a giant nonlinear resistance effect in the conducting organic salt theta-(BEDT-TTF)2CsCo(SCN)4, the voltage-current characteristics of which are essentially the same as those of a conventional thyristor. This intrinsic organic thyristor works as an inverter, generating an alternating current when a static direct-current voltage is applied. Whereas conventional thyristors consist of a series of diodes (their nonlinearity comes from interface effects at the p-n junctions), the present salt exhibits giant nonlinear resistance as a bulk phenomenon. We attribute the origin of this effect to the current-induced melting of insulating charge-order domains, an intrinsically non-equilibrium phenomenon in the sense that ordered domains are melted by a steady flow.

Journal Article↗

PubMed2001

Designer gene networks: Towards fundamental cellular control.

The engineered control of cellular function through the design of synthetic genetic networks is becoming plausible. Here we show how a naturally occurring network can be used as a parts list for artificial network design, and how model formulation leads to computational and analytical approaches relevant to nonlinear dynamics and statistical physics. We first review the relevant work on synthetic gene networks, highlighting the important experimental findings with regard to genetic switches and oscillators. We then present the derivation of a deterministic model describing the temporal evolution of the concentration of protein in a single-gene network. Bistability in the steady-state protein concentration arises naturally as a consequence of autoregulatory feedback, and we focus on the hysteretic properties of the protein concentration as a function of the degradation rate. We then formulate the effect of an external noise source which interacts with the protein degradation rate. We demonstrate the utility of such a formulation by constructing a protein switch, whereby external noise pulses are used to switch the protein concentration between two values. Following the lead of earlier work, we show how the addition of a second network component can be used to construct a relaxation oscillator, whereby the system is driven around the hysteresis loop. We highlight the frequency dependence on the tunable parameter values, and discuss design plausibility. We emphasize how the model equations can be used to develop design criteria for robust oscillations, and illustrate this point with parameter plots illuminating the oscillatory regions for given parameter values. We then turn to the utilization of an intrinsic cellular process as a means of controlling the oscillations. We consider a network design which exhibits self-sustained oscillations, and discuss the driving of the oscillator in the context of synchronization. Then, as a second design, we consider a synthetic network with parameter values near, but outside, the oscillatory boundary. In this case, we show how resonance can lead to the induction of oscillations and amplification of a cellular signal. Finally, we construct a toggle switch from positive regulatory elements, and compare the switching properties for this network with those of a network constructed using negative regulation. Our results demonstrate the utility of model analysis in the construction of synthetic gene regulatory networks. (c) 2001 American Institute of Physics.

Journal Article↗

PubMed2001

From 1/f noise to multifractal cascades in heartbeat dynamics.

We explore the degree to which concepts developed in statistical physics can be usefully applied to physiological signals. We illustrate the problems related to physiologic signal analysis with representative examples of human heartbeat dynamics under healthy and pathologic conditions. We first review recent progress based on two analysis methods, power spectrum and detrended fluctuation analysis, used to quantify long-range power-law correlations in noisy heartbeat fluctuations. The finding of power-law correlations indicates presence of scale-invariant, fractal structures in the human heartbeat. These fractal structures are represented by self-affine cascades of beat-to-beat fluctuations revealed by wavelet decomposition at different time scales. We then describe very recent work that quantifies multifractal features in these cascades, and the discovery that the multifractal structure of healthy dynamics is lost with congestive heart failure. The analytic tools we discuss may be used on a wide range of physiologic signals. (c) 2001 American Institute of Physics.

Journal Article↗

PubMed2004

Low-temperature susceptibility of concentrated magnetic fluids.

The initial susceptibility of concentrated magnetic fluids (ferrocolloids) has been experimentally investigated at low temperatures. The results obtained indicate that the interparticle dipole-dipole interactions can increase the susceptibility by several times as compared to the Langevin value. It is shown that good agreement between recent theoretical models and experimental observations can be achieved by introducing a correction for coefficients in the series expansion of susceptibility in powers of density and aggregation parameter. A modified equation for equilibrium susceptibility is offered to sum over corrections made by Kalikmanov (Statistical Physics of Fluids, Springer-Verlag, Berlin, 2001) and by B. Huke and M. Lucke (Phys. Rev. E 67, 051403, 2003). The equation gives good quantitative agreement with the experimental data in the wide range of temperature and magnetic particles concentration. It has been found that in some cases the magnetic fluid solidification occurs at temperature several tens of kelvins higher than the crystallization temperature of the carrier liquid. The solidification temperature of magnetic fluids is independent of particle concentration (i.e., magneto-dipole interparticle interactions) and dependent on the surfactant type and carrier liquid. This finding allows us to suggest that molecular interactions and generation of some large-scale structure from colloidal particles in magnetic fluids are responsible for magnetic fluid solidification. If the magnetic fluid contains the particles with the Brownian relaxation mechanism of the magnetic moment, the solidification manifests itself as the peak on the "susceptibility-temperature" curve. This fact proves the dynamic nature of the observed peak: it arises from blocking the Brownian mechanism of the magnetization relaxation.

Journal Article↗

PubMed2006

A free-energy landscape picture and Landau theory for the dynamics of disordered materials.

Landau's theory of phase transitions [Nature (London) 138, 840 (1936); Statistical Physics (Pergamon, London, 1959)] is adapted to treat independently relaxing regions in complex systems using nanothermodynamics. The order parameter we use governs the thermal fluctuations, not a specific static structure. We find that the entropy term dominates the thermal behavior, as is reasonable for disordered systems. Consequently, the thermal equilibrium occurs at the internal-energy maximum, so that the potential-energy minima have negligible influence on the dynamics. The dynamics involves normal thermal fluctuations about the free-energy minimum, with a time scale that is governed by the curvature of the internal-energy maximum. The temperature dependence of the fluctuations yields Vogel-Tamman-Fulcher-type [Phys. Z. 22, 645 (1921); J. Am. Ceram. Soc. 8, 339 (1925); Z. Anorg. Allg. Chem. 156, 245 (1926)] relaxation rates and approximate time-temperature superposition, consistent with the Williams-Landell-Ferry [J. Am. Chem. Soc. 77, 3701 (1955)] procedure for analyzing the dynamics of complex fluids, while the size dependence of the fluctuations provides an explanation for the distribution of relaxation times and heterogeneity that are found in glass-forming liquids, thus providing a unified picture for several features in the dynamics of disordered materials.

Journal Article↗

PubMed2002

Fractal dynamics in physiology: alterations with disease and aging.

According to classical concepts of physiologic control, healthy systems are self-regulated to reduce variability and maintain physiologic constancy. Contrary to the predictions of homeostasis, however, the output of a wide variety of systems, such as the normal human heartbeat, fluctuates in a complex manner, even under resting conditions. Scaling techniques adapted from statistical physics reveal the presence of long-range, power-law correlations, as part of multifractal cascades operating over a wide range of time scales. These scaling properties suggest that the nonlinear regulatory systems are operating far from equilibrium, and that maintaining constancy is not the goal of physiologic control. In contrast, for subjects at high risk of sudden death (including those with heart failure), fractal organization, along with certain nonlinear interactions, breaks down. Application of fractal analysis may provide new approaches to assessing cardiac risk and forecasting sudden cardiac death, as well as to monitoring the aging process. Similar approaches show promise in assessing other regulatory systems, such as human gait control in health and disease. Elucidating the fractal and nonlinear mechanisms involved in physiologic control and complex signaling networks is emerging as a major challenge in the postgenomic era.

Aging↗

PubMed2002

Predictability of catastrophic events: material rupture, earthquakes, turbulence, financial crashes, and human birth.

We propose that catastrophic events are "outliers" with statistically different properties than the rest of the population and result from mechanisms involving amplifying critical cascades. We describe a unifying approach for modeling and predicting these catastrophic events or "ruptures," that is, sudden transitions from a quiescent state to a crisis. Such ruptures involve interactions between structures at many different scales. Applications and the potential for prediction are discussed in relation to the rupture of composite materials, great earthquakes, turbulence, and abrupt changes of weather regimes, financial crashes, and human parturition (birth). Future improvements will involve combining ideas and tools from statistical physics and artificial/computational intelligence, to identify and classify possible universal structures that occur at different scales, and to develop application-specific methodologies to use these structures for prediction of the "crises" known to arise in each application of interest. We live on a planet and in a society with intermittent dynamics rather than a state of equilibrium, and so there is a growing and urgent need to sensitize students and citizens to the importance and impacts of ruptures in their multiple forms.

Climate↗

PubMed2003

Neuron recognition by parallel Potts segmentation.

Identifying neurons and their spatial coordinates in images of the cerebral cortex is a necessary step in the quantitative analysis of spatial organization in the brain. This is especially important in the study of Alzheimer's disease (AD), in which spatial neuronal organization and relationships are highly disrupted because of neuronal loss. To automate neuron recognition by using high-resolution confocal microscope images from human brain tissue, we propose a recognition method based on statistical physics that consists of image preprocessing, parallel image segmentation, and cluster selection on the basis of shape, optical density, and size. We segment a preprocessed digital image into clusters by applying Monte Carlo simulations of a q-state inhomogeneous Potts model. We then select the range of Potts segmentation parameters to yield an ideal recognition of simplified objects in the test image. We apply our parallel segmentation method to control individuals and to AD patients and achieve recognition of 98% (for a control) and 93% (for an AD patient), with at most 3% false clusters.

Alzheimer Disease↗

PubMed2002

Stochastic and mesoscopic models for tropical convection.

A new way to parametrize certain aspects of tropical convection through stochastic and mesoscopic models is developed here. The technical idea is to adapt tools from statistical physics and materials science to model important unresolved features of tropical convection. This new strategy consists of modeling the unresolved effects of convective inhibition in a coarse mesh mesoscopic parametrization through a "heat bath" model involving a stochastic spin flip model with very natural interaction rules for convective inhibition combined with a suitable external potential defined by the coarse mesh values. In turn, the values of the order parameter from this heat bath alter the vertical mass flux in regions of deep convection. Both stochastic and systematic deterministic mesoscopic parametrizations are developed here. The deterministic mesoscopic models derived in this fashion exhibit new phenomena such as multiple radiative equilibria in suitable parameter regimes. The simplest first numerical experiments reported here with the mesoscopic deterministic parametrization qualitatively reproduce several key features of the observational record regarding convectively coupled tropical waves. The systematic stochastic modeling strategy proposed here could also be very useful for capturing other features of tropical convection such as those involving cloud radiation feedbacks.

Models, Theoretical↗