Specific heat and partition function zeros for the dimer model on the checkerboard B lattice: Finite-size effects.

There are three possible classifications of the dimer weights on the bonds of the checkerboard lattice and they are denoted as checkerboard A, B, and C lattices [Phys. Rev. E 91, 062139 (2015)PLEEE81539-375510.1103/PhysRevE.91.062139]. The dimer model on the checkerboard B and C lattices has much richer critical behavior compared to the dimer model on the checkerboard A lattice. In this paper we study in full detail the dimer model on the checkerboard B lattice. The dimer model on the checkerboard B lattice has two types of critical behavior. In one limit this model is the anisotropic dimer model on rectangular lattice with algebraic decay of correlators and in another limit it is the anisotropic generalized Kasteleyn model with radically different critical behavior. We analyze the partition function of the dimer model on a 2M×2N checkerboard B lattice wrapped on a torus. We find very unusual behavior of the partition function zeros and the specific heat of the dimer model. Remarkably, the partition function zeros of finite-size systems can have very interesting structures, made of rings, concentric circles, radial line segments, or even arabesque structures. We find out that the number of the specific heat peaks and the number of circles of the partition function zeros increases with the system size. The lattice anisotropy of the model has strong effects on the behavior of the specific heat, dominating the relation between the correlation length exponent ν and the shift exponent λ, and λ is generally unequal to 1/ν (λ≠1/ν).

Finite-size corrections and scaling for the dimer model on the checkerboard lattice.

Lattice models are useful for understanding behaviors of interacting complex many-body systems. The lattice dimer model has been proposed to study the adsorption of diatomic molecules on a substrate. Here we analyze the partition function of the dimer model on a 2M×2N checkerboard lattice wrapped on a torus and derive the exact asymptotic expansion of the logarithm of the partition function. We find that the internal energy at the critical point is equal to zero. We also derive the exact finite-size corrections for the free energy, the internal energy, and the specific heat. Using the exact partition function and finite-size corrections for the dimer model on a finite checkerboard lattice, we obtain finite-size scaling functions for the free energy, the internal energy, and the specific heat of the dimer model. We investigate the properties of the specific heat near the critical point and find that the specific-heat pseudocritical point coincides with the critical point of the thermodynamic limit, which means that the specific-heat shift exponent λ is equal to ∞. We have also considered the limit N→∞ for which we obtain the expansion of the free energy for the dimer model on the infinitely long cylinder. From a finite-size analysis we have found that two conformal field theories with the central charges c=1 for the height function description and c=-2 for the construction using a mapping of spanning trees can be used to describe the dimer model on the checkerboard lattice.

Disorder profile of nebulin encodes a vernierlike position sensor for the sliding thin and thick filaments of the skeletal muscle sarcomere.

Nebulin is an about 1µm long intrinsically disordered scaffold for the thin filaments of skeletal muscle sarcomere. It is a multifunctional elastic protein that wraps around actin filament, stabilizes thin filaments, and regulates Ca-dependent actomyosin interactions. This study investigates whether the disorder profile of nebulin might encode guidelines for thin and thick filament interactions in the sarcomere of the skeletal muscle. The question was addressed computationally by analyzing the predicted disorder profile of human nebulin (6669 residues, ∼200 actin-binding repeats) by pondr and the periodicity of the A-band stripes (reflecting the locations of myosin-associated proteins) in the electron micrographs of the sarcomere. Using the detrended fluctuation analysis, a scale factor for the A-band stripe image data with respect to the nebulin disorder profile was determined to make the thin and thick filaments aligned to have maximum correlation. The empirical mode decomposition method was then applied to identify hidden periodicities in both the nebulin disorder profile and the rescaled A-band data. The decomposition reveals three characteristic length scales (45 nm, 100 nm, and 200 nm) that are relevant for correlational analysis. The dynamical cross-correlation analyses with moving windows at various sarcomere lengths depict a vernierlike design for both periodicities, thus enabling nebulin to sense position and fine tune sarcomere overlap. This shows that the disorder profile of scaffolding proteins may encode a guideline for cellular architecture.

Surface electromyography analysis of blepharoptosis correction by transconjunctival incisions.

Upper eyelid movement depends on the antagonistic actions of orbicularis oculi muscle and levator aponeurosis. Blepharoptosis is an abnormal drooping of upper eyelid margin with the eye in primary position of gaze. Transconjunctival incisions for upper eyelid ptosis correction have been a well-developed technique. Conventional prognosis however depends on clinical observations and lacks of quantitatively analysis for the eyelid muscle controlling. This study examines the possibility of using the assessments of temporal correlation in surface electromyography (SEMG) as a quantitative description for the change of muscle controlling after operation. Eyelid SEMG was measured from patients with blepharoptosis preoperatively and postoperatively, as well as, for comparative study, from young and aged normal subjects. The data were analyzed using the detrended fluctuation analysis method. The results show that the temporal correlation of the SEMG signals can be characterized by two indices associated with the correlation properties in short and long time scales demarcated at 3ms, corresponding to the time scale of neural response. Aging causes degradation of the correlation properties at both time scales, and patient group likely possess more serious correlation degradation in long-time regime which was improved moderately by the ptosis corrections. We propose that the temporal correlation in SEMG signals may be regarded as an indicator for evaluating the performance of eyelid muscle controlling in postoperative recovery.

Simplified lattice model for polypeptide fibrillar transitions.

Polypeptide fibrillar transitions are studied using a simplified lattice model, modified from the three-state Potts model, where uniform residues as spins, placed on a cubic lattice, can interact with neighbors to form coil, helical, sheet, or fibrillar structure. Using the transfer matrix method and numerical calculations, we analyzed the partition function and construct phase diagrams. The model manifests phase transitions among coil, helix, sheet, and fibril through parameterizing bond coupling energy ɛh,ɛs,ɛf, structural entropies sh,ss,sf of helical, sheet, and fibrillar states, and number density ρ. The phase diagrams show the transition sequence is basically governed by ɛh, ɛs, and ɛf, while the transition temperature is determined by the competition among ɛh, ɛs, and ɛf, as well as sh, ss, sf, and ρ. Furthermore, the fibrillation is accompanied with an abrupt phase transition from coil, helix, or sheet to fibril even for short polypeptide length, resembling the feature of nucleation-growth process. The finite-size effect in specific heat at transitions for the nonfibrillation case can be described by the scaling form of lattice model. With rich phase-transition properties, our model provides a useful reference for protein aggregation experiments and modeling.

The role of tryptophan in staphylococcal nuclease stability.

Staphylococcal nuclease (SNase) has a single Trp residue at position 140. Circular dichroism, intrinsic and ANS-binding fluorescence, chemical titrations and enzymatic assays were used to measure the changes of its structure, stability and activities as the Trp was mutated or replaced to other positions. The results show that W140 is critical to SNase structure, stability, and function. Mutants such as W140A, F61W/W140A, and Y93W/W140A have unfolding, corrupted secondary and tertiary structures, diminished structural stability and attenuated catalytic activity as compared to the wild type. The deleterious effects of W140 substitution cannot be compensated by concurrent changes at topographical locations of position 61 or 93. Local hydrophobicity defined as a sum of hydrophobicity around a given residue within a distance is found to be a relevant property to SNase folding and stability.

Thermostability of the N-terminal RNA-binding domain of the SARS-CoV nucleocapsid protein: experiments and numerical simulations.

Differential scanning calorimetry, circular dichroism spectroscopy, nuclear magnetic resonance spectroscopy, and numerical simulations were used to study the thermostability of the N-terminal RNA-binding domain (RBD) of the SARS-CoV nucleocapsid protein. The transition temperature of the RBD in a mixing buffer, composed of glycine, sodium acetate, and sodium phosphate with 100 mM sodium chloride, at pH 6.8, determined by differential scanning calorimetry and circular dichroism, is 48.74 degrees C. Experimental results showed that the thermal-induced unfolding-folding transition of the RBD follows a two-state model with a reversibility >90%. Using a simple Go-like model and Langevin dynamics we have shown that, in agreement with our experiments, the folding of the RBD is two-state. Theoretical estimates of thermodynamic quantities are in reasonable agreement with the experiments. Folding and thermal unfolding pathways of the RBD also were experimentally and numerically studied in detail. It was shown that the strand beta(1) from the N-terminal folds last and unfolds first, while the remaining beta-strands fold/unfold cooperatively.

Enveloping triangulation method for detecting internal cavities in proteins and algorithm for computing their surface areas and volumes.

Detection and quantitative characterization of the internal cavities in proteins remain an important topic in studying protein structure and function. Here we propose a new analytical method for detecting the existence of cavities in proteins. The method is based on constructing the special enveloping triangulation enclosing the cavities. Based on this method, we develop an algorithm and a fortran package, CAVE, for computing volumes and surface areas of cavities in proteins. We first test our method and algorithm in some artificial systems of spheres and find that the calculated results are consistent with exact results. Then we apply the package to compute volumes and surface areas of cavities for some protein structures in the Protein Data Bank. We compare our calculated results with those obtained by some other methods and find that our approach is reliable.

Multiple nucleic acid binding sites and intrinsic disorder of severe acute respiratory syndrome coronavirus nucleocapsid protein: implications for ribonucleocapsid protein packaging.

The nucleocapsid protein (N) of the severe acute respiratory syndrome coronavirus (SARS-CoV) packages the viral genomic RNA and is crucial for viability. However, the RNA-binding mechanism is poorly understood. We have shown previously that the N protein contains two structural domains--the N-terminal domain (NTD; residues 45 to 181) and the C-terminal dimerization domain (CTD; residues 248 to 365)--flanked by long stretches of disordered regions accounting for almost half of the entire sequence. Small-angle X-ray scattering data show that the protein is in an extended conformation and that the two structural domains of the SARS-CoV N protein are far apart. Both the NTD and the CTD have been shown to bind RNA. Here we show that all disordered regions are also capable of binding to RNA. Constructs containing multiple RNA-binding regions showed Hill coefficients greater than 1, suggesting that the N protein binds to RNA cooperatively. The effect can be explained by the "coupled-allostery" model, devised to explain the allosteric effect in a multidomain regulatory system. Although the N proteins of different coronaviruses share very low sequence homology, the physicochemical features described above may be conserved across different groups of Coronaviridae. The current results underscore the important roles of multisite nucleic acid binding and intrinsic disorder in N protein function and RNP packaging.

Phase statistics approach to human ventricular fibrillation.

Ventricular fibrillation (VF) is known to be the most dangerous cardiac arrhythmia, frequently leading to sudden cardiac death (SCD). During VF, cardiac output drops to nil and, unless the fibrillation is promptly halted, death usually ensues within minutes. While delivering life saving electrical shocks is a method of preventing SCD, it has been recognized that some, though not many, VF episodes are self-terminating, and understanding the mechanism of spontaneous defibrillation might provide newer therapeutic options for treatment of this otherwise fatal arrhythmia. Using the phase statistics approach, recently developed to study financial and physiological time series, here, we reveal the timing characteristics of transient features of ventricular tachyarrhythmia (mostly VF) electrocardiogram (ECG) and find that there are three distinct types of probability density function (PDF) of phase distributions: uniform (UF), concave (CC), and convex (CV). Our data show that VF patients with UF or CC types of PDF have approximately the same probability of survival and nonsurvival, while VF patients with CV type PDF have zero probability of survival, implying that their VF episodes are never self-terminating. Our results suggest that detailed phase statistics of human ECG data may be a key to understanding the mechanism of spontaneous defibrillation of fatal VF.

Hydrophobic condensation and modular assembly model of protein folding.

Despite several decades of intense study, protein folding problem remains elusive. In this paper, we review current knowledge and the prevailing thinking in the field, and summarize our work on the in vitro folding of a typical small globular protein, staphylococcal nuclease (SNase). Various thermodynamic and kinetic methods have been employed to determine the energetic and construct the energy landscape of folding. Data presented include, but not limit to, the identification of intermediate states, time courses of their spread and convergence on the landscape, and finally the often ignored step, the refinement of the overall conformation and hence the activation of the enzyme. Our goal is to have a complete perspective of the folding process starting from its initial unfolded state to the fully active native state. Analysis leads to these findings: the folding starts with the condensation of the hydrophobic side chains in different locales of the peptide chain. The newly forged hydrophobic environment facilitates formation of helix- and sheet-like frameworks at different domains. Consolidation and inter-docking of these frameworks or domains then stabilizes the overall conformation and refines the structure to activate the enzyme. Based on these observations we favor folding-by-parts and propose a modular assembly model for the in vitro folding of SNase.

Compact dimension of denatured states of staphylococcal nuclease.

Fluorescence and circular dichroism stopped-flow have been widely used to determine the kinetics of protein folding including folding rates and possible folding pathways. Yet, these measurements are not able to provide spatial information of protein folding/unfolding. Especially, conformations of denatured states cannot be elaborated in detail. In this study, we apply the method of fluorescence energy transfer with a stopped-flow technique to study global structural changes of the staphylococcal nuclease (SNase) mutant K45C, where lysine 45 is replaced by cysteine, during folding and unfolding. By labeling the thiol group of cysteine with TNB (5,5'-dithiobis-2-nitrobenzoic acid) as an energy acceptor and the tryptophan at position 140 as a donor, distance changes between the acceptor and the donor during folding and unfolding are measured from the efficiency of energy transfer. Results indicate that the denatured states of SNase are highly compact regardless of how the denatured states (pH-induced or GdmCl-induced) are induced. The range of distance changes between two probes is between 25.6 and 25.4 A while it is 20.4 A for the native state. Furthermore, the folding process consists of three kinetic phases while the unfolding process is a single phase. These observations agree with our previous sequential model: N(0) left arrow over right arrow D(1) left arrow over right arrow D(2) left arrow over right arrow D(3) (Chen et al., J Mol Biol 1991;220:771-778). The efficiency of protein folding may be attributed to initiating the folding process from these compact denatured structures.

Empirical mode decomposition and synchrogram approach to cardiorespiratory synchronization.

We use the empirical mode decomposition method to decompose experimental respiratory signals into a set of intrinsic mode functions (IMFs), and consider one of these IMFs as a respiratory rhythm. We then use the Hilbert spectral analysis to calculate the instantaneous phase of the IMF. Heartbeat data are finally incorporated to construct the cardiorespiratory synchrogram, which is a visual tool for inspecting synchronization. We perform analysis on 20 data sets collected by the Harvard medical school from ten young (21-34 years old) and ten elderly (68-81 years old) rigorously screened healthy subjects. Our results support the existence of cardiorespiratory synchronization. We also investigate the origin of the cardiorespiratory synchronization by addressing the problem of correlations between regularities of respiratory and cardiac signals. Our analysis shows that regularity of respiratory signals plays a dominant role in the cardiorespiratory synchronization.

Exact finite-size scaling functions for the interfacial tensions of the Ising model on planar lattices.

Exact finite-size scaling functions of the interfacial tensions are obtained for the Ising model with isotropic coupling on a set of M x N planar lattices, including square (sq), plane triangular (pt), and honeycomb (hc) lattices. The analyses of transitive behaviors at criticality revise the knowledge of the interfacial tensions as a function of the aspect ratio defined by R = M/N for R approaching to zero gradually. The amplitudes of the interfacial tensions for the sq, pt, and hc lattices are further shown to have relative proportions 1:square root of 3 / 2:square root of 3 which are related to the aspect ratios for the three lattices to have similar domains.

Phase distribution and phase correlation of financial time series.

The scaling, phase distribution, and phase correlation of financial time series are investigated based on the Dow Jones Industry Average and NASDAQ 10-min intraday data for a period from 1 Aug. 1997 to 31 Dec. 2003. The returns of the two indices are shown to have nice scaling behaviors and belong to stable distributions according to the criterion of Lévy's alpha stable distribution condition. An approach catching characteristic features of financial time series based on the concept of instantaneous phase is further proposed to study the phase distribution and correlation. Analysis of the phase distribution concludes that return time series fall into a class which is different from other nonstationary time series. The correlation between returns of the two indices probed by the distribution of phase difference indicates that there was a remarkable change of trading activities after the event of the 9/11 attack, and this change persisted in later trading activities.

Finite-size corrections and scaling for the triangular lattice dimer model with periodic boundary conditions.

We analyze the partition function of the dimer model on M x N triangular lattice wrapped on the torus obtained by Fendley, Moessner, and Sondhi [Phys. Rev. B 66, 214513, (2002)]. Based on such an expression, we then extend the algorithm of Ivashkevich, Izmailian, and Hu [J. Phys. A 35, 5543 (2002)] to derive the exact asymptotic expansion of the first and second derivatives of the logarithm of the partition function at the critical point and find that the aspect-ratio dependence of finite-size corrections and the finite-size scaling functions are sensitive to the parity of the number of lattice sites along the lattice axis.

Unzipping of DNA with correlated base sequence.

We consider force-induced unzipping transition for a heterogeneous DNA model with a correlated base sequence. Both finite-range and long-range correlated situations are considered. It is shown that finite-range correlations increase stability of DNA with respect to the external unzipping force. Due to long-range correlations the number of unzipped base pairs displays two widely different scenarios depending on the details of the base sequence: either there is no unzipping phase transition at all, or the transition is realized via a sequence of jumps with magnitude comparable to the size of the system. Both scenarios are different from the behavior of the average number of unzipped base pairs (non-self-averaging). The results can be relevant for explaining the biological purpose of correlated structures in DNA.

Universal finite-size scaling functions with exact nonuniversal metric factors.

Using exact partition functions and finite-size corrections for the Ising model on finite square, plane triangular, and honeycomb lattices and extending a method [J. Phys. 19, L1215 (1986)] to subtract leading singular terms from the free energy, we obtain universal finite-size scaling functions for the specific heat, internal energy, and free energy of the Ising model on these lattices with exact nonuniversal metric factors.