Ming-Chya Wu

ARVO: A Fortran package for computing the solvent accessible surface area and the excluded volume of overlapping spheres via analytic equations ✩

In calculating the solvation energy of proteins, the hydration effects, drug binding, molecular docking, etc., it is important to have an efficient and exact algorithms for computing the solvent accessible surface area and the excluded volume of macromolecules. Here we present a Fortran package based on the new exact analytical methods for computing volume and surface area of overlapping spheres. In the considered procedure the surface area and volume are expressed as surface integrals of the second kind over the closed region. Using the stereographic projection the surface integrals are transformed to a sum of double integrals which are reduced to the curve integrals. MPI Fortran version is described as well. The package is also useful for computing the percolation probability of continuum percolation models.

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 Lévys 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.

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.

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.

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.

Damped oscillations in the ratios of stock market indices

A stock market index is an average of a group of stock prices with weights. Different stock market indices derived from various combinations of stocks may share similar trends in certain periods, while it is not expected that there are fixed relations among them. Here we report our investigations on the daily index data of Dow Jones Industry Average (DJIA), NASDAQ, and S&P500 from 1971/02/05 to 2011/06/30. By analyzing the index ratios using the empirical mode decomposition, we find that the ratios NASDAQ/DJIA and S&500/DJIA, normalized to 1971/02/05, approached and then retained the values of 2 and 1, respectively. The temporal variations of the ratios consist of global trends and oscillatory components including a damped oscillation in 8-year cycle and damping factors of 7183 days (NASDAQ/DJIA) and 138471 days (S&P500/DJIA). Anomalies in the ratios, corresponding to significant increases and decreases of indices, only appear in the time scale less than an 8-year cycle. Detrended fluctuation analysis and multiscale entropy analysis of the components with cycles less than a half-year manifest a behavior of self-adjustment in the ratios, and the behavior in S&500/DJIA is more significant than in NASDAQ/DJIA.

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.

Exact partition functions of the Ising model on M ? N planar lattices with periodic?aperiodic boundary conditions

The Grassmann path integral approach is used to calculate exact partition functions of the Ising model on M × N square (sq), plane triangular (pt) and honeycomb (hc) lattices with periodic–periodic (pp), periodic–antiperiodic (pa), antiperiodic–periodic (ap) and antiperiodic–antiperiodic (aa) boundary conditions. The partition functions are used to calculate and plot the specific heat, C/kB, as a function of temperature, θ = kBT/J. We find that for the N × N sq lattice, C/kB for pa and ap boundary conditions are different from those for aa boundary conditions, but for the N × N pt and hc lattices, C/kB for ap, pa and aa boundary conditions have the same values. Our exact partition functions might also be useful for understanding the effects of lattice structures and boundary conditions on critical finite-size corrections of the Ising model.

CAVE: A package for detection and quantitative analysis of internal cavities in a system of overlapping balls: Application to proteins

We developed a software package (CAVE) in Fortran language to detect internal cavities in proteins which can be applied also to an arbitrary system of balls. The volume, the surface area and other quantitative characteristics of the cavities can be calculated. The code is based on the recently suggested enveloping triangulation algorithm [J. Busa et al., J. Comp. Chem. 30 (2009) 346] for computing volume and surface area of the cavity by analytical equations. Different standard sets of atomic radii can be used. The PDB compatible file containing the atomic coordinates must be stored on the disk in advance. Testing of the code on different proteins and artificial ball systems showed efficiency and accuracy of the algorithm. The program is fast. It can handle a system of several thousands of balls in the order of seconds on contemporary PCs. The code is open source and free.

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.