Direct Measurement of Local and Global Contributions in the Binding of Coformycin to Bovine Adenosine Deaminase

A general method is outlined that determines quantitatively the extent to which tight ligand binding to an enzyme active site is facilitated by the adoption of a stabler macromolecular conformation in the complex. The method therefore rejects the general assumption that competitive inhibitor binding to enzyme active sites involves only local (active site) interactions. The procedure involves comparing the unfolding transition state free energies of the free and complexed enzyme from physiological conditions. For the interaction of the transition state analog coformycin with bovine adenosine deaminase we observed that the binding free energy by the physiological enzyme was ~92% due to the assumption of a stabler enzyme conformation in the complex. The significance of these findings in terms of general enzyme catalysis is discussed.     

Direct measurement of local and global contributions in the binding of coformycin to bovine adenosine deaminase

A general method is outlined that determines quantitatively the extent to which tight ligand binding to an enzyme active site is facilitated by the adoption of a stabler macromolecular conformation in the complex. The method therefore rejects the general assumption that competitive inhibitor binding to enzyme active sites involves only local (active site) interactions. The procedure involves comparing the unfolding transition state free energies of the free and complexed enzyme from physiological conditions. For the interaction of the transition state analog coformycin with bovine adenosine deaminase we observed that the binding free energy by the physiological enzyme was approximately 92% due to the assumption of a stabler enzyme conformation in the complex. The significance of these findings in terms of general enzyme catalysis is discussed.     

A general method for constructing increment-decrement life tables that agree with the data

A general method for making increment-decrement life tables is presented. The method involves the finding of probabilities of transition between states, graduated to small intervals of time and age, that are consistent with (i.e., can reproduce) the data, whether the data consist of central age-state specific rates, or some other feature, such as state distributions of a real cohort. The method is then illustrated with a fetal loss life table.     

Calculation of mutational free energy changes in transition states for protein folding

Recent advances in experimental and computational methods have made it possible to determine with considerable accuracy the structures whose formation is rate limiting for the folding of some small proteins-the transition state ensemble, or TSE. We present a method to analyze and validate all-atom models of such structures. The method is based on the comparison of experimental data with the computation of the change in free energy of the TSE resulting from specific mutations. Each mutation is modeled individually in all members of an ensemble of transition state structures using a method originally developed to predict mutational changes in the stability of native proteins. We first apply this method to six proteins for which we have determined the TSEs with a technique that uses experimental mutational data (Phi-values) as restraints in the structure determination and find a highly significant correlation between the calculated free energy changes and those derived from experimental kinetic data. We then use the procedure to analyze transition state structures determined by molecular dynamics simulations of unfolding, again finding a high correlation. Finally, we use the method to estimate changes in folding rates of several hydrophobic core mutants of Fyn SH3. Taken together, these results show that the procedure developed here is a tool of general validity for analyzing, assessing, and improving the quality of the structures of transition states for protein folding.     

Transition probabilities for general birth–death processes with applications in ecology, genetics, and evolution

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with n current particles, a new particle is born with instantaneous rate λ(n) and a particle dies with instantaneous rate μ(n). Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics.     

Adsorption of polypeptides on solid surfaces. I. Effect of chain stiffness

The general method of obtaining the partition function and thermodynamic characteristics of polymer chains near an adsorbing surface, simulated by random walks on a lattice, is developed. The method takes into account the effect of short-range interactions in polymer chains, in particular, the chain stiffness and secondary structure. The theory of adsorption of chains of different stiffness is developed, and the process of adsorption which occurs when the external conditions change is shown to be always a second-order phase transition. The critical adsorption energy decreases and the sharpness of transition grows when the chain stiffness increases. A simple model of a chain with “virtual” steps is proposed which simplifies the treatment; the results obtained are in good agreement with exact theories. A general scheme of analysis of adsorption of chains with a given secondary structure is set forth and the analogy between the stiffness of a noncooperative chain and the presence of helical segments in a polypeptide chain is discussed.     

Ordered genotypes: an extended ITO method and a general formula for genetic covariance

Traditionally, the stochastic ITO transition matrices provide a simple general method for obtaining the joint genotype distribution and genotypic correlations between any specified pair of noninbred relatives. The ITO method has been widely used in modern genetic analysis; however, since it was originally derived for unordered genotypes, it is not very useful in some new applications -- for example, when one is modeling genomic imprinting and must keep track of the parental origin of alleles. To address these new, emerging problems, here we extend the ITO method to handle ordered genotypes. Our extended method is applied to calculate the covariance in unilineal and bilineal relatives under genomic imprinting, and some generalized linear functions of the transition matrices are given. Since the ITO method is limited to biallelic loci and to unilineal and bilineal relatives, we derive a general formula for calculating the genetic covariance using ordered genotypes for any type of relative pair.     

An illness-death process with time-dependent covariates

A general model for the illness-death stochastic process with covariates has been developed for the analysis of survival data. This model incorporates important baseline and time-dependent covariates in order to make an appropriate adjustment for the transition and survival probabilities. The follow-up period is subdivided into small intervals and a constant hazard is assumed for each interval. An approximation formula is derived to estimate the transition parameters when the exact transition time is unknown. The method developed is illustrated with data from a study on the prevention of the recurrence of a myocardial infarction and subsequent mortality, the Beta-Blocker Heart Attack Trial (BHAT). This method provides an analytical approach with which the effectiveness of the treatment can be compared between the placebo and propranolol treatment groups with respect to fatal and nonfatal events simultaneously.     

Liposome filtration. Dependence on transition temperature

Liposomes formed by vortexing and passed through polycarbonate surface retention membranes showed appreciable differences in filtration behavior depending on the temperature of filtration relative to the liposome gel-liquid crystal transition temperature. Below transition, liposomes were filterable and size distributions could be determined; the cumulative volume distributions were log-normal. Above transition, liposomes were not filterable: smaller liposomes were formed until a limiting size was reached. These results suggest that liquid crystal liposome size distributions cannot be determined by filtration. This filtration behavior is a physical property of liposomes, related to the gel-liquid crystal transition, not previously reported. This property could be exploited as a new method for controlling liposome size distributions, but the implications for lipid membranes, including biological membranes, are general.     

On the theory of the nematic phase and its possible relation to the mitotic spindle structure

Onsager's method of studying the nematic phase is developed for general molecular interactions. It is shown that the symmetry of the molecule helps determine the type of transition that occurs in passing from the isotropic phase to the anisotropic phase. The possible relation between the nematic phase and spindle structure is briefly discussed.     

Enzyme reaction rates and the stochastic theory of kinetics

The kinetics of an elementary reaction step are discussed from the viewpoint of the stochastic theory of chemical kinetics. The general form of the rate constant found in the stochastic approach is described, and compared with the expression from transition state theory. Whereas the stochastic theory predicts a rate enhancement in cases which are not adiabatic (in the quantum mechanical sense), transition state theory,which is essentially an adiabatic theory of reaction rates, does not permit inclusion of the effect. This effect can be expected to be of greater importance in cases of catalysis by structures, such as enzymes, containing large numbers of vibrational degrees of freedom (particularly low frequency ones) than in cases lacking such structures. The stochastic theory is more general than the transition state theory, the rate constant expression given by the latter being obtainable from the former when restrictive assumptions, including that of adiabaticity, are made. Interpretations of enzyme catalysis based on the transition state theory must thus be viewed as speculative.     

Determination of phase transition temperatures of lipids by light scattering

Various techniques have been proposed to specify the phase transition temperatures of surfactant molecules. The work reported herein deals with a new general method of T(c) determination based on the optical properties' modifications of aqueous surfactant solutions when the phase transitions occur in the phospholipid membrane. The shape alteration of supramolecular systems induced by the phase transition was correlated with the refraction and absorption coefficients of their aqueous dispersion. The mean count rate (average number of photons detected per second) measured with a Zetasizer Nano-S model ZEN1600 Dynamic Light Scattering Instrument, is representative of an emerging macroscopic phenomenon, but not directly size dependent and has been adapted to our expectations. Changes in the measured scattering intensity reflect changes in the optical properties of the material during temperature variations. Thus, this method allowed to specify the phase transition temperature of many natural or synthetic surfactants independently of their polar head or hydrophobic part.     

Miscibility of phosphatidylcholine binary mixtures in unilamellar vesicles: Phase equilibria

Summary Miscibility among phospholipids with different lipid chain-lengths or with different head groups has attracted a number of research efforts because of its significance in biological membrane structure and function. The general consensus about the miscibility of phosphatidylcholines with varying lipid chainlengths appears to be that binary mixtures of phospholipids with a difference of two carbon atoms in the lipid chain mix well at the main phase transition. Miscibility between phosphatidylcholines with differences of four carbon atoms appears to be inconclusive. Previous reports on the phase transition of binary phospholipid mixtures are concerned mainly with multilamellar vesicles and are mostly limited to the main transition. In the present study, unilamellar vesicles were used and miscibility in binary systems between dimyristoyl-, dipalmitoyl- and distearoyl-phosphatidylcholines at pretransition, as well as main transition temperatures was evaluated by constructing phase diagrams. Two methods were used to monitor the phase transitions: differential scanning microcalorimetry and optical absorbance methods. The optical method has the advantage that unilamellar vesicles of dilute phospholipid concentrations can be used. The liquidus and solidus phase boundaries were determined by the onset temperature of heating and cooling scans, respectively, because the completion temperature of a phase transition has no meaning in binary solutions. Dimyristoyl- and distearoyl-phosphatidylcholines. where the difference in the, lipid chain-length is four carbon atoms, mixed well even at pretransition temperature.     

The identity by descent process along the chromosome

The probabilities of the various possible identity by descent (IBD) states at a locus captures all the genealogical information for that locus for the set of individuals under consideration. Here we study the stochastic process of the IBD state as one moves across the genome of a set of individuals. In general it is no longer sufficient to specify the IBD state, one needs to increase the state space if one is to maintain the Markov property, as has been discussed by for instance McPeak and Sun [Am J Hum Genet 2000;66:1076-1094] and Browning and Browning [Theor Popul Biol 2002;62:1-8]. This paper discusses a general method of deriving the transition matrix for that Markov chain iteratively from one time point to a subsequent one. This method allows a considerable reduction in the size of the state space needed. The basic recursion is set out here and the application is illustrated by two specific examples.     

A discrete model with density dependent fast migration

The aim of this work is to develop an approximate aggregation method for certain non-linear discrete models. Approximate aggregation consists in describing the dynamics of a general system involving many coupled variables by means of the dynamics of a reduced system with a few global variables. We present discrete models with two different time scales, the slow one considered to be linear and the fast one non-linear because of its transition matrix depends on the global variables. In our discrete model the time unit is chosen to be the one associated to the slow dynamics, and then we approximate the effect of fast dynamics by using a sufficiently large power of its corresponding transition matrix. In a previous work the same system is treated in the case of fast dynamics considered to be linear, conservative in the global variables and inducing a stable frequency distribution of the state variables. A similar non-linear model has also been studied which uses as time unit the one associated to the fast dynamics and has the non-linearity in the slow part of the system. In the present work we transform the system to make the global variables explicit, and we justify the quick derivation of the aggregated system. The local asymptotic behaviour of the aggregated system entails that of the general system under certain conditions, for instance, if the aggregated system has a stable hyperbolic fixed point then the general system has one too. The method is applied to aggregate a multiregional Leslie model with density dependent migration rates.     

One-step metal-affinity purification of histidine-tagged proteins by temperature-triggered precipitation

The feature of elastin-like proteins (ELPs) to reversibly precipitate above their transition temperature was exploited as a general method for the purification of histidine (His)-tagged proteins. The principle of the single-step metal-affinity method is based on coordinated ligand-bridging between the modified ELPs and the target proteins. ELPs with repeating sequences of [(VPGVG)(2)(VPGKG)(VPGVG)(2)](21) were synthesized and the free amino groups on the lysine residues were modified by reacting with imidazole-2-carboxyaldehyde to incorporate the metal-binding ligands into the ELP bio- polymers. Biopolymers charged with Ni(2+) were able to interact with a His tag on the target proteins based on metal coordination chemistry. Purifications of two His-tagged enzymes, beta-D-galactosidase and chloramphenicol acetyltransferase, were used to demonstrate the utility of this general method and over 85% recovery was observed in both cases. The bound enzymes were easily released by addition of either EDTA or imidazole. The recovered ELPs were reused four times with no observable decrease in the purification performance.     

Predicting glass transition temperatures of polyarylethersulphones using QSPR methods

The technique of Quantitative Structure Property Relationships has been applied to the glass transition temperatures of polyarylethersulphones. A general equation is reported that calculates the glass transition temperatures with acceptable accuracy (correlation coefficients of between 90-67%, indicating an error of 10-30% with regard to experimentally determined values) for a series of 42 reported polyarylethersulphones. This method is quite simple in assumption and relies on a relatively small number of parameters associated with the structural unit of the polymer: the number of rotatable bonds, the dipole moment, the heat of formation, the HOMO eigenvalue, the molar mass and molar volume. For smaller subsets of the main group (based on families of derivatives containing different substituents) the model can be simplified further to an equation that uses the volume of the substituents as the principal variable.     

Kinetics of a multistate enzyme in a large oscillating field.

A simple, general, and efficient method for calculating the response of a set of coupled first-order (or pseudo-first-order) chemical reactions to an arbitrarily large periodic field is described. The method is applied to a four-state membrane transport enzyme that is electroconformationally coupled to an ac field, i.e., the enzyme has electric charges that move concomitantly with a conformational transition. The calculation is done both for enzymes in a planar membrane and for enzymes in the spherical membrane of a cell or vesicle in suspension.