Some Tools to Analyze Changes of Rhythms in Biological Time Series

The moving window principle applied to the khi-square periodogram allows, through local successive examinations, a comprehensive study of the biological time series. This method puts forward several cases of transition linked to environmental or physiological changes. Furthermore, we applied the Grassberger and Procaccia method (1983) for the analysis of more complex transition problems. The method helps to detect chaotic properties in behavioral activity rhythms.     

Estimation of the Transition/Transversion Ratio

A simple method for estimating the transition/transversion ratio was developed. This method can be applied to not only two sequences but also more than two sequences. The statistical properties of the method and some other methods were examined by numerical computation and computer simulation. The results obtained showed that, in terms of bias and variance, the new method gives a better estimate of the transition/transversion ratio than do the other examined methods. The new method was applied to human and chimpanzee mitochondrial control region sequences. Received: 22 September 1997 / Accepted: 1 November 1997     

General theoretical approach to the thermodynamic and kinetic properties of cooperative intramolecular transformations of linear biopolymers

A general method to calculate experimentally accessible thermodynamic and kinetic quantities for any type of cooperative transitions is developed. Special attention has been directed to transition curves and mean relaxation times. The procedure is applied to the most general case of nearest-neighbor cooperativity by using the linear Ising model and the matrix method of evaluation. The various potential types of end effects arid the resulting chain length dependences are discussed in detail. The significance of the theory with respect to the helix-coil transition of polypeptides as well as to the polyproline I-II transition is indicated.     

Dynamic domains: A simple method of analysing structural movements in proteins

A method is presented to analyse conformational changes in enzymes upon coenzyme and/or substrate binding. The method is based on a rigid body approximation for secondary structures and defines a dynamic domain as a collection of secondary structures which move together. The technique has been tested on a number of enzymes for which the conformation transition is well characterised. It was then applied to the analysis of two theoretically derived transition pathways for citrate synthase.     

Measuring the folding transition time of single RNA molecules

We describe a new, time-apertured photon correlation method for resolving the transition time between two states of RNA in folding--i.e., the time of the transition between states rather than the time spent in each state. Single molecule fluorescence resonance energy transfer and fluorescence correlation spectroscopy are used to obtain these measurements. Individual RNA molecules are labeled with fluorophores such as Cy3 and Cy5. Those molecules are then immobilized on a surface and observed for many seconds during which time the molecules spontaneously switch between two conformational states with different levels of flourescence resonance energy transfer efficiency. Single photons are counted from each fluorophore and cross correlated in a small window around a transition. The average of over 1000 cross correlations can be fit to a polynomial, which can determine transition times as short as the average photon emission interval. We applied the method to the P4-P6 domain of the Tetrahymena group I self-splicing intron to yield the folding transition time of 240 micros. The unfolding time is found to be too short to measure with this method.     

Time-resolved methods in biophysics. 3. Fluorescence lifetime correlation spectroscopy.

We present a thorough introduction into the recently developed fluorescence lifetime correlation spectroscopy (FLCS). The theoretical basis of FLCS is explained, and the method is applied to the study of a dynamic transition between two fluorescence lifetime states in a dye-protein complex.     

An effective way to determine the melting curve

A new ‘two-phase’ simulation method with which to accurately predict the melting curve is proposed. The method requires, as a starting configuration, generating a two-phase coexistence state by employing a suitable ensemble. Examining a change in volume ratio of the two phases upon varying temperature (pressure) under a fixed pressure (temperature) allows us to determine the phase transition point. The Clausius–Clapeyron relationship can then be implemented as a guide to predict the nearby phase transition point. The method was applied to determine the solid–liquid phase boundary of the modified Lennard–Jones system. A better accuracy, as that achieved by the non-equilibrium relaxation method (Asano Y, Fuchizaki K. J Phys Soc Jpn. 2017;86:025001), was obtained but with much less computational cost.     

Stochastic dynamic study of optical transition properties of single GFP-like molecules

Due to high fluctuations and quantum uncertainty, the processes of single-molecules should be treated by stochastic methods. To study fluorescence time series and their statistical properties, we have applied two stochastic methods, one of which is an analytic method to study the off-time distributions of certain fluorescence transitions and the other is Gillespie’s method of stochastic simulations. These methods have been applied to study the optical transition properties of two single-molecule systems, GFPmut2 and a Dronpa-like molecule, to yield results in approximate agreement with experimental observations on these systems. Rigorous oscillatory time series of GFPmut2 before it unfolds in the presence of denaturants have not been obtained based on the stochastic method used, but, on the other hand, the stochastic treatment puts constraints on the conditions under which such oscillatory behavior is possible. Furthermore, a sensitivity analysis is carried out on GFPmut2 to assess the effects of transition rates on the observables, such as fluorescence intensities.     

Interpretation of DSC data on protein denaturation complicated by kinetic and irreversible effects

Thermal denaturation of Kunitz soybean trypsin inhibitor (KTI) and ribulose-1,5-biphosphate carboxylase (RBPC) from tobacco leafs was studied by the method of high-sensitivity differential scanning calorimetry (HS-DSC). The dependence of the denaturation temperature on the heating rate reveals in the case of both proteins a non-equilibrium character of the denaturation transition in applied conditions. Developed kinetic approach allows the determination of an equilibrium transition temperature as well as the rate constants of denaturation and renaturation from the complex data of HS-DSC. This method was applied to the analysis of the pH-induced change of the conformational stability of KTI within pH range from 2.0 to 11.0. It allowed the determination of the pH dependencies: of the excess free energy of denaturation, of the activation enthalpy and entropy of denaturation as well as of the denaturation rate constant. Conclusions have been made suggesting the contribution of side-chain hydrogen bonds in the stabilisation of the native and activated states of KTI.     

Changes in the refractive index ellipsoid isotropies,symmetric anisotropies,and depolarization ratios of potassium hyaluronate solutions as a function of pH

A new method is presented for studying the tertiary and possibly the secondary structure of a biopolymer, which is applied to the pH-dependent structural transition of potassium hyaluronate solutions. The method involves a new application of Dirac dispersion theory polarization dependence measures to isotropic and anisotropic components of the refractive index ellipsoid. Changes in the dipole moment may also be observed by this method. The pH-induced changes in viscosity and optical properties of hyaluronic acid previously reported appear to be dependent on changes in secondary and tertiary structure.     

Yeast vitality determination based on intracellular NAD(P)H fluorescence measurement during aerobic-anaerobic transition

This work presents a yeast-cell vitality-assessment method based on on-line intracellular fluorescence measurement. The intracellular NAD(P)H fluorescence of a cell suspension is recorded during transition from aerobic to anaerobic conditions and the output signal is evaluated as a measure of yeast vitality (quality). This fluorescence method showed a highly satisfactory correlation with even low dead cell numbers where the acidification power test could not be applied.     

Conformational stability of biological polyelectrolytes: Evaluation of enthalpy and entropy changes of conformational transitions

A new method is proposed for the determination of the enthalpy and entropy changes of nonionic origin upon conformational transition of linear biopolyelectrolytes in solution. For all transition midpoints, defined by given temperature and ionic strength, the total free energy change of the system is zero, which means that the nonionic contribution to the free energy change is equal in value and opposite in sign to the polyelectrolytic one. The counterion condensation theory of linear polyelectrolytes provides for the appropriate analytical expression to be used in such calculations. Linear plots of the proper functions of the calculated free energy changes vs the proper functions of temperature allows for the determination of the enthalpic and entropic terms of the nonionic free energy change of transition. The method has been applied to the extensive available data of the ion-induced conformational change of κ-carrageenan, a linear sulfated galactan extracted from seaweeds. The method has proved very successful, with the results showing a remarkable convergency of the enthalpy values for different monovalent counterions. On the other hand, the above approach has made it possible to explain the known effect of counterion specificity on the transition by a small difference in the nonionic entropic contributions. © 1998 John Wiley & Sons, Inc. Biopoly 45: 203–216, 1998     

Polyelectrolytic aspects of the thermodynamics of conformational transition: κ‐carrageenan in formamide

A recently published method for the determination of the enthalpy and entropy changes of nonionic origin upon conformational transition of linear biopolyelectrolytes in solution [J. C. Benegas, A. Cesàro, R. Rizzo and S. Paoletti (1998) Biopolymers, Vol. 45, pp. 203–216] has been extended from the case of aqueous salt solutions to that of the organic solvent formamide (FA). The calculation have been applied to the case of the intramolecular transition of the K⁺ salt form of the sulfated polysaccharide κ‐carrageenan. The method proved to be effective in providing the desired data in FA, as it has been previously been successful for the water cases. The comparison between the predicted enthalpy change of transition and the microcalorimetric experimental one turned out to be excellent, thereby ensuring on the validity of the approach. © 1999 John Wiley & Sons, Inc. Biopoly 49: 127–130, 1999     

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.     

Electron-topological, energetic and π-electron delocalization analysis of ketoenamine-enolimine tautomeric equilibrium

The ketoenamine-enolimine tautometic equilibrium has been studied by the analysis of aromaticity and electron-topological parameters. The influence of substituents on the energy of the transition state and of the tautomeric forms has been investigated for different positions of chelate chain. The quantum theory of atoms in molecules method (QTAIM) has been applied to study changes in the electron-topological parameters of the molecule with respect to the tautomeric equilibrium in intramolecular hydrogen bond. Dependencies of the HOMA aromaticity index and electron density at the critical points defining aromaticity and electronic state of the chelate chain on the transition state (TS), OH and HN tautomeric forms have been obtained.     

Transition metal ion FRET to measure short-range distances at the intracellular surface of the plasma membrane

Biological membranes are complex assemblies of lipids and proteins that serve as platforms for cell signaling. We have developed a novel method for measuring the structure and dynamics of the membrane based on fluorescence resonance energy transfer (FRET). The method marries four technologies: (1) unroofing cells to isolate and access the cytoplasmic leaflet of the plasma membrane; (2) patch-clamp fluorometry (PCF) to measure currents and fluorescence simultaneously from a membrane patch; (3) a synthetic lipid with a metal-chelating head group to decorate the membrane with metal-binding sites; and (4) transition metal ion FRET (tmFRET) to measure short distances between a fluorescent probe and a transition metal ion on the membrane. We applied this method to measure the density and affinity of native and introduced metal-binding sites in the membrane. These experiments pave the way for measuring structural rearrangements of membrane proteins relative to the membrane.     

The influence of secondary interactions on complex stability and double proton transfer reaction in 2-[1H]-pyridone/2-hydroxypyridine dimers

The 2-[1H]-pyridone/2-hydroxypyridine tautomeric pair and its 6-substituted complexes have been studied with the use of DFT(M05) method. The intermolecular interaction energy has been calculated and discussed in the light of secondary interaction concept. The attractive secondary interactions of O/NH and O/OH type and OH/NH and OH/OH repulsions have been analyzed in terms of stabilizing or destabilizing influence on intermolecular behavior. The transition states of the double proton transfer reaction have been found and the energy of activation has been determined. The activation energy of the proton transfer reaction, geometry of the complexes and transition states show NH(2) and/or OH groups influence the properties of complexes and transition states. The HOMA index of aromaticity was applied to describe the π-electron delocalization in the heterocyclic rings.     

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.     

A new method to analyze postural stability during a transition task from double-leg stance to single-leg stance

Time to stabilization (TTS) has been introduced as a method to analyze dynamic postural stability during jump and landing tasks, but has also been applied during the transition task from double-leg stance (DLS) to single-leg stance (SLS). However, the application of the originally described TTS technique during the latter task has some important limitations. The first goal of this study was to present an adapted version of the TTS technique to provide an effective alternative method to better analyze postural stability during the transition from DLS to SLS. The second goal was to study the influence of pathology and different speeds on postural stability outcomes. Fifteen healthy control subjects and 15 subjects with chronic ankle instability (CAI) performed the transition task on their preferred speed and as fast as possible, with eyes open and with eyes closed. Subjects with CAI performed the transition significantly slower when moving at their preferred speed with eyes closed. The time subjects needed to reach a new stability point was not discriminative between groups and largely dependent on movement speed. However, the amount of sway after this new stability point was significantly increased in the CAI group and when eyes were closed. The results of this study suggest that subjects with CAI have a decreased ability to overcome the postural perturbation created by the voluntary movement from DLS to SLS. Focusing only on TTS during the transition from DLS to SLS may lead at least in some cases to misinterpretations when assessing postural stability.     

Unbiased estimation of evolutionary distance between nucleotide sequences

A new algorithm for estimating the number of nucleotide substitutions per site (i.e., the evolutionary distance) between two nucleotide sequences is presented. This algorithm can be applied to many estimation methods, such as Jukes and Cantor's method, Kimura's transition/transversion method, and Tajima and Nei's method. Unlike ordinary methods, this algorithm is always applicable. Numerical computations and computer simulations indicate that this algorithm gives an almost unbiased estimate of the evolutionary distance, unless the evolutionary distance is very large. This algorithm should be useful especially when we analyze short nucleotide sequences. It can also be applied to amino acid sequences, for estimating the number of amino acid replacements.