Ultrasonic study of the kinetics of counterion site binding in aqueous solutions of polyelectrolytes

The excess ultrasonic absorption due to counterion binding has been studied as a function of frequency for a series of polysalts in the range 1–150 MHz. All the relaxation spectra can be represented by a relaxation equation with two relaxation terms. The relaxation frequencies appear concentration independent and the relaxation amplitudes seem proportional to concentration. The low frequency relaxation process appears to depend mainly on the nature of the counterion while the high frequency relaxation process seems to be mostly dependent on the nature of the polyion. These results are quite similar to those obtained in ultrasonic studies of ion-pairing in solutions of divalent sulfates. The kinetic model used for the quantitative analysis of these results has been modified for polysalts through introducing the concept of“counterion condensation”. In this modified model the excess absorption is assigned to the perturbation by the ultrasonic waves of the equilibria between the three states of hydration of ths complex formed by a counterion and that part of the polyion where it is bound. Analytical expressions of the relaxation amplitudes have been derived using classical procedures for this modified kinetic model. In the case of cobalt-polyphosphate (Co-PP), the ultrasonic data together with the results of NMR measurements on either Co²⁺ or Co-PP have been used for the evaluation of the volume changes, the rate constants and the fractions of counterions in the three states of hydration involved in the binding equilibria. The volume changes obtained in this manner depend only slightly on the method of calculation and appear to be consistent with volume changes for outer-sphere and inner-sphere complex formation. These results are discussed.     

F?rster-type energy transfer as a probe for changes in local fluctuations of the protein matrix

Much evidence, on both theoretical and experimental sides, indicates the importance of local fluctuations (in energy levels, conformational substates, etc.) of the macromolecular matrix in the biological activity of proteins. We describe here a novel application of the F?rster-type energy-transfer process capable of monitoring changes both in local fluctuations and in conformational states of macromolecules. A new energy-transfer parameter, f, is defined as an average transfer efficiency, [E], normalized by the actual average quantum efficiency of the donor fluorescence, [phi D]. A simple oscillator model (for a one donor-one acceptor system) is presented to show the sensitivity of this parameter to changes in amplitudes of local fluctuations. The different modes of averaging (static, dynamic, and intermediate cases) occurring for a given value of the average transfer rate, [kt], and the experimental requirements as well as limitations of the method are also discussed. The experimental tests were performed on the ribonuclease T1-pyridoxamine 5'-phosphate conjugate (a one donor-one acceptor system) by studying the change of the f parameter with temperature, an environmental parameter expectedly perturbing local fluctuations of proteins. The parameter f increased with increasing temperature as expected on the basis of the oscillator model, suggesting that it really reflects changes of fluctuation amplitudes (significant changes in the orientation factor, k2, as well as in the spectral properties of the fluorophores can be excluded by anisotropy measurements and spectral investigations). Possibilities of the general applicability of the method are also discussed.     

Analysis of erythrocyte aggregation mechanism in presence of dextran and magnetic field by ultrasound scattering in blood

Aggregation of erythrocytes is studied as function of time during their sedimentation process under the gravitational field. The method is based on ultrasonic scattering from the various blood samples in presence and absence of inhomogeneous magnetic field (IMF) and dextran 70 (10%). The experimental arrangement is consisting of ultrasonic transmitter and receiver probes placed in mutually perpendicular direction intersecting at the sampling volume of blood located at the centre of the blood column. The temporal kinetic process is represented in terms of histograms of amplitudes and number of scattering fluctuations related to the size and motion of aggregates. The results show that the application of IMF influences the aggregation and sedimentation of erythrocytes. The aggregates thus formed sediment faster than that of control sample. The aggregate formation and their movements in presence of dextran 70 are slower than that of normal blood which may be attributed to the enhanced suspending medium viscosity and their interaction with erythrocytes.     

Statistical models of synaptic transmission evaluated using the expectation-maximization algorithm.

Amplitude fluctuations of evoked synaptic responses can be used to extract information on the probabilities of release at the active sites, and on the amplitudes of the synaptic responses generated by transmission at each active site. The parameters that describe this process must be obtained from an incomplete data set represented by the probability density of the evoked synaptic response. In this paper, the equations required to calculate these parameters using the Expectation-Maximization algorithm and the maximum likelihood criterion have been derived for a variety of statistical models of synaptic transmission. These models are ones where the probabilities associated with the different discrete amplitudes in the evoked responses are a) unconstrained, b) binomial, and c) compound binomial. The discrete amplitudes may be separated by equal (quantal) or unequal amounts, with or without quantal variance. Alternative models have been considered where the variance associated with the discrete amplitudes is sufficiently large such that no quantal amplitudes can be detected. These models involve the sum of a normal distribution (to represent failures) and a unimodal distribution (to represent the evoked responses). The implementation of the algorithm is described in each case, and its accuracy and convergence have been demonstrated.     

Relaxation processes and conformation of aquomethemoglobin.

We found out that the optical extinction E of MetHbH₂O, pH 6 depends non-monotonously on temperature in room temperature range. The corresponding more-component equilibrium was analysed by T-jump measurements. Three groups of relaxations were observed with relaxation rates differing by more than 7 decades. Newly discovered was a relaxation in the sec-time range. The stationary temperature dependence of E is quantitatively explained by the sum of the relaxation amplitudes. Modifications of the reactive SH-groups change the rate in the ms-time range and the stationary extinction. These changes are coupled: both observables depend characteristically on the specific modification.     

Quantitative analysis of G-actin transport in motile cells

Cell migration is based on an actin treadmill, which in turn depends on recycling of G-actin across the cell, from the rear where F-actin disassembles, to the front, where F-actin polymerizes. To analyze the rates of the actin transport, we used the Virtual Cell software to solve the diffusion-drift-reaction equations for the G-actin concentration in a realistic three-dimensional geometry of the motile cell. Numerical solutions demonstrate that F-actin disassembly at the cell rear and assembly at the front, along with diffusion, establish a G-actin gradient that transports G-actin forward “globally” across the lamellipod. Alternatively, if the F-actin assembly and disassembly are distributed throughout the lamellipod, F-/G-actin turnover is local, and diffusion plays little role. Chemical reactions and/or convective flow of cytoplasm of plausible magnitude affect the transport very little. Spatial distribution of G-actin is smooth and not sensitive to F-actin density fluctuations. Finally, we conclude that the cell body volume slows characteristic diffusion-related relaxation time in motile cell from ∼10 to ∼100 s. We discuss biological implications of the local and global regimes of the G-actin transport.     

Relaxation dynamics of the gel to liquid-crystalline transition of phosphatidylcholine bilayers. Effects of chainlength and vesicle size.

The relaxation kinetics of the gel to liquid-crystalline transition of five phosphatidylcholine (DC14PC to DC18PC) bilayer dispersions have been investigated using volume perturbation calorimetry, a steady-state technique which subjects a sample to sinusoidal changes in volume. Temperature and pressure responses to the volume perturbation are measured to monitor the relaxation to a new equilibrium position. The amplitude demodulation and phase shift of these observables are analyzed with respect to the perturbation frequency to yield relaxation times and amplitudes. In the limit of low perturbation frequency, the temperature and pressure responses are proportional to the equilibrium excess heat capacity and bulk modulus, respectively. At all temperatures, the thermal response data are consistent with a single primary relaxation process of the lipid. The less accurate bulk modulus data exhibit two relaxation times, but it is not clear whether they reflect lipid processes or are characteristic of the instrument. The observed thermal relaxation behavior of all multilamellar vesicles are quantitatively similar. The relaxation times vary from approximately 50 ms to 4 s, with a pronounced maximum at a temperature just greater than Tm, the temperature of the excess heat capacity maximum. Large unilamellar vesicles also exhibit a single relaxation process, but without a pronounced maximum in the relaxation time. Their relaxation time is approximately 80 ms over most of the transition range.     

On the influence of rapid periodic parameter oscillations on the long-term behaviour of cell metabolism

A skeleton model of energy metabolism of the living cell is considered in the form of kinetic equations. It is assumed that one intermediate metabolite can be rapidly shifted into a buffer reservoir and that the respective affinity constant changes periodically so that the metabolite is periodically withdrawn from and injected into the system. Investigation of the nonlinear system of differential equations with the periodic parameter by way of the Bogolyubov averaging method shows that the long-time energy state of the system may be changed drastically when the period is sufficiently short as compared with the characteristic metabolic events. In particular, the stabilization of a high-energy state by appropriate buffer shuttling is possible which cannot be maintained when the oscillations are stopped at any fixed parameter value. The result bears on the understanding of the influence of short-period rhythms on long-time behaviour of biosystems.     

Factors determining the sequence of oxidative decarboxylation of the 2- and 4-propionate substituents of coproporphyrinogen III by coproporphyrinogen oxidase in rat liver

The relaxation behaviour of a system of reactants equilibrated in the presence of pig heart lactate dehydrogenase was studied after pressure perturbation. Two relaxations were observed when protein fluorescence was recorded, but only the slower relaxation was apparent in observations of A340. The faster relaxation therefore involves transfer between free and enzyme-bound NADH, whereas the slower relaxation represents the reduction of NAD+. Both relaxations were observed in Tris buffer, where there is little effect of pressure on pH, and in phosphate buffer, where pH changes are significant; however, the amplitudes depended on the buffer used. The slower reciprocal relaxation time increases with increasing total enzyme concentration and decreases slightly with increasing NAD+ concentration. Computer simulations, based on a proposed mechanism, were compared with the experimentally determined amplitudes and relaxation times as a test of the mechanism.     

Dielectric behavior of polyelectrolytes. III. The role of counterion interactions

The role of the Coulomb forces between the counterions on the surface of polyelectrolytes on the dielectric response is analyzed. An estimate of the maximum dielectric increment (as a function of the number of counterions) is found as a function of the molecular length. The minimum-energy configuration of the counterions on a cylinder is found to be a double helix, suggesting the fundamental importance of electrostatic interactions in determining structure. Solutions of the dynamical equations for a few counterions indicate that a single mode dominates the relaxation which is enhanced by the inter-ion repulsions. A lower bound is found for this mode based on analysis of the system response for short lengths. Sum rules for the rates and amplitudes of the dipolar correlation function are derived and lead to an upper bound for the rate of the dominant mode. These bounds approach one another for the parameters characteristic of restriction fragments of DNA. This permits a prediction of the magnitude and time scale of the dielectric response.     

Hutchinson revisited: Patterns of density regulation and the coexistence of strong competitors

Ecologists have long been searching for mechanisms of species coexistence, particularly since G.E. Hutchinson raised the ‘paradox of the plankton’. A promising approach to solve this paradox and to explain the coexistence of many species with strong niche overlap is to consider over-compensatory density regulation with its ability to generate endogenous population fluctuations.Previous work has analysed the role of over-compensation in coexistence based on analytical approaches. Using a spatially explicit time-discrete simulation model, we systematically explore the dynamics and conditions for coexistence of two species. We go beyond the analytically accessible range of models by studying the whole range of density regulation from under- to very strong over-compensation and consider the impact of spatial structure and temporal disturbances. In particular, we investigate how coexistence can emerge in different types of population growth models.We show that two strong competitors are able to coexist if at least one species exhibits over-compensation. Analysing the time series of population dynamics reveals how the differential responses to density fluctuations of the two competitors lead to coexistence: The over-compensator generates density fluctuations but is the inferior competitor at strong amplitudes of those fluctuations; the competitor, therefore, becomes frequent and dampens the over-compensator's amplitudes, but it becomes inferior under dampened fluctuations.These species interactions cause a dynamic alternation of community states with long-term persistence of both species. We show that a variety of population growth models is able to reproduce this coexistence although the particular parameter ranges differ among the models. Spatial structure influences the probability of coexistence but coexistence is maintained for a broad range of dispersal parameters.The flexibility and robustness of coexistence through over-compensation emphasize the importance of nonlinear density dependence for species interactions, and they also highlight the potential of applying more flexible models than the classical Lotka-Volterra equations in community ecology.     

Oviductal isthmic motility patterns as monitored by polyview in unrestrained sows around ovulation

A method for monitoring oviductal isthmic motility in sows incorporating a computer programme (Polyview) was developed. This method was found to be reliable and easy for recording and analysing data. Isthmic motility patterns were monitored from 11 h prior to and up to 36 h after ovulation in 13 unrestrained multiparous sows during their second oestrus after weaning. The amplitudes and frequencies of phasic pressure fluctuations in relation to the hormonal profiles were also calculated. The isthmic motility patterns were regular before ovulation changing to wave patterns during the peri-ovulatory period and eventually to irregular patterns after ovulation. The amplitudes and frequencies of phasic pressure fluctuations were significantly higher (p<0.05) prior to and soon after ovulation than afterwards. Plasma oestradiol-17beta levels significantly (p<0.05) decreased before ovulation while plasma progesterone levels increased significantly (p<0.05) after ovulation. Despite a significant decrease in the plasma levels of oestradiol-17beta prior to ovulation, the amplitudes and frequencies of phasic pressure fluctuations remained high until shortly after ovulation. This could have been due to the endogenous levels of oestradiol-17beta bound to the nuclear oestradiol-17beta receptors that might still have been present in the isthmus. Conversely, the irregular isthmic motility patterns, the decline in the frequencies of phasic pressure fluctuations and amplitudes seen after ovulation may have been due to the rising plasma levels of progesterone. The amplitudes and frequencies of phasic pressure fluctuations were highest at the time when oestradiol-17beta levels were highest and when progesterone levels were low. It can be concluded that the changes in the isthmic motility patterns, amplitudes and frequencies of phasic pressure fluctuations in relation to the changes in the plasma levels of oestradiol-17beta and progesterone seen in the present study prior to and after ovulation indicate a possible role of the oviduct in regulating gamete transport.     

Near-critical phenomena in intracellular metabolite pools

The supply and consumption of metabolites in living cells are catalyzed by enzymes. Here we consider two of the simplest schemes where one substrate is eliminated through Michaelis-Menten kinetics, and where two types of substrates are joined together by an enzyme. It is demonstrated how steady-state substrate concentrations can change ultrasensitively in response to changes in their supply rates and how this is coupled to slow relaxation back to steady state after a perturbation. In the one-substrate system, such near-critical behavior occurs when the supply rate approaches the maximal elimination rate, and in the two-substrate system it occurs when the rates of substrate supply are almost balanced. As systems that operate near criticality tend to display large random fluctuations, we also carried out a stochastic analysis using analytical approximations of master equations and compared the results with molecular-level Monte Carlo simulations. It was found that the significance of random fluctuations was directly coupled to the steady-state sensitivity and that the two substrates can fluctuate greatly because they are anticorrelated in such a way that the product formation rate displays only small variation. Basic relations are highlighted and biological implications are discussed.     

Response to temporal parameter fluctuations in biochemical networks

Metabolic response coefficients describe how variables in metabolic systems, like steady state concentrations, respond to small changes of kinetic parameters. To extend this concept to temporal parameter fluctuations, we define spectral response coefficients that relate Fourier components of concentrations and fluxes to Fourier components of the underlying parameters. It is also straightforward to generalize other concepts from metabolic control theory, such as control coefficients with their summation and connectivity theorems. The first-order response coefficients describe forced oscillations caused by small harmonic oscillations of single parameters: they depend on the driving frequency and comprise the phases and amplitudes of the concentrations and fluxes. Close to a Hopf bifurcation, resonance can occur: as an example, we study the spectral densities of concentration fluctuations arising from the stochastic nature of chemical reactions. Second-order response coefficients describe how perturbations of different frequencies interact by mode coupling, yielding higher harmonics in the metabolic response. The temporal response to small parameter fluctuations can be computed by Fourier synthesis. For a model of glycolysis, this approximation remains fairly accurate even for large relative fluctuations of the parameters.     

Human upright posture control in a virtual visual environment

The sagittal and frontal components of the stabilogram were monitored in 14 healthy subjects standing on a rigid or pliant support under three different conditions of visual control: with the eyes opened (EO), with the eyes closed (EC), or in a virtual visual environment (VVE). Under the VVE conditions, the subjects looked at a three-dimensional image of elements of a room (a 3-D artificial room) that was generated by a computer and locked to the fluctuations of the body center of gravity (CG) so that the visual connection between body sway and shifts of the visual environment typical of normal visual conditions was reproduced. Frequency filtration of the fluctuations of the foot’s center of pressure (FCP) was used to isolate the movements of the vertical projection of the CG and determine the difference between these two variables. The changes in the variables (CG and FCP-CG) were estimated using spectral analysis followed by the calculation of the root mean square (RMS) amplitudes of their spectral fluctuations. In subjects standing on a rigid support, the RMS amplitudes of the spectra of both variables were the highest under the VVE and EC conditions and the lowest under the EO conditions. In subjects standing on a pliant support, body sway was considerably enhanced, which was accompanied by a different pattern of visual influences. The RMS values were the highest under the EC conditions and were lower by a factor of 2–2.5 under the EO and VVE conditions. Thus, it has been demonstrated that the cerebral structures controlling posture ignore the afferent input from the eyes under VVE conditions, if the subject is standing on a rigid support and the CG fluctuations are relatively small; however, this afferentation is efficiently used for maintaining the posture on a pliable support, when the body sway is substantially enhanced.     

Ultrasonic studies of proton-transfer reactions at the catalytic site of alpha-chymotrypsin

Ultrasonic relaxation measurements for alpha-chymotrypsin in phosphate, sulfite and arsenate buffers exhibit a high peak of absorption at neutral pH. The analysis is based on: comparison of the relaxation measurements for the enzyme and for the zymogen and inhibited enzyme; X-ray and neutron diffraction data, and high-resolution NMR data. The ultrasonic relaxation is shown to result mainly from a proton-transfer reaction that involves the histidine at the catalytic site (His-57). The question is raised of whether the enhanced ultrasonic effect observed in the enzyme is indicative of a property that plays a part in the catalytic activity.     

Role of Relaxation Time Scale in Noisy Signal Transduction

Intra-cellular fluctuations, mainly triggered by gene expression, are an inevitable phenomenon observed in living cells. It influences generation of phenotypic diversity in genetically identical cells. Such variation of cellular components is beneficial in some contexts but detrimental in others. To quantify the fluctuations in a gene product, we undertake an analytical scheme for studying few naturally abundant linear as well as branched chain network motifs. We solve the Langevin equations associated with each motif under the purview of linear noise approximation and derive the expressions for Fano factor and mutual information in close analytical form. Both quantifiable expressions exclusively depend on the relaxation time (decay rate constant) and steady state population of the network components. We investigate the effect of relaxation time constraints on Fano factor and mutual information to indentify a time scale domain where a network can recognize the fluctuations associated with the input signal more reliably. We also show how input population affects both quantities. We extend our calculation to long chain linear motif and show that with increasing chain length, the Fano factor value increases but the mutual information processing capability decreases. In this type of motif, the intermediate components act as a noise filter that tune up input fluctuations and maintain optimum fluctuations in the output. For branched chain motifs, both quantities vary within a large scale due to their network architecture and facilitate survival of living system in diverse environmental conditions.     

Pressure jump relaxation kinetics of frog skin open circuit voltage and short circuit current.

The relaxation kinetics of frog skin open circuit voltage, Voc, and short circuit current, Isc, was studied by analyzing the effects of subjecting the tissue to sudden increments of hydrostatic pressure. Both Voc and Isc are perturbed by the pressure jump. Changes in Voc can be resolved into three components: a rapid decrease (phase I), a second, additional decrease with time constant 2.2 s (phase II), and finally a very slow increase found only in some preparations. The amplitudes of phases I and II are linear in the range of pressures studied (less than 350 atm) and have respective pressure coefficients of -1.2.10(-4) atm-1 and 3.7.10(-4) atm-1. Under short circuit conditions, phases I and II persist. The pressure coefficients of the amplitudes of phases I and II, -4.3.10(-4) ATM-1 and -5.0.10(-4)ATM-1, respectively, are larger than those of Voc, but the time constant of phase II, 2.2 S, is the same. The sum of the amplitudes of phases I and II is directly proportional to Isc when it is inhibited with ouabain. It is argued that in both electrical states pressure perturbs the same transport mechanism giving rise to phases I and II of Voc and of Isc. The magnitude of the pressure coefficients of these processes implies that they arise from chemical reactions, rather than from simple, physical solution properties. Comparison of the pressure jump kinetics with the previous spectral analysis of the electrical fluctuations of frog skin suggests a common origin for both sets of phenomena.