Lednev's model: theory and experiment

The results of theoretical and experimental investigations of V.V. Lednev on interactions of weak and extremely weak magnetic fields with biosystems have been reviewed. The period since 1989, when the first version of the interference model has been suggested, until now has been considered. Some mathematical expressions, are presented, which have been published earlier in the papers that are now bibliographic rarity. The results of experimental investigations are also summarized that have been performed in this period under the supervision of V.V. Lednev in the laboratory of biophysics of intracellular regulation in the Institute of Theoretical and Experimental Biophysics of the Russian Academy of Sciences.     

Fosbury flop: predicting performance with a three-variable model

The goal of this study is to (a) find the most predictive anthropometric factors, (b) check the predictability of a new jumping motor test, and (c) predict Fosbury-flop (FFP) performance by using a multiregression analysis. The participants of this study were 49 girls (age 13.6 ± 0.48 years; height = 1.61 ± 0.07 m) and 68 boys (age 13.6 ± 0.47 years; height = 1.64 ± 0.10 m). We measured the height, the sitting height), the highest position touched by the hand in a standing position (HEIGHTARM), the highest position touched by the hand during a running 1-leg vertical jump with a semirestricted curved run-up (HMAX), and the best performance in the FFP. We then calculated the leg length (LEGLENGTH), the skelic index (ratio of legs length to the abdomen length, SKEL), the vertical performance (VP, difference between HMAX and HEIGHTARM). The ability level was deducted from the difference between (LEGLENGTH + VP) and FFP. Pearson correlation coefficients were calculated, and a multiple-regression analysis technique was applied to find the most predictive model (p < 0.05). The FFP was correlated with standing height (HEIGHT; r = 0.398; p < 0.05), HMAX (r = 0.707; p < 0.0005), ABILITY (r = 0.391; p < 0.005) but not with SKEL (r = 0.161; p = 0.01). The best multiple-regression model included HEIGHT, HMAX, and ABILITY with a high level of prediction (r2 = 0.94). In conclusion, the FFP performance can be predicted with equation: FFP = -0.618 HEIGHT + 0.898 HMAX + 0.669 ABILITY - 0.08. This equation is quite similar for both sexes, showing that 13-year-old girls and boys use the same method to jump high, which implies that the way to increase coordination or lower limb strength during training can be the same for junior boys and girls in high jump.     

Dielectrophoretic force: A comparison of theory and experiment

Because of the increasing use of dielectrophoresis in the dielectric characterization and sorting of living cells or their parts, it has become important to establish carefully the theoretical backgrounds for this effect. A comparison with experiment is made of the several versions of the theory for the dielectrophoretic force exerted by nonuniform electric fields upon a neutral object. The three fundamental approaches: the Maxwell-Strattonstress tensor, the effective dipole moment, and the ‘Helmholtz’ energy approach are presented along with the general solution given earlier by Pohl and Crane. These are found to agree closely with experiment in predicting the dielectrophoretic force upon various rods hung in specially shaped (isomotive) field distributions. On the other hand, an alternative formulation based upon a debatable assignment of fields local to the dipoles gave a good fit to the experimental data only for materials of very low permittivity, and fitted poorly in the case of highly polarizable materials. An improved derivation of the theory for stable dielectrophoretic levitation is also presented. This phenomenon is of particular interest in that it is based upon an apparent violation of the Earnshaw's theorem, and is useful in the study of the dielectric properties of individual living cells.     

Topological analysis of chaos in a three-variable biochemical model

A three-variable biochemical prototype involving two enzymes with autocatalytic regulation proposed by Decroly and Goldbeter (1987) is analyzed using a topological approach. A two-branched manifold, a so-called template, is thus identified. For certain control parameter values, this template is a horseshoe template with a global torsion of two half-turns. This implies that the bifurcation diagram can be described using the usual sequences associated with a unimodal map with a differentiable maximum as well as exemplified by the logistic map. Moreover, a type-I intermittency associated with a saddle-node bifurcation is exhibited. The dynamics from a single time series are also investigated to determine whether it is possible to investigate the dynamics of this biochemical model from the measure of a single concentration.     

Dynamics of proteins in crystals: comparison of experiment with simple models

The dynamic behavior of proteins in crystals is examined by comparing theory and experiments. The Gaussian network model (GNM) and a simplified version of the crystallographic translation libration screw (TLS) model are used to calculate mean square fluctuations of C(alpha) atoms for a set of 113 proteins whose structures have been determined by x-ray crystallography. Correlation coefficients between the theoretical estimations and experiment are calculated and compared. The GNM method gives better correlation with experimental data than the rigid-body libration model and has the added benefit of being able to calculate correlations between the fluctuations of pairs of atoms. By incorporating the effect of neighboring molecules in the crystal the correlation is further improved.     

Interplay of charge distribution and conformation in peptides: comparison of theory and experiment

We assessed the correlation between charge distribution and conformation of flexible peptides by comparing the theoretically calculated potentiometric-titration curves of two model peptides, Ac-Lys5-NHMe (a model of poly-L-lysine) and Ac-Lys-Ala11-Lys-Gly2-Tyr-NH2 (P1) in water and methanol, with the experimental curves. The calculation procedure consisted of three steps: (i) global conformational search of the peptide under study using the electrostatically driven Monte Carlo (EDMC) method with the empirical conformational energy program for peptides (ECEPP)/3 force field plus the surface-hydration (SRFOPT) or the generalized Born surface area (GBSA) solvation model as well as a molecular dynamics method with the assisted model building and energy refinement (AMBER)99/GBSA force field; (ii) reevaluation of the energy in the pH range considered by using the modified Poisson-Boltzmann approach and taking into account all possible protonation microstates of each conformation, and (iii) calculation of the average degree of protonation of the peptide at a given pH value by Boltzmann averaging over conformations. For Ac-Lys5-NHMe, the computed titration curve agrees qualitatively with the experimental curve of poly-L-lysine in 95% methanol. The experimental titration curves of peptide P1 in water and methanol indicate a remarkable downshift of the first pK(a) value compared to the values for reference compounds (n-butylamine and phenol, respectively), suggesting the presence of a hydrogen bond between the tyrosine hydroxyl oxygen and the H(epsilon) proton of a protonated lysine side chain. The theoretical titration curves agree well with the experimental curves, if conformations with such hydrogen bonds constitute a significant part of the ensemble; otherwise, the theory predicts too small a downward pH shift.     

Contribution of vasomotion to vascular resistance: a comparison of arteries from virgin and pregnant rats

Intrinsic oscillatory activity, or vasomotion,within the microcirculation has many potential functions, includingmodulation of vascular resistance. Alterations in oscillatory activityduring pregnancy may contribute to the marked reduction in vascularresistance. The purpose of this study was1) to mathematically model theoscillatory changes in vessel diameter and determine the effect onvascular resistance and 2) tocharacterize the vasomotion in resistance arteries of pregnant andnonpregnant (virgin) rats. Mesenteric arteries were isolated fromSprague-Dawley rats and studied in a pressurized arteriograph.Mathematical modeling demonstrated that the resistance in a vessel withvasomotion was greater than that in a static vessel with the same meanradius. During constriction with the₁-adrenergic agonistphenylephrine, the amplitude of oscillation was less in the arteriesfrom pregnant rats. We conclude that vasomotor activity may provide amechanism to regulate vascular resistance and blood flow independent ofstatic changes in arterial diameter. During pregnancy the decrease invasomotor activity in resistance arteries may contribute to thereduction in peripheral vascular resistance.

     

Ionic strength dependence of localized contact formation between membranes: nonlinear theory and experiment.

Erythrocyte membrane surface or suspending phase properties can be experimentally modified to give either spatially periodic local contacts or continuous contact along the seams of interacting membranes. Here, for cells suspended in a solution of the uncharged polysaccharide dextran, the average lateral separation between localized contacts in spatially periodic seams at eight ionic strengths, decreasing from 0.15 to 0.065, increased from 0.65 to 3.4 micrometers. The interacting membranes and intermembrane aqueous layer were modeled as a fluid film, submitted to a disjoining pressure, responding to a displacement perturbation either through wave growth resulting in spatially periodic contacts or in perturbation decay, to give a plane continuous film. Measured changes of lateral contact separations with ionic strength change were quantitatively consistent with analytical predictions of linear theory for an instability mechanism dependent on the membrane bending modulus. Introduction of a nonlinear approach established the consequences of the changing interaction potential experienced by different parts of the membrane as the disturbance grew. Numerical solutions of the full nonlinear governing equations correctly identified the ionic strength at which the bifurcation from continuous seam to a stationary periodic contact pattern occurred and showed a decrease in lateral contact and wave crest separation with increasing ionic strength. The nonlinear approach has the potential to recognize the role of nonspecific interactions in initiating the localized approach of membranes, and then incorporate the contribution of specific molecular interactions, of too short a range to influence the beginning of perturbation growth. This new approach can be applied to other biological processes such as neural cell adhesion, phagocytosis, and the acrosome reaction.     

Unconfined compression of articular cartilage: nonlinear behavior and comparison with a fibril-reinforced biphasic model

Mechanical behavior of articular cartilage was characterized in unconfined compression to delineate regimes of linear and nonlinear behavior, to investigate the ability of a fibril-reinforced biphasic model to describe measurements, and to test the prediction of biphasic and poroelastic models that tissue dimensions alter tissue stiffness through a specific scaling law for time and frequency. Disks of full-thickness adult articular cartilage from bovine humeral heads were subjected to successive applications of small-amplitude ramp compressions cumulating to a 10 percent compression offset where a series of sinusoidal and ramp compression and ramp release displacements were superposed. We found all equilibrium behavior (up to 10 percent axial compression offset) to be linear, while most nonequilibrium behavior was nonlinear, with the exception of small-amplitude ramp compressions applied from the same compression offset. Observed nonlinear behavior included compression-offset-dependent stiffening of the transient response to ramp compression, nonlinear maintenance of compressive stress during release from a prescribed offset, and a nonlinear reduction in dynamic stiffness with increasing amplitudes of sinusoidal compression. The fibril-reinforced biphasic model was able to describe stress relaxation response to ramp compression, including the high ratio of peak to equilibrium load. However, compression offset-dependent stiffening appeared to suggest strain-dependent parameters involving strain-dependent fibril network stiffness and strain-dependent hydraulic permeability. Finally, testing of disks of different diameters and rescaling of the frequency according to the rule prescribed by current biphasic and poroelastic models (rescaling with respect to the sample's radius squared) reasonably confirmed the validity of that scaling rule. The overall results of this study support several aspects of current theoretical models of articular cartilage mechanical behavior, motivate further experimental characterization, and suggest the inclusion of specific nonlinear behaviors to models.     

The biomagnetic signature of a crushed axon. A comparison of theory and experiment.

The response of a crayfish medial giant axon to a nerve crush is examined with a biomagnetic current probe. The experimental data is interpreted with a theoretical model that incorporates both radial and axial ionic transport and membrane kinetics similar to those in the Hodgkin/Huxley model. Our experiments show that the effects of the crush are manifested statically as an elevation of the resting potential and dynamically as a reduction in the amplitude of the action current and potential, and are observable up to 10 mm from the crush. In addition, the normally biphasic action current becomes monophasic near the crush. The model reflects these observations accurately, and based on the experimental data, it predicts that the crush seals with a time constant of 45 s. The injury current density entering the axon through the crush is calculated to be initially on the order of 0.1 mA/mm2 and may last until the crush seals or until the concentration gradients between the intra- and extracellular spaces equilibrate.     

The magnetic field of a single axon. A comparison of theory and experiment.

The magnetic field and the transmembrane action potential of a single nerve axon were measured simultaneously. The volume conductor model was used to calculate the magnetic field from the measured action potential, allowing comparison of the model predictions with the experimental data. After analyzing the experiment for all systematic errors, we conclude that the shape of the magnetic field can be accurately predicted from the transmembrane potential and, more importantly, the shape of the transmembrane potential can be calculated from the magnetic field. The data are used to determine ri, the internal resistance per unit length of the axon, to be 19.3 +/- 1.9 k omega mm-1, implying a value for the internal conductivity of 1.44 +/- 0.33 omega -1 m-1. Magnetic measurements are compared with standard bioelectric techniques for studying nerve axons.     

Dynamics of protein folding: probing the kinetic network of folding-unfolding transitions with experiment and theory

The problem of spontaneous folding of amino acid chains into highly organized, biologically functional three-dimensional protein structures continues to challenge the modern science. Understanding how proteins fold requires characterization of the underlying energy landscapes as well as the dynamics of the polypeptide chains in all stages of the folding process. In recent years, important advances toward these goals have been achieved owing to the rapidly growing interdisciplinary interest and significant progress in both experimental techniques and theoretical methods. Improvements in the experimental time resolution led to determination of the timescales of the important elementary events in folding, such as formation of secondary structure and tertiary contacts. Sensitive single molecule methods made possible probing the distributions of the unfolded and folded states and following the folding reaction of individual protein molecules. Discovery of proteins that fold in microseconds opened the possibility of atomic-level theoretical simulations of folding and their direct comparisons with experimental data, as well as of direct experimental observation of the barrier-less folding transition. The ultra-fast folding also brought new questions, concerning the intrinsic limits of the folding rates and experimental signatures of barrier-less "downhill" folding. These problems will require novel approaches for even more detailed experimental investigations of the folding dynamics as well as for the analysis of the folding kinetic data. For theoretical simulations of folding, a main challenge is how to extract the relevant information from overwhelmingly detailed atomistic trajectories. New theoretical methods have been devised to allow a systematic approach towards a quantitative analysis of the kinetic network of folding-unfolding transitions between various configuration states of a protein, revealing the transition states and the associated folding pathways at multiple levels, from atomistic to coarse-grained representations. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.     

Dynamics of the Hck-SH3 domain: comparison of experiment with multiple molecular dynamics simulations

Molecular dynamics calculations provide a method by which the dynamic properties of molecules can be explored over timescales and at a level of detail that cannot be obtained experimentally from NMR or X-ray analyses. Recent work (Philippopoulos M, Mandel AM, Palmer AG III, Lim C, 1997, Proteins 28:481-493) has indicated that the accuracy of these simulations is high, as measured by the correspondence of parameters extracted from these calculations to those determined through experimental means. Here, we investigate the dynamic behavior of the Src homology 3 (SH3) domain of hematopoietic cell kinase (Hck) via 5N backbone relaxation NMR studies and a set of four independent 4 ns solvated molecular dynamics calculations. We also find that molecular dynamics simulations accurately reproduce fast motion dynamics as estimated from generalized order parameter (S2) analysis for regions of the protein that have experimentally well-defined coordinates (i.e., stable secondary structural elements). However, for regions where the coordinates are not well defined, as indicated by high local root-mean-square deviations among NMR-determined structural family members or high B-factors/low electron density in X-ray crystallography determined structures, the parameters calculated from a short to moderate length (less than 5-10 ns) molecular dynamics trajectory are dependent on the particular coordinates chosen as a starting point for the simulation.     

Membrane model of the regulation of proliferation: the theory and interpretation of an experiment

The role of cell surface physical organization in the cell cycle regulation is analyzed within the framework of the earlier proposed theory (Chernavskii et al., 1982). Two models of cell surface are considered: hard-frame fluid-mosaic model (latticemosaic) and the fluid-mosaic one. The former deals with normal cells. The existence of integral carcasse or "frame" which is formed by the essential part of cross-linked membrane components and may have at least two different conformational states is hypothesized. The second model describes membranes of tumour cells. With the latter theory any mitogen (excluding the restoration of nutrient depletion) reduces the mechanical tensile strength of the frame and stimulates the general structural rearrangement of the plasma membrane. There are only two conformational transitions during the cell cycle which serve as signals for the beginning of S and M phases. If the values of tensile strength are great enough and therefore the conformational transitions are impossible, the cells pass into the resting (prereplicative--G01, or premitotical--G02) state. Three types of experiments are interpreted in the proposed theory: a) on differences in the action of growth factors on normal and tumour cell cycle, b) on the necessary condition for mitogenicity of lectins, c) on the stimulation of proliferation by mechanical deformation of cells.     

Modulation of vasomotion in resistance arteries of JCR:LA-cp rats: a model of insulin resistance.

Obesity and insulin resistance are strongly associated with an increased risk of vascular disease. Vasomotion is the cyclic variation in the diameter of arteries and is a general feature of the vasculature that may have important physiological consequences. We tested the hypothesis that obesity - insulin resistance is associated with abnormal vasomotion by comparing obese, insulin-resistant JCR:LA-cp rats, known to develop vasculopathy, atherosclerosis, and ischemic lesions of the heart, with lean insulin-sensitive animals from the same strain. Vasomotion was assessed using isolated mesenteric arteries on a myograph system after preconstriction to 50% of maximal constriction with norepinephrine. The amplitude of vasomotion was enhanced by the presence of meclofenamate, a prostaglandin H synthase inhibitor, and was diminished by N(G)-nitro-L-arginine methyl ester (L-NAME), a nitric oxide synthase inhibitor. Removal of the endothelium essentially abolished vasomotion, and meclofenamate had no effect on de-endothelialized arteries. Frequency was not altered by either L-NAME or meclofenamate. Although pharmacological inhibition of nitric oxide and eicosanoid production clearly altered vasomotion, there was no difference in the amplitude or frequency of vasomotion in arteries from obese rats compared with lean rats. These results indicate that the endothelium plays a central role in modulating vasomotion, involving both enhancing and inhibiting effects, and that vasomotion is similar between obese, insulin-resistant and lean, insulin-sensitive rats.     

Acidic-basic properties of three alanine-based peptides containing acidic and basic side chains: comparison between theory and experiment

The purpose of this work was to evaluate the effect of the nature of the ionizable end groups, and the solvent, on their acid-base properties in alanine-based peptides. Hence, the acid-base properties of three alanine-based peptides: Ac-KK-(A)(7)-KK-NH(2) (KAK), Ac-OO-(A)(7)-DD-NH(2) (OAD), Ac-KK-(A)(7)-EE-NH(2) (KAE), where A, D, E, K, and O denote alanine, aspartic acid, glutamic acid, lysine, and ornithine, respectively, were determined in water and in methanol by potentiometry. With the availability of these data, the ability of two theoretical methods to simulate pH-metric titration of those peptides was assessed: (i) the electrostatically driven Monte Carlo method with the ECEPP/3 force field and the Poisson-Boltzmann approach to compute solvation energy (EDMC/PB/pH), and (ii) the molecular dynamics method with the AMBER force field and the Generalized Born model (MD/GB/pH). For OAD and KAE, pK(a1) and pK(a2) correspond to the acidic side chains. For all three compounds in both solvents, the pK(a1) value is remarkably lower than the pK(a) of a compound modeling the respective isolated side chain, which can be explained by the influence of the electrostatic field from positively charged ornithine or lysine side chains. The experimental titration curves are reproduced well by the MD/GB/pH approach, the agreement being better if restraints derived from NMR measurements are incorporated in the conformational search. Poorer agreement is achieved by the EDMC/PB/pH method.