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[Mathematical model of electromechanical coupling in the rat myocardium].

A mathematical modelling approach was used to study the negative staircase in the rat papillary muscle. This phenomenon was found to be associated with an excess of the steady-state Ca++-influx in the myocardium cells. The model with a single chamber intracellular Ca-pool simulates satisfactory the experimental data obtained with a standard set of parameter values. It is concluded that the rat myocardium sarcoplasmic reticulum is loaded by Ca++-ions which enter the cell as a potential-independent Ca-influx presumably.

Action Potentials↗

The two-dimensional IR nonlinear spectroscopy of a cyclic penta-peptide in relation to its three-dimensional structure.

A form of two-dimensional (2D) vibrational spectroscopy, which uses two ultrafast IR laser pulses, is used to examine the structure of a cyclic penta-peptide in solution. Spectrally resolved cross peaks occur in the off-diagonal region of the 2D IR spectrum of the amide I region, analogous to those in 2D NMR spectroscopy. These cross peaks measure the coupling between the different amide groups in the structure. Their intensities and polarizations relate directly to the three-dimensional structure of the peptide. With the help of a model coupling Hamiltonian, supplemented by density functional calculations, the spectra of this penta-peptide can be regenerated from the known solution phase structure. This 2D-IR measurement, with an intrinsic time resolution of less than 1 ps, could be used in all time regimes of interest in biology.

Amino Acid Sequence↗

Coupled production and transport of selenium vapor in unsaturated soil: evaluation by experiments and numerical simulation.

Volatilization of selenium (Se) from soil to the atmosphere involves several sequential chemical reactions that form volatile Se species, followed by transport of the gaseous Se through the soil. This paper describes a numerical model that simulates the chemical and physical processes governing the production and transport of Se vapor in unsaturated soil. The model couples the four Se species involved in the production of Se vapor through chemical reactions, and allows each to migrate through the soil by advection, liquid or vapor diffusion depending on its affinity for the dissolved or vapor phase. The coupled transformations and transport of the four Se species, i.e., selenate, selenite, elemental and organic Se, and Se vapor, were calculated based on the Crank-Nicolson finite difference method. The model was used to analyze fluxes of Se vapor measured from a soil amended with inorganic Se in the form of selenate and covered with unamended clean soil of various thicknesses. Evolution of Se vapor from the soil was very fast, with measurable amounts of Se detected within 24 h. The peak of Se volatilization, detected at the 6th day, reached 3.31 Se microgram/day for the uncovered soil, but was reduced to near the detection limit (0.05 microgram/day) in the presence of a 8- or 16-cm clean soil cover. With two reaction rate coefficients fitted to the data, the model described Se volatilization very well. The estimated rate coefficient of Se methylation was unexpectedly high, with a value of 0.167/day. The net volatilization of Se, however, was severely inhibited by the fast demethylation, i.e., the reverse reaction which converted volatile Se species back into nonvolatile forms. As a result, Se vapor only penetrated a few centimeters in the soil. The demethylation rate coefficient, assessed by independent transport experiments using dimethyl selenide, was estimated as 186.8/day, corresponding to a half-life of only 5.3 min for Se vapor. Results of this study indicated that rapid demethylation of Se vapor during its diffusive transport through a soil is probably an important limiting factor in the volatilization of Se under natural conditions.

Computer Simulation↗

CFD analysis of gas explosions vented through relief pipes.

Vent devices for gas and dust explosions are often ducted to safe locations by means of relief pipes. However, the presence of the duct increases the severity of explosion if compared to simply vented vessels (i.e. compared to cases where no duct is present). Besides, the identification of the key phenomena controlling the violence of explosion has not yet been gained. Multidimensional models coupling, mass, momentum and energy conservation equations can be valuable tools for the analysis of such complex explosion phenomena. In this work, gas explosions vented through ducts have been modelled by a two-dimensional (2D) axi-symmetric computational fluid dynamic (CFD) model based on the unsteady Reynolds Averaged Navier Stokes (RANS) approach in which the laminar, flamelet and distributed combustion models have been implemented. Numerical test have been carried out by varying ignition position, duct diameter and length. Results have evidenced that the severity of ducted explosions is mainly driven by the vigorous secondary explosion occurring in the duct (burn-up) rather than by the duct flow resistance or acoustic enhancement. Moreover, it has been found out that the burn-up affects explosion severity due to the reduction of venting rate rather than to the burning rate enhancement through turbulization.

Explosions↗

Structural models of osteogenesis imperfecta-associated variants in the COL1A1 gene.

Osteogenesis imperfecta (OI) is a genetic disease in which the most common mutations result in substitutions for glycine residues in the triple helical domain of the chains of type I collagen. Currently there is no way to use sequence information to predict the clinical OI phenotype. However, structural models coupled with biophysical and machine learning methods may be able to predict sequences that, when mutated, would be associated with more severe forms of OI. To build appropriate structural models, we have applied a high throughput molecular dynamic approach. Homotrimeric peptides covering 57 positions in which mutations are associated with OI were simulated both with and without mutations. Our models revealed structural differences that occur with different substituting amino acids. When mutations were introduced, we observed a decrease in helix stability, as caused by fewer main chain backbone hydrogen bonds, and an increase in main chain root mean square deviation and specifically bound water molecules.

Collagen Type I↗

Universality of chaotic rare fluctuations in a locally coupled phase map model.

Chaotic fluctuations of the order parameter in a coupled two-dimensional phase map model are numerically investigated. We discuss the system-size N dependence of the statistical properties of rare fluctuations observed in the transition range between the quasiordered chaotic state and the fully developed one. It is found that the normalized probability distribution function (PDF) has a unique functional form irrespective of N. The asymptotic form of the PDF is discussed in connection with the universal distribution for correlated systems proposed by Bramwell et al. [Nature (London) 396, 552 (1998)]. Moreover, it is observed that the power spectrum P(N)(omega) of rare fluctuations asymptotically takes the power-law form P(N)(omega) equivalent to omega(-(1+alpha)) (alpha=0.6 equivalent to 0.7) irrespective of N. This result suggests that the temporal correlation decays as a stretched exponential.

Journal Article↗

Modelling the fate and transport of nickel in the mersey estuary.

Modelling heavy metals in estuarine environments is extremely complex for various reasons; one of the primary complicating factors is that metals exist in two phases, dissolved and particulate bound. Dynamic changes in water chemistry, and in particular salinity, affect the partitioning of metals between the two phases and hence make it difficult to determine the relative fractions of each phase. A relatively simple approach was developed to relate variations in partition coefficient for Ni to salinity fluctuations in the Mersey Estuary. The functional relationship developed between partition coefficient and salinity departs from the traditional exponential type curve, providing a more realistic relationship.A numerical model was then developed for predicting the transport and distribution of Ni about the Mersey Estuary. The model couples transport of metals throughout the water along with incorporating the chemical processes controlling how nickel is fractioned between dissolved and particulate phases through the newly developed partition coefficient relationship. Model predictions of dissolved Ni along the longitudinal axis of the estuary were compared with measurements of Ni for two events; very good correlation was obtained between the model results and the data.

Biological Transport↗

Group velocity and dispersion model of coupled-cavity waveguides in photonic crystals.

A theoretical model of the group velocity, dispersion parameter, and dispersion slope of coupled-cavity waveguides in photonic crystals is reported. Results arising from closed-form expressions show a good agreement with simulation results obtained by employing a plane-wave expansion method. Coupled-cavity waveguides present interesting dispersion properties that may be employed in applications such as optical signal processing, dispersion compensation, and optical delay lines.

Journal Article↗

A mathematical and experimental study of ant foraging trail dynamics.

In this article, we present a mathematical model coupled to an experimental study of ant foraging trails. Our laboratory experiments on Tetramorium caespitum do not find a strong relationship between ant densities and velocities, a common assumption in traffic modeling. Rather, we find that higher order effects play a major role in observed behavior, and our model reflects this by including inertial terms in the evolution equation. A linearization of the resulting system yields left- and right-moving waves, in agreement with laboratory measurements. The linearized system depends upon Froude numbers reflecting a ratio of the energy stored in the foraging trail to the kinetic energy of the ants. The model predicts and the measurements support the existence of two distinct phase velocities.

Animal Communication↗

Numerical simulation of trace element transport on subsurface environment pollution in coal mine spoil.

An understanding of the dynamic behavior of trace elements leaching from coal mine spoil is important in predicting the groundwater quality. The relationship between trace element concentrations and leaching times, pH values of the media is studied. Column leaching tests conducted in the laboratory showed that there was a close correlation between pH value and trace element concentrations. The longer the leaching time, the higher the trace element concentrations. Different trace elements are differently affected by pH values of leaching media. A numerical model for water flow and trace element transport has been developed based on analyzing the characteristics of migration and transformation of trace elements leached from coal mine spoil. Solutions to the coupled model are accomplished by Eulerian-Lagrangian localized adjoint method. Numerical simulation shows that rainfall intensity determined maximum leaching depth. As rainfall intensity is 3.6ml/s, the outflow concentrations indicate a breakthrough of trace elements beyond the column base, with peak concentration at 90cm depth. And the subsurface pollution range has a trend of increase with time. The model simulations are compared to experimental results of trace element concentrations, with reasonable agreement between them. The analysis and modeling of trace elements suggested that the infiltration of rainwater through the mine spoil might lead to potential groundwater pollution. It provides theoretical evidence for quantitative assessment soil-water quality of trace element transport on environment pollution.

Coal Mining↗

Electronic and molecular structure of high-spin d4 complexes: experimental and theoretical study of the [Cr(D2O)6]2+ cation in Tutton's salts.

Variable-temperature spectroscopic and crystallographic studies on the chromium(II) Tutton's salts, (MI)2Cr(X2O)6(SO4)2, where MI = ND4+, Rb+, or Cs+, and X = H or D, are reported. Inelastic neutron scattering (INS) and multifrequency EPR experiments facilitate a rigorous definition of the ground-state electronic structure from 1.5 up to 296 K, which is unprecedented for a high-spin d4 complex. Modeling of the INS data using a conventional S = 2 spin Hamiltonian reveals a dramatic variation in the axial and rhombic zero-field-splitting parameters. For the ammonium salt, D and E are -2.454(3) and 0.087(3) cm(-1) at 10 K and -2.29(2) and 0.16(3) cm(-1) at 250 K, respectively. A temperature variation in the stereochemistry of the [Cr(D2O)6]2+ complex is also identified, with an apparent coalescence of the long and medium Cr-O bond lengths at temperatures above 150 K. The corresponding changes for the rubidium and cesium salts are notable, though less pronounced. The experimental quantities are interpreted using a 5Ee Jahn-Teller Hamiltonian, perturbed by anisotropic strain. It is shown that good agreement can be obtained only by employing a model in which the anisotropic strain is itself temperature dependent. A new theoretical approach for calculating variable-temperature EPR spectra of high-spin d4 complexes, developed within the 5Ee coupling model, is described. Differences between spin-Hamiltonian parameters determined by INS and EPR are consistent with those of the different time scales of the two techniques.

Journal Article↗

On the extent of localization of the energized membrane state in chromatophores from Rhodopseudomonas capsulata N22.

1. The principle of the double-inhibitor titration method for assessing competing models of electron transport phosphorylation is expounded. 2. This principle is applied to photophosphorylation by chromatophores from Rhodopseudomonas capsulata N22. 3. It is found that, in contrast to the predictions of the chemiosmotic coupling model, free energy transfer is confined to individual electron transport chain and ATP synthase complexes. 4. This conclusion is not weakened by arguments concerning, the degree of uncoupling in the native chromatophore preparation or the relative number of electron transport chain and ATP synthase complexes present. 5. Photophosphorylation is completely inhibited by the uncoupler SF 6847 at a concentration corresponding to 0.31 molecules per electron transport chain. 6. The apparent paradox is solved by the proposal, consistent with the available evidence on the mode of action of uncouplers, that uncoupler binding causes a co-operative conformation transition in the chromatophore membrane, which leads to uncoupling and which is not present in the absence of uncoupler.

Antimycin A↗

Variability in biological exposure indices using physiologically based pharmacokinetic modeling and Monte Carlo simulation.

By using physiologically based pharmacokinetic (PBPK) modeling coupled with Monte Carlo simulation, the interindividual variability in the concentrations of chemicals in a worker's exhaled breath and urine were estimated and compared with existing biological exposure indices (BEIs). The PBPK model simulated an exposure regimen similar to a typical workday, while exposure concentrations were set to equal the ambient threshold limit values (TLVs) of six industrial solvents (benzene, chloroform, carbon tetrachloride, methylene chloride, methyl chloroform, and trichloroethylene). Based on model predictions incorporating interindividual variability, the percentage of population protected was derived using TLVs as the basis for worker protection. Results showed that current BEIs may not protect the majority or all of the workers in an occupational setting. For instance, current end-expired air indices for benzene and methyl chloroform protect 95% and less than 10% of the worker population, respectively. Urinary metabolite concentrations for benzene, methyl chloroform, and trichloroethylene were also estimated. The current BEI recommendation for phenol metabolite concentration at the end-of-shift sampling interval was estimated to protect 68% of the worker population, while trichloroacetic acid (TCAA) and trichloroethanol (TCOH) concentrations for methyl chloroform exposure were estimated to protect 54% and 97%, respectively. The recommended concentration of TCAA in urine as a determinant of trichloroethylene exposure protects an estimated 84% of the workers. Although many of the existing BEIs considered appear to protect a majority of the worker population, an inconsistent proportion of the population is protected. The information presented in this study may provide a new approach for administrative decisions establishing BEIs and allow uniform application of biological monitoring among different chemicals.

Humans↗

Technical and structural support systems and nurse utilization: systems model.

There are two major components to nursing support systems: technical support systems, for the distribution of supplies and medicines to patients and for communication among hospital personnel, and structural support systems, for the organization of nursing staff-RNs, LPNs, and aides-into a systematic, working assignment pattern. Four hospital studies that used different combinations of technical and structural support systems were compared for the amount of time registered nurses were able to spend on direct patient care activities. It was found that a structural support system based on the primary nursing model, coupled with a decentralized technical support system, maximized direct patient care time.

Hospital Communication Systems↗

Realistically coupled neural mass models can generate EEG rhythms.

We study the generation of EEG rhythms by means of realistically coupled neural mass models. Previous neural mass models were used to model cortical voxels and the thalamus. Interactions between voxels of the same and other cortical areas and with the thalamus were taken into account. Voxels within the same cortical area were coupled (short-range connections) with both excitatory and inhibitory connections, while coupling between areas (long-range connections) was considered to be excitatory only. Short-range connection strengths were modeled by using a connectivity function depending on the distance between voxels. Coupling strength parameters between areas were defined from empirical anatomical data employing the information obtained from probabilistic paths, which were tracked by water diffusion imaging techniques and used to quantify white matter tracts in the brain. Each cortical voxel was then described by a set of 16 random differential equations, while the thalamus was described by a set of 12 random differential equations. Thus, for analyzing the neuronal dynamics emerging from the interaction of several areas, a large system of differential equations needs to be solved. The sparseness of the estimated anatomical connectivity matrix reduces the number of connection parameters substantially, making the solution of this system faster. Simulations of human brain rhythms were carried out in order to test the model. Physiologically plausible results were obtained based on this anatomically constrained neural mass model.

Brain Mapping↗

In silico prediction of ADME properties: are we making progress?

The use of computational models in the prediction of ADME properties of compounds is growing rapidly in drug discovery as the benefits they provide in throughput and early application in drug design are realized. In addition, there is an increasing range of models available, as model builders have advanced from the first-generation' models, which were predominantly focused on solubility, absorption and metabolism, to include models of other optimization factors such as HERG, glucuronyl transferase and drug transport proteins. This widening interest is now driving demand for developments in the component elements of model building, namely higher quality datasets, better molecular descriptors and more computational power, and the quality of models is improving rapidly as a consequence. Models generally have very high throughput and can be used with virtual structures. As a consequence, they can generate large quantities of data on large numbers of compounds. Thus, one consequence of the wider choice of models, coupled with their high throughput, is a growing need to integrate their output into collective analyses of molecules against pre-set criteria. This article comments on some of the recent developments in ADME models, and highlights the importance of integrating the data to aid compound selection in drug discovery projects.

Chemical Phenomena↗

The effect of torso impedance on epicardial and body surface potentials: a modeling study.

Experimental results have been published that report marked changes in measured epicardial potentials when the conductivity of the material surrounding the heart is altered. These reports raise a question as to the validity of the traditional two step, equivalent cardiac source approach to modeling the forward problem of electrocardiology as the equivalent source calculation occurs in what is effectively an isolated cardiac region. In the physical situation the heart is surrounded by a torso that contains many different tissue types with different conductivities and is certainly not isolated. Here, a fully coupled model of the problem is employed where the electrical pathways are continuous from a cellular level through to the body surface. This model is used to investigate the effects that torso inhomogeneities have on epicardial and body surface potentials, including comparisons with a traditional two step approach. In particular, it is shown that adding lungs changes the epicardial potentials by 17%, which is consistent with the reported experimental results. In none of the tested situations did the equivalent source approach completely reproduce the fully coupled results, supporting the notion that a fully coupled approach is required to properly solve the forward problem of electrocardiology.

Abdomen↗

Hydrodynamic models of viscous coupling between motile myosin and endoplasm in characean algae.

Cytoplasmic streaming in characean algae is thought to be driven by interaction between stationary subcortical actin bundles and motile endoplasmic myosin. Implicit in this mechanism is a requirement for some form of coupling to transfer motive force from the moving myosin to the endoplasm. Three models of viscous coupling between myosin and endoplasm are presented here, and the hydrodynamic feasibility of each model is analyzed. The results show that individual myosinlike molecules moving along the actin bundles at reasonable velocities cannot exert enough viscous pull on the endoplasm to account for the observed streaming. Attachment of myosin to small spherical organelles improves viscous coupling to the endoplasm, but results for this model show that streaming can be generated only if the myosin-spheres move along the actin bundles in a virtual solid line at about twice the streaming velocity. In the third model, myosin is incorporated into a fibrous or membranous network or gel extending into the endoplasm. This network is pulled forward as the attached myosin slides along the actin bundles. Using network dimensions estimated from published micrographs of characean endoplasm, the results show that this system can easily generate the observed cytoplasmic streaming.

Actins↗