BISEN: Biochemical Simulation Environment.

SUMMARY: The Biochemical Simulation Environment (BISEN) is a suite of tools for generating equations and associated computer programs for simulating biochemical systems in the MATLAB computing environment. This is the first package that can generate appropriate systems of differential equations for user-specified multi-compartment systems of enzymes and transporters accounting for detailed biochemical thermodynamics, rapid equilibria of multiple biochemical species and dynamic proton and metal ion buffering. AVAILABILITY: The software and a user manual (including several tutorial examples) are available at bbc.mcw.edu/BISEN.

Effect of binding in cyclic phosphorylation-dephosphorylation process and in energy transformation.

The effects of binding on the phosphorylation-dephosphorylation cycle (PDPC) - one of the key components of the signal transduction processes - is analyzed based on a mathematical model. The model shows that binding of proteins, forming a complex, diminishes the ultrasensitivity of the PDPC to the differences in activity between kinase and phosphatase in the cycle. It is also found that signal amplification depends upon the strength of the binding affinity of the protein (phosphorylated or dephosphorylated) to other proteins . It is also observed that the amplification of signal is not only dependent on phosphorylation potential but also on binding properties and resulting adjustments in binding energies.

Computational modeling predicts the structure and dynamics of chromatin fiber.

BACKGROUND: The compact form of the chromatin fiber is a critical regulator of fundamental processes such as transcription and replication. These reactions can occur only when the fiber is unraveled and the DNA strands contained within are exposed to interact with nuclear proteins. While progress on identifying the biochemical mechanisms that control localized folding and hence govern access to genetic information continues, the internal structure of the chromatin fiber, let alone the structural pathways for folding and unfolding, remain unknown. RESULTS: To offer structural insights into how this nucleoprotein complex might be organized, we present a macroscopic computer model describing the mechanics of the chromatin fiber on the polymer level. We treat the core particles as electrostatically charged disks linked via charged elastic DNA segments and surrounded by a microionic hydrodynamic solution. Each nucleosome unit is represented by several hundred charges optimized so that the effective Debye-Hückel electrostatic field matches the field predicted by the nonlinear Poisson-Boltzmann equation. On the basis of Brownian dynamics simulations, we show that oligonucleosomes condense and unfold in a salt-dependent manner analogous to the chromatin fiber. CONCLUSIONS: Our predicted chromatin model shows good agreement with experimental diffusion coefficients and small-angle X-ray scattering data. A fiber of width 30 nm, organized in a compact helical zigzag pattern with about 4 nucleosomes per 10 nm, naturally emerges from a repeating nucleosome folding motif. This fiber has a cross-sectional radius of gyration of R(c) = 8.66 nm, in close agreement with corresponding values for rat thymus and chicken erythrocyte chromatin (8.82 and 8.5 nm, respectively).

A database of thermodynamic quantities for the reactions of glycolysis and the tricarboxylic acid cycle.

Analysis of biochemical systems requires reliable and self-consistent databases of thermodynamic properties for biochemical reactions. Here a database of thermodynamic properties for the reactions of glycolysis and the tricarboxylic acid cycle is developed from measured equilibrium data. Species-level free energies of formation are estimated on the basis of comparing thermodynamic model predictions for reaction-level equilibrium constants to previously reported data obtained under different experimental conditions. Matching model predictions to the data involves applying state corrections for ionic strength, pH, and metal ion binding for each input experimental biochemical measurement. By archiving all of the raw data, documenting all model assumptions and calculations, and making the computer package and data available, this work provides a framework for extension and refinement by adding to the underlying raw experimental data in the database and/or refining the underlying model assumptions. Thus the resulting database is a refinement of preexisting databases of thermodynamics in terms of reliability, self-consistency, transparency, and extensibility.

Mitochondrial inner membrane electrophysiology assessed by rhodamine-123 transport and fluorescence.

Rhodamine-123 is widely used to make dynamic measurements of mitochondrial membrane potential both in vitro and in situ. Yet data interpretation is difficult due to a lack of quantitative understanding of how membrane potential and measured fluorescence are related. To develop such understanding, a model for dye transport across the mitochondrial inner membrane and partition into the membrane was developed. The model accounts for experimentally measured dye self-quenching and was integrated into a model of mitochondrial electrophysiology to estimate transients in mitochondrial membrane potential from kinetic fluorescence measurements. Our analysis indicates that (i) R123 fluorescence peaks at concentrations near 50 microM due to self-quenching; (ii) measured fluorescence intensity and membrane potential are related by a non-linear calibration curve sensitive to certain experimental details, including total concentration of dye and mitochondria in suspensions; and (iii) the time courses of membrane potential and electron transport fluxes following a perturbation (i.e. addition of ADP) significantly differ from observed transients in fluorescence intensity. These findings are consistent with the model predictions that mitochondria display a characteristic time of response to changes in substrate concentration of less than 0.1 s, corresponding to the time scale over which the rate of ATP synthesis changes to meet changes in ADP concentration.

Metabolic futile cycles and their functions: a systems analysis of energy and control.

It has long been hypothesised that futile cycles in cellular metabolism are involved in the regulation of biochemical pathways. Following the work of Newsholme and Crabtree, a quantitative theory was developed for this idea based on open-system thermodynamics and metabolic control analysis. It is shown that the stoichiometric sensitivity of an intermediary metabolite concentration with respect to changes in steady-state flux is governed by the effective equilibrium constant of the intermediate formation, and the equilibrium can be regulated by a futile cycle. The direction of the shift in the effective equilibrium constant depends on the direction of operation of the futile cycle. High stoichiometric sensitivity corresponds to ultrasensitivity of an intermediate concentration to net flow through a pathway; low stoichiometric sensitivity corresponds to super-robustness of concentration with respect to changes in flux. Both cases potentially play important roles in metabolic regulation. Futile cycles actively shift the effective equilibrium by expending energy; the magnitude of changes in effective equilibria and sensitivities is a function of the amount of energy used by a futile cycle. This proposed mechanism for control by futile cycles works remarkably similar to kinetic proofreading in biosynthesis. The sensitivity of the system is also intimately related to the rate of concentration fluctuations of intermediate metabolites. The possibility of different roles for the two major mechanisms within cellular biochemical regulation, namely reversible chemical modifications via futile cycles and shifting equilibrium by macromolecular binding, are discussed.

Computational framework for generating transport models from databases of microvascular anatomy.

Quantitative descriptions of transport and exchange in physiological systems should make use of the emerging wealth of data on vascular anatomic structure. These descriptions may take the form of computational models which then must be incorporated into the comprehensive database of knowledge of microcirculatory physiology being developed under the title, The Microcirculation Physiome Project. Toward this end we present a simple and efficient computational method for simulating transport (advection, permeation, diffusion) in tissues containing microvascular structures of arbitrary complexity. The method is convenient because transport is simulated on a regular Cartesian lattice, and efficient because features of the anatomy are resolved within individual volume elements of the lattice. As a result, relatively low-resolution lattices yield accurate results. Therefore the method provides a feasible approach for studying a general class of transport problems in the context of realistic representations of vascular anatomy.

The fractal nature of myocardial blood flow emerges from a whole-organ model of arterial network.

Mammalian hearts exhibit a heterogeneous spatial distribution of blood flows, but flows in near-neighbor regions correlate strongly. Also, tracer (15)O-water washout after injection into the inflow shows a straight log-log relationship between outflow concentration and time. To uncover the role of the arterial network in governing these phenomena, morphometric data were used to construct a mathematical model of the coronary arterial network of the pig heart. The model arterial network, built in a simplified three-dimensional representation of tissue geometry, satisfies the statistical morphometric data on segment lengths, diameters and connectivities reported for real arterial networks. The model uses an avoidance algorithm to position successive vascular segments in the network. Assuming flows through the network to be steady, the calculated regional flow distributions showed (1) the degree of heterogeneity observed in normal hearts; (2) spatial self-similarity in local flows; (3) fractal spatial correlations, all with the same fractal dimension found in animal studies; (4) pressure distributions along the model arterial network comparable to those observed in nature, with maximal resistances in small vessels. In addition, the washout of intravascular tracer showed tails with power law slopes that fitted h(t) = at(-alpha-1) with the exponents alpha = 2 for the reconstructed networks compared with those from experimental outflow concentration-time curves with alpha = 2.1+/-0.3. Thus, we concluded that the fractal nature of spatial flow distribution in the heart, and of temporal intravascular washout, are explicable in terms of the morphometry of the coronary network.

Modeling salt-mediated electrostatics of macromolecules: the discrete surface charge optimization algorithm and its application to the nucleosome.

Much progress has been achieved on quantitative assessment of electrostatic interactions on the all-atom level by molecular mechanics and dynamics, as well as on the macroscopic level by models of continuum solvation. Bridging of the two representations-an area of active research-is necessary for studying integrated functions of large systems of biological importance. Following perspectives of both discrete (N-body) interaction and continuum solvation, we present a new algorithm, DiSCO (Discrete Surface Charge Optimization), for economically describing the electrostatic field predicted by Poisson-Boltzmann theory using a discrete set of Debye-Hückel charges distributed on a virtual surface enclosing the macromolecule. The procedure in DiSCO relies on the linear behavior of the Poisson-Boltzmann equation in the far zone; thus contributions from a number of molecules may be superimposed, and the electrostatic potential, or equivalently the electrostatic field, may be quickly and efficiently approximated by the summation of contributions from the set of charges. The desired accuracy of this approximation is achieved by minimizing the difference between the Poisson-Boltzmann electrostatic field and that produced by the linearized Debye-Hückel approximation using our truncated Newton optimization package. DiSCO is applied here to describe the salt-dependent electrostatic environment of the nucleosome core particle in terms of several hundred surface charges. This representation forms the basis for modeling-by dynamic simulations (or Monte Carlo)-the folding of chromatin. DiSCO can be applied more generally to many macromolecular systems whose size and complexity warrant a model resolution between the all-atom and macroscopic levels.

Fractal 15O-labeled water washout from the heart.

To characterize the washout of water from the heart, we used a flow-limited (not diffusion- or permeability-limited) marker for blood-tissue exchange, namely, tracer-labeled water. Experiments were performed by injecting 15O-labeled water into the inflow to isolated blood-perfused rabbit hearts and by recording the tracer content in the heart and in the outflow simultaneously for up to 5 minutes. The data exhibit a particular combination of power law forms: (1) The downslopes of the residue and outflow curves were both power law functions, with the residue diminishing as t-alpha and the outflow as t-alpha-1, where alpha is interpreted to be the dimensionless exponent of a fractal power law relation characterizing the self-similarity inherent in each curve. (2) The fractional escape rate, given by the outflow curve divided by the residue curve, diminished almost exactly as t-1. In 18 sets of curves, alpha averaged 2.21 +/- 0.27. These results lead to an improved method for extrapolating the downslopes of indicator dilution curves to estimate their areas and therefore the blood flows. The evidence also points strongly to the conclusions that myocardial water washout is a fractal process and that stirred tank models are inappropriate for the heart.

Advection and diffusion of substances in biological tissues with complex vascular networks.

For highly diffusive solutes the kinetics of blood-tissue exchange is only poorly represented by a model consisting of sets of independent parallel capillary-tissue units. We constructed a more realistic multicapillary network model conforming statistically to morphometric data. Flows through the tortuous paths in the network were calculated based on constant resistance per unit length throughout the network and the resulting advective intracapillary velocity field was used as a framework for describing the extravascular diffusion of a substance for which there is no barrier or permeability limitation. Simulated impulse responses from the system, analogous to tracer water outflow dilution curves, showed flow-limited behavior over a range of flows from about 2 to 5 ml min(-1) g(-1), as is observed for water in the heart in vivo. The present model serves as a reference standard against which to evaluate computationally simpler, less physically realistic models. The simulated outflow curves from the network model, like experimental water curves, were matched to outflow curves from the commonly used axially distributed models only by setting the capillary wall permeability-surface area (PS) to a value so artifactually low that it is incompatible with the experimental observations that transport is flow limited. However, simple axially distributed models with appropriately high PSs will fit water outflow dilution curves if axial diffusion coefficients are set at high enough values to account for enhanced dispersion due to the complex geometry of the capillary network. Without incorporating this enhanced dispersion, when applied to experimental curves over a range of flows, the simpler models give a false inference that there is recruitment of capillary surface area with increasing flow. Thus distributed models must account for diffusional as well as permeation processes to provide physiologically appropriate parameter estimates.

Power-law kinetics of tracer washout from physiological systems.

Recent studies suggest that the tail of the washout of tracer-labeled substances from physiological systems can exhibit power-law behavior. In this work we develop a theoretical interpretation of the power-law behavior of the flow-limited washout of tracer-labeled water from the myocardium. Using minimal assumptions concerning the complicated structure of the coronary network we show that the washout from a heterogeneous flow system is given by h(t) approximately equal to A x p1 (V/t)(-beta), where beta is close to 3, p1 is the probability density of flows through the system, V is a constant volume associated with each pathway, and A is a constant. This prediction fits observed power-law washout behavior of tracer water in the heart. This theory is general enough to lead us to speculate that close examination of transport in other heterogeneity-perfused systems is likely to reveal similar power-law behavior.

Modeling advection and diffusion of oxygen in complex vascular networks.

A realistic geometric model for the three-dimensional capillary network geometry is used as a framework for studying the transport and consumption of oxygen in cardiac tissue. The nontree-like capillary network conforms to the available morphometric statistics and is supplied by a single arterial source and drains into a pair of venular sinks. We explore steady-state oxygen transport and consumption in the tissue using a mathematical model which accounts for advection in the vascular network, nonlinear binding of dissolved oxygen to hemoglobin and myoglobin, passive diffusion of freely dissolved and protein-bound oxygen, and Michaelis-Menten consumption in the parenchymal tissue. The advection velocity field is found by solving the hemodynamic problem for flow throughout the network. The resulting system is described by a set of coupled nonlinear elliptic equations, which are solved using a finite-difference numerical approximation. We find that coupled advection and diffusion in the three-dimensional system enhance the dispersion of oxygen in the tissue compared to the predictions of simplified axially distributed models, and that no "lethal corner," or oxygen-deprived region occurs for physiologically reasonable values for flow and consumption. Concentrations of 0.5-1.0 mM myoglobin facilitate the transport of oxygen and thereby protect the tissue from hypoxia at levels near its P50, that is, when local oxygen consumption rates are close to those of delivery by flow and myoglobin-facilitated diffusion, a fairly narrow range.

The mechanical and metabolic basis of myocardial blood flow heterogeneity.

Precise measurements of regional myocardial blood flow heterogeneity had to be developed before one could seek causation for the heterogeneity. Deposition techniques (particles or molecular microspheres) are the most precise, but imaging techniques have begun to provide high enough resolution to allow in vivo studies. Assigning causation has been difficult. There is no apparent association with the regional concentrations of energy-related enzymes or substrates, but these are measures of status, not of metabolism. There is statistical correlation between flow and regional substrate uptake and utilization. Attribution of regional flow variation to vascular anatomy or to vasomotor control appears not to be causative on a long-term basis. The closest relationships appear to be with mechanical function, but one cannot say for sure whether this is related to ATP hydrolysis at the crossbridge or associated metabolic reactions such as calcium uptake by the sarcoplasmic reticulum.