Hierarchical modeling of phenolic ligand binding to 2Zn--insulin hexamers.

Phenolic ligands, e.g., phenol and m-cresol, bind to 2Zn(II)-insulin hexamers and induce a conformational change at the N-terminus of the B-chain for each monomer. The binding of these phenolic ligands to 2Zn(II)-insulin hexamers has been studied by isothermal titrating calorimetry (ITC). The binding isotherms were modeled and thermodynamic parameters were quantified using a novel, flexible algorithm that permitted the development of a hierarchical series of physical models. With the insulin hexamer represented as a dimer of trimers, the modeling demonstrated that ligand binding is highly cooperative in nature, both intra- and inter-trimer. The isotropic inter-trimer cooperativity was dominant and negative in every system studied, with initial binding constants typically an order of magnitude greater for the binding of ligands to the first trimer relative to the second. The inter-trimer cooperatively estimated from the modeling of solution calorimetry data is consistent with a T6 <--> T3R3 <--> R6 equilibrium first proposed from crystallographic investigations. Intra-trimer cooperatively was present only in the enthalpy coefficient space, not in the equilibrium coefficient space, and therefore, less of a factor. The order of binding affinity for the ligands studied in resorcinol >> phenol > or = m-cresol as determined from their overall free energies of binding to the 2Zn(II)-insulin hexamer (-26.6, -23.4, and -23.4 kcal/mol, respectively) and their intrinsic binding constants (8780, 5040, and 3370 L/mol, respectively) at 14 degrees C. The temperature dependence of phenol binding to 2Zn(II)-insulin hexamer was modeled. Increasing temperature decreased the magnitude of both the intrinsic binding constant and the inter-trimer was cooperatively. The second phase of the ITC binding profile was also found to be highly temperature dependent. At lower temperatures the second phase is endothermic but gradually decreases with increasing temperature and subsequently becomes exothermic. This effect is attributed to loss of water from the hydration shell of the insulin hexamer with increasing temperature and consequently reduces the entropic contributions to the T <--> R transition in the phenol/2Zn(II)-insulin hexamer system.

Nonlinear dynamics in cardiac conduction.

Electrical conduction in the heart shows many phenomena familiar from nonlinear dynamics. Among these phenomena are multiple basins of attraction, phase locking, and perhaps period-doubling bifurcations and chaos. We describe a simple cellular-automation model of electrical conduction which simulates normal conduction patterns in the heart as well as a wide range of disturbances of heart rhythm. In addition, we review the application of percolation theory to the analysis of the development of complex, self-sustaining conduction patterns.

Applications of a detailed model of cardiac conduction to ventricular dysrhythmogenesis.

In order to study transitions from normal patterns of electrical activity to abnormal patterns, such as ventricular activation, one requires a means to represent the state of myocardial electrical activation in a few parameters. Two parameters are presented here: 1) the net vorticity index (NVI) which is a measure of the net vorticity in a given region, and 2) the wavefront fractionation index (WFI), which is a measure of perturbations in the propagation of the electrical activation through the myocardium. Both parameters are topological measures in that normal propagation is condensed to a zero state, irrespective of smooth changes in wavefront orientation or shape. Several examples are demonstrated using a computer simulation of cardiac conduction. Potential applications to clinical diagnosis using experimentally obtainable data are discussed.

Computer simulation of fibrillation threshold measurements and electrophysiologic testing procedures.

A finite element model of cardiac conduction was used to simulate two experimental protocols: 1) fibrillation threshold measurements and 2) clinical electrophysiologic (EP) testing procedures. The model consisted of a cylindrical lattice whose properties were determined by four parameters: element length, conduction velocity, mean refractory period, and standard deviation of refractory periods. Different stimulation patterns were applied to the lattice under a given set of lattice parameter values and the response of the model was observed through a simulated electrocardiogram. The studies confirm that the model can account for observations made in experimental fibrillation threshold measurements and in clinical EP testing protocols.

A time dependent anatomically detailed model of cardiac conduction.

In order to understand the determinants of transitions in cardiac electrical activity from normal patterns to dysrhythmias such as ventricular fibrillation, we are constructing an anatomically and physiologically detailed finite element simulation of myocardial electrical propagation. A healthy human heart embedded in paraffin was sectioned to provide a detailed anatomical substrate for model calculations. The simulation of propagation includes anisotropy in conduction velocity due to fiber orientation as well as gradients in conduction velocities, absolute and relative refractory periods, action potential duration and electrotonic influence of nearest neighbors. The model also includes changes in the behaviour of myocardial tissue as a function of the past local activity. With this model, we can examine the significance of fiber orientation and time dependence of local propagation parameters on dysrhythmogenesis.

A statistical test for comparing several nucleotide sequences.

A statistical test useful for the simultaneous comparison of nucleotide sequences is presented. A likelihood ratio test is derived, examples demonstrated, and tables of critical values are provided.