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Hysteresis, oscillations, and pattern formation in realistic biochemical systems governed by P.D.E.s are considered from both numerical and mathematical points of view. Analysis of multiple steady states in the case of hysteresis, and bifurcation theory in the cases of oscillations and pattern formation, account for the observed numerical results. The possibility to realize these systems experimentally is their main interest, thus bringing further arguments in favor of theories explaining basic biological phenomena by diffusion and reaction.

We present methods for using the generalpurpose network analysis program, SPICE, to construct computer models of excitable membrane displaying Hodgkin-Huxley-like kinetics. The four non-linear partial differential equations of Hodgkin and Huxley (H-H; 1952) are implemented using electrical circuit elements. The H-H rate constants, a and ß, are approximated by polynomial functions rather than exponential functions, since the former are handled more efficiently by SPICE. The process of developing code to implement the H-H sodium conductance is described in detail. The Appendix contains a complete listing of the code required to simulate an H-H action potential. The behavior of models so constructed is validated by comparison with the space-clamped and propagating action potentials of Hodgkin and Huxley. SPICE models of multiply branched axons were tested and found to behave as predicted by previous numerical solutions for propagation in inhomogeneous axons. New results are presented for two cases. First, a detailed, anatomically based model is constructed of group Ia input to an a-motoneuron with an excitable soma, a myelinated axon and passive dendrites. Second, we simulate interactions among clusters of mixed excitable and passive dendritic spines on an idealized neuron. The methods presented in this paper and its companion (Segev et al. 1985) should permit neurobiologists to construct and explore models which simulate much more closely the real morphological and physiological characteristics of nerve cells.

We describe the application of a popular and widely available electrical circuit simulation program called SPICE to modeling the electrical behavior of neurons with passive membrane properties and arbitrarily complex dendritic trees. Transient responses may be calculated at any location in the cell model following current, voltage or conductance perturbations at any point. A numbering method is described for binary trees which is helpful in transforming complex dendritic structures into a coded list of short cylindrical dendritic segments suitable for input to SPICE. Individual segments are modeled as isopotential compartments comprised of a parallel resistor and capacitor, representing the transmembrane impedance, in series with one or two core resistors. Synaptic current is modeled by a current source controlled by the local membrane potential and an “alpha-shaped” voltage, thus simulating a conductance change in series with a driving potential. Extensively branched test cell circuits were constructed which satisfied the equivalent cylinder constraints (Rall 1959). These model neurons were perturbed by independent current sources and by synaptic currents. Responses calculated by SPICE are compared with analytical results. With appropriately chosen model parameters, extremely accurate transient calculations may be obtained. Details of the SPICE circuit elements are presented, along with illustrative examples sufficient to allow implementation of passive nerve cell models on a number of common computers. Methods for modeling excitable membrane are presented in the companion paper (Bunow et al. 1985).

Three antibody reagents that neutralize primary human immunodeficiency virus type 1 (HIV-1) isolates were tested for magnitude and breadth of neutralization when used alone or in double or triple combinations. Hyperimmune anti-HIV immunoglobulin (HIVIG) is derived from the plasma of HIV-1-infected donors, and monoclonal antibodies (MAbs) 2F5 and 2G12 bind to distinct regions of the HIV-1 envelope glycoprotein. The antibodies were initially tested against a panel of 15 clade B HIV-1 isolates, using a single concentration that is achievable in vivo (HIVIG, 2,500 microg/ml; MAbs, 25 microg/ml). Individual antibody reagents neutralized many of the viruses tested, but antibody potency varied substantially among the viruses. The virus neutralization produced by double combinations of HIVIG plus 2F5 or 2G12, the two MAbs together, or the triple combination of HIVIG, 2F5, and 2G12 was generally equal to or greater than that predicted by the effect of individual antibodies. Overall, the triple combination displayed the greatest magnitude and breadth of neutralization. Synergistic neutralization was evaluated by analyzing data from dose-response curves of each individual antibody reagent compared to the triple combination and was demonstrated against each of four viruses tested. Therefore, combinations of polyclonal and monoclonal anti-HIV antibodies can produce additive or synergistic neutralization of primary HIV-1 isolates. Passive immunotherapy for treatment or prophylaxis of HIV-1 should consider mixtures of potent neutralizing antibody reagents to expand the magnitude and breadth of virus neutralization.