Stabilized intermediate redox states of cytochrome c are generated by radiolytic reduction of initially oxidized enzyme in glass matrices at liquid nitrogen temperature. In the intermediate states the heme group is reduced by hydrated electrons, whereas the protein conformation is restrained close to its oxidized form by the low-temperature glass matrix. The intermediate and stable redox states of cytochrome c at neutral and alkaline pH are studied by low-temperature resonance Raman spectroscopy using excitations in resonance with the B (Soret) and Q1 (beta) optical transitions. The assignments of the cytochrome c resonance Raman bands are discussed. The observed spectral characteristics of the intermediate states as well as of the alkaline transition in the oxidized state are interpreted in terms of oxidation-state marker modes, spin-state marker modes, heme iron--axial ligand stretching modes, totally symmetric in-plane porphyrin modes, nontotally symmetric in-plane modes, and out-of-plane modes.

The kinetics of thermally activated processes are studied by the nonstationary solutions of the Fokker–Planck equation, or Kramers’ equation, for a particle moving in a bistable potential and coupled to a heat bath. An alternate direction implicit method is formulated and used to determine the time evolution of the probability density function and probability density current in the phase space for a large range of the strength of coupling to the heat bath. In addition to the rate constant in a first-order rate equation, corresponding to the lowest real eigenvalue in an eigenfunction expansion, transient processes corresponding to higher and complex eigenvalues are also studied. The results for strong coupling to the heat bath are compared to those obtained from the Smoluchowski equation. The present results are also used to evaluate the accuracy of previous treatments.

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It is shown that a low-dimensional model neuron with a response time constant smaller than the membrane time constant closely reproduces the activity and excitability behavior of a detailed conductance-based model of Hodgkin-Huxley type. The fast response of the activity variable also makes it possible to reduce the model to a one-dimensional model, in particular for typical conditions. As an example, the reduction to a single-variable model from a multivariable conductance-based model of a neocortical pyramidal cell with somatic input is demonstrated. The conditions for avoiding a spurious damped oscillatory response to a constant input are derived, and it is shown that a limit-cycle response cannot occur. The capability of the low-dimensional model to approximate higher-dimensional models accurately makes it useful for describing complex dynamics of nets of interconnected neurons. The simplicity of the model facilitates analytic studies, elucidations of neurocomputational mechanisms, and applications to large-scale systems.