A graph method is developed to solve Schwinger–Dyson equations for electron transfer reactions in biological molecules. Feynman diagrams provide a convenient technique for the calculation of self-energy. Multiple pathway mechanisms of electron transfer can be examined by splitting of the graphical representation into clusters in case of rate-limiting steps. The approximation of weak hopping greatly simplifies the problem of calculating Green functions, which powerfully express a number of characteristics of the process of electron transfer such as the spectral density of states and the correlational function. Rules of graph transformations are derived, and applied to calculate Green matrix elements corresponding to a single hydrogen bond-coupled path in polypeptides, and to the case of the through-backbone pathway. The relation between cluster graphs and Feynman diagrams in locator representation is discussed. Formulas up to the second-order perturbations for linear structure of the cluster graph are given. Calculations of the electron transfer rate dependence on donor–acceptor distance are presented. It is shown that taking into account the second-order perturbation makes the dependence of the logarithm of the electron transfer rate on donor–acceptor distance nonlinear. This effect is especially significant for large distances.

For many years, membrane potential (Vm) and input resistance have been used to characterize the electrophysiological nature of a seal (barrier) that forms at the cut end of a transected axon or other extended cytoplasmic structure. Data from a mathematical and an analog model of a transected axon and other theoretical considerations show that steady-state values of Vm and input resistance measured from any cable-like structure provide a very equivocal assessment of the electrical barrier (seal) at the cut end. Extracellular assessments of injury currents almost certainly provide a better electrophysiological measure of the status of plasma membrane sealing because measurements of these currents do not depend on the cable properties of extended cytoplasmic processes after transection.

We applied the formalism of double-time Green's functions to the problem of electron transfer from donor (D) to acceptor (A) through large macromolecules. The finite size of a system does not allow the use of momentum representation. For a tight-binding (Huckel-like) Hamiltonian we obtained the Dyson equation. The equation for Green's functions is linear and does not require one to go to higher order ones, which makes analysis of large protein molecules quite feasible. In this paper we analyze the structure of important double-time correlation functions, which will allow us to investigate time-dependent features of long-range electron transfer. We find explicit solutions of Dyson equations for some special cases. Our next 'vhich will provide a useful tool to investigate the general case of large paper will be dkdicaied to a graphical technique macromolecules.Electron transfer between localized sites is an important problem in some physical, chemical, and biological phenomena.' It is found that in living systems electron transfer occurs over large distances. For example, in the case of the photosynthesis the absorption of light by chlorophyll promotes an electron along an electrontransport chain mode up of a sequence of sites. We consider these sites to correspond to the structure of polypeptide chains. The chemical and biological problems deal with electron propagation from one center of an individual molecule to an acceptor. The problem is to estimate the rate of this transfer.The many-body technique, developed in solid-state physics and statistical mechanics, may successfully be applied to the problem under investigation. Especially promising will be (we believe) the application of so-called double-time Green's functions developed some time ago. They are especially effective in the case of nonequilibrium quantum statistical mechanics, and electron transport is essentially a nonequilibrium quantum mechanical process. The difference in technique which we will describe here and usually used in the solid-state many-body technique is that we cannot use the momentum representation but must, rather, work in direct spatial representation.da Gama was the first to use Green's function formalism in a model for the through-bond electronic interaction between electron donor and acceptor in proteins.I0The model which we adopt here is that of an electron donor (D), an electron acceptor (A), and a chain of amino acids. For each group we will assign a site of the chain and a subsequent orbital energy Ti. We will use the grand canonical ensemble, and therefore, chemical potentials enters here. The electron intersite interaction is not restricted to first neighbors and is represented by the hopping transfer potentials 6) In this paper we concern ourselves with only the electronic part of the Hamiltonian. We will discuss the ionic part elsewhere.In what follows we will adopt a tight-binding (Huckel-like) Hamiltonian, written in secondary quantized form 'Hopping" integrals vj are taken here to be nonrandom functions of r y Here we ...

Results of approximate integral equation calculations both for the square-well and Lennard-Jones fluids in the supercritical region are reported, and a comparison with Percus–Yevick and hypernetted chain theories is made. A relation between the effective diameter of particles and values of the mean force potential along the line of vanishing of solutions has been found.