The maturation of HIV-1 protease precursor studied by discrete molecular dynamics.

The equilibrium properties of a HIV-1-protease precursor are studied by means of an efficient molecular dynamics scheme, which allows for the simulation of the folding of the protein monomers and their dimerization into an active form and compare them with those of the mature protein. The results of the model provide, with atomic detail, an overall account of several experimental findings, including the NMR conformation of the mature dimer, the calorimetric properties of the system, the effects of the precursor tail on the dimerization constant, the secondary chemical shifts of the monomer, and the paramagnetic relaxation enhancement data associated with the conformations of the precursor. It is found that although the mature protein can dimerize in a unique, single way, the precursor populates several dimeric conformations in which monomers are always native-like, but their binding can be non-native.

Equilibrium and Response Properties of the Integrate-and-Fire Neuron in Discrete Time.

The integrate-and-fire neuron with exponential postsynaptic potentials is a frequently employed model to study neural networks. Simulations in discrete time still have highest performance at moderate numerical errors, which makes them first choice for long-term simulations of plastic networks. Here we extend the population density approach to investigate how the equilibrium and response properties of the leaky integrate-and-fire neuron are affected by time discretization. We present a novel analytical treatment of the boundary condition at threshold, taking both discretization of time and finite synaptic weights into account. We uncover an increased membrane potential density just below threshold as the decisive property that explains the deviations found between simulations and the classical diffusion approximation. Temporal discretization and finite synaptic weights both contribute to this effect. Our treatment improves the standard formula to calculate the neuron's equilibrium firing rate. Direct solution of the Markov process describing the evolution of the membrane potential density confirms our analysis and yields a method to calculate the firing rate exactly. Knowing the shape of the membrane potential distribution near threshold enables us to devise the transient response properties of the neuron model to synaptic input. We find a pronounced non-linear fast response component that has not been described by the prevailing continuous time theory for Gaussian white noise input.