A simulation method is presented for the demographic and genetic variation of age structured haploid populations. First, we use matrix analytic methods to derive an equilibrium distribution for the age class sizes conditioned on the total population size. Knowledge of this distribution eliminates the need of a burn-in time in simulations. Next, we derive the distribution of the alleles at a polymorphic locus in various age classes given the allele frequencies in the total population and the age size composition. For the time dynamics, we start by simulating the dynamics for the total population. In order to generate the inheritance of the alleles, we derive their distribution conditionally on the simulated population sizes. This method enables a fast simulation procedure of multiple loci in linkage equilibrium.
In this paper we propose an effective method to estimate the intrinsic values in an immobilized enzyme system, i.e., Michaelis constant K(m) and the maximum reaction rate V(m). We combine three techniques: (1) the non-linear least square method for estimating the kinetic values, (2) orthogonal collocation with the Gauss integration method, and (3) Newton-Raphson method (NRM) or S-system method (SSM) as Newton-like method. We build a procedure to combine the first two methods to estimate the unknown kinetic values in a system. We apply this procedure to solve the intrinsic kinetic parameters determination problem in an immobilized enzyme systems following Michaelis-Menten reaction. To demonstrate the effectiveness of the current method, we test their convergence performance in detail. The results show that the basin of attraction in the current method is extremely enlarged compared with that of the S-system alone. We suggest that the current method is one of the most effective ways to solve fairly complicated biochemical reaction systems in general.
A powerful methodology for analyzing post-synaptic currents recorded from central neurons is presented. An unknown quantity of transmitter molecules released from presynaptic terminals by electrical stimulation of nerve fibers generates a post-synaptic response at the synaptic site. The current induced at the synaptic junction is assumed to rise rapidly and decay slowly with its peak amplitude being proportional to the number of released transmitter molecules. The signal so generated is then distorted by the cable properties of the dendrite, modeled as a time-invariant, linear filter with unknown parameters. The response recorded from the cell body of the neuron following the electrical stimulation is contaminated by zero-mean, white, Gaussian noise. The parameters of the signal are then evaluated from the observation sequence using a quasi-profile likelihood estimation procedure. These parameter values are then employed to deconvolve each measured post-synaptic response to produce an optimal estimate of the transmembrane current flux. From these estimates we derive the amplitude of the synaptic current and the relative amount of transmitter molecules that elicited each response. The underlying amplitude fluctuations in the entire data sequence are investigated using a non-parametric technique based on kernel smoothing procedures. The effectiveness of the new methodology is illustrated in various simulation examples.
A three-state Markov model taking into account clinical signs of malaria infections by P. falciparum is described. The three states considered are the noninfected (state 0), the infected exhibiting no clinical signs (state 1), and the infected with clinical signs (state 2). Methods for estimating the transition rates from longitudinal data are indicated. This model was used to assess the effect on children of an intervention trial on the use of mosquito nets impregnated with insecticide. The trial was conducted in West Africa (Burkina Faso) between 1985 and 1987. The analysis showed that the intervention was most effective on transition rates between state 1 and state 2.
