Mathematical analysis of a basic model for epidermal wound healing

The stimuli for the increase in epidermal mitosis during wound healing are not fully known. We construct a mathematical model which suggests that biochemical regulation of mitosis is fundamental to the process, and that a single chemical with a simple regulatory effect can account for the healing of circular epidermal wounds. The numerical results of the model compare well with experimental data. We investigate the model analytically by making biologically relevant approximations. We then obtain travelling wave solutions which provide information about the accuracy of these approximations and clarify the roles of the various model parameters.     

Effect of pH on successive foam and sonic droplet fractionation of a bromelain-invertase mixture

A droplet fractionation method was previously developed to concentrate a dilute nonfoaming protein solution. In that earlier study with invertase, it was demonstrated that droplets created by ultrasonic energy waves could be enriched up to 8 times that of the initial dilute invertase solution. In this study, a mixture of bromelain (a foaming protein) and invertase (a nonfoaming protein) is investigated as a preliminary step to determine if droplet fractionation can also be used to separate a non-foaming protein from foaming proteins. The foaming mixture containing bromelain is first removed by bubbling the binary mixture with air. After the foam is removed, the protein rich air-water interfacial layer is skimmed off (prior to droplet fractionation) so as not to interfere with the subsequent droplet production from the remaining bulk liquid, rich in non-foaming protein. Finally, sonic energy waves are then applied to this residual bulk liquid to recover droplets containing the non-foaming protein, presumed to be invertase. The primary control variable used in this droplet fractionation process is the pH, which ranged for separate experiments between 2 and 9. It was observed that the maximum overall protein partition coefficients of 5 and 4 were achieved at pH 2 and 4, respectively, for the initial foaming experiment followed by the post foaming droplet fractionation experiment.     

The Analysis of Synaptically Generated Traveling Waves

Mathematical and computational models for the propagation of activity in excitatorily coupled neurons are simulated and analyzed. The basic measurable quantity—velocity—is found for a wide class of models. Numerical bifurcation techniques, asymptotic analysis, and numerical simulations are used to show that there are distinct scaling laws for the velocity as a function of a variety of parameters. In particular, the obvious linear relationships between speed and spatial spread or synaptic decay rate are shown. More surprisingly, it is shown that the velocity scales as a power law with synaptic coupling strength and that the exponent is dependent only on the rising phase of the synapse.