Adaptive mutations in Escherichia coli as a model for the multiple mutational origins of tumors.

The cells in most tumors are found to carry multiple mutations; however, based upon mutation rates determined by fluctuation tests, the frequency of such multiple mutations should be so low that tumors are never detected within human populations. Fluctuation tests, which determine the cell-division-dependent mutation rate per cell generation in growing cells, may not be appropriate for estimating mutation rates in nondividing or very slowly dividing cells. Recent studies of time-dependent, "adaptive" mutations in nondividing populations of microorganisms suggest that similar measurements may be more appropriate to understanding the mutation origins of tumors. Here I use the ebgR and ebgA genes of Escherichia coli to measure adaptive mutation rates where multiple mutations are required for rapid growth. Mutations in either ebgA or ebgR allow very slow growth on lactulose (4-O-beta-D-galactosyl-D-fructose), with doubling times of 3.2 and 17.3 days, respectively. However, when both mutations are present, cells can grow rapidly with doubling times of 2.7 hr. I show that during prolonged (28-day) selection for growth on lactulose, the number of lactulose-utilizing mutants that accumulate is 40,000 times greater than can be accounted for on the basis of mutation rates measured by fluctuation tests, but is entirely consistent with the time-dependent adaptive mutation rates measured under the same conditions of prolonged selection.

A feedback-controlled ensemble model of the stress-responsive hypothalamo-pituitary-adrenal axis

The present work develops and implements a biomathematical statement of how reciprocal connectivity drives stress-adaptive homeostasis in the corticotropic (hypothalamo-pituitary-adrenal) axis. In initial analyses with this interactive construct, we test six specific a priori hypotheses of mechanisms linking circadian (24-h) rhythmicity to pulsatile secretory output. This formulation offers a dynamic framework for later statistical estimation of unobserved in vivo neurohormone secretion and within-axis, dose-responsive interfaces in health and disease. Explication of the core dynamics of the stress-responsive corticotropic axis based on secure physiological precepts should help to unveil new biomedical hypotheses of stressor-specific system failure.

Active control of waves in a cochlear model with subpartitions.

Multiscale asymptotic methods developed previously to study macromechanical wave propagation in cochlear models are generalized here to include active control of a cochlear partition having three subpartitions, the basilar membrane, the reticular lamina, and the tectorial membrane. Activation of outer hair cells by stereocilia displacement and/or by lateral wall stretching result in a frequency-dependent force acting between the reticular lamina and basilar membrane. Wavelength-dependent fluid loads are estimated by using the unsteady Stokes' equations, except in the narrow gap between the tectorial membrane and reticular lamina, where lubrication theory is appropriate. The local wavenumber and subpartition amplitude ratios are determined from the zeroth order equations of motion. A solvability relation for the first order equations of motion determines the subpartition amplitudes. The main findings are as follows: The reticular lamina and tectorial membrane move in unison with essentially no squeezing of the gap; an active force level consistent with measurements on isolated outer hair cells can provide a 35-dB amplification and sharpening of subpartition waveforms by delaying dissipation and allowing a greater structural resonance to occur before the wave is cut off; however, previously postulated activity mechanisms for single partition models cannot achieve sharp enough tuning in subpartitioned models.