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.

A model of multiplicative neural responses in parietal cortex.

Visual responses of neurons in parietal area 7a are modulated by a combined eye and head position signal in a multiplicative manner. Neurons with multiplicative responses can act as powerful computational elements in neural networks. In the case of parietal cortex, multiplicative gain modulation appears to play a crucial role in the transformation of object locations from retinal to body-centered coordinates. It has proven difficult to uncover single-neuron mechanisms that account for neuronal multiplication. Here we show that multiplicative responses can arise in a network model through population effects. Specifically, neurons in a recurrently connected network with excitatory connections between similarly tuned neurons and inhibitory connections between differently tuned neurons can perform a product operation on additive synaptic inputs. The results suggest that parietal responses may be based on this architecture.