Epitaxial Growth of a Thin Layer of Putative Cancer Cells under Limited Resources and in the Presence of an Alkylating Agent

The dynamics of the Eden cluster in a 32x32 lattice is implemented using a stochastic model. A single-type of cells solid tumor is assumed. Duplication is probabilistic, and occurs when there is room in the immediate surroundings of a cell, otherwise the cell is inhibited by contact. The growth is epitaxial, the shape of the cluster is disk-like; the ratio between the numbers of perimeter cells; and bulk cells decreases as the cluster grows. Percolation is flagged by an inflection in the rate of growth. We assume that the inflection point actually flags a shortage of nutrients, thereafter the rate of growth decreases to zero. Cancer cells in culture, when deprived of nutrients, actually exhibit a similar behavior. Under the logistic hypothesis, the lattice contains nutrients to sustain the growth up to 1024 cells. The model is expanded to include a drug that pollutes the environment. The drug is an alkylating agent that hinders duplication, eventually causing the death of the cell. The logistic equation accounts for drug consumption. The probability of duplication with the drug decreases as the drug is consumed, eventually leading to relapse. Relapses and survival times are investigated as a function of the dose injected.

Cognitive aspects of chaos in random networks

A special case of deterministic chaos that is independent of the architecture of the connections has been observed in a computer model of a purely excitatory neuronal network. Chaos onsets when the level of connectivity is critically low. The results indicate a typical period-doubling route to chaos as the connectivity decreases. A cognitive interpretation of such type of chaos, based on information theory and phase-transitions, is proposed.

The amelioration of olfactory acuity upon sexual maturation might affect food preferences

Upon sexual maturation, olfactory acuity in women ameliorates and starts oscillating across the cycle. During ovulation, mean olfactory threshold is 30 times lower than during bleeding. Interestingly, menstruated women undergo maleodorant trimethylaminuria. We argued that olfactory amelioration during ovulation might concur to a mating strategy, whereas olfactory impairment during bleeding might protect women against self-refusal. Testosterone and its 17β-estradiol derivative might be responsible for the synchronization of these menstrual events. Furthermore, we posed the question whether olfactory detection amelioration upon sexual maturation might provoke a change in food preferences, for instance a reduction in fish consumption. A preliminary survey in Italy provided encouraging results: 15-44 year-old women have lower fish consumption than 3-14 year-old girls. Surprisingly, men exhibited the same behaviour, so new olfactory tests as well as testosterone measurements are under way.

Dynamics of cell membrane passive depolarization: a phase portrait

Does a persistent blockage of the ionic pumps bring cell membrane voltage to zero? This apparently trivial question of basic cellular Biology stirred up an intriguing problem of nonlinear dynamics. A 3-ion model based on continuity and charge conservation proves that membrane voltage actually sets on a negative value, meaning that chemical equilibrium is never reached, rather an inversion of the Na+ concentration gradient occurs, usually hours after the blockage of the pumps. Experimental tests carried out with PC12 cells incubated with Oubaine for a period of 24 hours show an increase of cytosolic Na+ of about 266 mM/l with respect to a control sample. The result is compatible with an inversion of the Na+ gradient, which eventually brings the membrane voltage to a negative value. Reactivation of the Na+-K+ pumps even after a prolonged period of blockage (late repolarization) should lead to repolarization and revival of the cell. In the 3D space of the ionic concentrations, the dynamics of passive depolarization reveals an intriguing topology, all trajectories being stacked in parallel planes, each set ending to a unique fixed point via an infinitely dense set of lines. The dynamics of repolarization has a different phase portrait, especially in the case of late repolarization. Thus, a sequence of depolarization- repolarization cycles may result in a path wandering in the phase space, or in a closed loop, depending on the timing of the sequence.

The cost of an action potential

Neuronal modules, or 'cell-assemblies', comprising millions of mutually interconnected cells have been postulated to form the basis of many functions of the brain, such as mood, sleep, hunger, vigilance, and more. Depending on the extent of the module, neurocommunication in cell-assemblies might exceed metabolic resources. A medium-size (10000 neurons) module would require at least 10 J per l of brain, based on a calculated cost of an isolated action potential (AP) of 10(11)-10(12) molecules of ATP per cm(2) of cell membrane, with an absolute minimum of 10(6) ATP at a node of Ranvier. The figure matches the cost of depolarizing the unmyelinated axon of the large monopolar cell in the blowfly retina. A circuit model of the cell membrane, based on abrupt changes of Na(+) and K(+) conductances, is used to emulate the AP and to assess the resulting ionic unbalance. The cost of an AP is equated to the metabolic energy necessary to fuel ATP-based pumps that restore intracellular K(+). The high metabolic demand of a cell-assembly suggests that less expensive means of neurocommunication may be involved, such as non-synaptic diffusion neurotransmission (NDN), which would comply with a proposed law of conservation of space and energy in the brain.

Multidimensional electrocutaneous stimulation

Probing the subjective response to a five-parameter electrocutaneous stimulus has revealed a noisy perceptual space. A method for reducing the noise is hypothesized and experimentally tested by comparing the intensity discrimination thresholds along and off the energy gradient. Preliminary results show a reduction of the threshold of up to 60% when stimulating along the gradient. The method is exploited to implement an optimal intensity control in an electrotactile vision-substitution device.

Brain cell microenvironment effects on neuron excitability and basal metabolism

In a model of neurons in a brain cell assembly, changes in volume of the extracellular space affect neuronal excitability and basal metabolism. A widely applicable coefficient of excitability with respect to a variation of the volume fraction has been determined. Calculations suggest that chloride increases membrane stability by indirectly promoting an acceleration of the metabolic pumping rate as a response to a diminished extracellular volume fraction. Volume fraction changes induced by cell swelling in a compact and highly tortuous microenvironment may play a role in epilepsy and, following brain damage, in cell death and recovery.

Nerve length and volume in synaptic vs diffusion neurotransmission: a model

Non-synaptic diffusion neurotransmission (NDN) may be an important factor in brain space and energy conservation, especially within cell assemblies and for mass sustained functions. We have illustrated the extreme cases of total synaptic and total ND neurotransmission for the purpose of noting the differences between the two. For these modeling studies, in which we assume assemblies of 1000 to 100 000 cells supplied by at least one fiber and a single synapse from each of the other cells, each cell assembly would have approximately 200 m to 8000 km of nerve fibers more than when innervated by diffusion. For coeruleo-cortical synaptic innervation, linking each to a common origin (the locus coeruelus), the fiber lengths are 38 cm (1000 cells) to 170 m (100,000 cells). It is likely , however, that neuronal arrays include both 'wireless' (NDN) as well as synaptic intercellular communication systems.