Ongoing synaptic activity, ever present in cortical neurons, may vary widely in its amplitude and characteristics, potentially having a strong influence on neuronal processing. Intracellular recordings in layer 5 pyramidal cells in prefrontal and visual cortical slices maintained in vitro revealed spontaneous periods of synaptic bombardment. Testing the responsiveness of these cortical cells to synaptic inputs or the injection of artificial excitatory postsynaptic conductances of various amplitudes revealed that background synaptic activity dramatically increased the probability of response to small inputs, decreased the slope of the input-output curve, and decreased both the latency and jitter of action potential activation. Examining the effects of different components of synaptic barrages (namely, depolarization, increase in membrane conductance, and increase in membrane potential variance) revealed that the effects observed were dominated by the membrane depolarization and increase in variance. Depolarization increased the peak cross-correlation between injected complex in vivo-like waveforms through enhancement of responsiveness to small inputs, whereas increases in variance did so through a shift in firing mode from one of threshold detection to probabilistic discharge. These results indicate that rapid increases in neuronal responsiveness, as well as increases in spike timing precision, can be achieved through balanced barrages of excitatory and inhibitory synaptic activity.

Recently, in a beautiful set of experiments, it has been shown that a Ncd mutant, NK11, which lacks directionality in its individual motion, was able to exhibit a new kind of directed motion in motility assays (Endow, S. A. & Higuchi, H. (2000) Nature (London) 406, 913-916): the filaments keep a given velocity for a while and then suddenly move in the opposite direction with similar velocity. We show that these observations nicely illustrate the concept of dynamic transitions in motor collections introduced earlier in the case of an infinite number of motors. We investigate the experimentally relevant case of a finite number of motors both when directionality is present (kinesins, myosins, Ncd) and absent (NK11). Using a symmetric two-state model, we demonstrate that bidirectional motion is the signature of a dynamic transition that results from the collective behavior of many motors acting on the same filament. For motors exhibiting directional bias individually, an asymmetric two-state model is appropriate. In that case, dynamic transitions exist for motor collections in the presence of an external force. We give predictions for the dependence of motion on ATP concentration, external forces, and the number of motors involved. In particular, we show that the reversal time grows exponentially with the number of motors per filament. Motor proteins such as kinesins and myosins are driven by ATP hydrolysis and are able to generate motion and perform work against external forces (1). A given type of motor has a particular directionality of motion along its track filament. Most kinesins move toward the plus end of microtubules (2), but Ncd moves toward the minus end (3). The opposite directionality of closely related motors such as Ncd and conventional kinesins has raised a lot of interest (4 -6). Artificial constructs have been built to determine ways to control the directionality of motors. A chimera composed of a conventional kinesin with a Ncd motor domain exhibited motion toward the minus end (7). Recently, a Ncd mutant NK11, which differs from Ncd only by 1 aa in the region of the neck, was described. This mutant apparently lacked a welldefined directionality as an individual motor, but in motility assay experiments it could generate bidirectional motion of filaments in both the plus and minus directions (8). A given microtubule reversed its direction of motion after time intervals of up to 1 min and exhibited characteristic velocities of similar magnitude in opposite directions. Motility assays, which provide a convenient tool for the study of the directionality of motors, typically involve the simultaneous action of many motors at any given time (2, 9, 10). Individual motor molecules, however, can be studied by manipulating motorcoated beads with optical traps (11-13). These single-molecule experiments reveal different behaviors for Ncd and NK11: whereas Ncd clearly exhibits characteristic displacements of typically 6 nm directed toward the minus end of the filament, NK11 produces displacements of a similar s...

It has been shown experimentally that contact interactions may influence the migration of cancer cells. Previous works have modelized this thanks to stochastic, discrete models (cellular automata) at the cell level. However, for the study of the growth of real-size tumors with several million cells, it is best to use a macroscopic model having the form of a partial differential equation (PDE) for the density of cells. The difficulty is to predict the effect, at the macroscopic scale, of contact interactions that take place at the microscopic scale. To address this, we use a multiscale approach: starting from a very simple, yet experimentally validated, microscopic model of migration with contact interactions, we derive a macroscopic model. We show that a diffusion equation arises, as is often postulated in the field of glioma modeling, but it is nonlinear because of the interactions. We give the explicit dependence of diffusivity on the cell density and on a parameter governing cell-cell interactions. We discuss in detail the conditions of validity of the approximations used in the derivation, and we compare analytic results from our PDE to numerical simulations and to some in vitro experiments. We notice that the family of microscopic models we started from includes as special cases some kinetically constrained models that were introduced for the study of the physics of glasses, supercooled liquids, and jamming systems.