Regulatory inhibition of biological tissue mineralization by calcium phosphate through post-nucleation shielding by fetuin-A.

In vertebrates, insufficient availability of calcium and inorganic phosphate ions in extracellular fluids leads to loss of bone density and neuronal hyper-excitability. To counteract this problem, calcium ions are usually present at high concentrations throughout bodily fluids-at concentrations exceeding the saturation point. This condition leads to the opposite situation where unwanted mineral sedimentation may occur.

Mathematical approaches to modeling of cortical spreading depression.

Migraine with aura (MwA) is a debilitating disease that afflicts about 25%-30% of migraine sufferers. During MwA, a visual illusion propagates in the visual field, then disappears, and is followed by a sustained headache. MwA was conjectured by Lashley to be related to some neurological phenomenon.

A mathematical model of the metabolic and perfusion effects on cortical spreading depression.

Cortical spreading depression (CSD) is a slow-moving ionic and metabolic disturbance that propagates in cortical brain tissue. In addition to massive cellular depolarizations, CSD also involves significant changes in perfusion and metabolism-aspects of CSD that had not been modeled and are important to traumatic brain injury, subarachnoid hemorrhage, stroke, and migraine. In this study, we develop a mathematical model for CSD where we focus on modeling the features essential to understanding the implications of neurovascular coupling during CSD.

A continuum neuronal model for the instigation and propagation of cortical spreading depression.

Cortical spreading depression (CSD) waves can occur in the cortices of various brain structures and are associated with the spread of depression of the electroencephalogram signal. In this paper, we present a continuum neuronal model for the instigation and spreading of CSD. Our model assumes that the brain-cell microenvironment can be treated as a porous medium consisting of extra- and intracellular compartments.

Restricted diffusion in cellular media: (1+1)-dimensional model.

We consider the diffusion of molecules in a one-dimensional medium consisting of a large number of cells separated from the extra-cellular space by permeable membranes. The extra-cellular space is completely connected and allows unrestricted diffusion of the molecules. Furthermore, the molecules can diffuse within a given cell, i.

Traveling waves in coupled reaction-diffusion models with degenerate sources.

We consider a general system of coupled nonlinear diffusion equations that are characterized by having degenerate source terms and thereby not having isolated rest states. Using a general form of physically relevant source terms, we derive conditions that are required to trigger traveling waves when a stable uniform steady-state solution is perturbed by a highly localized disturbance. We show that the degeneracy in the source terms implies that traveling waves have a number of surprising properties that are not present for systems with nondegenerate source terms.

Prediction of mRNA polyadenylation sites by support vector machine.

mRNA polyadenylation is responsible for the 3' end formation of most mRNAs in eukaryotic cells and is linked to termination of transcription. Prediction of mRNA polyadenylation sites [poly(A) sites] can help identify genes, define gene boundaries, and elucidate regulatory mechanisms. Current methods for poly(A) site prediction achieve moderate sensitivity and specificity.

Spatial buffering mechanism: mathematical model and computer simulations.

It is generally accepted that the spatial buffering mechanism is important to buffer extracellular-space potassium in the brain-cell microenviron- ment. In the past, this phenomenon, generally associated with glial cells, has been treated analytically and numerically using a simplified one-dimensional description. The present study extends the previous research by using a novel numerical scheme for the analysis of potassium buffering mechanisms in the extracellular brain-cell microenvironment.

Membrane resonance and stochastic resonance modulate firing patterns of thalamocortical neurons.

We examined the interactions of subthreshold membrane resonance and stochastic resonance using whole-cell patch clamp recordings in thalamocortical neurons of rat brain slices, as well as with a Hodgkin-Huxley-type mathematical model of thalamocortical neurons. The neurons exhibited the subthreshold resonance when stimulated with small amplitude sine wave currents of varying frequency, and stochastic resonance when noise was added to sine wave inputs. Stochastic resonance was manifest as a maximum in signal-to-noise ratio of output response to subthreshold periodic input combined with noise.

The influences of Ih on temporal summation in hippocampal CA1 pyramidal neurons: a modeling study.

Recent experimental and theoretical studies have found that active dendritic ionic currents can compensate for the effects of electrotonic attenuation. In particular, temporal summation, the percentage increase in peak somatic voltage responses invoked by a synaptic input train, is independent of location of the synaptic input in hippocampal CA1 pyramidal neurons under normal conditions. This independence, known as normalization of temporal summation, is destroyed when the hyperpolarization-activated current, Ih, is blocked [Magee JC (1999a), Nature Neurosci.

Resonances and noise in a stochastic Hindmarsh-Rose model of thalamic neurons.

Thalamic neurons exhibit subthreshold resonance when stimulated with small sine wave signals of varying frequency and stochastic resonance when noise is added to these signals. We study a stochastic Hindmarsh-Rose model using Monte-Carlo simulations to investigate how noise, in conjunction with subthreshold resonance, leads to a preferred frequency in the firing pattern. The resulting stochastic resonance (SR) exhibits a preferred firing frequency that is approximately exponential in its dependence on the noise amplitude.