Diffusion in sparse networks: linear to semi-linear crossover

We consider random networks whose dynamics is described by a rate equation, with transition rates $w_{nm}$ that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient $D$. In one dimension it is well known that $D$ can display an abrupt percolation-like transition from diffusion ($D>0$) to sub-diffusion (D=0). A question arises whether such a transition happens in higher dimensions. Numerically $D$ can be evaluated using a resistor network calculation, or optionally it can be deduced from the spectral properties of the system. Contrary to a recent expectation that is based on a renormalization-group analysis, we deduce that $D$ is finite; suggest an "effective-range-hopping" procedure to evaluate it; and contrast the results with the linear estimate. The same approach is useful for the analysis of networks that are described by quasi-one-dimensional sparse banded matrices.Comment: 13 pages, 4 figures, proofed as publishe

Paradoxical Signaling by a Secreted Molecule Leads to Homeostasis of Cell Levels

SummaryA widespread feature of extracellular signaling in cell circuits is paradoxical pleiotropy: the same secreted signaling molecule can induce opposite effects in the responding cells. For example, the cytokine IL-2 can promote proliferation and death of T cells. The role of such paradoxical signaling remains unclear. To address this, we studied CD4+ T cell expansion in culture. We found that cells with a 30-fold difference in initial concentrations reached a homeostatic concentration nearly independent of initial cell levels. Below an initial threshold, cell density decayed to extinction (OFF-state). We show that these dynamics relate to the paradoxical effect of IL-2, which increases the proliferation rate cooperatively and the death rate linearly. Mathematical modeling explained the observed cell and cytokine dynamics and predicted conditions that shifted cell fate from homeostasis to the OFF-state. We suggest that paradoxical signaling provides cell circuits with specific dynamical features that are robust to environmental perturbations

V-I characteristics in the vicinity of order-disorder transition in vortex matter

The shape of the V-I characteristics leading to a peak in the differential resistance r_d=dV/dI in the vicinity of the order-disorder transition in NbSe2 is investigated. r_d is large when measured by dc current. However, for a small Iac on a dc bias r_d decreases rapidly with frequency, even at a few Hz, and displays a large out-of-phase signal. In contrast, the ac response increases with frequency in the absence of dc bias. These surprisingly opposite phenomena and the peak in r_d are shown to result from a dynamic coexistence of two vortex matter phases rather than from the commonly assumed plastic depinning.Comment: 12 pages 4 figures. Accepted for publication in PRB rapi

Ataxia and the olivo-cerebellar module

Ataxia is a neurological symptom characterized by abnormal movement, due to cerebellar malfunction. Although the cause of the malfunction varies, from mutations in calcium or potassium channels to progressive degeneration of cerebellar tissue, the neurological symptoms of cerebellar-related ataxia are similar. In this short review we present a model that portrays the olivo-cerebellar system as a generator of temporal patterns. We then use the model to explain how mutations in different ionic channels located in different parts of the cerebellar system can result in similar neurological symptom

Axonal Pruning Is Actively Regulated by the Microtubule-Destabilizing Protein Kinesin Superfamily Protein 2A

Extensive axonal pruning and neuronal cell death are critical events for the development of the nervous system. Like neuronal cell death, axonal elimination occurs in discrete steps; however, the regulators of these processes remain mostly elusive. Here, we identify the kinesin superfamily protein 2A (KIF2A) as a key executor of microtubule disassembly and axonal breakdown during axonal pruning. Knockdown of Kif2a, but not other microtubule depolymerization or severing proteins, protects axonal microtubules from disassembly upon trophic deprivation. We further confirmed and extended this result to demonstrate that the entire degeneration process is delayed in neurons from the Kif2a knockout mice. Finally, we show that the Kif2a-null mice exhibit normal sensory axon patterning early during development, but abnormal target hyperinnervation later on, as they compete for limited skin-derived trophic support. Overall, these findings reveal a central regulatory mechanism of axonal pruning during development