General technique of calculating drift velocity and diffusion coefficient in arbitrary periodic systems

We develop a practical method of computing the stationary drift velocity V and the diffusion coefficient D of a particle (or a few particles) in a periodic system with arbitrary transition rates. We solve this problem both in a physically relevant continuous-time approach as well as for models with discrete-time kinetics, which are often used in computer simulations. We show that both approaches yield the same value of the drift, but the difference between the diffusion coefficients obtained in each of them equals V*V/2. Generalization to spaces of arbitrary dimension and several applications of the method are also presented.Comment: 12 pages + 2 figures, RevTeX. Submitted to J. Phys. A: Math. Ge

Ground State Entropy of Potts Antiferromagnets: Bounds, Series, and Monte Carlo Measurements

We report several results concerning $W(\Lambda,q)=\exp(S_0/k_B)$, the exponent of the ground state entropy of the Potts antiferromagnet on a lattice $\Lambda$. First, we improve our previous rigorous lower bound on $W(hc,q)$ for the honeycomb (hc) lattice and find that it is extremely accurate; it agrees to the first eleven terms with the large-$q$ series for $W(hc,q)$. Second, we investigate the heteropolygonal Archimedean $4 \cdot 8^2$ lattice, derive a rigorous lower bound, on $W(4 \cdot 8^2,q)$, and calculate the large-$q$ series for this function to $O(y^{12})$ where $y=1/(q-1)$. Remarkably, these agree exactly to all thirteen terms calculated. We also report Monte Carlo measurements, and find that these are very close to our lower bound and series. Third, we study the effect of non-nearest-neighbor couplings, focusing on the square lattice with next-nearest-neighbor bonds.Comment: 13 pages, Latex, to appear in Phys. Rev.

Eml1 loss impairs apical progenitor spindle length and soma shape in the developing cerebral cortex

The ventricular zone (VZ) of the developing cerebral cortex is a pseudostratified epithelium that contains progenitors undergoing precisely regulated divisions at its most apical side, the ventricular lining (VL). Mitotic perturbations can contribute to pathological mechanisms leading to cortical malformations. The HeCo mutant mouse exhibits subcortical band heterotopia (SBH), likely to be initiated by progenitor delamination from the VZ early during corticogenesis. The causes for this are however, currently unknown. Eml1, a microtubule (MT)-associated protein of the EMAP family, is impaired in these mice. We first show that MT dynamics are perturbed in mutant progenitor cells in vitro. These may influence interphase and mitotic MT mechanisms and indeed, centrosome and primary cilia were altered and spindles were found to be abnormally long in HeCo progenitors. Consistently, MT and spindle length regulators were identified in EML1 pulldowns from embryonic brain extracts. Finally, we found that mitotic cell shape is also abnormal in the mutant VZ. These previously unidentified VZ characteristics suggest altered cell constraints which may contribute to cell delamination

Connectomics and molecular imaging in neurodegeneration.

Our understanding on human neurodegenerative disease was previously limited to clinical data and inferences about the underlying pathology based on histopathological examination. Animal models and in vitro experiments have provided evidence for a cell-autonomous and a non-cell-autonomous mechanism for the accumulation of neuropathology. Combining modern neuroimaging tools to identify distinct neural networks (connectomics) with target-specific positron emission tomography (PET) tracers is an emerging and vibrant field of research with the potential to examine the contributions of cell-autonomous and non-cell-autonomous mechanisms to the spread of pathology. The evidence provided here suggests that both cell-autonomous and non-cell-autonomous processes relate to the observed in vivo characteristics of protein pathology and neurodegeneration across the disease spectrum. We propose a synergistic model of cell-autonomous and non-cell-autonomous accounts that integrates the most critical factors (i.e., protein strain, susceptible cell feature and connectome) contributing to the development of neuronal dysfunction and in turn produces the observed clinical phenotypes. We believe that a timely and longitudinal pursuit of such research programs will greatly advance our understanding of the complex mechanisms driving human neurodegenerative diseases.The Molecular Imaging of Neurodegeneration Cologne (MINC) Symposium was partly funded by the Deutsche Forschungsgemeinschaft (DFG) awarded to Dr. Thilo van Eimeren (EI 892/5-1). The Deutsche Forschungsgemeinschaft (DFG) also awarded funding to Dr. Alexander Drzezga (DR442/91)

Many-particle interference beyond many-boson and many-fermion statistics

Identical particles exhibit correlations even in the absence of inter-particle interaction, due to the exchange (anti)symmetry of the many-particle wavefunction. Two fermions obey the Pauli principle and anti-bunch, whereas two bosons favor bunched, doubly occupied states. Here, we show that the collective interference of three or more particles leads to a much more diverse behavior than expected from the boson-fermion dichotomy known from quantum statistical mechanics. The emerging complexity of many-particle interference is tamed by a simple law for the strict suppression of events in the Bell multiport beam splitter. The law shows that counting events are governed by widely species-independent interference, such that bosons and fermions can even exhibit identical interference signatures, while their statistical character remains subordinate. Recent progress in the preparation of tailored many-particle states of bosonic and fermionic atoms promises experimental verification and applications in novel many-particle interferometers.Comment: 12 pages, 5 figure

De Novo Growth Zone Formation from Fission Yeast Spheroplasts

Eukaryotic cells often form polarized growth zones in response to internal or external cues. To understand the establishment of growth zones with specific dimensions we used fission yeast, which grows as a rod-shaped cell of near-constant width from growth zones located at the cell tips. Removing the cell wall creates a round spheroplast with a disorganized cytoskeleton and depolarized growth proteins. As spheroplasts recover, new growth zones form that resemble normal growing cell tips in shape and width, and polarized growth resumes. Regulators of the GTPase Cdc42, which control width in exponentially growing cells, also control spheroplast growth zone width. During recovery the Cdc42 scaffold Scd2 forms a polarized patch in the rounded spheroplast, demonstrating that a growth zone protein can organize independent of cell shape. Rga4, a Cdc42 GTPase activating protein (GAP) that is excluded from cell tips, is initially distributed throughout the spheroplast membrane, but is excluded from the growth zone after a stable patch of Scd2 forms. These results provide evidence that growth zones with normal width and protein localization can form de novo through sequential organization of cellular domains, and that the size of these growth zones is genetically controlled, independent of preexisting cell shape

Mitotic Spindle Orients Perpendicular to the Forces Imposed by Dynamic Shear

Orientation of the division axis can determine cell fate in the presence of morphogenetic gradients. Understanding how mitotic cells integrate directional cues is therefore an important question in embryogenesis. Here, we investigate the effect of dynamic shear forces on confined mitotic cells. We found that human epithelial cells (hTERT-RPE1) as well as MC3T3 osteoblasts align their mitotic spindle perpendicular to the external force. Spindle orientation appears to be a consequence of cell elongation along the zero-force direction in response to the dynamic shear. This process is a nonlinear response to the strain amplitude, requires actomyosin activity and correlates with redistribution of myosin II. Mechanosteered cells divide normally, suggesting that this mechanism is compatible with biological functions