Statistical Mechanics Characterization of Neuronal Mosaics

The spatial distribution of neuronal cells is an important requirement for achieving proper neuronal function in several parts of the nervous system of most animals. For instance, specific distribution of photoreceptors and related neuronal cells, particularly the ganglion cells, in mammal's retina is required in order to properly sample the projected scene. This work presents how two concepts from the areas of statistical mechanics and complex systems, namely the \emph{lacunarity} and the \emph{multiscale entropy} (i.e. the entropy calculated over progressively diffused representations of the cell mosaic), have allowed effective characterization of the spatial distribution of retinal cells.Comment: 3 pages, 1 figure, The following article has been submitted to Applied Physics Letters. If it is published, it will be found online at http://apl.aip.org

On the Potential of the Excluded Volume and Auto-Correlation as Neuromorphometric Descriptors

This work investigates at what degree two neuromorphometric measurements, namely the autocorrelation and the excluded volume of a neuronal cell can influence the characterization and classification of such a type of cells. While the autocorrelation function presents good potential for quantifying the dendrite-dendrite connectivity of cells in mosaic tilings, the excluded volume, i.e. the amount of the surround space which is geometrically not accessible to an axon or dendrite, provides a complementary characterization of the cell connectivity. The potential of such approaches is illustrated with respect to real neuronal cells.Comment: 15 pages, 6 figure

Cell shape analysis of random tessellations based on Minkowski tensors

To which degree are shape indices of individual cells of a tessellation characteristic for the stochastic process that generates them? Within the context of stochastic geometry and the physics of disordered materials, this corresponds to the question of relationships between different stochastic models. In the context of image analysis of synthetic and biological materials, this question is central to the problem of inferring information about formation processes from spatial measurements of resulting random structures. We address this question by a theory-based simulation study of shape indices derived from Minkowski tensors for a variety of tessellation models. We focus on the relationship between two indices: an isoperimetric ratio of the empirical averages of cell volume and area and the cell elongation quantified by eigenvalue ratios of interfacial Minkowski tensors. Simulation data for these quantities, as well as for distributions thereof and for correlations of cell shape and volume, are presented for Voronoi mosaics of the Poisson point process, determinantal and permanental point processes, and Gibbs hard-core and random sequential absorption processes as well as for Laguerre tessellations of polydisperse spheres and STIT- and Poisson hyperplane tessellations. These data are complemented by mechanically stable crystalline sphere and disordered ellipsoid packings and area-minimising foam models. We find that shape indices of individual cells are not sufficient to unambiguously identify the generating process even amongst this limited set of processes. However, we identify significant differences of the shape indices between many of these tessellation models. Given a realization of a tessellation, these shape indices can narrow the choice of possible generating processes, providing a powerful tool which can be further strengthened by density-resolved volume-shape correlations.Comment: Chapter of the forthcoming book "Tensor Valuations and their Applications in Stochastic Geometry and Imaging" in Lecture Notes in Mathematics edited by Markus Kiderlen and Eva B. Vedel Jense

Pattern Formation and Organization of Epithelial Tissues

Developmental biology is a study of how elaborate patterns, shapes, and functions emerge as an organism grows and develops its body plan. From the physics point of view this is very much a self-organization process. The genetic blueprint contained in the DNA does not explicitly encode shapes and patterns an animal ought to make as it develops from an embryo. Instead, the DNA encodes various proteins which, among other roles, specify how different cells function and interact with each other. Epithelial tissues, from which many organs are sculpted, serve as experimentally- and analytically-tractable systems to study patterning mechanisms in animal development. Despite extensive studies in the past decade, the mechanisms that shape epithelial tissues into functioning organs remain incompletely understood. This thesis summarizes various studies we have done on epithelial organization and patterning, both in abstract theory and in close contact with experiments. A novel mechanism to establish cellular left-right asymmetry based on planar polarity instabilities is discussed. Tissue chirality is often assumed to originate from handedness of biological molecules. Here we propose an alternative where it results from spontaneous symmetry breaking of planar polarity mechanisms. We show that planar cell polarity (PCP), a class of well-studied mechanisms that allows epithelia to spontaneously break rotational symmetry, is also generically capable of spontaneously breaking reflection symmetry. Our results provide a clear interpretation of many mutant phenotypes, especially those that result in incomplete inversion. To bridge theory and experiments, we develop quantitative methods to analyze fluorescence microscopy images. Included in this thesis are algorithms to selectively project intensities from a surface in z-stack images, analysis of cells forming short chain fragments, analysis of thick fluorescent bands using steerable ridge detector, and analysis of cell recoil in laser ablation experiments. These techniques, though developed in the context of zebrafish retina mosaic, are general and can be adapted to other systems. Finally we explore correlated noise in morphogenesis of fly pupa notum. Here we report unexpected correlation of noise in cell movements between left and right halves of developing notum, suggesting that feedback or other mechanisms might be present to counteract stochastic noise and maintain left-right symmetry.PHDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138800/1/hjeremy_1.pd

Anisotropic Müller glial scaffolding supports a multiplex lattice mosaic of photoreceptors in zebrafish retina

Abstract Background The multiplex, lattice mosaic of cone photoreceptors in the adult fish retina is a compelling example of a highly ordered epithelial cell pattern, with single cell width rows and columns of cones and precisely defined neighbor relationships among different cone types. Cellular mechanisms patterning this multiplex mosaic are not understood. Physical models can provide new insights into fundamental mechanisms of biological patterning. In earlier work, we developed a mathematical model of photoreceptor cell packing in the zebrafish retina, which predicted that anisotropic mechanical tension in the retinal epithelium orients planar polarized adhesive interfaces to align the columns as cone photoreceptors are generated at the retinal margin during post-embryonic growth. Methods With cell-specific fluorescent reporters and in vivo imaging of the growing retinal margin in transparent juvenile zebrafish we provide the first view of how cell packing, spatial arrangement, and cell identity are coordinated to build the lattice mosaic. With targeted laser ablation we probed the tissue mechanics of the retinal epithelium. Results Within the lattice mosaic, planar polarized Crumbs adhesion proteins pack cones into a single cell width column; between columns, N-cadherin-mediated adherens junctions stabilize Müller glial apical processes. The concentration of activated pMyosin II at these punctate adherens junctions suggests that these glial bands are under tension, forming a physical barrier between cone columns and contributing to mechanical stress anisotropies in the epithelial sheet. Unexpectedly, we discovered that the appearance of such parallel bands of Müller glial apical processes precedes the packing of cones into single cell width columns, hinting at a possible role for glia in the initial organization of the lattice mosaic. Targeted laser ablation of Müller glia directly demonstrates that these glial processes support anisotropic mechanical tension in the planar dimension of the retinal epithelium. Conclusions These findings uncovered a novel structural feature of Müller glia associated with alignment of photoreceptors into a lattice mosaic in the zebrafish retina. This is the first demonstration, to our knowledge, of planar, anisotropic mechanical forces mediated by glial cells.https://deepblue.lib.umich.edu/bitstream/2027.42/139592/1/13064_2017_Article_96.pd

Hyperuniformity and its Generalizations

Disordered many-particle hyperuniform systems are exotic amorphous states characterized by anomalous suppression of large-scale density fluctuations. Here we substantially broaden the hyperuniformity concept along four different directions. This includes generalizations to treat fluctuations in the interfacial area in heterogeneous media and surface-area driven evolving microstructures, random scalar fields, divergence-free random vector fields, as well as statistically anisotropic many-particle systems and two-phase media. Interfacial-area fluctuations play a major role in characterizing the microstructure of two-phase systems , physical properties that intimately depend on the geometry of the interface, and evolving two-phase microstructures that depend on interfacial energies (e.g., spinodal decomposition). In the instances of divergence-free random vector fields and statistically anisotropic structures, we show that the standard definition of hyperuniformity must be generalized such that it accounts for the dependence of the relevant spectral functions on the direction in which the origin in Fourier space (nonanalyticities at the origin). Using this analysis, we place some well-known energy spectra from the theory of isotropic turbulence in the context of this generalization of hyperuniformity. We show that there exist many-particle ground-state configurations in which directional hyperuniformity imparts exotic anisotropic physical properties (e.g., elastic, optical and acoustic characteristics) to these states of matter. Such tunablity could have technological relevance for manipulating light and sound waves in ways heretofore not thought possible. We show that disordered many-particle systems that respond to external fields (e.g., magnetic and electric fields) are a natural class of materials to look for directional hyperuniformity.Comment: In pres

Pharmacological Or Genetic Targeting Of Transient Receptor Potential (TRP) Channels Can Disrupt The Planarian Escape Response

In response to noxious stimuli, planarians cease their typical ciliary gliding and exhibit an oscillatory type of locomotion called scrunching. We have previously characterized the biomechanics of scrunching and shown that it is induced by specific stimuli, such as amputation, noxious heat, and extreme pH. Because these specific inducers are known to activate Transient Receptor Potential (TRP) channels in other systems, we hypothesized that TRP channels control scrunching. We found that chemicals known to activate TRPA1 (allyl isothiocyanate (AITC) and hydrogen peroxide) and TRPV (capsaicin and anandamide) in other systems induce scrunching in the planarian species Dugesia japonica and, except for anandamide, in Schmidtea mediterranea. To confirm that these responses were specific to either TRPA1 or TRPV, respectively, we tried to block scrunching using selective TRPA1 or TRPV antagonists and RNA interference (RNAi) mediated knockdown. Unexpectedly, co-treatment with a mammalian TRPA1 antagonist, HC-030031, enhanced AITC-induced scrunching by decreasing the latency time, suggesting an agonistic relationship in planarians. We further confirmed that TRPA1 in both planarian species is necessary for AITC-induced scrunching using RNAi. Conversely, while co-treatment of a mammalian TRPV antagonist, SB-366791, also enhanced capsaicin-induced reactions in D. japonica, combined knockdown of two previously identified D. japonica TRPV genes (DjTRPVa and DjTRPVb) did not inhibit capsaicin-induced scrunching. RNAi of DjTRPVa/DjTRPVb attenuated scrunching induced by the endocannabinoid and TRPV agonist, anandamide. Overall, our results show that although scrunching induction can involve different initial pathways for sensing stimuli, this behavior’s signature dynamical features are independent of the inducer, implying that scrunching is a stereotypical planarian escape behavior in response to various noxious stimuli that converge on a single downstream pathway. Understanding which aspects of nociception are conserved or not across different organisms can provide insight into the underlying regulatory mechanisms to better understand pain sensation