Spatial and Temporal Sensing Limits of Microtubule Polarization in Neuronal Growth Cones by Intracellular Gradients and Forces

Neuronal growth cones are the most sensitive amongst eukaryotic cells in responding to directional chemical cues. Although a dynamic microtubule cytoskeleton has been shown to be essential for growth cone turning, the precise nature of coupling of the spatial cue with microtubule polarization is less understood. Here we present a computational model of microtubule polarization in a turning neuronal growth cone (GC). We explore the limits of directional cues in modifying the spatial polarization of microtubules by testing the role of microtubule dynamics, gradients of regulators and retrograde forces along filopodia. We analyze the steady state and transition behavior of microtubules on being presented with a directional stimulus. The model makes novel predictions about the minimal angular spread of the chemical signal at the growth cone and the fastest polarization times. A regulatory reaction-diffusion network based on the cyclic phosphorylation-dephosphorylation of a regulator predicts that the receptor signal magnitude can generate the maximal polarization of microtubules and not feedback loops or amplifications in the network. Using both the phenomenological and network models we have demonstrated some of the physical limits within which the MT polarization system works in turning neuron.Comment: 7 figures and supplementary materia

High accuracy computation with linear analog optical systems: a critical study

High accuracy optical processors based on the algorithm of digital multiplication by analog convolution (DMAC) are studied for ultimate performance limitations. Variations of optical processors that perform high accuracy vector-vector inner products are studied in abstract and with specific examples. It is concluded that the use of linear analog optical processors in performing digital computations with DMAC leads to impractical requirements for the accuracy of analog optical systems and the complexity of postprocessing electronics

Optical computing: introduction by the guest editors to the feature in the 1 May 1988 issue

The feature in the 1 May 1988 issue of Applied Optics includes a collection of papers originally presented at the 1987 Lake Tahoe Topical Meeting on Optical Computing. These papers emphasize digital optical computing systems, optical interconnects, and devices for optical computing, but analog optical processing is considered as well

Three methods for performing Hankel transforms

Three methods for performing Hankel transforms with optical or digital processors are described. The first method is applicable when the input data is available in Cartesian (x-y) format and uses the close connection between generalized Hankel transform and the two dimensional Fourier transform in Cartesian coordinates. The second method is useful when the input data is in polar (r - theta) format and uses change of variables to perform the nth order Hankel transform as a correlation integral. The third method utilizes the von Neumann addition theorem for Bessel functions to extract the Hankel coefficients from a correlation between the radial part of the input and a Bessel function. Initial experimental results obtained for optical implementation of the first two methods are presented

Modelling Nuclear Body Dynamics in Living Cells by 4-D Microscopy, Image Analysis and Simulation

The work presented here demonstrates rules of and validates models for nuclear body (NB) dynamics. Simulation tools developed in the course of this work can be used in future work to generate hypotheses about related aspects of nuclear architecture. Initially I examined the mobility of vimentin nuclear bodies bodies (VNB) in interphase by single particle tracking and analysis of fluorescence images from 4-D confocal laser scanning microscopy (CLSM). These synthetic nuclear bodies are observed in cells transfected with labelled nuclear-targeted Xenopus laevis vimentin. Analysis shows that VNBs undergo anomalous diffusion in the nuclei, independent of metabolic energy. Individual bodies display either one of the three modes of diffusion -- directed, restricted or simple. The consistency of modes and magnitudes of diffusion constants between VNBs and bona fide nuclear bodies points to a generic mechanism that mediates and regulates the mobility of nuclear bodies. Since the results of diffusion analysis of VNBs did not agree with a simple diffusion model, I tested the alternative interchromosomal domain (ICD) compartment model. The ICD model predicts that in interphase cell nuclei, individual decompacted chromosomes do not intermingle, but are separated by a significant interchromatin space forming a network of channels. These networks could affect the mobility of nuclear bodies. Monte Carlo simulations that predict the effects of channels and other obstructions on NB diffusion were tested, but they could not explain deviation from ideal behaviour. Fitting an empirical model of `critical diffusion' produced similar results. Therefore the ICD model as a purely obstructing network of channels needs modification, to possibly include binding. To examine the role of chromatin density in intra-nuclear diffusion, I employed multidimensional fluorescence recovery after photobleaching (FRAP) in living cells. The influence of chromatin density on diffusive mobility of the nuclear yellow fluorescent protein (YFP) appears marginal. A 2-D diffusion simulation to better characterize the experiment provides a tool to produce `diffusion maps' of the nucleus. The related aspect of nuclear body integrity and dynamics was examined for the distribution of topoisomerase II beta (TopoIIb), which localizes preferentially in the nucleolus. The experimentally observed diffusion and binding dynamics were formulated as a compartment model and fitted to the experiments. The model topology, flux constants and residence times estimates could be validated, providing a predictive model of TopoIIb dynamics By demonstrating that VNB diffusion is anomalous and consistent with other bona fide NBs, I have revealed a mechanism that regulates NB mobility. The diffusion of these bodies deviates however from ideal diffusion, and can be explained by neither the effect of chromatin density on molecular diffusion, nor the different models of NB diffusion. I have shown that binding rather than diffusion appears to determine nuclear body localization and dynamics, as in the case of TopoIIb. Nuclear bodies and nuclear architecture has been recently hypothesized as emerging from simple local interactions. The predictive model for TopoIIb distribution dynamics provides evidence for this. The models presented here, are in keeping with the increasing trend to abstract nuclear dynamics as mathematical models. It is hoped that the work presented here will contribute to the effort of arriving at an integrated model for nuclear bodies and therefore better understanding nuclear architecture