Session H29: Focus Session: Physical Aspects of Morphogenesis: Computational Approaches

From Genes to Morphogenetic Movements: How Cell-level Modeling Makes such Connections Possible

New understanding provided by computational modeling makes it possible to identify, in detail, the sequence of events by which gene expression gives rise to specific morphogenetic movements. Convergent extension (CE), an important developmental process in which embryonic tissues undergo self-driven narrowing in one in-plane direction and expansion in the other, is one such example. CE is triggered by gene expression and, in amphibian gastrulae, involves cephalocaudal (CC) gradients of the morphogens Xbra and Chordin and signalling molecules that include planar cell polarity (PCP) and Wnt/Ca2+ (Nature 2004, 430: 305-306). When these pathways have established suitable biochemical conditions, cellular protrusions called lamellipodia, which previously arose with random orientations, form preferentially in the mediolateral (ML) direction. To investigate whether lamellipodium action has the mechanical capacity to drive cell intercalation and its attendant cell reshaping, the cell-level finite element model of Chen and Brodland (ASME J. Biomech. Eng., 2000, 122: 394-401) was modified so that lamellipodia could originate from randomly selected cells, connect to next-neighboring cells in the ML direction and then contract. The simulations show that lamellipodia with these characteristics can, indeed, drive CE and that adjacent tissue must resist ML narrowing in order for characteristically elongated cells to result, predictions that have been confirmed experimentally. When these meso-scale findings are integrated with tissue- and whole-embryo mechanics, multi-scale ``mechanical pathways'' become evident. These pathways, in turn, interface directly with known biochemical pathways to produce an unbroken causal sequence from gene expression to specific morphogentic movements.   

Myxobacteria Fruiting Body Formation

Myxobacteria are social bacteria that swarm and glide on surfaces, and feed cooperatively. When starved, tens of thousands of cells change their movement pattern from outward spreading to inward concentration; they form aggregates that become fruiting bodies, inside which cells differentiate into nonmotile, environmentally resistant spores. Traditionally, cell aggregation has been considered to imply chemotaxis, a long-range cell interaction mediated by diffusing chemicals. However, myxobacteria aggregation is the consequence of direct cell-contact interactions. I will review our recent efforts in modeling the fruiting body formation of Myxobacteria, using lattice gas cellular automata models that are based on local cell-cell contact signaling. These models have reproduced the individual phases in Myxobacteria development such as the rippling, streaming, early aggregation and the final sporulation; the models can be unified to simulate the whole developmental process of Myxobacteria.   

Quantifying the Intercellular Forces during \textit{Drosophila} Morphogenesis

In many models of morphogenesis, cellular movements are driven by differences in interfacial tension along cell-cell boundaries. We have developed a microsurgical method to determine these tensions in living fruit fly (\textit{Drosophila}) embryos. Cell edges in these embryos are labeled with green fluorescent protein chimeras; and line scan images that intersect several cell edges are recorded with a laser-scanning confocal microscope at a time resolution of 2 ms. While recording these scans, a Q-switched Nd:YAG laser is used to cut a single cell edge. The recoil of adjacent cell edges is evident in the line scans and the time-dependent cell edge positions are extracted using custom ImageJ plugins based on the Lucas-Kanade algorithm. The post-incision recoil velocities of cell edges are determined by fitting the cell edge positions to a double exponential function. In addition, a power spectrum analysis of cell-edge position fluctuations is used to determine the viscous damping constant. In the regime of low Reynolds number, the tension along a cell-cell boundary is well-approximated by the product of the viscous damping constant and the initial recoil velocity of adjacent cell edges. We will present initial results from two stages of \textit{Drosophila} development -- germ band retraction and early dorsal closure.   

Mechanisms of Biological Neural Network Development

Functionality of the nervous system depends to a large extent on the precise patterns of connections between neurons. Neuronal connections form during development when neurons send out axons which migrate to their targets. We will describe briefly how such networks form including guidance by diffusible cues and the influence of nerve fiber bundling on network growth and form.   

Upregulation of Tissue Dynamics in Response to UV Laser Perturbations

We investigate tissue dynamics {\it in vivo} using a steerable UV-laser microbeam coupled to a scanning laser confocal microscope. We follow a stage in the morphogenesis of the fruit fly known as dorsal closure, which largely occurs in 2D. Dorsal closure is a consequence of four biological processes that are coordinated in space and are synchronized in time. During dorsal closure, two advancing flanks of epidermal tissue demarcate an eye-shaped opening on the dorsal side of the embryo, exposing the underlying amnioserosa tissue. As closure progresses, the two flanks of epidermal tissue approach each other and, via an adhesion mediated process, ``zip'' to form seams at the two canthi, i.e. the corners of the opening. In our studies, we target the microbeam to selectively remove specific tissues and track the resulting dynamics. We account for the results with a quantitative model. When we inhibit zipping by repeatedly targeting the microbeam to one canthus, we find evidence for an increase in the zipping rate of the seam at the other, unperturbed canthus. The upregulation occurs in a region remote from the tissue targeted by the microbeam and involves many cells. This upregulation of zipping is an example of a compensatory mechanism that ensures successful closure and highlights the resiliency of dorsal closure to perturbations. Supported by the NIH (GM33830 and GM61240).   

Pattern Scaling Achieved by Oppositely Directed Morphogen Gradients

Morphogens are proteins, often produced in a localised region, whose concentrations spatially demarcate regions of differing gene expression in developing embryos. The boundaries of expression must be set accurately and in proportion to the size $L$ of the developing field; this cannot be accomplished by a single one-dimensional gradient. Here, we show how a pair of morphogens produced at opposite ends of a developing field can solve the pattern-scaling problem. In the most promising scenario, two morphogens interact according to $A+B\rightarrow\emptyset$ and the switch occurs according to the absolute concentration of the first gradient. In this case scaling occurs in a window of developing-field sizes centred at a few times the morphogen decay length.   

Shape and Size of the Fission Yeast Nucleus are governed by Equilibrium Mechanics

Nuclear morphogenesis in the asexual reproduction of \textit{Schizosaccharomyces pombe} (fission yeast) consists of two stages: (i) volume-doubling growth, in which a round nucleus inflates uniformly, and (ii) division, in which the nucleus undergoes shape changes from round to oblong to peanut to dumbbell before it resolves into two smaller, round daughter nuclei, driven by the formation and elongation of a microtubule-based spindle within the nucleus. The combined volume of the daughter nuclei immediately after division is the same as the volume of the single nucleus at the onset of division. Consequently, the nuclear envelope (NE) area must increase by 26\% during division. We are developing a model in order to determine the mechanics governing these shape and size changes. It is based on current knowledge of the nuclear structure, insight from normal and abnormal nuclei, and concepts from the mechanics governing lipid-bilayer membranes. We predict that (a) the NE prefers to be flat, (b) the NE is under tension, (c) the nucleus has an internal pressure, (d) nuclear growth is governed by the Law of Laplace, and (e) some abnormal nuclei behave like vesicles with encapsulated microtubules.   

A surprising answer in the search for a comprehensive health protection exposure metric for radiofrequency (RF) fields

Matter can interact with light in 3 different ways (known by 1910): by absorption of energy [\it thermal \rm hazard] or by absorption of linear momentum (radiation pressure) or of angular momentum (torque) or of both [\it nonthermal \rm hazards].$^{1,2}$ The same is true for RF fields; indeed, microwave wattmeters may operate on a momentum absorption principle.$^{3,4}$ But most RF health protection standards today are based solely on \it thermal \rm effects, ignoring nonthermal effects. Formal expressions for scientifically valid exposure metrics will be presented. It will be shown that nonthermal effects depend on field frequency, polarization and spatial configuration as well as on field strength, so a \it general \rm metric valid for \it all \rm fields may not exist. But with some approximations, the \it magnetic induction current \rm may constitute an adequate \it practical \rm exposure metric for RF fields. $^1$M. Lundquist, BAPS \bf 50\rm (1):620(2005). $^2 $M. Lundquist, BAPS \bf 50\rm (1):1178(2005). $^3$A. L. Cullen, Proc. IEE \bf 99\rm Pt4(2):100-110(Apr 1952). $^4$A. L. Cullen \& I. M. Stephenson, Proc. IEE \bf 99\rm Pt4(4):294-301(Dec 1952).   

Nonlinear Analysis of Electromyography Time Series of Low Back Muscles

We have calculated the mean-square displacement $\Delta (t)$ from the EMG time series and have found that increases diffusively, $\Delta ( t) \sim t$, for short times $t < 10 \mbox{ms}$, and shows a plateau-like behavior, $\Delta (t) \sim t^{0}$, for interintermediate times $10 \, \mbox{ms} < t < 0.5 , \mbox{s}$. The plateau-like behavior implies the presence of correlations in the signal. We characterize these correlations and relate them to properties of the power spectrum of the signal.