An experimental and computational study of the effect of ActA polarity on the speed of Listeria monocytogenes actin-based motility.

Listeria monocytogenes is a pathogenic bacterium that moves within infected cells and spreads directly between cells by harnessing the cell's dendritic actin machinery. This motility is dependent on expression of a single bacterial surface protein, ActA, a constitutively active Arp2,3 activator, and has been widely studied as a biochemical and biophysical model system for actin-based motility. Dendritic actin network dynamics are important for cell processes including eukaryotic cell motility, cytokinesis, and endocytosis. Here we experimentally altered the degree of ActA polarity on a population of bacteria and made use of an ActA-RFP fusion to determine the relationship between ActA distribution and speed of bacterial motion. We found a positive linear relationship for both ActA intensity and polarity with speed. We explored the underlying mechanisms of this dependence with two distinctly different quantitative models: a detailed agent-based model in which each actin filament and branched network is explicitly simulated, and a three-state continuum model that describes a simplified relationship between bacterial speed and barbed-end actin populations. In silico bacterial motility required a cooperative restraining mechanism to reconstitute our observed speed-polarity relationship, suggesting that kinetic friction between actin filaments and the bacterial surface, a restraining force previously neglected in motility models, is important in determining the effect of ActA polarity on bacterial motility. The continuum model was less restrictive, requiring only a filament number-dependent restraining mechanism to reproduce our experimental observations. However, seemingly rational assumptions in the continuum model, e.g. an average propulsive force per filament, were invalidated by further analysis with the agent-based model. We found that the average contribution to motility from side-interacting filaments was actually a function of the ActA distribution. This ActA-dependence would be difficult to intuit but emerges naturally from the nanoscale interactions in the agent-based representation.

An agent-based model contrasts opposite effects of dynamic and stable microtubules on cleavage furrow positioning.

From experiments by Foe and von Dassow (Foe, V.E., and G. von Dassow. 2008. J. Cell Biol. 183:457-470) and others, we infer a molecular mechanism for positioning the cleavage furrow during cytokinesis. Computer simulations reveal how this mechanism depends on quantitative motor-behavior details and explore how robustly this mechanism succeeds across a range of cell sizes. The mechanism involves the MKLP1 (kinesin-6) component of centralspindlin binding to and walking along microtubules to stimulate cortical contractility where the centralspindlin complex concentrates. The majority of astral microtubules are dynamically unstable. They bind most MKLP1 and suppress cortical Rho/myosin II activation because the tips of unstable microtubules usually depolymerize before MKLP1s reach the cortex. A subset of astral microtubules stabilizes during anaphase, becoming effective rails along which MKLP1 can actually reach the cortex. Because stabilized microtubules aim statistically at the equatorial spindle midplane, that is where centralspindlin accumulates to stimulate furrow formation.

In silico reconstitution of Listeria propulsion exhibits nano-saltation.

To understand how the actin-polymerization-mediated movements in cells emerge from myriad individual protein-protein interactions, we developed a computational model of Listeria monocytogenes propulsion that explicitly simulates a large number of monomer-scale biochemical and mechanical interactions. The literature on actin networks and L. monocytogenes motility provides the foundation for a realistic mathematical/computer simulation, because most of the key rate constants governing actin network dynamics have been measured. We use a cluster of 80 Linux processors and our own suite of simulation and analysis software to characterize salient features of bacterial motion. Our "in silico reconstitution" produces qualitatively realistic bacterial motion with regard to speed and persistence of motion and actin tail morphology. The model also produces smaller scale emergent behavior; we demonstrate how the observed nano-saltatory motion of L. monocytogenes,in which runs punctuate pauses, can emerge from a cooperative binding and breaking of attachments between actin filaments and the bacterium. We describe our modeling methodology in detail, as it is likely to be useful for understanding any subcellular system in which the dynamics of many simple interactions lead to complex emergent behavior, e.g., lamellipodia and filopodia extension, cellular organization, and cytokinesis.

Design and constraints of the Drosophila segment polarity module: robust spatial patterning emerges from intertwined cell state switches.

The Drosophila segment polarity genes constitute the last tier in the segmentation cascade; their job is to maintain the boundaries between parasegments and provide positional "read-outs" within each parasegment for the entire developmental history of the animal. These genes constitute a relatively well-defined network with a relatively well-understood patterning task. In a previous publication (von Dassow et al. 2000. Nature 406:188-192) we showed that a computer model predicts the segment polarity network to be a robust boundary-making device. Here we elaborate those findings. First, we explore the constraints among parameters that govern the network model. Second, we test architectural variants of the core network, and show that the network tolerates a wide variety of adjustments in design. Third, we evaluate several topologically identical models that incorporate more or less molecular detail, finding that more-complex models perform noticeably better than simplified ones. Fourth, we discuss two instances in which the failure of the network model to behave in a life-like fashion highlights mechanistic details that need further experimental investigation. We conclude with an explanation of how the segment polarity network can be understood as an interwoven conspiracy of simple dynamical elements, several bistable switches and a homeostat. The robustness with which the network as a whole maintains a spatial regime of stable cell state emerges from generic dynamical properties of these simple elements.

Ingeneue: a versatile tool for reconstituting genetic networks, with examples from the segment polarity network.

Here we describe a software tool for synthesizing molecular genetic data into models of genetic networks. Our software program Ingeneue, written in Java, lets the user quickly turn a map of a genetic network into a dynamical model consisting of a set of ordinary differential equations. We developed Ingeneue as part of an ongoing effort to explore the design and evolvability of genetic networks. Ingeneue has three principal advantages over other available mathematical software: it automates instantiation of the same network model in each cell in a 2-D sheet of cells; it constructs model equations from pre-made building blocks corresponding to common biochemical processes; and it automates searches through parameter space, sensitivity analyses, and other common tasks. Here we discuss the structure of the software and some of the issues we have dealt with. We conclude with some examples of results we have achieved with Ingeneue for the Drosophila segment polarity network.

Robustness, flexibility, and the role of lateral inhibition in the neurogenic network.

BACKGROUND: Many gene networks used by developing organisms have been conserved over long periods of evolutionary time. Why is that? We showed previously that a model of the segment polarity network in Drosophila is robust to parameter variation and is likely to act as a semiautonomous patterning module. Is this true of other networks as well? RESULTS: We present a model of the core neurogenic network in Drosophila. Our model exhibits at least three related pattern-resolving behaviors that the real neurogenic network accomplishes during embryogenesis in Drosophila. Furthermore, we find that it exhibits these behaviors across a wide range of parameter values, with most of its parameters able to vary more than an order of magnitude while it still successfully forms our test patterns. With a single set of parameters, different initial conditions (prepatterns) can select between different behaviors in the network's repertoire. We introduce two new measures for quantifying network robustness that mimic recombination and allelic divergence and use these to reveal the shape of the domain in the parameter space in which the model functions. We show that lateral inhibition yields robustness to changes in prepatterns and suggest a reconciliation of two divergent sets of experimental results. Finally, we show that, for this model, robustness confers functional flexibility. CONCLUSIONS: The neurogenic network is robust to changes in parameter values, which gives it the flexibility to make new patterns. Our model also offers a possible resolution of a debate on the role of lateral inhibition in cell fate specification.

Polarized basolateral cell motility underlies invagination and convergent extension of the ascidian notochord.

We use 3D time-lapse analysis of living embryos and laser scanning confocal reconstructions of fixed, staged, whole-mounted embryos to describe three-dimensional patterns of cell motility, cell shape change, cell rearrangement and tissue deformation that accompany formation of the ascidian notochord. We show that notochord formation involves two simultaneous processes occurring within an initially monolayer epithelial plate: The first is invagination of the notochord plate about the axial midline to form a solid cylindrical rod. The second is mediolaterally directed intercalation of cells within the plane of the epithelial plate, and then later about the circumference of the cylindrical rod, that accompanies its extension along the anterior/posterior (AP) axis. We provide evidence that these shape changes and rearrangements are driven by active extension of interior basolateral notochord cell edges directly across the faces of their adjacent notochord neighbors in a manner analogous to leading edge extension of lamellapodia by motile cells in culture. We show further that local edge extension is polarized with respect to both the AP axis of the embryo and the apicobasal axis of the notochord plate. Our observations suggest a novel view of how active basolateral motility could drive both invagination and convergent extension of a monolayer epithelium. They further reveal deep similarities between modes of notochord morphogenesis exhibited by ascidians and other chordate embryos, suggesting that cellular mechanisms of ascidian notochord formation may operate across the chordate phylum.