Quantifying the roles of space and stochasticity in computer simulations for cell biology and cellular biochemistry.

Most of the fascinating phenomena studied in cell biology emerge from interactions among highly organized multimolecular structures embedded into complex and frequently dynamic cellular morphologies. For the exploration of such systems, computer simulation has proved to be an invaluable tool, and many researchers in this field have developed sophisticated computational models for application to specific cell biological questions. However, it is often difficult to reconcile conflicting computational results that use different approaches to describe the same phenomenon. To address this issue systematically, we have defined a series of computational test cases ranging from very simple to moderately complex, varying key features of dimensionality, reaction type, reaction speed, crowding, and cell size. We then quantified how explicit spatial and/or stochastic implementations alter outcomes, even when all methods use the same reaction network, rates, and concentrations. For simple cases, we generally find minor differences in solutions of the same problem. However, we observe increasing discordance as the effects of localization, dimensionality reduction, and irreversible enzymatic reactions are combined. We discuss the strengths and limitations of commonly used computational approaches for exploring cell biological questions and provide a framework for decision making by researchers developing new models. As computational power and speed continue to increase at a remarkable rate, the dream of a fully comprehensive computational model of a living cell may be drawing closer to reality, but our analysis demonstrates that it will be crucial to evaluate the accuracy of such models critically and systematically.

Comparison of quantitative methods for cell-shape analysis.

Morphology is an important large-scale manifestation of the global organizational and physiological state of cells, and is commonly used as a qualitative or quantitative measure of the outcome of various assays. Here we evaluate several different basic representations of cell shape - binary masks, distance maps and polygonal outlines - and different subsequent encodings of those representations - Fourier and Zernike decompositions, and the principal and independent components analyses - to determine which are best at capturing biologically important shape variation. We find that principal components analysis of two-dimensional shapes represented as outlines provide measures of morphology which are quantitative, biologically meaningful, human interpretable and work well across a range of cell types and parameter settings.

A kinematic description of the trajectories of Listeria monocytogenes propelled by actin comet tails.

The bacterial pathogen Listeria monocytogenes propels itself in the cytoplasm of the infected cells by forming a filamentous comet tail assembled by the polymerization of the cytoskeletal protein actin. Although a great deal is known about the molecular processes that lead to actin-based movement, most macroscale aspects of motion, including the nature of the trajectories traced out by the motile bacteria, are not well understood. Here, we present 2D trajectories of Listeria moving between a glass-slide and coverslip in a Xenopus frog egg extract motility assay. We observe that the bacteria move in a number of fascinating geometrical trajectories, including winding S curves, translating figure eights, small- and large-amplitude sine curves, serpentine shapes, circles, and a variety of spirals. We then develop a dynamic model that provides a unified description of these seemingly unrelated trajectories. A key ingredient of the model is a torque (not included in any microscopic models of which we are aware) that arises from the rotation of the propulsive force about the body axis of the bacterium. We show that a large variety of trajectories with a rich mathematical structure are obtained by varying the rate at which the propulsive force moves about the long axis. The trajectories of bacteria executing both steady and saltatory motion are found to be in excellent agreement with the predictions of our dynamic model. When the constraints that lead to planar motion are removed, our model predicts motion along regular helical trajectories, observed in recent experiments.

Effects of intermediate filaments on actin-based motility of Listeria monocytogenes.

How does subcellular architecture influence the intracellular movements of large organelles and macromolecular assemblies? To investigate the effects of mechanical changes in cytoplasmic structure on intracellular motility, we have characterized the actin-based motility of the intracellular bacterial pathogen Listeria monocytogenes in normal mouse fibroblasts and in fibroblasts lacking intermediate filaments. The apparent diffusion coefficient of L. monocytogenes was two-fold greater in vimentin-null fibroblasts than in wild-type fibroblasts, indicating that intermediate filaments significantly restrict the Brownian motion of bacteria. However, the mean speed of L. monocytogenes actin-based motility was statistically identical in vimentin-null and wild-type cells. Thus, environmental drag is not rate limiting for bacterial motility. Analysis of the temporal variations in speed measurements indicated that bacteria in vimentin-null cells displayed larger fluctuations in speed than did trajectories in wild-type cells. Similarly, the presence of the vimentin meshwork influenced the turning behavior of the bacteria; in the vimentin-null cells, bacteria made sharper turns than they did in wild-type cells. Taken together, these results suggest that a network of intermediate filaments constrains bacterial movement and operates over distances of several microns to reduce fluctuations in motile behavior.

The making of a gradient: IcsA (VirG) polarity in Shigella flexneri.

The generation and maintenance of subcellular organization in bacteria is critical for many cell processes and properties, including growth, structural integrity and, in pathogens, virulence. Here, we investigate the mechanisms by which the virulence protein IcsA (VirG) is distributed on the bacterial surface to promote efficient transmission of the bacterium Shigella flexneri from one host cell to another. The outer membrane protein IcsA recruits host factors that result in actin filament nucleation and, when concentrated at one bacterial pole, promote unidirectional actin-based motility of the pathogen. We show here that the focused polar gradient of IcsA is generated by its delivery exclusively to one pole followed by lateral diffusion through the outer membrane. The resulting gradient can be modified by altering the composition of the outer membrane either genetically or pharmacologically. The gradient can be reshaped further by the action of the protease IcsP (SopA), whose activity we show to be near uniform on the bacterial surface. Further, we report polar delivery of IcsA in Escherichia coli and Yersinia pseudotuberculosis, suggesting that the mechanism for polar delivery of some outer membrane proteins is conserved across species and that the virulence function of IcsA capitalizes on a more global mechanism for subcellular organization.

Actin-based motility is sufficient for bacterial membrane protrusion formation and host cell uptake.

Shigella flexneri replicates in the cytoplasm of host cells, where it nucleates host cell actin filaments at one pole of the bacterial cell to form a 'comet tail' that propels the bacterium through the host's cytoplasm. To determine whether the ability to move by actin-based motility is sufficient for subsequent formation of membrane-bound protrusions and intercellular spread, we conferred the ability to nucleate actin on a heterologous bacterium, Escherichia coli. Previous work has shown that IcsA (VirG), the molecule that is necessary and sufficient for actin nucleation and actin-based motility, is distributed in a unipolar fashion on the surface of S. flexneri. Maintenance of the unipolar distribution of IcsA depends on both the S. flexneri outer membrane protease IcsP (SopA) and the structure of the lipopolysaccharide (LPS) in the outer membrane. We co-expressed IcsA and IcsP in two strains of E. coli that differed in their LPS structures. The E. coli were engineered to invade host cells by expression of invasin from Yersinia pseudotuberculosis and to escape the phagosome by incubation in purified listeriolysin O (LLO) from Listeria monocytogenes. All E. coli strains expressing IcsA replicated in host cell cytoplasm and moved by actin-based motility. Actin-based motility alone was sufficient for the formation of membrane protrusions and uptake by recipient host cells. The presence of IcsP and an elaborate LPS structure combined to enhance the ability of E. coli to form protrusions at the same frequency as S. flexneri, quantitatively reconstituting this step in pathogen intercellular spread in a heterologous organism. The frequency of membrane protrusion formation across all strains tested correlates with the efficiency of unidirectional actin-based movement, but not with bacterial speed.

Dendritic organization of actin comet tails.

Polymerization of actin filaments is necessary for both protrusion of the leading edge of crawling cells and propulsion of certain intracellular pathogens, and it is sufficient for generating force for bacterial motility in vitro. Motile intracellular pathogens are associated with actin-rich comet tails containing many of the same molecular components present in lamellipodia, and this suggests that these two systems use a similar mechanism for motility. However, available structural evidence suggests that the organization of comet tails differs from that of lamellipodia. Actin filaments in lamellipodia form branched arrays, which are thought to arise by dendritic nucleation mediated by the Arp2/3 complex. In contrast, comet tails have been variously described as consisting of short, randomly oriented filaments, with a higher degree of alignment at the periphery, or as containing long, straight axial filaments with a small number of oblique filaments. Because the assembly of pathogen-associated comet tails has been used as a model system for lamellipodial protrusion, it is important to resolve this apparent discrepancy. Here, using a platinum replica approach, we show that actin filament arrays in comet tails in fact have a dendritic organization with the Arp2/3 complex localizing to Y-junctions as in lamellipodia. Thus, comet tails and lamellipodia appear to share a common dendritic nucleation mechanism for protrusive motility. However, comet tails differ from lamellipodia in that their actin filaments are usually twisted and appear to be under significant torsional stress.

Systematic mutational analysis of the amino-terminal domain of the Listeria monocytogenes ActA protein reveals novel functions in actin-based motility.

The Listeria monocytogenes ActA protein acts as a scaffold to assemble and activate host cell actin cytoskeletal factors at the bacterial surface, resulting in directional actin polymerization and propulsion of the bacterium through the cytoplasm. We have constructed 20 clustered charged-to-alanine mutations in the NH2-terminal domain of ActA and replaced the endogenous actA gene with these molecular variants. These 20 clones were evaluated in several biological assays for phenotypes associated with particular amino acid changes. Additionally, each protein variant was purified and tested for stimulation of the Arp2/3 complex, and a subset was tested for actin monomer binding. These specific mutations refined the two regions involved in Arp2/3 activation and suggest that the actin-binding sequence of ActA spans 40 amino acids. We also identified a 'motility rate and cloud-to-tail transition' region in which nine contiguous mutations spanning amino acids 165-260 caused motility rate defects and changed the ratio of intracellular bacteria associated with actin clouds and comet tails without affecting Arp2/3 activation. Several unusual motility phenotypes were associated with amino acid changes in this region, including altered paths through the cytoplasm, discontinuous actin tails in host cells and the tendency to 'skid' or dramatically change direction while moving. These unusual phenotypes illustrate the complexity of ActA functions that control the actin-based motility of L. monocytogenes.

Dietary chloride does not correlate with urinary thromboxane in deoxycorticosterone acetate-treated rats.

Renal vascular resistance in deoxycorticosterone acetate (DOCA) salt-treated uninephrectomized rats is increased by high dietary chloride. Because DOCA salt-hypertensive rats exhibit an increased urinary excretion of thromboxane B2 (TXB2), a metabolite of thromboxane A2 (TXA2), the increased TXB2 excretion by DOCA salt-treated rats could relate to elevated dietary chloride, increased blood pressure, and/or the presence of intact renal tubules. We hypothesized that high NaCl intake, resulting in an elevated tubular chloride excretion, stimulates TXA2 production. A result of that production could be renal vasoconstriction. Baseline blood pressures were measured for 10 days, and then the rats were treated with DOCA (30 mg/kg) and fed (1) normal NaCl, (2) normal sodium with high chloride, or (3) high sodium chloride (NaCl) for 4.5 weeks. Next, the rats were uninephrectomized (1K) or unihydronephrectomized (1KHK) to yield one kidney without an intact tubular system and therefore no macula densa. Two and a half weeks later, urinary excretion of TXB2 was determined. DOCA-high NaCl-fed 1KHK or 1K rats had significant increases in systemic blood pressure to 172 +/- 12 and 190 +/- 5 mm Hg, respectively, compared with no significant increase in blood pressure among the other groups. Urinary TXB2 excretion was increased to 29 +/- 4 pg per 24 hours per gram of body weight in all DOCA-treated 1KHK and 1K animals regardless of diet compared with DOCA-treated animals with two intact kidneys (13 +/- 2 pg per 24 hours per gram of body weight). DOCA treatment in rats with one functional kidney results in the excretion of high levels of urinary TXB2 unrelated to dietary chloride load, blood pressure, or intact renal tubules.

Secrets of actin-based motility revealed by a bacterial pathogen.

Actin-based cell motility is a complex process involving a dynamic, self-organizing cellular system. Experimental problems initially limited our understanding of this type of motility, but the use of a model system derived from a bacterial pathogen has led to a breakthrough. Now, all the molecular components necessary for dynamic actin self-organization and motility have been identified, setting the stage for future mechanistic studies.

The polymerization motor.

Polymerization and depolymerization of actin filaments and microtubules are thought to generate force for movement in various kinds of cell motility, ranging from lamellipodial protrusion to chromosome segregation. This article reviews the thermodynamic and physical theories of how a nonequilibrium polymerization reaction can be used to transduce chemical energy into mechanical energy, and summarizes the evidence suggesting that actin polymerization produces motile force in several biological systems.

Cooperative symmetry-breaking by actin polymerization in a model for cell motility.

Polymerizing networks of actin filaments are capable of exerting significant mechanical forces, used by eukaryotic cells and their prokaryotic pathogens to change shape or to move. Here we show that small beads coated uniformly with a protein that catalyses actin polymerization are initially surrounded by symmetrical clouds of actin filaments. This symmetry is broken spontaneously, after which the beads undergo directional motion. We have developed a stochastic theory, in which each actin filament is modelled as an elastic brownian ratchet, that quantitatively accounts for the observed emergent symmetry-breaking behaviour. Symmetry-breaking can only occur for polymers that have a significant subunit off-rate, such as the biopolymers actin and tubulin.

Listeria monocytogenes exploits normal host cell processes to spread from cell to cell.

The bacterial pathogen, Listeria monocytogenes, grows in the cytoplasm of host cells and spreads intercellularly using a form of actin-based motility mediated by the bacterial protein ActA. Tightly adherent monolayers of MDCK cells that constitutively express GFP-actin were infected with L. monocytogenes, and intercellular spread of bacteria was observed by video microscopy. The probability of formation of membrane-bound protrusions containing bacteria decreased with host cell monolayer age and the establishment of extensive cell-cell contacts. After their extension into a recipient cell, intercellular membrane-bound protrusions underwent a period of bacterium-dependent fitful movement, followed by their collapse into a vacuole and rapid vacuolar lysis. Actin filaments in protrusions exhibited decreased turnover rates compared with bacterially associated cytoplasmic actin comet tails. Recovery of motility in the recipient cell required 1-2 bacterial generations. This delay may be explained by acid-dependent cleavage of ActA by the bacterial metalloprotease, Mpl. Importantly, we have observed that low levels of endocytosis of neighboring MDCK cell surface fragments occurs in the absence of bacteria, implying that intercellular spread of bacteria may exploit an endogenous process of paracytophagy.

Motility of ActA protein-coated microspheres driven by actin polymerization.

Actin polymerization is required for the generation of motile force at the leading edge of both lamellipodia and filopodia and also at the surface of motile intracellular bacterial pathogens such as Listeria monocytogenes. Local catalysis of actin filament polymerization is accomplished in L. monocytogenes by the bacterial protein ActA. Polystyrene beads coated with purified ActA protein can undergo directional movement in an actin-rich cytoplasmic extract. Thus, the actin polymerization-based motility generated by ActA can be used to move nonbiological cargo, as has been demonstrated for classical motor molecules such as kinesin and myosin. Initiation of unidirectional movement of a symmetrically coated particle is a function of bead size and surface protein density. Small beads (

Functional analysis of a rickettsial OmpA homology domain of Shigella flexneri icsA.

Shigella flexneri is a gram-negative bacterium that causes diarrhea and dysentery by invasion and spread through the colonic epithelium. Bacteria spread by assembling actin and other cytoskeletal proteins of the host into "actin tails" at the bacterial pole; actin tail assembly provides the force required to move bacteria through the cell cytoplasm and into adjacent cells. The 120-kDa S. flexneri outer membrane protein IcsA is essential for actin assembly. IcsA is anchored in the outer membrane by a carboxy-terminal domain (the beta domain), such that the amino-terminal 706 amino acid residues (the alpha domain) are exposed on the exterior of the bacillus. The alpha domain is therefore likely to contain the domains that are important to interactions with host factors. We identify and characterize a domain of IcsA within the alpha domain that bears significant sequence similarity to two repeated domains of rickettsial OmpA, which has been implicated in rickettsial actin tail formation. Strains of S. flexneri and Escherichia coli that carry derivatives of IcsA containing deletions within this domain display loss of actin recruitment and increased accessibility to IcsA-specific antibody on the surface of intracytoplasmic bacteria. However, site-directed mutagenesis of charged residues within this domain results in actin assembly that is indistinguishable from that of the wild type, and in vitro competition of a polypeptide of this domain fused to glutathione S-transferase did not alter the motility of the wild-type construct. Taken together, our data suggest that the rickettsial homology domain of IcsA is required for the proper conformation of IcsA and that its disruption leads to loss of interactions of other IcsA domains within the amino terminus with host cytoskeletal proteins.

Imaging techniques in microbiology.

Recent advances in optical imaging have dramatically expanded the capabilities of the light microscope and its usefulness in microbiology research. Some of these advances include improved fluorescent probes, better cameras, new techniques such as confocal and deconvolution microscopy, and the use of computers in imaging and image analysis. These new technologies have now been applied to microbiological problems with resounding success.