Force generation by actin polymerization II: the elastic ratchet and tethered filaments

The motion of many intracellular pathogens is driven by the polymerization of actin filaments. The propulsive force developed by the polymerization process is thought to arise from the thermal motions of the polymerizing filament tips. Recent experiments suggest that the nucleation of actin filaments involves a phase when the filaments are attached to the pathogen surface by a protein complex. Here we extend the "elastic ratchet model" of Mogilner and Oster to incorporate these new findings. We apply this "tethered ratchet" model to derive the force-velocity relation for Listeria and discuss relations of our theoretical predictions to experimental measurements. We also discuss "symmetry breaking" dynamics observed in ActA-coated bead experiments, and the implications of the model for lamellipodial protrusion in migrating cells.     

A Highlights from MBoC Selection: Diffusion of GPI-anchored proteins is influenced by the activity of dynamic cortical actin

Molecular diffusion at the surface of living cells is believed to be predominantly driven by thermal kicks. However, there is growing evidence that certain cell surface molecules are driven by the fluctuating dynamics of cortical cytoskeleton. Using fluorescence correlation spectroscopy, we measure the diffusion coefficient of a variety of cell surface molecules over a temperature range of 24–37°C. Exogenously incorporated fluorescent lipids with short acyl chains exhibit the expected increase of diffusion coefficient over this temperature range. In contrast, we find that GPI-anchored proteins exhibit temperature-independent diffusion over this range and revert to temperature-dependent diffusion on cell membrane blebs, in cells depleted of cholesterol, and upon acute perturbation of actin dynamics and myosin activity. A model transmembrane protein with a cytosolic actin-binding domain also exhibits the temperature-independent behavior, directly implicating the role of cortical actin. We show that diffusion of GPI-anchored proteins also becomes temperature dependent when the filamentous dynamic actin nucleator formin is inhibited. However, changes in cortical actin mesh size or perturbation of branched actin nucleator Arp2/3 do not affect this behavior. Thus cell surface diffusion of GPI-anchored proteins and transmembrane proteins that associate with actin is driven by active fluctuations of dynamic cortical actin filaments in addition to thermal fluctuations, consistent with expectations from an “active actin-membrane composite” cell surface.     

A mathematical model of the sarcomere mechanics of cross-striated muscle with consideration of the stretch and twist of actin filaments

A mathematical model of sarcomere mechanics, which takes into account the elongation of actin and myosin filaments and also twisting of the actin filaments in the sarcomere of striated muscle during contraction is presented. The model accounts for the experimentally observed phenomena of the stretch and twist of the actin filaments due to strong binding of myosin heads and the pulling force. Some model parameters were estimated from published experimental data. The results of modeling show that the twist of actin filaments can play a substantial role in the mechanical responses of contracting muscle fibers to step changes of their length.     

A neutral model with fluctuating population size and its effective size

We consider a diffusion model with neutral alleles whose population size is fluctuating randomly. For this model, the effects of fluctuation of population size on the effective size are investigated. The effective size defined by the equilibrium average heterozygosity is larger than the harmonic mean of population size but smaller than the arithmetic mean of population size. To see explicitly the effects of fluctuation of population size on the effective size, we investigate a special case where population size fluctuates between two distinct states. In some cases, the effective size is very different from the harmonic mean. For this concrete model, we also obtain the stationary distribution of the average heterozygosity. Asymptotic behavior of the effective size is obtained when the population size is large and/or autocorrelation of the fluctuation is weak or strong.     

Experimental evolution in fluctuating environments: tolerance measurements at constant temperatures incorrectly predict the ability to tolerate fluctuating temperatures

The ability to predict the consequences of fluctuating environments on species distribution and extinction often relies on determining the tolerances of species or genotypes in different constant environments (i.e. determining tolerance curves). However, very little is known about the suitability of measurements made in constant environments to predict the level of adaptation to rapidly fluctuating environments. To explore this question, we used bacterial clones adapted to constant or fluctuating temperatures and found that measurements across a range of constant temperatures did not indicate any adaptation to fluctuating temperatures. However, adaptation to fluctuating temperatures was only apparent if growth was measured during thermal fluctuation. Thus, tolerance curves based on measurements in constant environments can be misleading in predicting the ability to tolerate fast environmental fluctuations. Such complications could lead to false estimates of the genetic merits of genotypes and extinction risks of species due to climate change‐induced thermal fluctuations.     

The Hill model for binding myosin S1 to regulated actin is not equivalent to the McKillop-Geeves model

The Hill two-state cooperativity model and the McKillop-Geeves (McK-G) three-state model predict very similar binding traces of myosin subfragment 1 (S1) binding to regulated actin filaments in the presence and absence of calcium, and both fit the experimental data reasonably well [Chen et al., Biophys. J., 80, 2338-2349]. Here, we compared the Hill model and the McK-G model for binding myosin S1 to regulated actin against three sets of experimental data: the titration of regulated actin with S1 and the kinetics of S1 binding of regulated actin with either excess S1 to actin or excess actin to S1. Each data set was collected for a wide range of specified calcium concentrations. Both models were able to generate reasonable fits to the time course data and to titration data. The McK-G model can fit all three data sets with the same calcium-concentration-sensitive parameters. Only K(B) and K(T) show significant calcium dependence, and the parameters have a classic pCa curve. A unique set of the Hill model parameters was extremely difficult to estimate from the best fits of multiple sets of data. In summary, the McK-G cooperativity model more uniquely resolves parameters estimated from kinetic and titration data than the Hill model, predicts a sigmoidal dependence of key parameters with calcium concentration, and is simpler and more suitable for practical use.     

Constructing disease-specific gene networks using pair-wise relevance metric: Application to colon cancer identifies interleukin 8, desmin and enolase 1 as the central elements

Background

When purified phagosomes are incubated in the presence of actin under appropriate conditions, microfilaments start growing from the membrane in a process that is affected by ATP and the lipid composition of the membrane. Isolated phagosomes are metabolically active organelles that contain enzymes and metabolites necessary for lipid interconversion. Hence, addition of ATP, lipids, and actin to the system alter the steady-state composition of the phagosomal membrane at the same time that the actin nucleation is initiated. Our aim was to model all these processes in parallel.

Results

We compiled detailed experimental data on the effects of different lipids and ATP on actin nucleation and we investigated experimentally lipid interconversion and ATP metabolism in phagosomes by using suitable radioactive compounds. In a first step, a complex lipid network interconnected by chemical reactions catalyzed by known enzymes was modelled in COPASI (Complex Pathway Simulator). However, several lines of experimental evidence indicated that only the phosphatidylinositol branch of the network was active, an observation that dramatically reduced the number of parameters in the model. The results also indicated that a lipid network-independent ATP-consuming activity should be included in the model. When this activity was introduced, the set of differential equations satisfactorily reproduced the experimental data. On the other hand, a molecular mechanism connecting membrane lipids, ATP, and the actin nucleation process is still missing. We therefore adopted a phenomenological (black-box) approach to represent the empirical observations. We proposed that lipids and ATP influence the dynamic interconversion between active and inactive actin nucleation sites. With this simple model, all the experimental data were satisfactorily fitted with a single positive parameter per lipid and ATP.

Conclusion

By establishing an active 'dialogue' between an initial complex model and experimental observations, we could narrow the set of differential equations and parameters required to characterize the time-dependent changes of metabolites influencing actin nucleation on phagosomes. For this, the global model was dissected into three sub-models: ATP consumption, lipid interconversion, and nucleation of actin on phagosomal membranes. This scheme allowed us to describe this complex system with a relatively small set of differential equations and kinetic parameters that satisfactorily reproduced the experimental data.     

How depolymerization can promote polymerization: the case of actin and profilin

Rapid polymerization and depolymerization of actin filaments in response to extracellular stimuli is required for normal cell motility and development. Profilin is one of the most important actin‐binding proteins; it regulates actin polymerization and interacts with many cytoskeletal proteins that link actin to extracellular membrane. The molecular mechanism of profilin has been extensively considered and debated in the literature for over two decades. Here we discuss several accepted hypotheses regarding the mechanism of profilin function as well as new recently emerged possibilities. Thermal noise is routine in molecular world and unsurprisingly, nature has found a way to utilize it. An increasing amount of theoretical and experimental research suggests that fluctuation‐based processes play important roles in many cell events. Here we show how a fluctuation‐based process of exchange diffusion is involved in the regulation of actin polymerization.     

Actin-Myosin Viscoelastic Flow in the Keratocyte Lamellipod

The lamellipod, the locomotory region of migratory cells, is shaped by the balance of protrusion and contraction. The latter is the result of myosin-generated centripetal flow of the viscoelastic actin network. Recently, quantitative flow data was obtained, yet there is no detailed theory explaining the flow in a realistic geometry. We introduce models of viscoelastic actin mechanics and myosin transport and solve the model equations numerically for the flat, fan-shaped lamellipodial domain of keratocytes. The solutions demonstrate that in the rapidly crawling cell, myosin concentrates at the rear boundary and pulls the actin network inward, so the centripetal actin flow is very slow at the front, and faster at the rear and at the sides. The computed flow and respective traction forces compare well with the experimental data. We also calculate the graded protrusion at the cell boundary necessary to maintain the cell shape and make a number of other testable predictions. We discuss model implications for the cell shape, speed, and bi-stability.     

Effect of profilin on actin critical concentration: a theoretical analysis

To explain the effect of profilin on actin critical concentration in a manner consistent with thermodynamic constraints and available experimental data, we built a thermodynamically rigorous model of actin steady-state dynamics in the presence of profilin. We analyzed previously published mechanisms theoretically and experimentally and, based on our analysis, suggest a new explanation for the effect of profilin. It is based on a general principle of indirect energy coupling. The fluctuation-based process of exchange diffusion indirectly couples the energy of ATP hydrolysis to actin polymerization. Profilin modulates this coupling, producing two basic effects. The first is based on the acceleration of exchange diffusion by profilin, which indicates, paradoxically, that a faster rate of actin depolymerization promotes net polymerization. The second is an affinity-based mechanism similar to the one suggested in 1993 by Pantaloni and Carlier although based on indirect rather than direct energy coupling. In the model by Pantaloni and Carlier, transformation of chemical energy of ATP hydrolysis into polymerization energy is regulated by direct association of each step in the hydrolysis reaction with a corresponding step in polymerization. Thus, hydrolysis becomes a time-limiting step in actin polymerization. In contrast, indirect coupling allows ATP hydrolysis to lag behind actin polymerization, consistent with experimental results.     

Modeling of protein binary complexes using structural mass spectrometry data

In this article, we describe a general approach to modeling the structure of binary protein complexes using structural mass spectrometry data combined with molecular docking. In the first step, hydroxyl radical mediated oxidative protein footprinting is used to identify residues that experience conformational reorganization due to binding or participate in the binding interface. In the second step, a three-dimensional atomic structure of the complex is derived by computational modeling. Homology modeling approaches are used to define the structures of the individual proteins if footprinting detects significant conformational reorganization as a function of complex formation. A three-dimensional model of the complex is constructed from these binary partners using the ClusPro program, which is composed of docking, energy filtering, and clustering steps. Footprinting data are used to incorporate constraints-positive and/or negative-in the docking step and are also used to decide the type of energy filter-electrostatics or desolvation-in the successive energy-filtering step. By using this approach, we examine the structure of a number of binary complexes of monomeric actin and compare the results to crystallographic data. Based on docking alone, a number of competing models with widely varying structures are observed, one of which is likely to agree with crystallographic data. When the docking steps are guided by footprinting data, accurate models emerge as top scoring. We demonstrate this method with the actin/gelsolin segment-1 complex. We also provide a structural model for the actin/cofilin complex using this approach which does not have a crystal or NMR structure.     

Spreading dynamics of biomimetic actin cortices

Reconstituted systems mimicking cells are interesting tools for understanding the details of cell behavior. Here, we use an experimental system that mimics cellular actin cortices, namely liposomes developing an actin shell close to their inner membrane, and we study their dynamics of spreading. We show that depending on the morphology of the actin shell inside the liposome, spreading dynamics is either reminiscent of a bare liposome (in the case of a sparse actin shell) or of a cell (in the case of a continuous actin shell). We use a mechanical model that qualitatively accounts for the shape of the experimental curves. From the data on spreading dynamics, we extract characteristic times that are consistent with mechanical estimates. The mechanical characterization of such stripped-down experimental systems paves the way for a more complex design closer to a cell. We report here the first step in building an artificial cell and studying its mechanics.     

Are fluctuating asymmetry studies adequately sampled? Implications of a new model for size distribution

Previous work on fluctuating asymmetry (FA) has highlighted its controversial relationship with environmental stress and genetic architecture. While size-based measures of FA have been assumed to have half-normal distributions within populations, studies of model developmental mechanisms have suggested other plausible distributions for FA. We investigated the distribution of FA in large empirical data sets of wing shape and wing size asymmetry from three species of insects (cotton aphid Aphis gossipyii Glover, honeybee Apis mellifera, and long-legged fly Chrysosoma crinitus). Regardless of measurement method, FA was best described by a double Pareto-lognormal (DPLN) distribution or one of its limiting functional forms. To investigate convergence of mean sample FA to the population mean at various sample sizes, we sampled repeatedly under a DPLN distribution using parameter values that best fitted our data. Sample variances are much larger, and hence, convergence is slowed considerably with univariate or multivariate size-based measures of FA in contrast to a multivariate shape-based measure of FA. We suggest that much of the past work on FA may be undersampled, and we recommend using multivariate shape-based approaches or collecting larger data sets in future studies. We also discuss the implications of the DPLN distribution for understanding the developmental mechanisms underlying FA.     

The real-time monitoring of the thermal unfolding of tetramethylrhodamine-labeled actin

Modification of actin at Cys (374) with tetramethylrhodamine maleimide (TMR-actin) has been used for visualization of actin filaments and to produce high-resolution crystal structures of actin. We show that TMR-actin exhibits a 21% decrease in absorbance at 557 nm upon thermal unfolding, likely due to the movement of TMR to a more hydrophobic environment upon rapid unfolding and protein aggregation. We took advantage of this property to test models of actin protein unfolding. A transition temperature ( T m) of 60.2 +/- 0.2 degrees C for Ca (2+).ATP.TMR-actin was determined using A 557 and agreed with our own determinations employing different techniques and previous work with unlabeled actin. Our data show that the dependence of TMR-actin thermal stability on the bound nucleotide and cations follows a trend of Ca (2+).ATP > Mg (2+).ATP > Ca (2+).ADP > Mg (2+).ADP. The activation energies and frequency factors for the thermal unfolding of TMR-actin determined with two methods were in good agreement with those previously determined for unlabeled actin. We observed a biphasic trend in the T m of TMR-actin with increasing nucleotide concentrations, supporting a two-pathway model for actin protein unfolding where one pathway dominates at different concentrations of nucleotide. Additionally, TMR-actin bound by DNase I or gelsolin segment-1 exhibited elevated transition temperatures.     

Sequence dependence of DNA conformational flexibility

By using conformational free energy calculations, we have studied the sequence dependence of flexibility and its anisotropy along various conformational variables of DNA base pairs. The results show the AT base step to be very flexible along the twist coordinate. On the other hand, homonucleotide steps, GG(CC) and AA(TT), are among the most rigid sequences. For the roll motion that would correspond to a bend, the TA step is most flexible, while the GG(CC) step is least flexible. The flexibility of roll is quite anisotropic; the ratio of fluctuations toward the major and minor grooves is the largest for the GC step and the smallest for the AA(TT) and CG steps. Propeller twisting of base pairs is quite flexible, especially of A.T base pairs; propeller twist can reach 19 degrees by thermal fluctuation. We discuss the effect of electrostatic parameters, comparison with available experimental results, and biological relevance of these results.     

An integrative simulation model linking major biochemical reactions of actin-polymerization to structural properties of actin filaments

We report on an advanced universal Monte Carlo simulation model of actin polymerization processes offering a broad application panel. The model integrates major actin-related reactions, such as assembly of actin nuclei, association/dissociation of monomers to filament ends, ATP-hydrolysis via ADP-Pi formation and ADP-ATP exchange, filament branching, fragmentation and annealing or the effects of regulatory proteins. Importantly, these reactions are linked to information on the nucleotide state of actin subunits in filaments (ATP hydrolysis) and the distribution of actin filament lengths. The developed stochastic simulation modelling schemes were validated on: i) synthetic theoretical data generated by a deterministic model and ii) sets of our and published experimental data obtained from fluorescence pyrene-actin experiments. Build on an open-architecture principle, the designed model can be extended for predictive evaluation of the activities of other actin-interacting proteins and can be applied for the analysis of experimental pyrene actin-based or fluorescence microscopy data. We provide a user-friendly, free software package ActinSimChem that integrates the implemented simulation algorithms and that is made available to the scientific community for modelling in silico any specific actin-polymerization system.     

Gene set enrichment analysis: performance evaluation and usage guidelines

A central goal of biology is understanding and describing the molecular basis of plasticity: the sets of genes that are combinatorially selected by exogenous and endogenous environmental changes, and the relations among the genes. The most viable current approach to this problem consists of determining whether sets of genes are connected by some common theme, e.g. genes from the same pathway are overrepresented among those whose differential expression in response to a perturbation is most pronounced. There are many approaches to this problem, and the results they produce show a fair amount of dispersion, but they all fall within a common framework consisting of a few basic components. We critically review these components, suggest best practices for carrying out each step, and propose a voting method for meeting the challenge of assessing different methods on a large number of experimental data sets in the absence of a gold standard.