Purification of actin from fission yeast Schizosaccharomyces pombe and characterization of functional differences from muscle actin

Fission yeast Schizosaccharomyces pombe is an important genetic model organism for studying the mechanisms of endocytosis and cytokinesis. However, most work on the biochemical properties of fission yeast actin-binding proteins has been done with skeletal muscle actin for matters of convenience. When simulations of mathematical models of the mechanism of endocytosis were compared with events in live cells, some of the reactions appeared to be much faster than observed in biochemical experiments with muscle actin. Here, we used gelsolin affinity chromatography to purify actin from fission yeast. S. pombe actin shares many properties with skeletal muscle actin but has higher intrinsic nucleotide exchange rate, faster trimer nucleus formation, faster phosphate dissociation rate from polymerized actin, and faster nucleation of actin filaments with Arp2/3 complex. These properties close the gap between the biochemistry and predictions made by mathematical models of endocytosis in S. pombe cells.     

Advances in the mechanical modeling of filamentous actin and its cross-linked networks on multiple scales

The protein actin is a part of the cytoskeleton and, therefore, responsible for the mechanical properties of the cells. Starting with the single molecule up to the final structure, actin creates a hierarchical structure of several levels exhibiting a remarkable behavior. The hierarchy spans several length scales and limitations in computational power; therefore, there is a call for different mechanical modeling approaches for the different scales. On the molecular level, we may consider each atom in molecular dynamics simulations. Actin forms filaments by combining the molecules into a double helix. In a model, we replace molecular subdomains using coarse-graining methods, allowing the investigation of larger systems of several atoms. These models on the nanoscale inform continuum mechanical models of large filaments, which are based on worm-like chain models for polymers. Assemblies of actin filaments are connected with cross-linker proteins. Models with discrete filaments, so-called Mikado models, allow us to investigate the dependence of the properties of networks on the parameters of the constituents. Microstructurally motivated continuum models of the networks provide insights into larger systems containing cross-linked actin networks. Modeling of such systems helps to gain insight into the processes on such small scales. On the other hand, they call for verification and hence trigger the improvement of established experiments and the development of new methods.     

Effects of random hydrolysis on biofilament length distributions in a shared subunit pool

The sizes of filamentous structures in a cell are often regulated for many physiological processes. A key question in cell biology is how such size control is achieved. Here, we theoretically study the length distributions of multiple filaments, growing by stochastic assembly and disassembly of subunits from a limiting subunit pool. Importantly, we consider a chemical switching of subunits (hydrolysis) prevalent in many biofilaments like microtubules (MTs). We show by simulations of different models that hydrolysis leads to a skewed unimodal length distribution for a single MT. In contrast, hydrolysis can lead to bimodal distributions of individual lengths for two MTs, where individual filaments toggle stochastically between bigger and smaller sizes. For more than two MTs, length distributions are also bimodal, although the bimodality becomes less prominent. We further show that this collective phenomenon is connected with the nonequilibrium nature of hydrolysis, and the bimodality disappears for reversible dynamics. Consistent with earlier theoretical studies, a homogeneous subunit pool, without hydrolysis, cannot control filament lengths. We thus elucidate the role of hydrolysis as a control mechanism on MT length diversity.     

Hybrid simulation of cellular behavior

MOTIVATION: To be valuable to biological or biomedical research, in silico methods must be scaled to complex pathways and large numbers of interacting molecular species. The correct method for performing such simulations, discrete event simulation by Monte Carlo generation, is computationally costly for large complex systems. Approximation of molecular behavior by continuous models fails to capture stochastic behavior that is essential to many biological phenomena. RESULTS: We present a novel approach to building hybrid simulations in which some processes are simulated discretely, while other processes are handled in a continuous simulation by differential equations. This approach preserves the stochastic behavior of cellular pathways, yet enables scaling to large populations of molecules. We present an algorithm for synchronizing data in a hybrid simulation and discuss the trade-offs in such simulation. We have implemented the hybrid simulation algorithm and have validated it by simulating the statistical behavior of the well-known lambda phage switch. Hybrid simulation provides a new method for exploring the sources and nature of stochastic behavior in cells.     

A theoretical analysis of filament length fluctuations in actin and other polymers

Control of the structure and dynamics of the actin cytoskeleton is essential for cell motility and for maintaining the structural integrity of cells. Central to understanding the control of these features is an understanding of the dynamics of actin filaments, first as isolated filaments, then as integrated networks, and finally as networks containing higher-order structures such as bundles, stress fibers and acto-myosin complexes. It is known experimentally that single filaments can exhibit large fluctuations, but a detailed understanding of the transient dynamics involved is still lacking. Here we first study stochastic models of a general system involving two-monomer types that can be analyzed completely, and then we report stochastic simulations on the complete actin model with three monomer types. We systematically examine the transient behavior of filament length dynamics so as to gain a better understanding of the time scales involved in reaching a steady state. We predict the lifetime of a cap of one monomer type and obtain the mean and variance of the survival time of a cap at the filament end, which together determine the filament length fluctuations.     

Intermediate filaments mediate cytoskeletal crosstalk

Intermediate filaments, actin-containing microfilaments and microtubules are the three main cytoskeletal systems of vertebrate and many invertebrate cells. Although these systems are composed of distinctly different proteins, they are in constant and intimate communication with one another. Understanding the molecular basis of this cytoskeletal crosstalk is essential for determining the mechanisms that underlie many cell-biological phenomena. Recent studies have revealed that intermediate filaments and their associated proteins are important components in mediating this crosstalk.     

Collective dynamics of active cytoskeletal networks

Self organization mechanisms are essential for the cytoskeleton to adapt to the requirements of living cells. They rely on the intricate interplay of cytoskeletal filaments, crosslinking proteins and molecular motors. Here we present an in vitro minimal model system consisting of actin filaments, fascin and myosin-II filaments exhibiting pulsatile collective dynamics and superdiffusive transport properties. Both phenomena rely on the complex competition of crosslinking molecules and motor filaments in the network. They are only observed if the relative strength of the binding of myosin-II filaments to the actin network allows exerting high enough forces to unbind actin/fascin crosslinks. This is shown by varying the binding strength of the acto-myosin bond and by combining the experiments with phenomenological simulations based on simple interaction rules.     

Role of the cytoskeleton in the spreading process of epithelial cells

The role of microtubules and actin filaments in spreading of the IAR-2 cells isolated from the rat liver was studied. At the glass surface in the standard medium the cells rapidly assumed a discoidal form soon after inoculation. In the colcemid-containing medium the spreading is disturbed and delayed. In the cytochalasin D-containing medium the cells form two or more long processes. The effects of these drugs are reversible. It is supposed that microtubules are essential for sending cytoplasmic processes and stabilizing those processes and lamellae which have no numerous and stable contacts with the substrate, e.g., the processes which form at the early stages of spreading or the elongated processes of polarized cells. Bundles of actin microfilaments are essential, in particular, to ensure the discoidal form of epithelial cells. Microtubules appear to prevent the actin cytoskeleton contraction.     

An InCytes from MBC Selection: Roles of Formin Nodes and Myosin Motor Activity in Mid1p-dependent Contractile-Ring Assembly during Fission Yeast Cytokinesis

Two prevailing models have emerged to explain the mechanism of contractile-ring assembly during cytokinesis in the fission yeast Schizosaccharomyces pombe: the spot/leading cable model and the search, capture, pull, and release (SCPR) model. We tested some of the basic assumptions of the two models. Monte Carlo simulations of the SCPR model require that the formin Cdc12p is present in >30 nodes from which actin filaments are nucleated and captured by myosin-II in neighboring nodes. The force produced by myosin motors pulls the nodes together to form a compact contractile ring. Live microscopy of cells expressing Cdc12p fluorescent fusion proteins shows for the first time that Cdc12p localizes to a broad band of 30–50 dynamic nodes, where actin filaments are nucleated in random directions. The proposed progenitor spot, essential for the spot/leading cable model, usually disappears without nucleating actin filaments. α-Actinin ain1 deletion cells form a normal contractile ring through nodes in the absence of the spot. Myosin motor activity is required to condense the nodes into a contractile ring, based on slower or absent node condensation in myo2-E1 and UCS rng3-65 mutants. Taken together, these data provide strong support for the SCPR model of contractile-ring formation in cytokinesis.     

Deducing Underlying Mechanisms from Protein Recruitment Data

By using fluorescent labelling techniques, the distribution and dynamics of proteins can be measured within living cells, allowing to study in vivo the response of cells to a triggering event, such as DNA damage. In order to evaluate the reaction rate constants and to identify the proteins and reactions that are essential for the investigated process, mechanistic models are used, which often contain many proteins and associated parameters and are therefore underdetermined by the data. In order to establish criteria for assessing the significance of a model, we present here a systematic investigation of the information that can be reliably deduced from protein recruitment data, assuming that the complete set of reactions that affect the data of the considered protein species is not known. To this purpose, we study in detail models where one or two proteins that influence each other are recruited to a substrate. We show that in many cases the kind of interaction between the proteins can be deduced by analyzing the shape of the recruitment curves of one protein. Furthermore, we discuss in general in which cases it is possible to discriminate between different models and in which cases it is impossible based on the data. Finally, we argue that if different models fit experimental data equally well, conducting experiments with different protein concentrations would allow discrimination between the alternative models in many cases.     

The evolution of connectivity in metabolic networks

Processes in living cells are the result of interactions between biochemical compounds in highly complex biochemical networks. It is a major challenge in biology to understand causes and consequences of the specific design of these networks. A characteristic design feature of metabolic networks is the presence of hub metabolites such as ATP or NADH that are involved in a high number of reactions. To study the emergence of hub metabolites, we implemented computer simulations of a widely accepted scenario for the evolution of metabolic networks. Our simulations indicate that metabolic networks with a large number of highly specialized enzymes may evolve from a few multifunctional enzymes. During this process, enzymes duplicate and specialize, leading to a loss of biochemical reactions and intermediary metabolites. Complex features of metabolic networks such as the presence of hubs may result from selection of growth rate if essential biochemical mechanisms are considered. Specifically, our simulations indicate that group transfer reactions are essential for the emergence of hubs.     

Why do divalent metal ions either promote or inhibit enzymatic reactions? The case of BamHI restriction endonuclease from combined quantum-classical simulations

Divalent metal ions are essential to many enzymatic reactions involving nucleic acids, but their critical and specific role still needs to be uncovered. Restriction endonucleases are a prominent group of such metal-requiring enzymes. Large scale accurate simulations of Mg- and Ca-BamHI elucidate the mechanism of the catalytic reaction leading to DNA cleavage and show that it involves the concerted action of two metal ions and water molecules. It is also established that what is decisive for the dramatically different behavior of magnesium (a cocatalyst) and calcium (an inhibitor) are kinetic factors and not the properties of the prereactive states of the enzymes. A new perspective is opened for the understanding of the functional role of metal ions in biological processes.     

Sarcomeric pattern formation by actin cluster coalescence

Contractile function of striated muscle cells depends crucially on the almost crystalline order of actin and myosin filaments in myofibrils, but the physical mechanisms that lead to myofibril assembly remains ill-defined. Passive diffusive sorting of actin filaments into sarcomeric order is kinetically impossible, suggesting a pivotal role of active processes in sarcomeric pattern formation. Using a one-dimensional computational model of an initially unstriated actin bundle, we show that actin filament treadmilling in the presence of processive plus-end crosslinking provides a simple and robust mechanism for the polarity sorting of actin filaments as well as for the correct localization of myosin filaments. We propose that the coalescence of crosslinked actin clusters could be key for sarcomeric pattern formation. In our simulations, sarcomere spacing is set by filament length prompting tight length control already at early stages of pattern formation. The proposed mechanism could be generic and apply both to premyofibrils and nascent myofibrils in developing muscle cells as well as possibly to striated stress-fibers in non-muscle cells.     

Local motion analysis reveals impact of the dynamic cytoskeleton on intracellular subdiffusion

Intracellular transport is a complex interplay of ballistic transport along filaments and of diffusive motion, reliably delivering material and allowing for cell differentiation, migration, and proliferation. The diffusive regime, including subdiffusive, Brownian, and superdiffusive motion, is of particular interest for inferring information about the dynamics of the cytoskeleton morphology during intracellular transport. The influence of dynamic cytoskeletal states on intracellular transport are investigated in Dictyostelium discoideum cells by single particle tracking of fluorescent nanoparticles, to relate quantitative motion parameters and intracellular processes before and after cytoskeletal disruption. A local mean-square displacement (MSD) analysis separates ballistic motion phases, which we exclude here, from diffusive nanoparticle motion. In this study, we focus on intracellular subdiffusion and elucidate lag-time dependence, with particular focus on the impact of cytoskeleton compartments like microtubules and actin filaments. This method proves useful for binary motion state distributions. Experimental results are compared to simulations of a data-driven Langevin model with finite velocity correlations that captures essential statistical features of the local MSD algorithm. Specifically, the values of the mean MSD exponent and effective diffusion coefficients can be traced back to negative correlations of the motion's increments. We clearly identify both microtubules and actin filaments as the cause for intracellular subdiffusion and show that actin-microtubule cross talk exerts viscosifying effects at timescales larger than 0.2 s. Our findings might give insights into material transport and information exchange in living cells, which might facilitate gaining control over cell functions.     

EB-family proteins: Functions and microtubule interaction mechanisms

Microtubules are polymers of tubulin protein, one of the key components of cytoskeleton. They are polar filaments whose plus-ends usually oriented toward the cell periphery are more dynamic than their minus-ends, which face the center of the cell. In cells, microtubules are organized into a network that is being constantly rebuilt and renovated due to stochastic switching of its individual filaments from growth to shrinkage and back. Because of these dynamics and their mechanical properties, microtubules take part in various essential processes, from intracellular transport to search and capture of chromosomes during mitosis. Microtubule dynamics are regulated by many proteins that are located on the plus-ends of these filaments. One of the most important and abundant groups of plus-end-interacting proteins are EB-family proteins, which autonomously recognize structures of the microtubule growing plus-ends, modulate their dynamics, and recruit multiple partner proteins with diverse functions onto the microtubule plus-ends. In this review, we summarize the published data about the properties and functions of EB-proteins, focusing on analysis of their mechanism of interaction with the microtubule growing ends.     

Models of the Collective Behavior of Proteins in Cells: Tubulin, Actin and Motor Proteins

One of the most important issues of molecular biophysics is the complex and multifunctional behavior of the cell's cytoskeleton. Interiors of living cells are structurally organized by the cytoskeleton networks of filamentous protein polymers: microtubules, actin and intermediate filaments with motor proteins providing force and directionality needed for transport processes. Microtubules (MT's) take active part in material transport within the cell, constitute the most rigid elements of the cell and hence found many uses in cell motility (e.g. flagella andcilia). At present there is, however, no quantitatively predictable explanation of how these important phenomena are orchestrated at a molecular level. Moreover, microtubules have been demonstrated to self-organize leading to pattern formation. We discuss here several models which attempt to shed light on the assembly of microtubules and their interactions with motor proteins. Subsequently, an overview of actin filaments and their properties isgiven with particular emphasis on actin assembly processes. The lengths of actin filaments have been reported that were formed by spontaneous polymerization of highly purified actin monomers after labeling with rhodamine-phalloidin. The length distributions are exponential with a mean of about 7 μm. This length is independent of the initial concentration of actin monomer, an observation inconsistent with a simple nucleation-elongation mechanism. However, with the addition of physically reasonable rates of filament annealing and fragmenting, a nucleation-elongation mechanism can reproduce the observed average length of filaments in two types of experiments: (1) filaments formed from a wide range of highly purified actin monomer concentrations, and (2) filaments formed from 24 mM actin over a range of CapZ concentrations. In the final part of the paper we briefly review the stochastic models used to describe the motion of motor proteins on protein filaments. The vast majority of these models are based on ratchet potentials with the presence of thermal noise and forcing due to ATP binding and a subsequent hydrolysis. Many outstanding questions remain to be quantitatively addressed on a molecular level in order to explain the structure-to-function relationship for the key elements of the cytoskeleton discussed in this review. This revised version was published online in July 2006 with corrections to the Cover Date.     

Exploring the Dynamics of Cell Processes through Simulations of Fluorescence Microscopy Experiments

Fluorescence correlation spectroscopy (FCS) methods are powerful tools for unveiling the dynamical organization of cells. For simple cases, such as molecules passively moving in a homogeneous media, FCS analysis yields analytical functions that can be fitted to the experimental data to recover the phenomenological rate parameters. Unfortunately, many dynamical processes in cells do not follow these simple models, and in many instances it is not possible to obtain an analytical function through a theoretical analysis of a more complex model. In such cases, experimental analysis can be combined with Monte Carlo simulations to aid in interpretation of the data. In response to this need, we developed a method called FERNET (Fluorescence Emission Recipes and Numerical routines Toolkit) based on Monte Carlo simulations and the MCell-Blender platform, which was designed to treat the reaction-diffusion problem under realistic scenarios. This method enables us to set complex geometries of the simulation space, distribute molecules among different compartments, and define interspecies reactions with selected kinetic constants, diffusion coefficients, and species brightness. We apply this method to simulate single- and multiple-point FCS, photon-counting histogram analysis, raster image correlation spectroscopy, and two-color fluorescence cross-correlation spectroscopy. We believe that this new program could be very useful for predicting and understanding the output of fluorescence microscopy experiments.     

Dynamic movement of actin-like proteins within bacterial cells

Actin proteins are present in pro- and eukaryotes, and have been shown to perform motor-like functions in eukaryotic cells in a variety of processes. Bacterial actin homologues are essential for cell viability and have been implicated in the formation of rod cell shape, as well as in segregation of plasmids and whole chromosomes. We have generated functional green fluorescent protein fusions of all three Bacillus subtilis actin-like proteins (MreB, Mbl and MreBH), and show that all three proteins form helical filaments underneath the cell membrane, the pattern of which is distinct for each protein. Time-lapse microscopy showed that the filaments are highly dynamic structures. A number of separate filaments of MreB and Mbl continuously move through the cell along helical tracks underneath the cell membrane. The speed of extension of the growing end of filaments is within the range of known actin polymerization (0.1 microm/s), generating a potential poleward or centreward pushing velocity at 0.24 microm/min for MreB or Mbl, respectively. During nutritional downshift and a block in topoisomerase IV activity, the filaments rapidly disintegrated, showing that movement occurs only in growing cells. Contrary to Mbl and MreBH filaments, MreB filaments were generally absent in cells lacking DNA, providing a further distinction between the three orthologues.