ML-Space: hybrid spatial Gillespie and Brownian motion simulation at multiple levels, and a rule-based description language

Computer simulations of biological cells as well-stirred systems are well established but neglect the spatial distribution of key actors. In this thesis, a simulation algorithm "ML-Space" for spatial models with dynamic hierarchies is presented. It combines stochastic spatial algorithms in discretized space with individual particles moving in continuous space that have spatial extensions and can contain other particles. For formal descriptions of the systems to be simulated spatially, ML-Space provides a rule-based specification language.Computersimulationen mikrobiologischer Prozesse, bei denen eine homogene Verteilung der Akteure einer Zelle angenommen wird, sind gut etabliert. In dieser Arbeit wird ein räumlicher Simulationsalgorithmus "ML-Space" für Mehrebenenmodelle vorgestellt, der auch dynamische Hierarchien abdeckt. Er vereint stochastische räumliche Algorithmen in diskretisiertem Raum mit individuellen Partikeln mit kontinuierlichen Koordinaten, die andere Partikel enthalten können. Zur formalen Beschreibung der räumlich zu simulierenden Systeme bietet ML-Space eine regelbasierte Modellierungssprache

Quasi-oscillatory motion of single cells on micropatterns

Zellmigration spielt eine grundlegende Rolle bei Prozessen wie Embryogenese, der Immunantwort, Wundheilung und bei der Metastasierung von Krebs. Daher ist der Mechanismus der Zellmigration, insbesondere die Dynamik des Zytoskeletts, Aktinpolymerisierung und Reaktionsdiffusionsprozesse, von großem Interesse für die Lebenswissenschaften. Zellen sind hochkomplexe dynamische Systeme, die ihren Zustand ständig verändern, wodurch sich bestimmte Morphologien und Migrationsmodi ausprägen. Die resultierenden Migrationsmuster werden durch externe Faktoren beeinflusst, die unter klassischen Kulturbedingungen nicht kontrolliert sind. Eine zentrale Herausforderung bei der Untersuchung der Zellmigration ist daher die Entwicklung spezifischer Methoden, um die Wirkung einzelner Parameter, die das Zellverhalten regulieren, untersuchen zu können. Ein möglicher Weg, die Komplexität der Umgebung zu reduzieren, besteht darin, Mikrostrukturierungstechniken zu verwenden um Zellen auf eine definierte Mikroumgebung zu beschränken. Mit solchen Strukturen kann der Freiheitsgrad der Zellbewegung reduziert werden, was es ermöglicht gezielt spezifische Eigenschaften der Zellmigration zu studieren. Darüber hinaus kann man mit Mikrostrukturierungstechnologie Felder von einer großen Anzahl identischer funktioneller Oberflächenstrukturen herstellen und so Hochdurchsatzmessungen durchführen. Im ersten Teil dieser Arbeit werden Studien zu einem neu entdeckten quasi-oszillatorischen Migrationsmodus von Einzelzellen auf kreisförmigen Mikrostrukturen vorgestellt. Wir beobachten persistente polarisierte Zellen und gerichtete Pol-zu-Pol-Bewegungen innerhalb der Strukturen. Die Zellen depolarisieren auf einer Seite der Mikrostuktur, gefolgt von einer verzögerten Repolarisierung in entgegengesetzter Richtung. Weiter wird gezeigt, dass mehrere Zelllinien (z.B. MDCK-, Huh7-, MDA-MB-231-Zellen) diesen oszillierenden Migrationsmodus auf kreis-, ellipsen- und streifenförmigen Mikrostrukturen zeigen. Im Vergleich zu kreisförmigen und elliptischen Strukturen ist das Auftreten von Oszillationen auf Streifen gehäuft feststellbar. Streifen bieten eine ideale und einfache Plattform um neue Migrationsmuster von Zellen und um den molekularen Mechanismus, der der Dynamik des Zytoskeletts zugrunde liegt, zu studieren. Im zweiten Teil dieser Arbeit analysieren wir das Zellverhalten mit Hilfe der räumlichen Geschwindigkeitsverteilung und dem Frequenzspektrum der Bewegung. Die experimentellen Daten werden mit einem zellulären Potts-Modell verglichen, das ein minimales mechanistisches Modell des dynamischen Zytoskeletts enthält. Insbesondere betrachten wir die Dauer des Umkehrprozesses als Maß für die Dauer spontaner Repolarisierung von Zellen und für die Zeit, die das führende Lamellipodium benötigt um sich am Ende des Streifens zurück zu bilden. Mit LifeAct-GFP transfizierten Zellen und Streifen mit unterschiedlich geformten Enden lassen sich Veränderungen im Verhalten an den Enden beobachten. Dies zeigt, dass die Form der Streifenenden und damit die lokale Krümmung der Zellfront Einfluss auf die Aktinpolymerisation hat. Diese Arbeit zeigt, dass Streifen für die quantitative Untersuchung von Zellmigration nützlich sind und dass erweiterte zelluläre Potts-Modelle mit einfachen mechanistischen Regeln die unterschiedlichen Migrationsphänotypen von Zellen in einer beengten Umgebung erfassen können.Cell migration plays a fundamental role in processes such as embryogenesis, immune response, wound healing and cancer metastasis. Hence the mechanisms of cell migration in particularly cytoskeleton dynamics, actin assembly, and reaction diffusion processes have received great interest in life science. Cells are highly complex dynamic systems that constantly alter their states, which leads to emerging morphologies and migratory modes. The resulting migration patterns are influenced by external cues, which are uncontrolled under classic culture conditions. Thus, a key challenge of studying cell migration is the design of specific methods to disentangle the effect of separate parameter regulating cellular behavior. A possible way to reduce the complexity of the environment is to confine cells to a defined external microenvironment by applying micropatterning techniques. Using these geometries, the degree of freedom of the cell motion can be reduced, which allows selectively studying specific characteristics of cell migration. Moreover, micropatterning technology can realize large-scale arrays of functional surface coatings, so that high throughput measurements can be obtained. In the first part of this work, studies on a newly discovered quasi-oscillatory migration mode of single cells on isotropic circular-micropatterns are presented. We observe persistent polarized cell shapes and directed pole-to-pole motion within the patterns. Cells depolarize at one side of the given micropattern, followed by delayed repolarization progressing towards the opposite side. We then show that several cell lines (e.g. MDCK, Huh7, MDA-MB-231 cells) exhibit the oscillatory migration mode on circular-shaped, ellipse-shaped, and stripe-shaped micropatterns respectively. Compared to circular and ellipse patterns, stripe-shaped microlanes enhance the occurrence of oscillations. Microlanes provide an ideal and simple platform for the exploration of emerging migration patterns of cells and the molecular mechanisms underlying cell cytoskeleton dynamics. In the second part of this work, we analyze cell motility by the spatial velocity distribution and frequency spectrum. The experimental data are compared to a Cellular Potts model that includes a minimal mechanistic model of the dynamical cytoskeleton. In particular, we evaluate the “reversal time” as a measure for spontaneous repolarization of cells as well as the time required to quench the leading lamellipodium at the microlane ends. Using LifeAct-GFP transfected cells and microlanes with differently shaped geometric ends, we found distinct scenarios at the leading edge showing that the tip geometry and hence the local deformation of the leading edge has an effect on actin polymerization. This work shows that microlanes are useful for quantitative assessment of cell migration and that extended Cellular Potts models with simple mechanistic rules capture the distinct migration phenotypes in confinement

Kinetics of fragmentation and dissociation of two-strand protein filaments: Coarse-grained simulations and experiments.

While a significant body of investigations have been focused on the process of protein self-assembly, much less is understood about the reverse process of a filament breaking due to thermal motion into smaller fragments, or depolymerization of subunits from the filament ends. Indirect evidence for actin and amyloid filament fragmentation has been reported, although the phenomenon has never been directly observed either experimentally or in simulations. Here we report the direct observation of filament depolymerization and breakup in a minimal, calibrated model of coarse-grained molecular simulation. We quantify the orders of magnitude by which the depolymerization rate from the filament ends koff is larger than fragmentation rate k- and establish the law koff/k- = exp[(ε‖ - ε⊥)/kBT] = exp[0.5ε/kBT], which accounts for the topology and energy of bonds holding the filament together. This mechanism and the order-of-magnitude predictions are well supported by direct experimental measurements of depolymerization of insulin amyloid filaments.This research was supported by the ERC, EPSRC, BBSRC, and the Newman Foundation.This is the author accepted manuscript. The final version is available from the American Institute of Physics via http://dx.doi.org/10.1063/1.496236

Sarcomere Lattice Geometry Influences Cooperative Myosin Binding in Muscle

In muscle, force emerges from myosin binding with actin (forming a cross-bridge). This actomyosin binding depends upon myofilament geometry, kinetics of thin-filament Ca2+ activation, and kinetics of cross-bridge cycling. Binding occurs within a compliant network of protein filaments where there is mechanical coupling between myosins along the thick-filament backbone and between actin monomers along the thin filament. Such mechanical coupling precludes using ordinary differential equation models when examining the effects of lattice geometry, kinetics, or compliance on force production. This study uses two stochastically driven, spatially explicit models to predict levels of cross-bridge binding, force, thin-filament Ca2+ activation, and ATP utilization. One model incorporates the 2-to-1 ratio of thin to thick filaments of vertebrate striated muscle (multi-filament model), while the other comprises only one thick and one thin filament (two-filament model). Simulations comparing these models show that the multi-filament predictions of force, fractional cross-bridge binding, and cross-bridge turnover are more consistent with published experimental values. Furthermore, the values predicted by the multi-filament model are greater than those values predicted by the two-filament model. These increases are larger than the relative increase of potential inter-filament interactions in the multi-filament model versus the two-filament model. This amplification of coordinated cross-bridge binding and cycling indicates a mechanism of cooperativity that depends on sarcomere lattice geometry, specifically the ratio and arrangement of myofilaments

Space dependent adhesion forces mediated by transient elastic linkages : new convergence and global existence results

In the first part of this work we show the convergence with respect to an asymptotic parameter {\epsilon} of a delayed heat equation. It represents a mathematical extension of works considered previously by the authors [Milisic et al. 2011, Milisic et al. 2016]. Namely, this is the first result involving delay operators approximating protein linkages coupled with a spatial elliptic second order operator. For the sake of simplicity we choose the Laplace operator, although more general results could be derived. The main arguments are (i) new energy estimates and (ii) a stability result extended from the previous work to this more involved context. They allow to prove convergence of the delay operator to a friction term together with the Laplace operator in the same asymptotic regime considered without the space dependence in [Milisic et al, 2011]. In a second part we extend fixed-point results for the fully non-linear model introduced in [Milisic et al, 2016] and prove global existence in time. This shows that the blow-up scenario observed previously does not occur. Since the latter result was interpreted as a rupture of adhesion forces, we discuss the possibility of bond breaking both from the analytic and numerical point of view

Cytoskeleton and Cell Motility

The present article is an invited contribution to the Encyclopedia of Complexity and System Science, Robert A. Meyers Ed., Springer New York (2009). It is a review of the biophysical mechanisms that underly cell motility. It mainly focuses on the eukaryotic cytoskeleton and cell-motility mechanisms. Bacterial motility as well as the composition of the prokaryotic cytoskeleton is only briefly mentioned. The article is organized as follows. In Section III, I first present an overview of the diversity of cellular motility mechanisms, which might at first glance be categorized into two different types of behaviors, namely "swimming" and "crawling". Intracellular transport, mitosis - or cell division - as well as other extensions of cell motility that rely on the same essential machinery are briefly sketched. In Section IV, I introduce the molecular machinery that underlies cell motility - the cytoskeleton - as well as its interactions with the external environment of the cell and its main regulatory pathways. Sections IV D to IV F are more detailed in their biochemical presentations; readers primarily interested in the theoretical modeling of cell motility might want to skip these sections in a first reading. I then describe the motility mechanisms that rely essentially on polymerization-depolymerization dynamics of cytoskeleton filaments in Section V, and the ones that rely essentially on the activity of motor proteins in Section VI. Finally, Section VII is devoted to the description of the integrated approaches that have been developed recently to try to understand the cooperative phenomena that underly self-organization of the cell cytoskeleton as a whole.Comment: 31 pages, 16 figures, 295 reference

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

Cells are strongly out-of-equilibrium systems driven by continuous energy supply. They carry out many vital functions requiring active transport of various ingredients and organelles, some being small, others being large. The cytoskeleton, composed of three types of filaments, determines the shape of the cell and plays a role in cell motion. It also serves as a road network for the so-called cytoskeletal motors. These molecules can attach to a cytoskeletal filament, perform directed motion, possibly carrying along some cargo, and then detach. It is a central issue to understand how intracellular transport driven by molecular motors is regulated, in particular because its breakdown is one of the signatures of some neuronal diseases like the Alzheimer. We give a survey of the current knowledge on microtubule based intracellular transport. We first review some biological facts obtained from experiments, and present some modeling attempts based on cellular automata. We start with background knowledge on the original and variants of the TASEP (Totally Asymmetric Simple Exclusion Process), before turning to more application oriented models. After addressing microtubule based transport in general, with a focus on in vitro experiments, and on cooperative effects in the transportation of large cargos by multiple motors, we concentrate on axonal transport, because of its relevance for neuronal diseases. It is a challenge to understand how this transport is organized, given that it takes place in a confined environment and that several types of motors moving in opposite directions are involved. We review several features that could contribute to the efficiency of this transport, including the role of motor-motor interactions and of the dynamics of the underlying microtubule network. Finally, we discuss some still open questions.Comment: 74 pages, 43 figure

Self-organized density patterns of molecular motors in arrays of cytoskeletal filaments

The stationary states of systems with many molecular motors are studied theoretically for uniaxial and centered (aster-like) arrangements of cytoskeletal filaments using Monte Carlo simulations and a two-state model. Mutual exclusion of motors from binding sites of the filaments is taken into account. For small overall motor concentration, the density profiles are exponential and algebraic in uniaxial and centered filament systems, respectively. For uniaxial systems, exclusion leads to the coexistence of regions of high and low densities of bound motors corresponding to motor traffic jams, which grow upon increasing the overall motor concentration. These jams are insensitive to the motor behavior at the end of the filament. In centered systems, traffic jams remain small and an increase in the motor concentration leads to a flattening of the profile, if the motors move inwards, and to the build-up of a concentration maximum in the center of the aster if motors move outwards. In addition to motors density patterns, we also determine the corresponding patterns of the motor current.Comment: 48 pages, 8 figure

Computational model combined with in vitro experiments to analyse mechanotransduction during mesenchymal stem cell adhesion.

The shape that stem cells reach at the end of adhesion process influences their differentiation. Rearrangement of cytoskeleton and modification of intracellular tension may activate mechanotransduction pathways controlling cell commitment. In the present study, the mechanical signals involved in cell adhesion were computed in in vitro stem cells of different shapes using a single cell model, the so-called Cytoskeleton Divided Medium (CDM) model. In the CDM model, the filamentous cytoskeleton and nucleoskeleton networks were represented as a mechanical system of multiple tensile and compressive interactions between the nodes of a divided medium. The results showed that intracellular tonus, focal adhesion forces as well as nuclear deformation increased with cell spreading. The cell model was also implemented to simulate the adhesion process of a cell that spreads on protein-coated substrate by emitting filopodia and creating new distant focal adhesion points. As a result, the cell model predicted cytoskeleton reorganisation and reinforcement during cell spreading. The present model quantitatively computed the evolution of certain elements of mechanotransduction and may be a powerful tool for understanding cell mechanobiology and designing biomaterials with specific surface properties to control cell adhesion and differentiation