Simulating the kinesin walk : towards a definitive theory

Dementia is a set of incurable, fatal diseases characterised by irreversible degeneration of the brain. One theory of its cause is the failure of intracellular transport in the axons of the neurons that compose the brain. Kinesin is a key motor transporting vital cargo along the axon. We know that this motor is a bipedal engine stepping forward along a polypeptide track but it is too small and fast for this motion to be observed using current experimental techniques. The stepping detail is therefore open to debate. This study firstly addresses the question of how kinesin steps and secondly pilots a possible method for investigating transport disruption in silico. To investigate the detail of stepping, a program has been designed and built to simulate kinesin traversing its track along a section of axon. The motor is modelled as simple, interacting agents obeying rules abstracted from known chemical and binding properties of its components. The agent-based method has proven useful and efficient on the small scale and has potential for simulating the larger and more complex system of axonal transport. This would enable investigation of transport failure in the context of finding a cure for dementia. A new model of kinesin stepping has been formulated as a consequence of performing virtual experiments using the simulation. Analysis of in vivo and in vitro experimental studies shows that the model accounts for a wide range of published results, explaining many findings. New experiments are suggested to test the model based on its falsifiable predictions. The principal conclusion of this study is that kinesin stepping is rectified Brownian motion

Multivalent Random Walkers:A computational model of superdiffusive transport at the nanoscale

We present a stochastic model and numerical simulation framework for a synthetic nanoscale walker that can be used to transport materials and information at superdiffusive rates in artificial molecular systems. Our \emph{multivalent random walker} model describes the motion of a walker with a rigid, inert body and flexible, enzymatic legs. A leg can bind to and irreversibly modify surface-bound chemical substrate sites arranged as nanoscale tracks. As the legs attach to, modify, and detach from the sites, the walker moves along these tracks. Walkers are symmetrical and the tracks they walk on are unoriented, yet we show that under appropriate kinetic constraints the walkers can transform the chemical free energy in the surface sites into directional motion, and can do ordered work against an external load force. This shows that multivalent random walkers are a new type of molecular motor, useful for directional transport in nanoscale systems. We model the motion of multivalent random walkers as a continuous-time discrete-state Markov process. States in the process correspond to the chemical state of the legs and surface sites, and transitions represent discrete chemical changes of legs binding to, unbinding from, and modifying the surface sites. The Markov property holds because we let the mechanical motion of the body and unattached legs come to equilibrium in between successive chemical steps, thus the transitions depend only on the current chemical state of the surface sites and attached legs. This coarse-grained model of walker motion allows us to use both equilibrium and non-equilibrium Markov chain Monte Carlo simulation techniques. The Metropolis-Hastings algorithm approximates the motion of a walker\u27s body and legs at a mechanical equilibrium, while the kinetic Monte Carlo algorithm simulates the transient chemical dynamics of the walker stepping across the surface sites. Using these numerical techniques, we find that MVRWs move superdiffusively in the direction of unmodified substrate sites when there is a residence time bias between modified and unmodified sites. This superdiffusive motion persists when opposed by external load forces, showing that multivalent random walkers are \emph{molecular motors} that can transform chemical free energy into ordered mechanical work. To produce these results we devised a distributed object-oriented framework for parallel simulation and analysis of the MVRW model. We use an object-relational mapping to persistently maintain all simulation-related objects as tuples in a relational database. We present a new object-relational mapping technique called the \emph{natural entity framework} which disambiguates the semantics of object identity and uniqueness in the relational and object-oriented programming models. Using the natural entity framework we are able to guarantee the uniqueness of mappings between data stored as objects in the relational database and external data stored in non-transactionally-secured HDF5 data files

Stochastic spatial modelling of DNA methylation patterns and moment-based parameter estimation

In the first part of this thesis, we introduce and analyze spatial stochastic models for DNA methylation, an epigenetic mark with an important role in development. The underlying mechanisms controlling methylation are only partly understood. Several mechanistic models of enzyme activities responsible for methylation have been proposed. Here, we extend existing hidden Markov models (HMMs) for DNA methylation by describing the occurrence of spatial methylation patterns with stochastic automata networks. We perform numerical analysis of the HMMs applied to (non-)hairpin bisulfite sequencing KO data and accurately predict the wild-type data from these results. We find evidence that the activities of Dnmt3a/b responsible for de novo methylation depend on the left but not on the right CpG neighbors. The second part focuses on parameter estimation in chemical reaction networks (CRNs). We propose a generalized method of moments (GMM) approach for inferring the parameters of CRNs based on a sophisticated matching of the statistical moments of the stochastic model and the sample moments of population snapshot data. The proposed parameter estimation method exploits recently developed moment-based approximations and provides estimators with desirable statistical properties when many samples are available. The GMM provides accurate and fast estimations of unknown parameters of CRNs. The accuracy increases and the variance decreases when higher-order moments are considered.Im ersten Teil der Arbeit führen wir eine Analyse für spatielle stochastische Modelle der DNA Methylierung, ein wichtiger epigenetischer Marker in der Entwicklung, durch. Die zugrunde liegenden Mechanismen der Methylierung werden noch nicht vollständig verstanden. Mechanistische Modelle beschreiben die Aktivität der Methylierungsenzyme. Wir erweitern bestehende Hidden Markov Models (HMMs) zur DNA Methylierung durch eine Stochastic Automata Networks Beschreibung von spatiellen Methylierungsmustern. Wir führen eine numerische Analyse der HMMs auf bisulfit-sequenzierten KO Datens¨atzen aus und nutzen die Resultate, um die Wildtyp-Daten erfolgreich vorherzusagen. Unsere Ergebnisse deuten an, dass die Aktivitäten von Dnmt3a/b, die überwiegend für die de novo Methylierung verantwortlich sind, nur vom Methylierungsstatus des linken, nicht aber vom rechten CpG Nachbarn abhängen. Der zweite Teil befasst sich mit Parameterschätzung in chemischen Reaktionsnetzwerken (CRNs). Wir führen eine Verallgemeinerte Momentenmethode (GMM) ein, die die statistischen Momente des stochastischen Modells an die Momente von Stichproben geschickt anpasst. Die GMM nutzt hier kürzlich entwickelte, momentenbasierte Näherungen, liefert Schätzer mit wünschenswerten statistischen Eigenschaften, wenn genügend Stichproben verfügbar sind, mit schnellen und genauen Schätzungen der unbekannten Parameter in CRNs. Momente höherer Ordnung steigern die Genauigkeit des Schätzers, während die Varianz sinkt

Simulating the kinesin walk : towards a definitive theory

Dementia is a set of incurable, fatal diseases characterised by irreversible degeneration of the brain. One theory of its cause is the failure of intracellular transport in the axons of the neurons that compose the brain. Kinesin is a key motor transporting vital cargo along the axon. We know that this motor is a bipedal engine stepping forward along a polypeptide track but it is too small and fast for this motion to be observed using current experimental techniques. The stepping detail is therefore open to debate. This study firstly addresses the question of how kinesin steps and secondly pilots a possible method for investigating transport disruption in silico. To investigate the detail of stepping, a program has been designed and built to simulate kinesin traversing its track along a section of axon. The motor is modelled as simple, interacting agents obeying rules abstracted from known chemical and binding properties of its components. The agent-based method has proven useful and efficient on the small scale and has potential for simulating the larger and more complex system of axonal transport. This would enable investigation of transport failure in the context of finding a cure for dementia. A new model of kinesin stepping has been formulated as a consequence of performing virtual experiments using the simulation. Analysis of in vivo and in vitro experimental studies shows that the model accounts for a wide range of published results, explaining many findings. New experiments are suggested to test the model based on its falsifiable predictions. The principal conclusion of this study is that kinesin stepping is rectified Brownian motion.EThOS - Electronic Theses Online ServiceEngineering and Physical Sciences Research Council (EPSRC)GBUnited Kingdo

Using the Features of Brownian Motion to Characterize the Nuclear Pore Complex, Molecular Robots, and Antimony-Doped Tin Oxide.

Brownian motion is the apparently random motion of small particles in a solution that results from the bombardment of molecules within the solution. The theoretical understanding of this motion was developed by Einstein in the early 1900s. Since then, features of Brownian motion, such as the fact that Brownian motion can be modeled using a random walk, or the fact that ensemble mean squared displacement (MSD) can be used to determine a diffusion coefficient and type of diffusive behavior, have been utilized to characterize a vast array of systems that are both naturally occurring and synthetic. In this thesis, I characterize three different types of systems using features of Brownian motion: naturally occurring nuclear pore complexes, synthetic molecular robots that are based on naturally occurring bipedal molecular walkers, and synthetic conductive nanoporous antimony-doped tin oxide (ATO). For the nuclear pore complex, the diffusion of particles through each region of the complex was modeled using a random walk in order to help determine the relative diffusion coefficients of the three regions. For the molecular robots, the movement of the robots was modeled using a more advanced random-walk simulation that utilizes the Gillespie algorithm; the movement of the robots was evaluated based on the MSDs, and the results were used to characterize the directional bias in the walking mechanism of the robots. For the ATO, fluorescent particles were monitored as they underwent Brownian motion while diffusing through the nanopores; MSDs were used to determine that these particles are embedded in the nanopores and that the diffusion coefficient depended in an unexpected way on the potential applied across the material.PhDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/99910/1/michelot_1.pd

Nonequilibrium statistical physics applied to biophysical cellular processes

The methods of statistical physics are increasingly being employed in a range of interdisciplinary areas. In particular, aspects of complex biological processes have been elucidated by bringing the problems down to the level of simple interactions studied in a statistical sense. In nonequilibrium statistical physics, a one dimensional lattice model known as the totally asymmetric simple exclusion processes (TASEP) has become prominent as a tool for modelling various cellular transport processes. Indeed the context in which the TASEP was first introduced (MacDonald et. al., 1968) was to model ribosome motion along mRNA during protein synthesis. In this work I study a variation of the TASEP in which particles hop along a one dimensional lattice which extends as they reach the end. We introduce this model to describe the unique growth dynamics of filamentous fungi, whereby a narrow fungal filament extends purely from its tip region while being supplied with growth materials from behind the tip. We find that the steady state behaviour of our model reflects that of the TASEP, however there is an additional phase where a dynamic shock is present in the system. I show through Monte Carlo simulation and theoretical analysis that the qualitative behaviour of this model can be predicted with a simple mean-field approximation, while the details of the phase behaviour are accurate only in a refined approximation which takes into account some correlations. I also discuss a further refined mean-field approximation and give a heuristic argument for our results. Next I present an extension of the model which allows the particles to interact with a second lattice, on which they diffuse in either direction. A first order meanfield continuum approximation suggests that the steady states of this system will exhibit some novel behaviour. Through Monte Carlo simulation I discuss the qualitative changes that arise due to the on-off dynamics. Finally I study a model for a second biological phenomenon: the length fluctuations of microtubules. The model describes stochastic polymerisation events at the tip of a microtubule. Using a mean-field theory, we find a transition between regimes where the microtubule grows on average, and where the length remains finite. For low rates of polymerisation and depolymerisation, the transition is in good agreement with Monte Carlo simulation

A stochastic automaton model for simulating kinesin processivity

Motivation: Cellular interactions of kinesin-1, an adenosine triphosphate (ATP)-driven motor protein capable of undergoing multiple steps on a microtubule (MT), affect its mechanical processivity, the number of steps taken per encounter with MT. Even though the processivity of kinesin has been widely studied, a detailed study of the factors that affect the stepping of the motor along MT is still lacking.Results: We model the cellular interactions of kinesin as a probabilistic timed automaton and use the model to simulate the mechanical processivity of the motor. Theoretical analysis suggests: (i) backward stepping tends to be powered by ATP hydrolysis, rather than ATP synthesis, (ii) backward stepping powered by ATP synthesis is more likely to happen with limiting ATP concentration ([ATP]) at high loads and (iii) with increasing load the frequency of backward stepping powered by ATP hydrolysis at high [ATP] is greater than that powered by ATP synthesis at limiting [ATP]. Together, the higher frequency of backward stepping powered by ATP hydrolysis than by ATP synthesis is found to be a reason for the more dramatic falling of kinesin processivity with rising load at high [ATP] compared with that at low [ATP]. Simulation results further show that the processivity of kinesin can be determined by the number of ATP hydrolysis and synthesis kinetic cycles taken by the motor before becoming inactive. It is also found that the duration of a backward stepping cycle at high loads is more likely to be less than that of a forward stepping cycle