Intra-cellular transport by single-headed kinesin KIF1A: effects of single-motor mechano-chemistry and steric interactions

In eukaryotic cells, many motor proteins can move simultaneously on a single microtubule track. This leads to interesting collective phenomena like jamming. Recently we reported ({\it Phys. Rev. Lett. {\bf 95}, 118101 (2005)}) a lattice-gas model which describes traffic of unconventional (single-headed) kinesins KIF1A. Here we generalize this model, introducing a novel interaction parameter $c$, to account for an interesting mechano-chemical process which has not been considered in any earlier model. We have been able to extract all the parameters of the model, except $c$, from experimentally measured quantities. In contrast to earlier models of intra-cellular molecular motor traffic, our model assigns distinct ``chemical'' (or, conformational) states to each kinesin to account for the hydrolysis of ATP, the chemical fuel of the motor. Our model makes experimentally testable theoretical predictions. We determine the phase diagram of the model in planes spanned by experimentally controllable parameters, namely, the concentrations of kinesins and ATP. Furthermore, the phase-separated regime is studied in some detail using analytical methods and simulations to determine e.g. the position of shocks. Comparison of our theoretical predictions with experimental results is expected to elucidate the nature of the mechano-chemical process captured by the parameter $c$.Comment: 17 pages including 14 embedded EPS figures; accepted for publication in Physical Review

Dynamic heterogeneity as a strategy of stem cell self-renewal.

To maintain cycling adult tissue in homeostasis the balance between proliferation and differentiation of stem cells needs to be precisely regulated. To investigate how stem cells achieve perfect self-renewal, emphasis has been placed on models in which stem cells progress sequentially through a one-way proliferative hierarchy. However, investigations of tissue regeneration have revealed a surprising degree of flexibility, with cells normally committed to differentiation able to recover stem cell competence following injury. Here, we investigate whether the reversible transfer of cells between states poised for proliferation or differentiation may provide a viable mechanism for a heterogeneous stem cell population to maintain homeostasis even under normal physiological conditions. By addressing the clonal dynamics, we show that such models of "dynamic heterogeneity" may be equally capable of describing the results of recent lineage tracing assays involving epithelial tissues. Moreover, together with competition for limited niche access, such models may provide a mechanism to render tissue homeostasis robust. In particular, in 2D epithelial layers, we show that the mechanism of dynamic heterogeneity avoids some pathological dependencies that undermine models based on a hierarchical stem/progenitor organization.Engineering and Physical Sciences Research CouncilThis is the author accepted manuscript. It is currently under an indefinite embargo pending publication by the National Academy of Sciences

Stochastic modeling of active biological transport in inhomogeneous environments

This thesis considers systems of actively driven particles on biased tracks in inhomogeneous environments. One example is vehicular- and pedestrian traffic. The main focus of this work, however, is on modeling collective directed motion of molecular motors involved in protein production or the transport of cargo on intracellular filaments. Transport on inhomogeneous tracks exhibits a jamming transition that emerges if the particle current attains the transport capacity of a bottleneck, which marks the maximum current. Jamming can be observed in traffic, but also for molecular motors. An analytical scheme to predict the transport capacity and critical parameters of this transition is developed. The presented models apply to tracks with slow sites (defects). These can for example be induced by biomedical drugs. In the context of intracellular traffic, defects are presently discussed as a cause of several diseases, e.g. Alzheimer\u27s disease. Particular codons on mRNA can also slow down ribosomes. Furthermore, transport on (filament-) networks is investigated. It is shown that particle clusters emerge. In contrast to regular networks or diffusion limited (reversible) aggregation, inhomogeneous networks exhibit a scale-free distribution of cluster sizes. This result can help to distinguish microscopic dynamics and structures by analyzing macroscopic particle cluster patterns. Applied to clusters of membrane proteins that promote the internalization of toxins, an analysis of clusters might improve the understanding of toxic pathways.Diese Arbeit behandelt Systeme aktiv getriebener Teilchen auf gerichteten Pfaden in inhomogenen Umgebungen. Ein Beispiel ist Straßenverkehr. Hauptgesichtspunkt ist jedoch die Modellierung gerichteter kollektiver Bewegung von molekularen Motoren bei Proteinproduktion oder Transport auf intrazellulären Filamenten. Auf inhomogenen Bahnen können Staus auftreten, wenn die Transportkapazität eines Engpasses (Maximalwert des Stromes) erreicht wird. Staus können sowohl im Verkehr, als auch bei molekularen Motoren beobachtet werden. Es wird eine Analytische Methode zur Vorhersage von Transportkapazität und kritischen Parametern für Staubildung entwickelt. Das Model kann auf Systeme mit langsamen Stellen (Defekte) angewandt werden, die z.B. durch künstliche Wirkstoffe erzeugt werden. Es wird vermutet, dass Defekte in intrazellulärem Transport Auslöser von Krankheiten wie z.B. der Alzheimerkrankheit seien. Bestimmte Kodone können aus erdem Ribosomen auf mRNA bremsen. Zusätzlich wird Transport in (Filament-) Netzwerken untersucht. Es wird gezeigt, dass Teilchen-Cluster entstehen. Im Gegensatz zu regulären Netzen oder (reversibler) diffusionsbegrenzter Aggregation, weisen inhomogene Netze eine skalenfreie Grössenverteilung auf. Diese Ergebnisse können helfen, von makroskopischen Cluster-Mustern auf mikroskopische Strukturen und Dynamik zu schliessen. Im Hinblick auf Membranprotein-Cluster, die die Aufnahme von Toxinen fördern, kann eine Untersuchung der Cluster das Verständnis der Internalisierung von Toxinen verbessern

Totally asymmetric exclusion process with site-wise dynamic disorder

We propose an extension of the totally asymmetric simple exclusion process (TASEP) in which particles hopping along a lattice can be blocked by obstacles that dynamically attach/detach from lattice sites. The model can be thought as TASEP with site-wise dynamic disorder. We consider two versions of defect dynamics: (i) defects can bind to any site, irrespective of particle occupation, (ii) defects only bind to sites which are not occupied by particles (particle-obstacle exclusion). In case (i) there is a symmetric, parabolic-like relationship between the current and particle density, as in the standard TASEP. Case (ii) leads to a skewed relationship for slow defect dynamics. We also show that the presence of defects induces particle clustering, despite the translation invariance of the system. For open boundaries the same three phases as for the standard TASEP are observed, albeit the position of phase boundaries is affected by the presence of obstacles. We develop a simple mean-field theory that captures the model's quantitative behaviour for periodic and open boundary conditions and yields good estimates for the current-density relationship, mean cluster sizes and phase boundaries. Lastly, we discuss an application of the model to the biological process of gene transcription.Comment: submitted to J. Phys.

Disordered driven lattice gases with boundary reservoirs and Langmuir kinetics

The asymmetric simple exclusion process with additional Langmuir kinetics, i.e. attachment and detachment in the bulk, is a paradigmatic model for intracellular transport. Here we study this model in the presence of randomly distributed inhomogeneities ('defects'). Using Monte Carlo simulations, we find a multitude of coexisting high- and low-density domains. The results are generic for one-dimensional driven diffusive systems with short-range interactions and can be understood in terms of a local extremal principle for the current profile. This principle is used to determine current profiles and phase diagrams as well as statistical properties of ensembles of defect samples.Comment: submitted for publishin

Mixed population of competing TASEPs with a shared reservoir of particles

We introduce a mean-field theoretical framework to describe multiple totally asymmetric simple exclusion processes (TASEPs) with different lattice lengths, entry and exit rates, competing for a finite reservoir of particles. We present relations for the partitioning of particles between the reservoir and the lattices: these relations allow us to show that competition for particles can have non-trivial effects on the phase behavior of individual lattices. For a system with non-identical lattices, we find that when a subset of lattices undergoes a phase transition from low to high density, the entire set of lattice currents becomes independent of total particle number. We generalize our approach to systems with a continuous distribution of lattice parameters, for which we demonstrate that measurements of the current carried by a single lattice type can be used to extract the entire distribution of lattice parameters. Our approach applies to populations of TASEPs with any distribution of lattice parameters, and could easily be extended beyond the mean-field case.Comment: 12 pages, 8 figure

Phase diagram and edge effects in the ASEP with bottlenecks

We investigate the totally asymmetric simple exclusion process (TASEP) in the presence of a bottleneck, i.e. a sequence of consecutive defect sites with reduced hopping rate. The influence of such a bottleneck on the phase diagram is studied by computer simulations and a novel analytical approach. We find a clear dependence of the current and the properties of the phase diagram not only on the length of the bottleneck, but also on its position. For bottlenecks near the boundaries, this motivates the concept of effective boundary rates. Furthermore the inclusion of a second, smaller bottleneck far from the first one has no influence on the transport capacity. These results will form the basis of an effective description of the disordered TASEP and are relevant for the modelling of protein synthesis or intracellular transport systems where the motion of molecular motors is hindered by immobile blocking molecules.Comment: accepted by Physica

Single-Bottleneck Approximation for Driven Lattice Gases with Disorder and Open Boundary Conditions

We investigate the effects of disorder on driven lattice gases with open boundaries using the totally asymmetric simple exclusion process as a paradigmatic example. Disorder is realized by randomly distributed defect sites with reduced hopping rate. In contrast to equilibrium, even macroscopic quantities in disordered non-equilibrium systems depend sensitively on the defect sample. We study the current as function of the entry and exit rates and the realization of disorder and find that it is, in leading order, determined by the longest stretch of consecutive defect sites (single-bottleneck approximation, SBA). Using results from extreme value statistics the SBA allows to study ensembles with fixed defect density which gives accurate results, e.g. for the expectation value of the current. Corrections to SBA come from effective interactions of bottlenecks close to the longest one. Defects close to the boundaries can be described by effective boundary rates and lead to shifts of the phase transitions. Finally it is shown that the SBA also works for more complex models. As an example we discuss a model with internal states that has been proposed to describe transport of the kinesin KIF1A.Comment: submitted to J. Stat. Mec

Mutational pathway determines whether drug gradients accelerate evolution of drug-resistant cells

Drug gradients are believed to play an important role in the evolution of bacteria resistant to antibiotics and tumors resistant to anti-cancer drugs. We use a statistical physics model to study the evolution of a population of malignant cells exposed to drug gradients, where drug resistance emerges via a mutational pathway involving multiple mutations. We show that a non-uniform drug distribution has the potential to accelerate the emergence of resistance when the mutational pathway involves a long sequence of mutants with increasing resistance, but if the pathway is short or crosses a fitness valley, the evolution of resistance may actually be slowed down by drug gradients. These predictions can be verified experimentally, and may help to improve strategies for combatting the emergence of resistance.Comment: 6 pages, 3 figures, final version before acceptance to Phys. Rev. Letters. P.G and B.W contributed equally to this wor