Asymptotic Analysis of Microtubule-Based Transport by Multiple Identical Molecular Motors

We describe a system of stochastic differential equations (SDEs) which model the interaction between processive molecular motors, such as kinesin and dynein, and the biomolecular cargo they tow as part of microtubule-based intracellular transport. We show that the classical experimental environment fits within a parameter regime which is qualitatively distinct from conditions one expects to find in living cells. Through an asymptotic analysis of our system of SDEs, we develop a means for applying in vitro observations of the nonlinear response by motors to forces induced on the attached cargo to make analytical predictions for two parameter regimes that have thus far eluded direct experimental observation: 1) highly viscous in vivo transport and 2) dynamics when multiple identical motors are attached to the cargo and microtubule

Unraveling the intricacies of spatial organization of the ErbB receptors and downstream signaling pathways

Faced with the complexity of diseases such as cancer which has 1012 mutations, altering gene expression, and disrupting regulatory networks, there has been a paradigm shift in the biological sciences and what has emerged is a much more quantitative field of biology. Mathematical modeling can aid in biological discovery with the development of predictive models that provide future direction for experimentalist. In this work, I have contributed to the development of novel computational approaches which explore mechanisms of receptor aggregation and predict the effects of downstream signaling. The coupled spatial non-spatial simulation algorithm, CSNSA is a tool that I took part in developing, which implements a spatial kinetic Monte Carlo for capturing receptor interactions on the cell membrane with Gillespies stochastic simulation algorithm, SSA, for temporal cytosolic interactions. Using this framework we determine that receptor clustering significantly enhances downstream signaling. In the next study the goal was to understand mechanisms of clustering. Cytoskeletal interactions with mobile proteins are known to hinder diffusion. Using a Monte Carlo approach we simulate these interactions, determining at what cytoskeletal distribution and receptor concentration optimal clustering occurs and when it is inhibited. We investigate oligomerization induced trapping to determine mechanisms of clustering, and our results show that the cytoskeletal interactions lead to receptor clustering. After exploring the mechanisms of clustering we determine how receptor aggregation effects downstream signaling. We further proceed by implementing the adaptively coarse grained Monte Carlo, ACGMC to determine if \u27receptor-sharing\u27 occurs when receptors are clustered. In our proposed \u27receptor-sharing\u27 mechanism a cytosolic species binds with a receptor then disassociates and rebinds a neighboring receptor. We tested our hypothesis using a novel computational approach, the ACGMC, an algorithm which enables the spatial temporal evolution of the system in three dimensions by using a coarse graining approach. In this framework we are modeling EGFR reaction-diffusion events on the plasma membrane while capturing the spatial-temporal dynamics of proteins in the cytosol. From this framework we observe \u27receptor-sharing\u27 which may be an important mechanism in the regulation and overall efficiency of signal transduction. In summary, I have helped to develop predictive computational tools that take systems biology in a new direction.\u2

Collective Behaviour of Polar Active Matter in Two Dimensions

Self-organization is a common way of forming functional structures in biology. It involves biochemical signalling pathways, triggered by a host of external conditions, that alter the mechnical properties of the individual constituents. These changes then propagate up in scale and, via changes in the self-organization, alter the biological function. In this work, we investigate self-organization and pattern formation due to self-propulsion in biological systems. The aim is to understand and map the collective dynamics in terms of mechanical properties of single constituents. We study dense ensembles of self-propelled vesicles that act as models for motile cells and ensembles of self-propelled semiflexible filaments that mimic actin filaments and microtubules in motility assays. Both systems are made of polar and active objects that possess extended shapes with an associated flexibility. We explore the collective dynamics in both systems as a function of activity, flexibility, and interactions between objects. Epithelial tissue serves as barrier for tissues and organs. To achieve this function, epithelial cells are typically tightly-packed, spatially well-ordered, and non-motile. However, a set of conditions can turn epithelial cells motile. During vertebrate embryonic development, wound healing, and cancer metastasis, cells become motile to rearrange the tissue, heal the wound, or travel away from the primary tumor, respectively. In vitro experiments on motile cell monolayers furthermore revealed a jamming transition in which an initially motile, fluid-like tissue undergoes a dynamic arrest. We study such motility transitions of dense cell monolayers in a minimal model approach. We go beyond existing models by including finite extension and flexibility of cells. To this end, we develop a novel computational model of cells as active vesicles that incorporates cell motility, cell-cell adhesions, compressibility, and flexibility. Increasing motility strength and decreasing cell-cell adhesions, area compression modulus, and bending rigidity lead to fluidization of the monolayer. In between the jammed and completely fluid- like states, we identify an active turbulence regime where cell motion is dominated by the formation of vortices. We thus uncover deformability-driven motility transitions and predict an active turbulent state for motile cell monolayers. In a second part, we study the collective behaviour of self-propelled semiflexible filaments by introducing self-propulsion as a constant magnitude force acting tangentially along the bonds of each filament. The combination of polymer properties, excluded-volume interactions, and self-propulsion leads to distinct phases as a function of rigidity, activity, and aspect ratio of individual filaments. We identify a transition from a free-swimming phase to a frozen steady state wherein strongly propelled filaments form spirals at a regime of low rigidity and high aspect ratio. Filaments form clusters of various sizes depending on rigidity and activity. In particular, we observe that filaments form small and transient clusters at low rigidities while stiffer filaments organize into giant clusters. However, as activity increases further, the clustering of filaments displays a reentrant phase behaviour where giant clusters melt, due to the strong propulsion forces bending the filaments. Our results highlight the role of mechanical properties and the finite extent of the constituents on the collective motion patterns. Cells and filaments display different symmetry properties at high densities due to structural differences. Filaments show an effective nematic symmetry, which results in an active turbulence regime characterized by half-integer topological defects. Cells, with polar symmetry, exhibit an active turbulence phase dominated by vortices

Psr1p interacts with SUN/sad1p and EB1/mal3p to establish the bipolar spindle

Regular Abstracts - Sunday Poster Presentations: no. 382During mitosis, interpolar microtubules from two spindle pole bodies (SPBs) interdigitate to create an antiparallel microtubule array for accommodating numerous regulatory proteins. Among these proteins, the kinesin-5 cut7p/Eg5 is the key player responsible for sliding apart antiparallel microtubules and thus helps in establishing the bipolar spindle. At the onset of mitosis, two SPBs are adjacent to one another with most microtubules running nearly parallel toward the nuclear envelope, creating an unfavorable microtubule configuration for the kinesin-5 kinesins. Therefore, how the cell organizes the antiparallel microtubule array in the first place at mitotic onset remains enigmatic. Here, we show that a novel protein psrp1p localizes to the SPB and plays a key role in organizing the antiparallel microtubule array. The absence of psr1+ leads to a transient monopolar spindle and massive chromosome loss. Further functional characterization demonstrates that psr1p is recruited to the SPB through interaction with the conserved SUN protein sad1p and that psr1p physically interacts with the conserved microtubule plus tip protein mal3p/EB1. These results suggest a model that psr1p serves as a linking protein between sad1p/SUN and mal3p/EB1 to allow microtubule plus ends to be coupled to the SPBs for organization of an antiparallel microtubule array. Thus, we conclude that psr1p is involved in organizing the antiparallel microtubule array in the first place at mitosis onset by interaction with SUN/sad1p and EB1/mal3p, thereby establishing the bipolar spindle.postprin

Removal of antagonistic spindle forces can rescue metaphase spindle length and reduce chromosome segregation defects

Regular Abstracts - Tuesday Poster Presentations: no. 1925Metaphase describes a phase of mitosis where chromosomes are attached and oriented on the bipolar spindle for subsequent segregation at anaphase. In diverse cell types, the metaphase spindle is maintained at a relatively constant length. Metaphase spindle length is proposed to be regulated by a balance of pushing and pulling forces generated by distinct sets of spindle microtubules and their interactions with motors and microtubule-associated proteins (MAPs). Spindle length appears important for chromosome segregation fidelity, as cells with shorter or longer than normal metaphase spindles, generated through deletion or inhibition of individual mitotic motors or MAPs, showed chromosome segregation defects. To test the force balance model of spindle length control and its effect on chromosome segregation, we applied fast microfluidic temperature-control with live-cell imaging to monitor the effect of switching off different combinations of antagonistic forces in the fission yeast metaphase spindle. We show that spindle midzone proteins kinesin-5 cut7p and microtubule bundler ase1p contribute to outward pushing forces, and spindle kinetochore proteins kinesin-8 klp5/6p and dam1p contribute to inward pulling forces. Removing these proteins individually led to aberrant metaphase spindle length and chromosome segregation defects. Removing these proteins in antagonistic combination rescued the defective spindle length and, in some combinations, also partially rescued chromosome segregation defects. Our results stress the importance of proper chromosome-to-microtubule attachment over spindle length regulation for proper chromosome segregation.postprin