Document Type



Doctor of Philosophy



First Adviser

Vavylonis, Dimitrios

Other advisers/committee members

Gunton, Jim; Hickman, A. Peet; Jagota, Anand; Ou-Yang, Daniel


In this thesis I study the diffusion and reaction of the Arp2/3 complex, capping protein, and actin protein in the cytoplasm of eukaryotic cells with computational modeling in order to study the turnover of protein within the lamellipodium. The Arp2/3 complex and capping protein are important regulators of the actin network in the lamellipodium. The Arp2/3 complex nucleates branches of new actin filaments off the sides of existing filaments, while capping protein is a protein that attaches to the end of existing actin filaments and stops them from polymerizing further at that end. My research consists of three separate projects. First, I study the kinetics of the Arp2/3 complex and capping protein through a reaction diffusion model that has been motivated from previous modeling work by Smith et al. which uses SiMS (Single Molecule Speckle microscopy) data from Naoki Watanabe (Kyoto University). In this work I utilize this model to run simulations of FRAP (Fluorescence Recovery After Photobleaching) which are then compared with experimental data from Lai et al. and Kapustina et al. Second, I developed a reaction diffusion model for actin that models turnover of actin in the lamellipodium which also utilizes SiMS data in order to compare to experimental photoactivation data from Eric Vitriol and James Zheng (Emory University). This model includes effects of knocking down Thymosin β4 on actin kinetics within the lamellipodium. Third, I developed a 3D whole cell model with particle diffusion. This model accounts for the effect of geometry of the cell on the kinetics of actin where our previous model and simulation mentioned above did not. It also accounts for kinetics and turnover of actin within the cell center while our previous models mentioned above only accounted for actin within the lamellipodium. In the first part, we study the distribution of capping protein (CP) and Arp2/3 protein complex that regulate actin polymerization in the lamellipodium through capping and nucleation of free barbed ends. We modeled the kinetics of capping protein and Arp2/3 complex in the lamellipodium using data from prior SiMS microscopy experiments. In these experiments, slowly-diffusing proteins appear as extended “clouds” while proteins bound to the actin filament network appear as speckles that undergo retrograde flow. Speckle appearance and disappearance events correspond to assembly and dissociation from the actin filament network and speckle lifetimes correspond to the dissociation rate. We use the measured rates of capping protein and Arp2/3 complex in a Monte Carlo simulation that includes particles in association with a filament network and diffuse in the cytoplasm. We consider two separate pools of diffuse proteins, representing fast and slowly-diffusing species. Accounting for the observed slowly-diffusing cytoplasmic pool of capping protein with diffusion coefficients on the order of 0.5 μm^2/s, which could represent severed actin filament fragments or membrane-bound capping protein, leads to gradients in the diffuse pool. We show that the results of models with such slow diffusion coefficients are consistent with prior FRAP experiments. By comparing single molecule data to prior FRAP experiments of the Arp2/3 complex, we provide estimates for the ratio of bound to diffuse complexes and calculate conditions where Arp2/3 recycling by diffusion may become limiting. We discuss the implications of slowly diffusing populations and suggest experiments to distinguish among mechanisms that influence long range transport. Second, we have developed a diffusion-reaction model useful generally for actin in the lamellipodium with three distinct diffusive species of actin: recycled, cytoplasmic, and membrane-bound actin. The actin bound to the actin network can dissociate into recycled actin, R, which could be the slowly diffusing oligomers mentioned above. The recycled actin can reversibly rebind to the network or become faster diffusing cytoplasmic actin, G_C, with a lifetime τ_R. Fast diffusing cytoplasmic actin, G_C, can reversibly bind to the network or become bound to the membrane with a spatially dependent rate, k(x), where x is the distance from the leading edge of the cell. Then the membrane bound protein, G_M, can either bind to the network, or it can turn back into fast diffusing cytoplasmic protein, G_C, with a lifetime, τ_M. The rates for the diffuse pools of actin to become bound actin are calculated using SiMS data. This model is described by a set of partial differential equations. These partial differential equations are solved by allowing them to relax using the Monte Carlo method in a 2D particle simulation. FRAP and photoactivation can be modeled with this simulation by deleting particles in a region of interest (or outside the ROI) and advancing the simulation in time. Our 2D particle simulation is then propagated through time using the Monte Carlo method. In this section we conclude that diffusion is fast enough for delivery of diffuse actin to the leading edge of the cell and suggest that Thymosin β4 aids in the fast diffusion of diffuse actin through the lamellipodium to the leading edge of the cell.Third, we created a 3D model of the whole cell that includes only reaction and diffusion of actin. In doing this, we show that diffusion is sufficient for movement of actin to various parts of the cell without the need for an active transport mechanism which has been a matter of debate. The diffusion, however, is close to limiting. In the lamellipodium of our simulated cell we use a previously established model (from the previous two sections) which includes two diffuse pools of actin, one which is slowly diffusing and the other which diffuses more quickly, as well as a pool representing actin bound to the filamentous network. One difference is that we adjust this model to fit a circular geometry for the lamellipodium around the whole cell. We also consider actin in the cell center which is either diffuse or in filamentous form and can react to become the other state. The filamentous actin in the cell center is assumed to be either cortical actin or stress fibers. In this model the rates in which actin reacts to become another pool are taken from measurements done by SiMS and FRAP. With this whole cell model we are then able to simulate photoactivation and FRAP in various parts of the cell to compare with experiment and show that diffusion and reaction can account for the effects seen in these studies with the ratio of polymerized actin to diffuse actin in the cell middle being an important factor. We discuss the implications for the proposal of the existence of diffuse actin specifically targeted to cell sub-compartments.

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