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Microtubule dynamics Vladimir Rodionov

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The goal of this project is to develop a comprehensive computational tool for modeling cytoskeletal dynamics using two complementary approaches: detailed discrete modeling and coarse-grain continuous approximation. The biological problem of regulation of intracellular transport by dynamics of the cytoskeleton is being used as a test bed for validation of this computational tool.

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Melanosomes are captured by growing MT plus-ends during aggregation

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Stabilization of microtubules inhibits pigment aggregation

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Aggregation Low cAMP Actin Filaments Granule M D K CLIP-170

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Aggregation Low cAMP Actin Filaments Granule M D K CLIP-170

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Microtubule statesGranule states Computational model for pigment aggregation → Model includes dynamically unstable microtubules (MTs) interacting with melanosomes Microtubules: → MTs are modeled as radial lines with minus ends fixed at the cell center and dynamic plus ends extended to the periphery → plus end can either move towards the periphery with velocity v +, (MT growth, state M + ), toward the center with velocity v - (MT shortening, state M - ), or pause (state M 0 ) Melanosomes: → a melanosome either undergoes actin-dependent random walks (state G), or is bound to MT → the MT-bound states of a melanosome include plus-end runs (G + ), minus-end runs (G - ), and pauses (G 0 ) Wiring diagram: → wiring diagram for MT states with rates q 1 – q 6 (left) is coupled to melanosome transitions with rates k 1 – k 6 (right) through the collision-controlled binding of the melanosome to a growing MT tip → all rates are found from experimental data → Model includes dynamically unstable microtubules (MTs) interacting with melanosomes Microtubules: → MTs are modeled as radial lines with minus ends fixed at the cell center and dynamic plus ends extended to the periphery → plus end can either move towards the periphery with velocity v +, (MT growth, state M + ), toward the center with velocity v - (MT shortening, state M - ), or pause (state M 0 ) Melanosomes: → a melanosome either undergoes actin-dependent random walks (state G), or is bound to MT → the MT-bound states of a melanosome include plus-end runs (G + ), minus-end runs (G - ), and pauses (G 0 ) Wiring diagram: → wiring diagram for MT states with rates q 1 – q 6 (left) is coupled to melanosome transitions with rates k 1 – k 6 (right) through the collision-controlled binding of the melanosome to a growing MT tip → all rates are found from experimental data Model includes dynamically unstable microtubules (MTs) interacting with melanosomes. Microtubules: MTs are modeled as radial lines with minus ends fixed at the cell center and dynamic plus ends extended to the periphery. Plus end can either move towards the periphery with velocity v+, (MT growth, state M+), toward the center wth velocity v- (MT shortening, state M-), or pause (state M0). Binding of melanosomes to MTs occur at a short distance (3 m or less) from the tip. Melanosomes: A melanosome either undergoes actin-dependent random walks (state G), or is bound to MT. The MT-bound states of a melanosome include plus-end runs (G+), minus-end runs (G-), and pauses (G0). Wiring diagram: Wiring diagram for MT states with rates q1 – q6 (left) is coupled to melanosome transitions with rates k1 – k6 (right) through the collision-controlled binding of the melanosome to a growing MT tip. All rates are found from experimental data.

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Parameters used in the computational model for pigment aggregation Notation Values GFPTaxol EB3- GFP GFP- CLIP tail GFP- CLIP head GFP- Lis1 Cell radius (μm)R20 Diffusion of unbound melanosome (μm 2 /s) D4x10 -3 Melanosome radius (μm)RgRg 0.25 MT cross-section (μm)δ0.025 Nucleus radius (μm)a4 Rate constant for M - → M + (s -1 ) q2q2 0.0520.0430.050.0280.0420.065 Rate constant for M - → M 0 (s -1 ) q3q3 0.0080.1920.0080.0030.0050.009 Rate constant for M + → M 0 (s -1 ) q5q5 0.0120.2060.009 0.0070.013 Rate constant for M 0 → M - (s -1 ) q4q4 0.090.0340.0960.0570.0850.079 Rate constant for M 0 → M + (s -1 ) q6q6 0.1610.0530.1420.2470.1570.15 Rate constant for M + → M - (s -1 ) q1q1 0.0440.0290.0390.0230.0330.053 Rate constants for G - → G + (s -1 ) k2k2 0.587 0.6230.9880.5540.703 Rate constants for G - → G 0 (s -1 ) k3k3 0.374 0.2780.3820.2860.299 Rate constants for G + → G 0 (s -1 ) k5k5 0.274 0.1630.2680.1970.151 Rate constants for G 0 → G - (s -1 ) k4k4 0.8 0.9650.7630.9090.917 Rate constants for G 0 → G + (s -1 ) k6k6 0.176 0.1590.2370.1670.149 Rate constants for G + → G - (s -1 ) k1k1 1.948 2.2182.2322.0762.185 Simulation time step (s) tt 10 -3 Total number of melanosomesNgNg 770 Total number of MTsNmNm 370 Velocity of melanosome minus-end runs (μm/s) 0.344 0.3820.3510.3430.376 Velocity of melanosome plus-end runs (μm/s) 0.345 0.3420.3230.3270.354 Velocity of MT growth (μm/s)0.1670.0590.1710.2250.2930.153 Velocity of MT shortening (μm/s)0.1850.0580.1880.2690.3360.175

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Spatial stochastic simulations of MT dynamics and intracellular transport Dynamic MTs (control)Stabilized MTs (taxol treatment )

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The results of spatial stochastic simulations agree with experimental data

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Dynamic parametersDispersed stateAggregated state Growth duration (s) 27.3417.99 Growth length (μm) 6.132.59 Growth rate (μm/s) 0.230.16 Shortening duration (s) 24.5511.86 Shortening length (μm) 7.722.06 Shortening rate (μm/s) 0.250.18 Catastrophe frequency (s -1 ) 0.030.04 Rescue frequency (s -1 ) 0.0460.085 Pause duration (s) 3.454.42 Number of analyzed MTs4060 Number of analyzed cells813 Granule aggregation signals change major parameters of MT dynamic instability, and these changes accelerate pigment aggregation Dynamic parametersDispersed stateAggregated state Growth duration (s) 27.3417.99 Growth length (μm) 6.132.59 Growth rate (μm/s) 0.230.16 Shortening duration (s) 24.5511.86 Shortening length (μm) 7.722.06 Shortening rate (μm/s) 0.250.18 Catastrophe frequency (s -1 ) 0.030.04 Rescue frequency (s -1 ) 0.0460.085 Pause duration (s) 3.454.42 Number of analyzed MTs4060 Number of analyzed cells813 Dynamic parametersDispersed stateAggregated state Growth duration (s) 27.3417.99 Growth length (μm) 6.132.59 Growth rate (μm/s) 0.230.16 Shortening duration (s) 24.5511.86 Shortening length (μm) 7.722.06 Shortening rate (μm/s) 0.250.18 Catastrophe frequency (s -1 ) 0.030.04 Rescue frequency (s -1 ) 0.0460.085 Pause duration (s) 3.454.42 Number of analyzed MTs4060 Number of analyzed cells813 Dynamic parametersDispersed stateAggregated state Growth duration (s) 27.3417.99 Growth length (μm) 6.132.59 Growth rate (μm/s) 0.230.16 Shortening duration (s) 24.5511.86 Shortening length (μm) 7.722.06 Shortening rate (μm/s) 0.250.18 Catastrophe frequency (s -1 ) 0.030.04 Rescue frequency (s -1 ) 0.0460.085 Pause duration (s) 3.454.42 Number of analyzed MTs4060 Number of analyzed cells813 Dynamic parametersDispersed stateAggregated state Growth duration (s) 27.3417.99 Growth length (μm) 6.132.59 Growth rate (μm/s) 0.230.16 Shortening duration (s) 24.5511.86 Shortening length (μm) 7.722.06 Shortening rate (μm/s) 0.250.18 Catastrophe frequency (s -1 ) 0.030.04 Rescue frequency (s -1 ) 0.0460.085 Pause duration (s) 3.454.42 Number of analyzed MTs4060 Number of analyzed cells813 Dynamic parameters Dispersed state Aggregated state Growth duration (s) 27.3417.99 Growth length (μm) 6.132.59 Growth rate (μm/s) 0.230.16 Shortening duration (s) 24.5511.86 Shortening length (μm) 7.722.06 Shortening rate (μm/s) 0.250.18 Catastrophe frequency (s -1 ) 0.030.04 Rescue frequency (s -1 ) 0.0460.085 Pause duration (s) 3.454.42 Number of analyzed MTs4060 Number of analyzed cells813 Aggregation Dynamics parameters as for dispersed state parameters as for aggregated state Aggregation Dynamics parameters as for dispersed state parameters as for aggregated state Aggregation Dynamics parameters as for dispersed state parameters as for aggregated state Aggregation Dynamics parameters as for dispersed state parameters as for aggregated state Aggregation Dynamics parameters as for dispersed state parameters as for aggregated state Aggregation Dynamics parameters as for dispersed state parameters as for aggregated state

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Conclusion We have developed stochastic model for microtubule dynamics, and validated the model in an experiment. Lomakin, A., Semenova, I., Zalyapin, I., Kraikivski, P., Nadezhdina, E., Slepchenko, B.M., Akhmanova, A., and Rodionov. V. (2009). CLIP-170-dependent capture of membrane organelles by microtubules initiates minus-end directed transport. Dev. Cell 17, 323-333.

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Plans for the next year Discrete and coarse-grain stochastic approaches for modeling dynamics of actin filaments and microtubules will be further developed.

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Dispersion High cAMP Actin Filaments Granule M D K

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Dispersion High cAMP Actin Filaments Granule M D K

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