Multiple Scales in Molecular Motor Models. Nanoscale Kinesin. - PowerPoint PPT Presentation

Multiple Scales in Molecular Motor Models. John Fricks Overview Multiple Scales in Molecular Motor Models. Nanoscale Kinesin. Important Quantities of Interest. John Fricks Common Models. Our Model(s). Biological Dept of Statistics Results. Penn State University Mesoscale University Park, PA Multiple Motors Common Models. The Fourth Erich L. Lehmann Symposium A Simple Model. Biological Rice University Results. May 9, 2011

Multiple Acknowledgements. Scales in Molecular Motor Models. John Fricks Overview Nanoscale Kinesin. • Nanoscale Important Quantities of • William Hancock (PSU Bioengineering) Interest. Common • Matthew Kutys (NIH/University of North Carolina) Models. Our Model(s). • John Hughes (PSU Statistics → Minnesota Biostatistics) Biological Results. • NSF/NIH joint program in mathematical biology Mesoscale • Mesoscale Multiple Motors • Avanti Athreya (Duke Mathematics) Common Models. • Peter Kramer (RPI Mathematical Sciences) A Simple Model. Biological • Scott McKinley (U Florida Mathematics) Results. • NSF via SAMSI

Multiple Overview. Scales in Molecular Motor Models. John Fricks Overview Nanoscale • The Biology. Kinesin. Important Quantities of • Nanoscale Models Interest. Common • Common Models. Models. Our Model(s). • Our Model(s). Biological Results. • Biological Results. Mesoscale Multiple • Mesoscale Models and Multiple Motors Motors • Common Models. Common Models. A Simple Model. • A Simple Model. Biological Results. • Averaging and Asymptotics. • Biological Results.

Multiple Molecular Motors. Scales in Molecular Motor Models. John Fricks Overview Nanoscale Kinesin. Important Quantities of Interest. Common Models. Our Model(s). Biological Results. Mesoscale Multiple Motors Common Models. A Simple Model. Biological Results.

Multiple Scales. Scales in Molecular Motor Models. John Fricks Overview Nanoscale Kinesin. Important Quantities of Interest. Common Models. Our Model(s). Biological Results. Mesoscale Multiple Motors Common Models. A Simple Model. Biological Results.

Multiple Who Cares? Scales in Molecular Motor Models. John Fricks Overview Nanoscale Kinesin. • When an axon is severed from a dendrite, it must be Important Quantities of Interest. regenerated. Common Models. Our Model(s). • The microtubules near the regeneration site realign in a Biological Results. mixed polarity. Mesoscale Multiple • Why do they do this? Motors Common • What effect does this have on kinesin transport? Models. A Simple Model. Biological • How is this regulated? At the nanoscale? Results.

Multiple Examples of Data. Scales in Molecular Motor Models. John Fricks Overview Nanoscale Kinesin. Important Quantities of Interest. Common Models. Our Model(s). Biological Results. Mesoscale Multiple Motors Common Models. A Simple Model. Biological Results.

Multiple An Artist’s Rendering of Experiment. Scales in Molecular Motor Models. John Fricks Overview Nanoscale Kinesin. Important Quantities of Interest. Common Models. Our Model(s). Biological Results. Mesoscale Multiple Motors Common Models. A Simple Model. Biological Results. Block Lab:http://www.stanford.edu/group/blocklab/kinesin/kinesin.html

Multiple The Important Biological Points. Scales in Molecular Motor Models. John Fricks Overview Nanoscale • “Hand over hand” stepping mechanism. Kinesin. Important • 8 nanometer steps with 1 ATP per step. Quantities of Interest. Common • Length of step determined by the physical structure of Models. Our Model(s). Biological microtubule. Results. Mesoscale • Back steps are rare. Multiple Motors • Kinetics + Constrained Diffusion. Common Models. • Free head detachment. A Simple Model. Biological • ATP binding. Results. • ATP hydrolysis. • Free head attachment.

Multiple The Kinesin Cartoon. Scales in Molecular Motor Models. John Fricks Overview Nanoscale Kinesin. Important Quantities of Interest. Common Models. Our Model(s). Biological Results. Mesoscale Multiple Motors Common Models. A Simple Model. Biological Results.

Multiple Engineered Motors. Scales in Molecular Motor Models. • Extensions can range from less than 1 nm up to 12 nm. John Fricks • Hackney and Hancock–extensions reduced processivity. Overview • Hancock–velocity was reduced. Nanoscale Kinesin. • Yildiz et al–processivity was unaffected and velocity was Important Quantities of Interest. reduced. Common Models. Our Model(s). Biological Results. Mesoscale Multiple Motors Common Models. A Simple Model. Biological Results.

Multiple Necklinker Extension. Scales in Molecular Motor Models. John Fricks Overview Nanoscale Kinesin. Important Quantities of Interest. Common Models. Our Model(s). Biological Results. Mesoscale Multiple Motors Common Models. A Simple Model. Biological Results. Yildiz, A. and Tomishige, M. and Gennerich, A. and Vale, R.D. Intramolecular Strain Coordinates Kinesin Stepping Behavior along Microtubules.

Multiple Important Quantities of Interest. Scales in Molecular Motor Models. John Fricks • Asymptotic Velocity Overview E [ X ( t )] X ( t ) Nanoscale V a = lim or V a = lim Kinesin. t →∞ t t →∞ t Important Quantities of Interest. • Effective Diffusion Common Var [ X ( t )] Models. D eff = lim Our Model(s). t →∞ 2 t Biological Results. or the quantity which ensures Mesoscale Multiple X ( t ) − V a t Motors √ 2 D eff t Common Models. A Simple Model. Biological converges to a standard normal. Results. • Randomness Parameter R = 2 D eff LV a • Processivity ν the number of random steps taken before detachment.

Multiple The Models. Scales in Molecular Motor Models. Pure kinetics model–a discrete space Markov chain. John Fricks • Fails to account for the physical movement of heads. Overview Nanoscale Kinesin. Important Quantities of Interest. Common Models. Our Model(s). Biological Results. Mesoscale Multiple Motors Common Models. A Simple Model. Biological Results.

Multiple The Models. Scales in Molecular Motor Models. John Fricks Overview Nanoscale Kinesin. Important Stochastic Differential Equation Model Quantities of Interest. Common • Brownian particle in a periodic potential. Models. Our Model(s). Biological • dX ( t ) = a ( X ( t )) dt + σ dB ( t ) Results. Mesoscale • Fails to account for two individual heads. Multiple Motors • Fails to coordinate physical movement and chemical Common Models. A Simple Model. kinetics. Biological Results.

Multiple The Models. Scales in Molecular Motor Models. John Fricks Overview Nanoscale Kinesin. Important Quantities of Interest. Common Flashing Ratchet Models. Our Model(s). • dX ( t ) = a K ( t ) ( X ( t )) dt + σ dB ( t ) Biological Results. • Accounts for both chemical and physical states. Mesoscale Multiple Motors • How can these be coordinated? Common Models. A Simple Model. Biological Results.

Multiple The Kinesin Cartoon. Scales in Molecular Motor Models. John Fricks Overview Nanoscale Kinesin. Important Quantities of Interest. Common Models. Our Model(s). Biological Results. Mesoscale Multiple Motors Common Models. A Simple Model. Biological Results.

Multiple Our Model. Scales in Molecular Motor Models. John Fricks Overview Nanoscale Kinesin. • What about incorporating diffusion of the free head into Important Quantities of the model? Interest. Common Models. • State 1 corresponds to having both heads bound. Our Model(s). Biological Results. • State 2 corresponds to the head having become free Mesoscale Tethered diffusion with a negative or neutral bias. Multiple Motors • State 3 and state 4 mean ATP has been bound Common Models. A Simple Model. A conformational change causes there to be a forward bias Biological Results. and less compliant spring.

Multiple Our Model. Scales in Molecular Motor Models. John Fricks • The position of the free motor head is governed by the following Overview equation. Nanoscale � t Kinesin. Y ( t ) = y + a K ( s ) ( Y ( s )) ds + σ B ( s ) Important Quantities of 0 Interest. where K ( t ) is the process corresponding to state events. Common Models. Our Model(s). • Associate with each binding site a binding process Biological Results. �� t � Mesoscale g j ( Y ( s )) ds N j Multiple Motors 0 Common Models. where the N j are independent standard Poisson processes A Simple Model. (independent of B also). Biological Results. • The time until we return to (chemical) state one ( τ ) would then be the time for one of these clocks to fire. • We define Y ( τ ) to be the location of the binding site associated with the binding process which fires first.