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Can Microtubule Dynamics Be Explained Using the Geometry Characteristic of the B-Lattice? Maria J. Schilstra 1 , John J. Correia 2 , and Stephen R.Martin 3 1 STRI, University of Hertfordshire, College Lane, Hatfield AL10 9AB, UK; [email protected]; 2 University of Mississippi Medical Center, Jackson, MS, USA; 3 MRC-National Institute for Medical Research, London, UK Microtubules (MTs) Hollow polymers of the -tubulin dimer (Tb) Principal component of the mitotic spindle and interphase cytoskeleton MT dynamics (“dynamic instability“) Phases of sustained growth alternating with phases of rapid shrinkage Abrupt phase transitions Lifetimes of the growing and shrinking states exponentially distributed Assembly-coupled GTP to GDP hydrolysis Hydrolysis of the -Tb cofactor, occurs upon incorporation of Tb into the MT lattice Catalysed by the -subunit of the longitudinal neighbouring Tb Changes the affinity of Tb for its neighbours in the lattice Tb-GTP “Cap” Proposed layer(s) of Tb-GTP at one or both ends of a growing MT Observations Lattice examples Lattice Binding site Helical symmetry -1, 12 -9, 4 -4, 9 -12, 1 Type A A B B Nr 1 9 4 12 Examples from a series of twelve 13-protofilament models with different regular (no seams) helical symmetries (- ends). Odd Nr: A-lattice; even Nr: B-lattice. Lattices have varying numbers of Tb binding sites. A- and B- lattices have different binding site configurations. Rationale Accurate interpretation of experimental data and prediction of the effects of microtubule-targeted anti-mitotic drugs, which in vitro suppress microtubule dynamics, and in vivo also interfere with the action of spindle dynamics regulators, requires a clear picture of the events that occur at the microtubule ends. Aim Early models of microtubule dynamics were based on the assumption that the dimers are packed in a so-called A-lattice. These models closely mimicked the observed in-vitro dynamics of microtubule - ends, using a minimum number of assumptions and parameters. However, it now seems likely that the dimers are mostly arranged in a B- lattice, often with a seam at which the lattice regularity is broken. Reproducing the characteristic biphasic behaviour with B- lattice-cum-seam models has been far more problematic. Here, we revisit the early minimal model to investigate whether the dynamic behaviour of A-lattice and B-lattice microtubules is fundamentally different. Binding site configurations TT DD TD DT Type A B Upon Tb binding to or dissociation from a binding site 1 longitudinal -, and 2 lateral - (A), or 1 -, and 1 - bond (B) are formed or broken A-lattices 0 3 6 9 12 0 0.1 0.2 0.3 0.4 0.5 Number of Tubulin-GTP in cap Fraction 0 3 6 9 12 0 0.1 0.2 0.3 0.4 0.5 Number of Tubulin-GTP in cap Fraction 0 250 500 750 1000 0 2 4 6 8 Time Length (mm) -200 -100 0 100 0.001 0.01 0.1 1 Rate Cumulative frequency A9 ~1.9 binding sites 0 250 500 750 1000 0 2 4 6 8 Time Length (mm) -400 -200 0 200 0.001 0.01 0.1 1 Rate Cumulative frequency A1 ~3.7 binding sites Typical length trajectoriesAverage cap sizeCumulative rate distribution 0 2 4 6 8 10 12 0.1 1 10 100 1000 Symmetry nr Cc 0 2 4 6 8 10 12 0 0.25 0.5 Symmetry nr f 0 2 4 6 8 10 12 0 1 2 3 4 5 Symmetry nr nSites Tb concentration at which there is no net growth (Critical concentration, Cc) Average number of binding sites at Cc Fraction of association events that are followed by a dissociation event at Cc Paramet er set k off TT k off TD k off DD k off DT Dissociation constants Changes in bond strength affect the dissociation rate constants. All association rate constants are 1. EP0 and EP2 are the parameters for equilibrium polymers (MTs in which GTP hydrolysis does not result in affinity changes). 1 3 2 EP1 EP2 1 1 1 1 100 100 1 10 1 100 1 100 10 1 100 100 100 100 1 100 terpretation and conclusions Legend Tb-GTP (, green; , red) Tb-GDP (, green, , pink) Lateral bond direction Bond whose strength changes upon GTP hydrolysis Hydrolysis rule Hydrolysis of the -Tb cofactor GTP takes place immediately after Tb has been fully incorporated in the lattice. It potentially changes the strength of 2 (A) or 1 (B) existing lateral bond. A B 0 3 6 9 12 0 0.1 0.2 0.3 0.4 0.5 Number of Tubulin-GTP in cap Fraction 0 250 500 750 1000 0 1 2 Time Length (mm) -200 -100 0 100 0.001 0.01 0.1 1 Rate Cumulative frequency B4 ~1.9 binding sites B12 ~4.5 binding sites Typical trajectories Average cap size Cumulative rate distribution 0 2 4 6 8 10 12 0.1 1 10 100 1000 Symmetry nr Cc 0 2 4 6 8 10 12 0 0.25 0.5 Symmetry nr f 0 2 4 6 8 10 12 0 1 2 3 4 5 Symmetry nr nSites Tb concentration at which there is no net growth (Critical concentration, Cc) Average number of binding sites at Cc Fraction of association events that are followed by a dissociation event at Cc 0 3 6 9 12 0 0.1 0.2 0.3 0.4 0.5 Number of Tubulin-GTP in cap Fraction -400 -300 -200 -100 0 10 0 0.001 0.01 0.1 1 Rate Cumulative frequency 0 250 500 750 1000 0 1 2 Time Length (mm) B-lattices Dynamic behaviour and thus Cc depend strongly on : Lattice symmetry Binding site characteristics Symmetry of changes in bond strength upon GTP hydrolysis Maximum possible growth and shrinkage rates depend on Cc -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 A9 A1 B4 B12 Effective rates at Cc Growth S h r i n k a g e Effective rate = Normalized rate Maximum or minimum rate Normalized rate = Average rate Number of binding sites -30 -20 -10 0 10 20 30 -150 -100 -50 0 50 100 150 A9 A1 B4 B12 Normalized rates at Cc Growth S h r i n k a g e Relative variability = Std dev on growth rate Growth rate 0.1 1 10 100 A9 A1 B4 B12 Growth rate variability at Cc Relative variability Growth phase lifetime = 1 Catastrophe frequency 1 10 100 1000 A9 A1 B4 B12 Growth phase lifetime at Cc Lifetime 0 5 10 15 20 25 30 35 40 45 50 -100 -50 0 50 A1, DT/TT = 10 Minimum rate Maximum rate B12, DT/TT = 100 Growth rate dependence on [Tb-GTP] free Normalized growth rate [Tb-GTP] free Achieved rates depend on: Binding site configuration: A-type or B-type) = k off DT /k off TD : indicative of symmetry in effect of GTP hydrolysis nSites: total number of binding sites Normalized steady state growth rates achieved in A-lattice geometries generally are higher than those in B-lattices Lattices in which the effect of GTP-hydrolysis is symmetric (A- lattices with = 1; all B- lattices are asymmetric as the TD configuration never occurs) are the most efficient growers: the average growth rates they achieve come closest to the maximum possible rate. Lattices in which the effect of GTP-hydrolysis is symmetric also exhibit the most uniform growth. Growth in the B-lattices and A- lattices with 1 is generally much more erratic (notice the log scale). (Exception is the highly dynamic A9/001 (blue) lattice, in which the growth phase is very short lived, see right) The GTP cap in lattices in which the effect of GTP-hydrolysis is symmetric are significantly more prone to catastrophe, and thus less stable than the B-lattices and most A-lattice configurations with 1 (notice the log scale).
