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A possible model is analyzed for the maintenance of attachment of a shortening microtubule (MT) to a kinetochore. In this model it is assumed that a MT is inserted and held in a sleeve or channel of the outer layer of a kinetochore while subunits are lost from the MT tip through the central layer of the kinetochore. A second problem considered is the… (More)

Recent experimental data on the equilibrium binding of myosin subfragment 1 (S-1) to regulated actin filaments in the presence and in the absence of Ca(2+) are analyzed by using a linear Ising model. In the model, each tropomyosin-troponin unit (including seven sites on the actin filament) can be in one of two possible states, which have different intrinsic… (More)

Earlier Monte Carlo studies on a single-helix model of the GTP cap at the end of a microtubule are extended here to a more realistic five-start helix model of the microtubule end. As in the earlier work, phase changes occur at the microtubule end: the end is either capped with GTP and growing slowly or uncapped and shortening rapidly, and these two regimes… (More)

Examination of Monte Carlo kinetic simulations, based on a realistic set of microscopic rate constants that apply to the end of a microtubule with a GTP cap, suggests that the end of a microtubule alternates between two quasimacroscopic phases. In one phase, the microtubule end has a GTP cap that fluctuates in size; in the other phase, the GTP cap has been… (More)

An introductory analysis is provided for the two-phase macroscopic kinetic model of the end of a microtubule. Some general relations are derived for one end of a very long microtubule in solution but the main results refer to the steady-state properties of microtubules grown on nucleated sites, as in the experiments of Mitchison and Kirschner [Mitchison, T.… (More)

Under conditions where microtubule nucleation and growth are fast (i.e., high magnesium ion and tubulin concentrations and absence of glycerol), microtubule assembly in vitro exhibits an oscillatory regime preceding the establishment of steady state. The amplitude of the oscillations can represent greater than 50% of the maximum turbidity change and… (More)

The origin of the two-phase (cap, no cap) macroscopic kinetic model of the end of a microtubule is reviewed. The model is then applied to a new theoretical problem, namely, the Mitchison-Kirschner [Mitchison, T. & Kirschner, M. W. (1984) Nature (London) 312, 237-242] experiment in which aggregated microtubules in solution spontaneously decrease in number… (More)

It is shown by use of an extremely simple explicit two-state model that two basic ideas may be sufficient to understand at least qualitatively the sensitive activation of isometric muscle contraction by Ca2+. (a) Ca2+ binds much more strongly on troponin if myosin is already attached to actin. The steady state analogue of this is that the single rate… (More)

The method of making Monte Carlo calculations of the velocity of fast axonal transport is described and applied in a relatively simple case. These illustrative calculations are supplemented by a differential equation solution of the same problem, valid as an asymptotic limit. The latter treatment is closely related to the theory of muscle contraction.

The general procedure is discussed for calculating the velocity of a vesicle along a microtubule. The formalism used previously for isotonic contraction in muscle (with multiple actin sites for a given cross-bridge) can be employed. However, some modifications must be made: (i) the kinetic diagram must include a state in which kinesin is absent from a… (More)