Identifying the motive force is central to explaining chromosome motions during mitosis. Presently, there is no consensus on what it is. The author has proposed a minimal assumptions model for the dynamics of post-attachment chromosome motions based on nanoscale electrostatics. Given the electrical properties of tubulin and the dynamic instability of microtubules, it is possible to account for prometaphase post-attachment, metaphase, and anaphase chromosome motions within a comprehensive model. The model addresses all of the following in a unified manner: Efficiency of aster and spindle assembly and the motive force for the motion of asters and forming half-spindles. Chromatid pair attachment. Motion of monovalently attached chromatid pairs. Motion of bivalently attached chromatid pairs and chromosome congression. Metaphase chromatid pair oscillations. Chromatid separation and anaphase-A chromosome motion. Anaphase-B pole separation. An ab-initio calculation of the maximum tension force exerted by a microtubule during mitosis that falls within the experimental range. Poleward force generation of chromosomes at poles with associated microtubule flux.

Electrostatic Considerations in Mitosis

By L. John Gagliardi

iUniverse, Inc.

Copyright © 2009 L. John Gagliardi
All right reserved.
ISBN: 978-1-4401-7378-3

Contents

1 Introduction......................................................................71.1 Preliminary considerations......................................................71.2 Some cellular electrostatics....................................................101.3 Spindle assembly and dynamics...................................................151.4 Summary.........................................................................192 Electrostatics in Nuclear Envelope Breakdown......................................212.1 Mechanical equilibrium of a nuclear envelope....................................212.2 Equilibrium of membrane charge clusters.........................................252.3 Electrostatics in nuclear envelope disassembly..................................282.4 Energy considerations in nuclear envelope disassembly...........................302.5 Electrostatics in nuclear envelope reassembly...................................322.6 Summary.........................................................................343 Electrostatic Force in Poleward Chromosome Motions................................363.1 Introduction....................................................................363.2 Electrostatic microtubule disassembly force at cell poles.......................373.3 Electrostatic microtubule disassembly force at kinetochores.....................433.4 Penetrating microtubules at a centrosome........................................493.5 Summary.........................................................................504 Induced Charge in Poleward Motions................................................524.1 Introduction....................................................................524.2 Induced charge on centrosomes and kinetochores..................................534.3 Electrostatic microtubule disassembly force at cell poles.......................574.4 Electrostatic microtubule disassembly force at kinetochores.....................604.5 Summary.........................................................................635 Electrostatics in Mitotic Chromosome Motions......................................655.1 Introduction....................................................................655.2 Antipoleward nanoscale electrostatic assembly force.............................685.3 Prometaphase and metaphase chromosome motions...................................715.4 Anaphase-A chromosome motion....................................................765.5 Anaphase-B chromosome motion....................................................795.6 Summary.........................................................................82A Some results from electrostatics..................................................85B Debye theory of counterion screening..............................................87C Electrostatic stress..............................................................92D Equation 2.1......................................................................94E Equation 2.10.....................................................................96F Bibliography......................................................................99

Chapter One

Introduction

1.1 Preliminary considerations

Although the current paradigm in cell biology has been quite successful in solving a number of problems in the understanding of cell structure and function, important problems remain open. Some of the most notable of these are in the area of cell division. Given the constraints wittingly or unwittingly imposed by the molecular biology paradigm, it would seem that models of mitotic motions and events have become more and more complex, and therefore-to this observer at least-more and more unsatisfactory.

It may be helpful at this point to give an example. It is a common parlor trick to attract small bits of paper by a charged hard rubber hair comb. This motion is simply explained in terms of the known negative charge on the comb attracting the nearer induced positive charge on the bits of paper with the paper bits remaining overall electrically neutral and the displaced negative charges farther from the comb. There is no need to identify the specific molecules in the paper (or in the comb, for that matter) that are responsible for the attractive force and the subsequent motion. In fact, since the charged comb will attract many different kinds of paper as well as many other substances, attempting to identify the molecules in the various substances is counterproductive to explaining what is happening. Similarly, as will be discussed later, chromosome and other mitotic motions can be described in terms of electric charge distributions. However before this can be done, one must first establish that electrostatic force is significant within cells in spite of counterion screening.

The electromagnetic interaction is primarily responsible for the structure of matter from atoms to objects. Much of physics, all of chemistry, and most of biology are in this realm of sizes. Primitive eukaryotic cells had to divide prior to the evolution of very many biological mechanisms, and it is reasonable to assume that basic physics and chemistry played dominant roles in both mitosis (nuclear division) and cytokinesis (cytoplasmic division). It is proposed that nanoscale electrostatic interactions played a major role in the dynamics of cell division in primitive cells, and that the fundamental solutions to the problem of cell division that were found by primitive cells may largely persist in modern eukaryotic cells.

The mitotic spindle is responsible for the segregation of sister chromatids during cell division. Chromosomes are attached to the spindle with their kinetochores [Euteneuer and McIntosh, 1981] attached to the plus ends of microtubules [Rieder, 1982; Bergen et al., 1980]. Chromosome movement is dependent on kinetochore-microtubule dynamics: a chromosome can move toward a pole only when its kinetochore is connected to microtubules emanating from that pole [Nicklas and Kubai, 1985]. A number of experimental studies have been undertaken to obtain information regarding microtubule dynamics, force production, and kinetochore function in mitotic cells. These experiments have revealed that the spindle can produce more force than is actually required to move a chromosome at the observed speeds for post-attachment movements, and that the force for the poleward motion of chromosomes can be localized at or near kinetochores [Nicklas, 1983; Mitchison et al., 1986; Gorbsky et al., 1987; Nicklas, 1989; Mitchison, 1989; Alexander and Rieder, 1991; Inoue and Salmon, 1995] or at spindle poles [Mitchison and Salmon, 1992; Maddox et al., 2002; Zhang and Chen, 2003]. Quite some time ago, M. S. Cooper addressed a possible link between endogenous electrostatic fields and the eukaryotic cell cycle [Cooper, 1979]. An early review by Jaffe and Nuccitelli [Jaffe and Nuccitelli, 1977] focused on the possible influence of relatively steady electric fields on the control of growth and development in cells and tissues.

Microtubules continually assemble and disassemble, so the turnover of tubulin is ongoing. The characteristics of microtubule lengthening (polymerization) and shortening (depolymerization) follow a pattern known as "dynamic instability": that is, at any given instant some of the microtubules are growing, while others are undergoing rapid breakdown. In general, the rate at...