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[4.] Microscale Electrostatics in Mitosis, Journal of Electrostatics, vol. 54, 210-232 (2002b).
Comments on biophysics research
In spite of a series of ingenious experiments over the last 25 - 30 years,
the causes for most of the mitotic
motions remains unclear. The
expectation of many researchers in the field had been that molecular
motors would eventually be shown to be the motive force for
chromosome motions. This may be changing. Several new models
have been proposed recently that are either electrostatic in nature
or leave the precise mechanism for force generation unspecified
in a simulation that introduces a number of adjustable parameters.
The current paradigm in molecular biology requires that specific molecules, and/or molecular geometries, for force generation be identified. However, it is possible to account for mitotic motions in terms of experimentally known cellular electric charge distributions interacting over nanometer distances. This is the approach that I have taken in the series of papers listed here.
The known charge in mitotic chromosome motions resides at kinetochores, centrosomes, and on chromosome arms. In 2002 and 2005 papers, I argued that indirect experimental evidence indicates that pole-facing "plates" of kinetochores manifest positive charge (see references  and  above) that interacts with negative charge at and near the plus ends of microtubules to generate force for poleward chromosome movements. A number of recent experiments have now implicated positively charged molecules in kinetochores in establishing a dynamic coupling to microtubules for force generation during mitosis.
Assuming positive charge at kinetochores, and negative charge at and near the free plus ends of microtubules, it is possible to derive a magnitude of the maximum (tension) force per microtubule for poleward chromosome motions that falls within the experimental range . In the above-mentioned papers I also proposed that indirect experimental evidence is consistent with negative charge on centrosomes. Recent direct experimental measurements have confirmed this [Hormeno S. et al., Biophys. J. 97 (2009) 1022].
A major advantage of focusing on known cellular charge distributions is that it appears to offer the possibility of discovering a minimal assumptions comprehensive model for post-attachment chromosome motions. A model of this sort can point the way to the eventual discovery of specific molecules, and their biochemistries, that are responsible for the various mitotic motions. This is what is happening. As mentioned above, recent experiments have shown that kinetochore molecules that bind with microtubules are positively charged, and that force for chromosome motions may be due to electrostatic interactions between these molecules and negative charge on microtubules. These discoveries might have been made sooner if the above mentioned papers had been duly noted.
The recent experimental verification of net negative charge on centrosomes implies that expression of positive charge on free minus microtubule ends will be favored. This is because of the lower local pH vicinal to the centrosome matrix as well as positive charge induction. Additionally, the beta monomers that crown minus ends are known to contain considerable positive charge. The interaction of this charge with a negatively charged centrosome may be responsible for polar poleward force generation. A calculation of the force per microtubule assuming permanent charge falls within the experimental range . Although a calculation of induced charge on a microtubule minus end is difficult because of the geometry, a reciprocal calculation of the induced charge on a centrosome matrix from charge at the free end of a microtubule is relatively straightforward, yields the same order of magnitude for the polar force per microtubule, and falls within the experimental range .
As mentioned above, electrostatic models within the molecular biology paradigm are being sought (or advanced) to explain recent experiments suggesting that highly basic kinetochore molecules interact with negative charge on microtubules to couple kinetochores to microtubules. As in the situation involving models that center partially or wholly on simulations, these approaches are quite complex in their assumptions and primarily attempt to address one or two mitotic motions, most notably poleward force generation at kinetochores. Critical experimental observations such as the "slip-clutch" mechanism [Maiato et al., 2004], observations of calcium ion concentration on anaphase-A chromosome motion [Zhang et al., 1990], and polar generation of force for poleward chromosome motions are not addressed. In the comprehensive model that I have proposed (, , , ; Gagliardi, 2009 (book)), interactions between stably bound, volume charge distributions can account for these, as well as poleward force generation at kinetochores.
[ Maiato H., DeLuca J., Salmon E.D., Earnshaw W.C. 2004. J. Cell Science,
vol. 117, p. 5461. ]
Regarding molecular motor contributions to mitotic motions,
it is generally thought that molecular motors are likely to be
involved in the sliding microtubule sidewall "capture" motion of
chromatid pairs. The case for molecular motors as the cause for
post-attachment chromosome motions is considerably less convincing.
[ Zhang D.H., Callaham D.A., Hepler P.K. 1990. J. Cell Biol., vol. 111, p. 171. ]
As discussed above, identifying the motive force is central to explaining chromosome motions during mitosis. Presently, there is no consensus on what it is. I have proposed a minimal assumptions model for post-attachment chromosome movements based on the dynamic instability of microtubules and nanoscale electrostatics. Given the electrical properties of (tubulin and) microtubules, and charge distributions on kinetochores, centrosome matrices and chromosome arms, as well as the pH-dependent dynamics of microtubules, it is possible to account for prometaphase post-attachment, metaphase, and anaphase chromosome motions within a comprehensive model that addresses all of the following in a unified manner:
1. Efficiency of aster and spindle assembly and the motive force for the
motion of asters and forming spindles
( , p.222 ).*
*See above links to numbered references. Page numbers in references 1
and 3 refer to the preprint versions linked to
this website, and differ from the actual page numbers in the Journal
of Electrostatics and Physical Review E papers.
2. Chromatid pair attachment ( , p. 12 ).
3. Motion of monovalently attached chromatid pairs ( , pp. 320 & 321; , pp. 12 & 13 ).
4. Motion of bivalently attached chromatid pairs; congression ( , pp. 321 & 322; , pp. 13 & 14 ).
5. Metaphase chromatid pair oscillations ( , p. 322; , pp. 14 & 15 ).
6. Anaphase-A chromosome motion ( , pp. 19-21; , pp. 322 & 323 ).
7. Anaphase-B pole separation ( , pp. 21 & 22; , pp. 228-230 ).
8. Poleward force generation at poles with associated microtubule flux is explained by the same microtubule nanoscale electrostatic disassembly force as at kinetochores ( ,  ).
9. The timing and sequencing of the above motions ( ; ; book, Chapter 5; also see Chapter 5 Summary for a capsule version.)
10. An "ab initio" theoretical calculation of the tension force exerted by a microtubule during mitosis that falls within the experimental range ( , pp. 16-18; , pp. 315-318 ).