Graduate School in Nonlinear Science

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MIDIT                               OFD                           CATS
Modelling, Nonlinear Dynamics       Optics and Fluid Dynamics     Chaos and Turbulence Studies
and Irreversible Thermodynamics     Risø National Laboratory      Niels Bohr Institute and 
Technical University of Denmark     Building 128                  Department of Chemistry
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4 Lectures on the Cytoskeleton

by Jack Tuszynski
Department of Physics
University of Alberta
Edmonton, Canada

MIDIT-seminars 426-429

December, 1998
at MIDIT, IMM Building 305, room 053

Abstract: In this series of lectures I will describe several key aspects of the functioning of the cell's cytoskeleton with special emphasis placed on the behaviour of microtubules.

Lecture 1: Introductory Aspects of Cell Biophysics
Tuesday December 15, 1998 at 11.00 (note the time)
MIDIT Seminar 426

Life is the ultimate example of a complex dynamical system. A living organism develops through a sequence of interlocking transformations involving an immense number of components which are themselves made up of molecular subsystems. Yet when they are combined into a larger functioning unit (e.g. a cell), then so-called emergent properties arise. For the past several decades, biologists have greatly advanced the understanding of how living systems work by focussing on the structure and function of constituent molecules such as DNA. Understanding what the parts of a complex machinery are made of, however, does not explain how the system works as a whole.

Conceptual advances in physics, (the development of nonlinear paradigms), vast improvements in the experimental techniques of molecular and cell biology (electron microscopy, AFM), and exponential progress in computational techniques have brought us to a unique point in the history of science where the expertise of researchers representing diverse areas of science can be brought to bear on the main unsolved puzzle of life, namely how cells divide. Cell biophysics is one of the frontier areas of biology where size dimensions, time scales and physical properties overlap with those explored by condensed matter physicists like myself, especially those involved in the so-called nano-scale soft-matter systems. Through the use of physical concepts and computer simulations, chemical kinetics equations and structural biochemical data I wish to describe how to model the key biological functions including. the division of a cell.

Lecture 2: The Cytoplasm and the Cytoskeleton
Wednesday December 16, 1998 at 14.00
MIDIT Seminar 427

Contrary, to early perceptions, the cytoplasm is not a viscous soup-like amorphous substance but a highly organized, multi-component, dynamic network of interconnected protein polymers suspended in a dielectrically active liquid medium.

Interiors of living cells are structurally organized by the cytoskeleton networks of filamentous protein polymers: microtubules, actin and intermediate filaments.

MT's are hollow cylinders 25 nm in diameter whose lengths may range from hundreds of nm to micrometers. They typically contain 13 protofilaments built from proteins called tubulin. Each subunit is a polar, 8 nm dimer which comprises two 4 nm, 55 kilodalton monomers known as alpha and beta tubulin. The tubulin dimers are arranged in a hexatic lattice which is slightly twisted and has a pronounced vertical "seam". Microtubules are involved in a number of important cellular functions: (a) material transport (through the use of motor proteins), (b) signal transduction, (c) cell motiltiy (cilia and flagella), (d) cell division (mitotic spindles). Microtubules constitute the most rigid elements of the cell and have found many uses in cell motility. Since MT's play the key role in mitosis, new cancer therapies are being developed (e.g. the use of taxol in the treatment of ovarian and breast cancers) which directly target microtubule assembly processes. It is, therefore, of crucial importance to our understanding of molecular level cell functioning to be able to quantify some of the most dominant processes that govern MT behavior. The assembly and disassembly processes of MT's both in vivo and in vitro have been extensively studied in recent years. The onset of assembly is crucially dependent on: (a) the temperature range, (b) the concentration of tubulin in the cytoplasm, (c) the supply of biochemical energy in the form of GTP. Individual microtubules exhibit an irregular temporal pattern of assembly and disassembly which has been termed a dynamic instability with its attendant features of catastrophes and rescues. Above a concentration threshold, MT ensembles, however, show a quasi-periodic, regular pattern of damped oscillations. This indicates that interactions between individual microtubules must play a crucial role in affecting this drastic change in behavior. Both polymerized and unpolymerized monomers bind either GTP or GDP. Upon assembly, the energy of hydrolysis from GTP to GDP is imparted to the tubulin subunits but its fate is unknown. We believe that at least part of this relatively large amount of energy is stored in an MT in the form of stacking fault energy which, when a critical amount is exceeded, can be released in the form of an earthquake-like collapse of the entire MT structure. Furthermore, MT's and their individual dimers possess dipole moments . Thus, MT's are electrets , i.e. oriented assemblies of dipoles which are predicted to have piezoelectric properties of great significance to signalling. We show how to develop master equation models of MT assembly and disassembly and compare them with the available experimental both in vitro and in vivo. We will also examine the crossover from a single MT (irregular) evolution dynamics to the damped oscillatory behaviour seen in MT ensembles. Finally, we provide a general overview of possible dipolar effects in the organization and interactions of microtubules, their assemblies and related cytoskeletal structures. We have given some direct as well as indirect evidence for an important role electric dipoles and possibly electric currents may play at a subcellular level, especially as it pertains to the functioning of microtubules.

Lecture 3: Biopolymer Networks, Mitosis and Tensegrity
Thursday December 17, 1998 at 14.00
MIDIT Seminar 428

It has been recently emphasized that microtubule networks play an essential role in cellular self-organization phenomena which include reaction-diffusion instabilities in the mechanisms of cytoskeletal self-organization. We believe that dipole-dipole interactions are crucial in the mechanism of self-organization of the cytoskeleton which is so prominent in mitosis which is one of the most fundamental processes in the development of higher organisms. Mitosis insures genetic continuity since the new daughter cells have exactly the same number and kind of chromosomes as the original mother cell and the same genetic instructions are passed on. This process can be divided into 5 or 6 basic stages: interphase, prophase, (late prophase/prometaphase), metaphase, anaphase and telophase which are briefly discussed in this lecture. An essential component of mitosis is the formation of a mitotic spindle made up of dynamic microtubules which spatially organize and then separate the divided chromosomes. The mitotic spindle morphogenesis poses a serious physical problem due to a combination of deterministic and stochastic behaviour present. Although the mitotic apparatus has to be functionally very precise, its assembly is accomplished without a detailed blueprint; the construction of the mitotic spindle is thus an example of a stochastic phenomenon where random molecular processes play a crucial role. Assembly of microtubules and the mitotic spindle is currently being modelled mathematically using the principles of polymer physics and chemical kinetics. To understand fully the way living systems form and function (including the mechanism of cell division), we need to uncover the basic principles that guide biological organization. Physicists still know relatively little about the forces that guide atoms to self-assemble into molecules. Biochemists know even less about how groups of molecules join together to create living cells and tissues. However, remarkably many natural systems are constructed using a common form of architecture known as tensegrity, a term which refers to a system that stabilizes itself mechanically because of the way in which tensional and compressive forces are distributed and balanced within itself. Tensegrity structures are mechanically stable because of the way the entire structure distributes and balances mechanical stresses and not because of the strength of individual members. Since tension is continuously transmitted across all structural members, a global increase in tension is balanced by an increase in compression within members distributed throughout the structure. The interiors of living cells contain an internal framework called the cytoskeleton, composed of three different types of protein polymers, i.e. actin, intermediate filaments and microtubules. Cells get their shape from tensegrity due not only to the cytoskeleton's microfilaments but also from the extracellular matrix - the anchoring scaffolding to which cells are naturally secured in the body. Although the cytoskeleton is surrounded by membranes and penetrated by viscous fluid, it is this hard-wired network of molecular struts and cables that stabilizes cell shape. The microtubules are compressed, rigid elements. the actin filaments are tensile. The existence of a tensegrity force balance provides a means to integrate mechanics and biochemistry at the molecular level and it suggests that the structure of the cell's cytoskeleton can be changed by altering the balance of physical forces transmitted across the cell surface. Therefore, there can be a dynamical interplay between the cytoskeletal geometry and the kinetics of biochemical reactions including gene activation. Remarkably, by simply modifying their shape, cells could switch between different genetic programs. Cells that spread flat became more likely to divide, whereas round cells may activate a death program celled apoptosis . When cells are neither too extended nor too retracted, they neither divide nor die but, instead, differentiate themselves in a tissue-specific manner.

Lecture 4: Signalling, Information and Mass Transfer Incuding Motor Proteins
Friday December 18, 1998 at 14.00
MIDIT Seminar 429

Biomolecules sometimes behave like electronic elements and their structure allows to process information. Proteins of a cell membrane are able to receive and decipher even very weak electromagnetic signals. The proces implicated in these abilities has been termed "resonance electroconformational coupling" and it involves an AC electric field of a defined amplitude and frequency which induces resonantly oscllations of a protein conformer. Can MTs also transport information by conducting a wave of coherent conformational change? Can MTs store information by showing a mosaic of conformational states? Such functions for MTs have been suggested by several scientists. Some evidence links the cytoskeleton with information processing and cognitive function. In order to examine the usefulness of MT's as biological information processors we must first evaluate the information capacity within each of the three dielectric phases identified. These results can be used to find the optimal conditions for the MT's to function as an information storage device. In this context it is interesting to note the distinction between MT's residing in the axon of nerve cells and those in other types of cells. It appears that the latter configure themselves preferentially parrallel to electric field gradients which, in turn are oriented perpendicular to the membrane walls. On the other hand, MT's inside the axons are subjected to perpendicular electric fields due to the action potential.

In the second half of the lecture we discuss mass transport and force generation in the cell via motor protein motion along microtubule protofilaments. The model we then propose assumes the presence of an effective potential due to electrostatic effects which has a different character in the direction parallel to the protofilament from the direction perpendicular to the protofilament axis.

Along the filament axis it resembles the so-called washboard potential frequently used in the physics of semiconductors and superconductors.We discuss the physical mechanisms involved in each of the steps of motor protein motion and derive requisite differential equations of motion for the motor protein. Finally, we compare our results with a host of experimental data such as the dependence of the average velocity on the ATP concentration, the effects of externally applied electric fields and temperature.