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 Building 321 P.O. Box 49 University of Copenhagen DK-2800 Lyngby DK-4000 Roskilde DK-2100 Copenhagen Ø Denmark Denmark Denmark
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.