Random walks and cell size
Paul S. Agutter
1
and Denys N. Wheatley
2
*
Summary
For many years, it has been believed that diffusion is the
principle motive force for distributing molecules within
the cell. Yet, our current information about the cell makes
this improbable. Furthermore, the argument that limita-
tions responsible for the relative constancy of cell sizeÐ
which seldom varies by more than a factor of 2, whereas
organisms can vary in mass by up to 10
24
Ðare based on
the limits of diffusion is questionable. This essay seeks to
develop an alternative explanation based on transport of
molecules along structural elements in the cytoplasm
and nucleus. This mechanism can better account for cell
size constancy, in light of modern biological knowledge
of the complex microstructure of the cell, than simple
diffusion. BioEssays 22:1018±1023, 2000.
ß 2000 John Wiley & Sons, Inc.
Introduction
The belief that diffusion can explain many aspects of
intracellular molecule movement is no longer tenable, since
classical (Fickian) diffusion theory cannot strictly apply to
conditions within the cell as we currently understand them.
(1±7)
Yet simple diffusion is still often invoked, or frequently (often
unwittingly) assumed, to explain intracellular transport of
macromolecules in eukaryotic cells.
(8)
The extensive evidence
against the diffusion theory will be discussed here and an
alternative viewpoint will be presented.
Since diffusion should no longer be taken as the ``natural''
explanation (by default) for any otherwise unexplained
transport process, many of our textbooks (e.g. Ref. 9) will
need to be rewritten. In some cases, however, this will occur
slowly and often reluctantly, because many authors are unable
to decide what to substitute for diffusion, as there is no
generally accepted alternative. In the past where diffusion was
patently insufficient to account for a particular phenomenon,
ad hoc supportive mechanisms were sometimes promulgated,
leading to concepts such as ``facilitated diffusion'', which
generally only served to hide our ignorance. In such cases, it
was assumed that, at some later stage, researchers would
elucidate the molecular mechanisms involved, since these
transport systems, being clearly directed and directional,
cannot be diffusional processes.
The ``fluid'' character of the cell internum has been re-
evaluated over the last generation; the idea of the cell as a bag
of aqueous solution is finally being replaced by an image of a
crowded and highly ordered cytoplasm.
(10,11)
Even metabolic
processes thought, as recently as 1970, to take place in bulk
aqueous solution are now attributed to organized enzyme
assemblies.
(12,13)
In turn, these assemblies do not just float
around like submarines in the same cellular sea as de Duve's
``cytonauts'',
(14)
but are tethered and closely integrated with
cytoskeletal structures to form a continuum.
(15)
It should be
appreciated, however, that this continuum is extremely
dynamic and any structure within it might have a very short
time constant of existence. A plethora of mathematical models
would be required to accommodate these circumstances
(6,7)
to a diffusion-based model.
(16,17)
Furthermore, one of the more
obvious features of the cytoplasm of the living cell seen down a
powerful modern microscope is that particles, granules and
organelles within it exhibit very little ``free movement''. In
contrast, Brownian motion becomes readily apparent within
superficial blebs or the main body of the cytoplasm in injured,
dying and dead cells. Presumably loss of function and death
are associated, inter alia, with failure to maintain the
infrastructure of cytoplasm. Once such (dynamic) structure
is lost, diffusion would dominate, as it does in any completely
fluid medium.
If diffusion on its own imposes severe limitations on the
functioning of the living cell above a certain size,
(9)
we have to
consider what alternative means of molecular movement are
generally superimposed upon this (inadequate) background
activity. We will use nucleocytoplasmic transport of mRNA and
related functions as our paradigm, which will lead to a
discussion on how such mechanisms might exert constraints
on cell size.
Extent to which random thermal movements
affect macromolecules in cells
Brownian motion of colloidal particles (and thermal motion of
solute molecules) are ineluctable phenomena in all fluid
media. Since the cell internum is not unreasonably regarded
as a fluid medium (even the erythrocyte is 63% water, oddly a
figure less than the water of hydration of a haemoglobin
crystal), the inference is that intracellular molecules and
multimacromolecular assemblies can, and undoubtedly do,
diffuse. We accept it as indisputable that random thermal
1018 BioEssays 22.11 BioEssays 22:1018±1023, ß 2000 John Wiley & Sons, Inc.
1
Formerly at the Department of Biological Sciences, Napier University,
Edinburgh, Scotland.
2
Department of Cell Pathology, University of Aberdeen, Aberdeen,
Scotland.
*Correspondence to: Dr. Denys N. Wheatley, Department of Cell
Pathology, University of Aberdeen, 581 King Street, Aberdeen, AB24
5UA, Scotland, UK. E-mail: wheatley@aberdeen.ac.uk
Problems and paradigms