Biology Reference
In-Depth Information
a protein with a hydrophobic part it exists in a steady state
with a membrane-bound and a cytosolic fraction. It is
important to stress that both kind of state are caused by
dynamic and often cyclic processes, which are mediated by
further binding partners. Guanine nucleotide binding is
regulated by guanine nucleotide exchange factors (GEFs)
and GTPase-activating proteins (GAPs), while scaffolds
such as BEM1 increase the proximity of CDC42 and its
GEF CDC24. Under 'normal' cellular circumstances these
reactions are balanced out to remain stable. However, since
BEM1-binding
time the spatial organization triggers new downstream
components. Specifically, the formation of microtubules
into the mitotic spindle is a necessary step before micro-
tubule-binding proteins can separate chromosomes, but
timing does not imply causality, because the underlying
processes can be interlinked. In all these examples the
scientific goal to determine the exact configuration of the
process, be it a snapshot (in time) or a zoom-in (in space)
needs to be tempered with knowledge of the bigger picture
to avoid postulating a standalone cause for a situation
emerging from a complex interplay of spatiotemporal
dynamics.
is CDC42-GTP dependent
and
the
CDC42
CDC24 complex favors CDC42-GTP
binding, this positive feedback carries the potential to
switch CDC42 activity and recruitment to a different mode.
As Turing described for coupled reaction-diffusion systems
[7] , a shift in a parameter (e.g., expression level of CDC42)
can destabilize a system, akin to a running car being shifted
into gear. If the cell operates in this mode, a random fluc-
tuation of CDC42-GTP can amplify into a sharp localiza-
tion and can in the process deplete the cell of cytosolic
CDC24 via diffusion. This is a method of communication,
because it stops distant, less-pronounced spikes in CDC42-
GTP concentration from growing further, delivering the
'message' that there exists a more successful competitor in
the neighborhood. The result again is a stable dynamic
cyclic process of binding/unbinding, albeit with a different
localization pattern. The cytosol in this example serves two
functions: in the inactive mode it smoothes the random
fluctuations because of its rapid exchange of material. In
the active mode its role is a medium for fast information
transfer to suppress other sites of CDC42 localization if the
fastest-growing site can, via CDC24 depletion, 'commu-
nicate' its success faster than the growth rate of its
competitors. However, the cytosol can only achieve this in
the presence of its complement: the plasma membrane with
its reduced dimensionality which acts as a template for
processes on a different timescale than in the cytosol.
Another example for this principle is the generation of
a cell-spanning gradient by anchoring the point source of
activity at a specific site as in Fus3-phosphorylation in
yeast, or pheromonally activated transmembrane receptors
in the PM that diffuse at a timescale different from the
spreading of their activity signal. In both cases perturba-
tions of the steady state occur at the smallest relevant
scale
BEM1
e
e
SPATIOTEMPORAL MODELING
OF CELLULAR PROCESSES
Abstraction of a biological phenomenon means that its
observation must be quantified and transferred into the
common language of mathematics, independent of
observer or instrument. With an equation that describes
a hypothesis of the process and a set of numbers that
describe a context, the outcome of a new experiment can be
predicted and the actual results compared. This functions as
a test of whether the abstraction of a process was valid. A
misconception has long been perpetuated that complete
knowledge of the parts of the process at its smallest scale
can be extrapolated to the end result. In case of a simple
chemical reaction it is impractical to consider the collision
frequency of single molecules and their electrostatic
interaction forces to derive the stoichiometry and speed of
this reaction because of Avogadro's number of molecules.
But the large number of interacting molecules in a small
volume also saves the day, as an abstract value for the
probability of a reaction to occur and the initial concen-
trations adequately describe the outcome of the reaction.
Thus, in understanding a dynamic process we choose
a level of abstraction and formulate partial differential
equations (PDEs), which describe the dynamics of the
system at this level. Mathematically, a differential equation
assumes that by dividing space and time into infinitesimally
small elements, realistic behavior can be predicted if the
current state is known. As is usually the case, if there are no
analytical solutions numerical methods are employed.
Here, the elements of time and space are chosen small
enough to guarantee accuracy, but large enough so that the
future state of the system to be modeled can be calculated
in a reasonable timeframe. Non-linear dynamics and chaos
theory (as used to describe turbulent flow, weather, etc.),
however, have illustrated the limitation of this approach. If
the system is sufficiently interconnected and has enough
components, small computational errors propagate and
accumulate so that the systemmay end up in different states
depending on the initial conditions. In other words, local
post-translational modification in the form of, for
example, phosphorylation of an amino-acidic residue.
Furthermore, in both examples these minute changes can be
responsible for a change in the cell's fate, be it differenti-
ation, proliferation or death. Mitosis is an example where
the spatially homogeneous nucleus of eukaryotic cells
undergoes dramatic organization, which starts with mitotic
spindle assembly and chromosome separation and leads to
cytokinesis. In each of these processes multiple interaction
networks govern the spatial restructuring, while at the same
e
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