Biology Reference
In-Depth Information
DIMENSIONALITY EFFECTS IN
BIOCHEMICAL REACTIONS
The term 'cell', from the Latin for 'small room', describes
the compartmentalization that enables life by confining
reactions and thereby shielding them from the entropic
effects of diffusion. The 'wall' of this 'small room' is the
plasma membrane (PM),which in addition to defining the
enclosed volume provides a reaction surface where local
densities of reactants and products are higher. The PM
comprises the organizational point of origin for bidirec-
tional communication that integrates the intracellular state
with the extracellular context via networks of inter-
connected interacting protein ensembles
[2]
.Asa2D
surface, reactions and matter exchange function signifi-
cantly differently from the enclosed cytosolic volume. A
chemical example of this difference is the Beloussov
even 60 years after its discovery
is not entirely under-
stood. When this system is modeled, the large number of
parameters yields a parameter space which is simply too
large to analyze systematically. However, sensible simpli-
fications yield an easy set of reactions that are closely
related to the Lotka
e
Volterra equations, which govern
e
predator
prey systems and form a cornerstone of
biophysics and theoretical biology. These equations can be
solved numerically in 2D and yield results that match the
experiments closely with a manageable number of param-
eters. To introduce another layer of complexity, perturbing
the system by adding methanol to the Petri dish hampers
the periodic structures in such a way that they become
frazzled and unstable. This chaotic behavior cannot be
understood simply by looking at the waves, as they appear
two-dimensional when seen from above, and necessitates
expanding the model to include more parameters about the
wave's 3D shape (
Figure 17.1
).
e
e
Zhabotinski reaction (BZ reaction), the prototype of
a chemical oscillator, which consists of about 40 chemical
reaction steps. In a well-stirred beaker, the color of the
solution oscillates with a fixed period between two states
(
Figure 17.1
). However, if 'spread' thin in a Petri dish, the
reactants become an excitable medium
[3]
. Starting from
a global excitable state, small hotspots of excitation (either
triggered externally, or amplified from random fluctuation
of the initial context) spread in concentric spiral waves,
which can be reset by shaking the dish.
This example of self-organization in a lifeless/non-
biological system has a striking impact on cellular biology
and the way we try experimentally and theoretically to
approach biological problems. The three main components
of the BZ reaction, cerium sulfate, malonic acid and
potassium bromate dissolved in sulfuric acid, are interact-
ing far from equilibrium at the expense of energy. The
interaction is sufficiently complex that the chemistry,
which occurs in each point of the dish at a given time
TOWARDS A SYSTEMIC UNDERSTANDING
OF CELLULAR BIOLOGY
As humans, we are limited in our ability to fully understand
any system in its totality without intense study. As a foun-
dation of science we typically apply three fundamental
techniques: reductionism, abstraction and generalization.
Compartmentalization is an example of reductionism: we
divide a problem into subsets with few critical components
in each subset. For the critical components of a given
subset, we collect experimental observations to formulate
abstract rules that allow us to generalize the behavior of
that subset to include the behavior of a different subset
following similar rules. Herein lies the strength of the
scientific principle and its danger: it allows us to deal with
complicated systems by narrowing our focus until we lose
e
FIGURE 17.1
Beloussov
e
Zhabotinski reaction.
Left panel: Experimental snapshot of the BZ reaction.
Top row: color change signifying the cyclic reaction
over a period of 20 s. Middle row: Progression of
a spiral wave of the BZ reaction confined in a 2D dish as
seen from above. Lower row: Adding methanol, the
periodicity of the reaction becomes unstable and wave
progression chaotic. This cannot be derived from the
2D projection. However, a cut in z-direction reveals that
consecutive wave-fronts tilt increasingly, until the front
of the following wave interferes with the back of the
preceding one. This comprises an example for the type
of Turing instability that leads to Turing patterns. Right
panel: Cellular automaton implementation of the BZ
reaction. The center column shows the local building
blocks of the simulation and their connection. The
displayed simulations (left and right column) are discretized to 300
300 of the small square cells depicted in the center column. The value of excitation
in a given cell is distributed among its neighbors. Depending on the local definition of the neighborhood, varying spiral patterns result. Top row: Regular
small or larger neighborhoods lead to too-regular large-scale patterns. Bottom row: Adding a stochastic position to the centers of each square, local
neighborhoods become warped to a varying degree (left: 10% variation; right: 50% variation).
time
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Experiment
Simulation
