Biology Reference
In-Depth Information
interaction modes than traditional engineering applications such as elec-
tronic circuits or fluid mechanics.
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In a direct numerical simulation, all
degrees of freedom need to be explicitly tracked. In continuous systems,
each point in space adds additional degrees of freedom, leading to an infi-
nite number of dimensions. Such systems have to be discretized, i.e. the
number of degrees of freedom needs to be reduced to a computationally
feasible amount, which is done by selecting certain representative dimen-
sions. Only these are then tracked in the simulation, approximating the
behavior of the full, infinite-dimensional system. Discretizations must be
consistent, i.e. the discretized system has to converge to the full system
if the number of explicitly tracked degrees of freedom goes to infinity.
Discrete biological systems already have a finite number of degrees of
freedom and can sometimes be simulated directly. If the number of degrees
of freedom is too large, as is e.g. the case when tracking the motion of all
atoms in a protein, we do, however, again have to reduce them in order
for simulations to be feasible. This can be done by collecting several
degrees of freedom into one and only tracking their collective behavior.
These so-called “coarse graining” methods greatly reduce the computa-
tional cost and allow simulations of very large, high-dimensional systems
such as patches of lipid bilayers with embedded proteins,
33,34
or actin fil-
aments.
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Coarse graining thus allows extending the capabilities of
molecular simulations to time and length scales of biological interest.
2.2. Regulation
In biological systems, little is left to chance, which might seem surprising
given the inherently stochastic nature of molecular processes, environ-
mental influences, and phenotypic variability. These underlying fluctua-
tions are, however, in many cases a prerequisite for adaptive deterministic
behavior, as has been shown, for example, in gene regulation networks.
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In addition to such indirect regulation mediated by bistability and sto-
chastic fluctuations, feedback and feed-forward loops are ubiquitous in
biological systems. From signal transduction pathways in single cells to
Darwinian evolution, regulatory mechanisms play important roles.
Results from control theory tell us that such loops can alter the dynamic
behavior of a system, change its stability or robustness, or give rise to
