Biology Reference
In-Depth Information
simulations currently done consider about 10
10
atoms over one nanosecond.
In order to model a complete cell, we would need a simulation about
100 000 times larger, running over a millionfold longer time interval.
This would result in a simulation at least 10
11
times bigger than what can
currently be done. This is certainly not feasible and will remain so for
many years to come. Even if one could simulate the whole system at full
resolution, the results would be of questionable value. The amount of
data generated by such a simulation would be vast, and the interesting
macroscopic phenomena that we are looking for would mostly be masked
by noise from the small scales. In order to treat coupled systems, we thus
have to use multi-scale models
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and formulations at the appropriate
level of detail.
2.6. Temporal Plasticity
While the analysis of high-dimensional, nonlinear systems is already compli-
cated as such, the systems themselves also frequently change over time in
biological applications. In a mathematical model, this is reflected by jumps
in the dynamic equations or by coefficients and functions that change over
time. During its dynamics, the system can change its behavior or switch to
a different mode. For example, the dynamics of many processes in cells
depend on the cell cycle, physiological processes in organisms alter their
dynamics depending on age or disease, and environmental changes affect
the dynamic behavior of ecosystems. Such systems are called “plastic” or
“time-varying”. Dealing with time-varying systems, or equations that
change their structure over time, is an open issue in numerical simulations.
Consistency of the solution at the switching points must be ensured in order
to prevent the simulation method from becoming unstable.
2.7. Nonequilibrium
According to the second law of thermodynamics, entropy can only
increase. Life evades this decay by feeding on negative entropy.
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The dis-
crepancy between life and the fundamental laws of thermodynamics has
puzzled scientists for a long time. It can only be explained by assuming
that living systems are not in equilibrium. Most of statistical physics and
