Biology Reference
In-Depth Information
thermodynamics has been developed for equilibrium situations and,
hence, does not readily apply to living systems. Phenomena such as the
establishment of cell polarity or the organization of the cell membrane
can only be explained when accounting for nonequilibrium processes
such as vesicular recycling.
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Due to our incomplete knowledge of the
theoretical foundations of nonequilibrium processes, they are much
harder to understand. Transient computer simulations are often the sole
method available for their study.
3. Spatiotemporal Modeling Techniques
Dynamic spatiotemporal systems can be described in various ways,
depending on the required level of detail and fidelity. We distinguish
three dimensions of description: phenomenological vs. physical, discrete
vs. continuous, and deterministic vs. stochastic. The three axes are inde-
pendent and all combinations are possible. Depending on the chosen sys-
tem description, different modeling techniques are available. Figure 2
gives an overview of the most frequently used ones as well as examples of
dynamic systems that could be described with them.
3.1. Phenomenological vs.Physical Models
Phenomenological models reproduce or approximate the overall behav-
ior of a system without resolving the underlying mechanisms. Such mod-
els are useful if one is interested in analyzing the reaction of the system
to a known perturbation, without requiring information about how this
reaction is brought about. This is in contrast to physical models, which
faithfully reproduce the mechanistic functioning of the system. Physical
models thus allow predicting the system behavior in new, unseen situa-
tions, and they give information about how things work. Physical mod-
els are based on first principles or laws from physics.
3.2. Discrete vs.Continuous Models
The discrete vs. continuous duality relates to the spatial resolution of the
model. In a discrete model, each constituent of the system is explicitly
