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The Biologist Toolbox: Drawing Systems

30 March 2018

Systems Theory was invented in the middle of the last century by the biologist Ludwig von Bertalanffy, as a way to understand the complexities of life. Today we could think that systems theory was created by engineers or psychologists, who use them frequently. But it is really a tool for biologists. We do not need to look further than the dogma of molecular biology to see that it is just a system.

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A system is a group of items that are interconnected and affect each other. We can apply this perspective in biology (transcription regulation, metabolism, signaling), chemistry (reactions), ecology (population dynamics), economy and electronics. For example, systems used in economy have been found to be equivalent to systems in hydraulics and electronicsFor another nice example see F.A.Firestone. “A New Analogy Between Mechanical and Electrical Systems.” Journal of the Acoustical Society of America, 1933, 249–67. . As the Business Dictionary says in the definition of systems:

Systems underlie every phenomenon and all are part of a larger system. Together, they allow understanding and interpretation of the universe as a meta-system of interlinked wholes, and organize our thoughts about the world.

Although different types of systems (from a cell to the human body, soap bubbles to galaxies, ant colonies to nations) look very different on the surface, they have remarkable similarities

Every system has items and interactions. They are often represented by networks where the nodes represent the items and the links represent interactions. Here we are going to use a slightly different representation.

We will represent any system with a network with two kinds of nodes: circles and boxes. Circles will represent the items, boxes will represent their interactions. Circles are connected to boxes with arrows (one-direction links) and vice-versa. There cannot be arrows between circles or between boxes, only between nodes of different shape. There can be more than one arrow between boxes and circles, in any directionThe technical name of this kind of network is directed bipartite multigraph. .

Drawing a system in this way allow us to make a complete and precise description of the items and interactions. That help us to communicate the model with other people. It also help us to analyze and simulate the system, and to determine its characteristics.

This abstract representation allows us to see the system in a general way, that help us to see the analogy with other systems arising from different areas.

How to draw the system

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Example of a simple system.
Boxes represent the processes that make the items quantities change. Circles represent the items that can change.

The arrows going into a box show which items are required for the process. The items that point towards a process are the inputs that will be consumed by the process. When a item is consumed by a process, the item quantity gets smaller.

The arrows going out of a box show which are the products of the process. The quantity of these items is going to increase with the process.

Lets illustrate this with a simple example. Our system is a flask with bacterial cells and food, and we want to see how the cell colony grows through time. We will assume that the cells need food to replicate. Moreover, the replication rate is proportional to the food availability.

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Figure 1. A model of the cell growth system.
There is a single process in this system: cell replication. This process takes one cell and delivers two. Therefore there is one arrow from cells to replication and two arrows back.

Since we assumed that the cells need food to replicate, there should be an arrow from food to replication. The network representing our system looks like Figure 1.

References

Koch, Ina. “Petri Nets - A Mathematical Formalism to Analyze Chemical Reaction Networks.” Molecular Informatics 29, no. 12 (December 17, 2010): 838–43. doi:10.1002/minf.201000086.

Ludwig von Bertalanffy, “General System Theory: Foundations, Development, Applications” New York (1968): George Braziller, revised edition 1976: ISBN 0-8076-0453-4

Originally published at https://anaraven.bitbucket.io/blog/2018/drawing-systems.html