The living world teems with fascinating examples of collective dynamics, whether highly visual ensembles, such as flocks of starlings or schools of fish, or less accessible phenomena, such as the synchronization of neurons arising from their mutual interactions. For several decades, mathematical modeling has accompanied teams of biologists specializing in ethology, neuroscience or microbiology, helping them better grasp the interactions between individuals that best explain these movements at the scale of the whole group — a group that, in microbiology, can reach several hundred thousand individuals. The world of bacteria offers both a great diversity of collective movements (waves, branching patterns, synchronization, etc.), a very fine-grained knowledge of genetics and of molecular and cell biology, and, finally, remarkably precise data thanks to recent advances in microscopy.
Let's examine the process of building a model with an example: waves in populations of Escherichiacoli bacteria that travel together through heterogeneous environments, in search of food and cohesion.
A famous experiment
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In a 1966 paper published in the journal Science, the American biochemist Julius Adler describes an experiment in which a bacterial population moves as a tight band along a straight channel filled with water and nutrients (see below). The population density advances along the channel at constant speed, much as a huge crowd of demonstrators might move up a boulevard. The "engine" of this collective movement is attributed to chemotaxis, that is, the tendency of these bacteria to follow molecular signals, such as oxygen or nutrients. This experiment has been reproduced a great many times and still underpins our understanding of the collective dynamics of bacteria — how they search for nutrients and how they communicate with one another through chemical signals diffusing through the medium. Furthermore, this same experiment has provided the foundation for an entire body of modeling, analysis and numerical simulation work at the interface between mathematics and biology.
