Surely, every single day we experience phenomena that may appear to be mere coincidence; however, this phenomena are the product of certain key natural ingredients. For instance, in different online platforms you can encounter videos of several metronomes being placed on a table, set to oscillate in different frequencies and intensities. Nevertheless, passed enough time, we can observe that each and every single one of them comes and goes at the same oscillation speed and same intensity. These two quantities are essential to characterize the phenomenon known as: synchronization. In other words, synchronization happens when the frequency and range of several elements of an oscillatory system act in unison.
Where can synchronization be observed?
Synchronization occurs in nature more often than one may think; for example, when females of different mammal species coexist, they tend to synchronize their menstrual periods, similarly to pendulum clocks at home. In the following paragraphs, we will take a brief journey across a phenomenon that has profoundly fascinated the scientific community, given the immediate consequences it has in our daily lives. This phenomenon is usually known as: self-induction.
Self-induction is the regulation of genetic expression that allows communication within a cell population. In the case of bacteria, this mechanism consists of the communication between individuals of a population through molecules known as self-inductors. These molecules allow the bacterial population to explore in search of food or to defend themselves from adverse situations, all this through changes in the number of members in the community.
Concretely, self-induction is based on the production and delivery of self-inductors, which is directly proportional to the density of the bacteria population. In other words, when a population exceeds a certain threshold, the bacteria detect the presence of self-inductors and consequently, their genes responsible for population’s behavior are activated, which provokes other bacteria, unicellular organisms, to behave as a coordinated community, meaning: a multicellular organism.
An analogy of this phenomenon can be observed in a massive rock concert. Each attendee at this concert is an individual, when you reach a certain number of attendees, the music coordinates the dancing or jumping of the public. Alternatively, music corresponds to the signal sent by molecules to synchronously coordinate the behavior of each individual, similarly to observing a mexican wave at the stadium, as it is known in english speaking countries, as it travels across the bleachers.
The road so far
Self-induction was first observed in the 1970s by Nealson and Hastings, who watched how bioluminescent bacteria formed a symbiotic relationship with some squid species. When the bacteria population reaches a threshold, the genes of luminescence are expressed, allowing the squid to use that fluorescence as a defense mechanism against predators. A wide diversity of examples where self-induction is manifested exist in nature; such as the formation of biofilms: bacterial communities that offer resistance to antibiotics and predators, that algo cause difficulties for the water recyccling industry. Furthermore, in the medical field, the study of changes in behavior of cellular communities is crucial in the fight against pathogens and antibiotic production.
As a preliminary conclusion, the understanding of this biological mechanism can result in the development of medications that make difficult or even block the signals of the self-inductors, weakening their resistance to antibiotics or allowing professionals to develop less invasive treatments, in the case of some bacterial diseases, without the side effects that more aggressive medications have.
What tools do we have to understand nature?
Dynamical Systems and Bifurcation theory, branches of mathematics, are particularly relevant in the understanding of the dynamic and consequences of a certain phenomenon. Particularly, the self-induction phenomenon, which is why it can be approached from the focus of mathematic modeling. Meaning, this allows the characterization and discovery of essential ingredients for the coordination mechanism driven by self-inductors.
From an applied mathematics point of view, the theory of Dynamical Systems consists of a set of theoretical tools that allow the strict characterization of dynamical consequences of a determined interaction. Meanwhile, Bifurcation theory, deeply connected to the Dynamical Systems theory, is in charge of exploring and determining all the essential dynamic events that occur in a mathematic model. From a certain point of view, for example, one can consider a population of bacteria divided in two subpopulations: one positive and the other negatively regulated by a concentration of self-inductors, which are produced by the whole population. This way, three ingredients are distributed in different positions within a region (e.g. Petri dish). Thus being, the interactions that are sought to be understood are equivalent to studying a phenomenon of population synchronization given a process of communication site-to-site, which is defined by the concentration of self-inductors in each site and their properties of transportation to other sites.
The natural order and it’s chaotic model
The self-induction model, briefly described above, has a fundamental characteristic very interesting in the theorical point of view: the arise of homoclinical chaos. This is a concept somewhat technical, but still fascinating in the sense that, besides being a recently studied dynamical phenomenon, occurs when certain key conditions are satisfied when changing certain parameters in the system. These parameters correspond to characteristics not only related to the processing of self-inductors by bacteria, but also to the interaction between subpopulations. When this scenario happens, the dynamic consequences become unpredictable, which is a fundamental characteristic of chaos.
Having arrived to the end of this text, I would like to pose three questions that I consider interesting, therefore, relevant to answer.
(i) What is it needed to reach the critical bacteria density so that the whole population is to grow and decrease with similar range and frequency in unison?
(ii) What mechanisms can cause population fluctuations and on what characteristics of the interaction does it depend on?
(iii) If the self-induction model sketched out in the previous paragraphs offer chaotic behaviors, can they be observed through in silico? and what mechanisms regulate or limit them?
Víctor Francisco Breña Medina
Full time Professor