Nonlinear Dynamics in Biology & Biomedicine

The rapid development of new quantitative methods in biology and medicine, making it possible to measure in real-time quantities previously difficult to access (such as the activity of a gene), creates new modeling needs in these fields. However, the behaviors encountered are intrinsically non-linear such as bistability, saturation, or on the contrary, hyper-amplification, oscillations are frequently encountered. Their mathematical study must, therefore, be approached by suitable methods, stemming from the theory of dynamic systems and from nonlinear dynamics. In addition to technical tools, nonlinear dynamics provide a conceptual framework, which allows a better understanding of phenomena such as for example the synchronization of oscillators or the destabilization induced by a delay. Furthermore, the new tools developed to characterize complex (for example, chaotic) behaviors can be diverted to quantify the variability of living systems. Interaction is doubly beneficial. The new insights into biological problems can be brought by the mathematical approach. On the other hand, biology and medicine impose constraints that are different from other fields of application and can, therefore, inspire new methods.

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In biology, genetic regulation networks constitute complex sets of choices. If genome sequencing is now a reality, it is not enough to understand how living things work. Indeed, genes are not static objects, their activities are strongly coupled and vary over time, depending on cross-interactions and the environment. The map of molecular interactions linked to a given function is very complex. However, many works based on simple dynamic models give hope that we can isolate small modules involving some genes and proteins in mutual interaction, and thus understand the functioning of the original system from the coupling of these modules. The study of these complex assemblies often reveals elementary blocks made up of flip-flops made by bistable devices, self-maintained oscillators designed around negative feedback loops, and signaling cascades that propagate information between different modules. , which all have strongly non-linear responses.

Understanding how these modules work and communicate in order to efficiently and robustly perform biological functions is of crucial importance because regulatory networks control the fate of cells and underlie major biological phenomena. The cell division cycle, the understanding of which is essential both in its normal (development) and abnormal (cancer) aspects, the circadian clock which paces a large number of processes on the 24-hour scale, the somitic clock which spins the formation of the vertebrae are thus classic examples of genetic oscillators. Bistability phenomena are used by the cell to produce cellular memories or "checkpoints" beyond which no reversal is possible (cell division, programmed cell death, etc.).

Neuroscience

Neuroscience is also a large field of application of nonlinear dynamics, and this since the pioneering work of Hodgkin and Huxley on the modeling of the initiation and the propagation of action potentials in neurons. Understanding the phenomena of oscillation, waves, and synchronization in the complex and highly structured systems that are the assemblies of neurons that make up our brain and how they form the basis of elaborate processing of information is an essential issue. It is also a natural setting for studying the phenomena of self-organization. As with genetic networks, the interaction between noise and deterministic dynamics cannot be overlooked, and it is even likely that stochasticity is a key element of the machinery.

Cardiac dynamics, epidemiology, immunology, ecology are still other biological themes where dynamic aspects are important, and many medical questions are beginning to benefit from the systemic approaches which have been illustrated in the study of genetic networks. Finally, the biomedical systems (cardio-respiratory, cerebral systems, etc.) are characterized by oscillations, whose fluctuations reflect different physiological states. One of the challenges is not only to reliably link the different dynamic behaviors of these systems to the different physiological states. For this, it is necessary not only to have reliable measurements of variables representative of the states of the system but also to develop analysis techniques. The automatic does not require human intervention that allowing reliable discrimination of different physiological states. The challenges relate to an increased understanding of bio-medical dynamics allowing the development of expert systems that can provide diagnostic assistance for the hospital practitioner.

It is not a question here of approaching these systems from measurements on the living (of patients) and answering practical questions asked by doctors. Indeed, the theory of dynamic systems offers a battery of analysis techniques particularly suited to these complex systems. Its activities fall within the field of biomedical engineering and are related to the activities of the themes. The challenges relate to an increased understanding of bio-medical dynamics allowing the development of expert systems that can provide diagnostic assistance for the hospital practitioner. It is not a question here of approaching these systems from measurements on the living (of patients) and of answering practical questions asked by doctors. Indeed, the theory of dynamic systems offers a battery of analysis techniques particularly suited to these complex systems. Its activities fall within the field of biomedical engineering and are related to the activities of the themes. The challenges relate to an increased understanding of bio-medical dynamics allowing the development of expert systems that can provide diagnostic assistance for the hospital practitioner. It is not a question here of approaching these systems from measurements on the living (of patients) and answering practical questions asked by doctors. Indeed, the theory of dynamic systems offers a battery of analysis techniques particularly suited to these complex systems. Its activities fall within the field of biomedical engineering and are related to the activities of the themes.

It is not a question here of approaching these systems from measurements on the living (of patients) and of answering practical questions asked by doctors. Indeed, the theory of dynamic systems offers a battery of analysis techniques particularly suited to these complex systems. Its activities fall within the field of biomedical engineering and are related to the activities of the themes. It is not a question here of approaching these systems from measurements on the living (of patients) and answering practical questions asked by doctors. Indeed, the theory of dynamic systems offers a battery of analysis techniques particularly suited to these complex systems. Its activities fall within the field of biomedical engineering and are related to the activities of the theme.

Author: Vicki Lezama