报告题目：Building mathematical models in Systems Biology
The three lectures will examine how to build mathematical models in the field of Systems Biology.
The first lecture will be devoted to the modeling of periodic behavior in a metabolic pathway. Oscillations in glycolysis, discovered some five decades ago, continue to be investigated and still represent the prototype of periodic behavior in a biochemical system. The oscillations have a period of the order of a few minutes. They originate from the regulation of one enzyme reaction in the glycolytic pathway, catalyzed by phosphofructokinase (PFK). Mathematical models were proposed after the mechanism of this periodic phenomenon was identified experimentally. I will show how to build a two-variable model for glycolytic oscillations, and how to use phase plane analysis to account for key experimental observations in terms of limit cycle behavior. Extensions to a 3-variable model allow us to show how periodic oscillations can transform into complex oscillations or chaos.
2. Circadian clocks
The second lecture will be devoted to circadian oscillations, which occur in all eukaryotic organisms, and some bacterial species, with a period of about 24h. Circadian clocks allow living organisms to adapt to the alternation of day and night, which characterizes the periodicity of the environment on Earth. Mathematical models for the genetic regulatory network that underlies circadian rhythms will be presented. First, a relatively simple model for circadian oscillations in the fly Drosophila will be discussed, in terms of negative feedback exerted by the PER protein on the transcription of its own gene. This model had to be modified in view of additional experimental observations, which identified the role of the TIM protein in the circadian mechanism and clarified the molecular bases of the control of the circadian clock by light. More complex mathematical models were subsequently proposed for the mammalian circadian clock. These models clarify the molecular mechanism of the circadian clock and can also be used to address the dynamical bases of circadian clock-related physiological disorders in humans, such as the familial advanced sleep phase syndrome (FASPS).
3. The cell cycle
The third lecture will be devoted to modeling the cell cycle, first in amphibian embryonic cells and then in mammalian cells. Early cell cycles in frog embryos occur with a periodicity of about 30 min, and involve the regulation of an enzyme known as cyclin-dependent kinase, Cdk1 (also known as Cdc2). A 3-variable model shows that the negative feedback regulation of Cdc2 gives rise to periodic oscillations of the limit cycle type. Positive feedback is also present in the regulation of Cdc2 and is capable of producing bistability, i.e. the coexistence of two stable steady states in the same set of conditions. This example allows us to discuss the link between bistability and sustained oscillations. In mammalian cells, the cell cycle is more complex and involves the passage through the successive phases G1, S (DNA replication), G2 and M (mitosis, or cell division). A network of cyclin-dependent kinases (CDKs) controls the passage through these successive phases of the cell cycle. A mathematical model shows how the regulatory structure of the CDK network accounts for its temporal self-organization in the form of sustained oscillations of the limit cycle type. Because the cell cycle and the circadian clock are linked, numerical simulations indicate that unidirectional coupling can lead to entrainment of one oscillator by the other, while bidirectional coupling can readily lead to the robust synchronization of the two cellular rhythms.
After completing his Chemistry studies and his PhD in the group of Ilya Prigogine at the Université Libre de Bruxelles (ULB), Albert Goldbeter did postdoctoral work at the Weizmann Instute of Science (Rehovot, Israel) and at the University of California (Berkeley, USA) before returning to ULB. His research pertains to the analysis of threshold phenomena in cellular regulation and to the mathematical modeling of the mechanism of cellular rhythms, such as metabolic oscillations in yeast, cyclic AMP oscillations and waves in Dictyostelium cells, the segmentation clock, Calcium oscillations, circadian clocks in Drosophila and mammals, and the cell cycle in amphibian embryonic cells and in mammalian cells. For his pioneering work on the mathematical modeling of biological processes he received in 2010 the Quinquennial Prize for Exact Fundamental Sciences from the Belgian Science Foundation (FNRS). He is member (since 2001) and former Director of the Classe des Sciences (Science Division) of the Académie Royale de Belgique (Royal Academy of Belgium, ARB).