Biological functions and functional modules originated in structure of chemical reaction network

Abstract: In living cells, chemical reactions are connected by sharing their products and substrates, and form a complex network system. Biological functions arise from the dynamics of chemical reaction networks, and are regulated by changes in the amount/activity of enzymes that catalyze reactions in the system. In this talk, I will introduce our recent theoretical approach to determine the behaviors of chemical reaction systems caused by changes in the amount/activity of enzymes, based solely on network topology. (1) We found that the qualitative response of chemical concentrations (and reaction fluxes) to changes in enzyme amount/activity can be determined from the network structure alone. (2) Non-zero responses are localized to finite ranges in a network, and each range is determined by a subnetwork called a “buffering structure”. The buffering structure is defined by the following equation from local topology of a network 𝜒≔−(# of chemicals)+(# of reactions)−(# of cycles)+(# of conserved quantities)=0 where the index 𝜒 is analogous to the Euler characteristic. We proved that any perturbation of a reaction parameter inside a buffering structure only affects the concentrations and fluxes inside the buffering structure, and does not affect the concentrations and fluxes outside. Finally, (3) buffering structures govern the bifurcation of the steady state of a reaction network. The bifurcation behaviors are localized to finite regions within a network, and these regions are again determined by buffering structures. These results imply that the buffering structures may be the origin of the modularity of biological functions derived from reaction networks. We applied this method to the cell cycle system and demonstrated that the regulation of different checkpoints is achieved by buffering structures.

References

Mochizuki A. & Fiedler B. (2015) J. Theor. Biol. 367, 189-202.

Okada T. & Mochizuki A. (2016) Phys. Rev. Lett. 117, 048101

Okada T. & Mochizuki A. (2017) Phys. Rev. E 96, 022322

Yamauchi, Hishida, Okada, Mochizuki (2024) Phys. Rev. Research 6, 023150

Yamauchi, et al. (In preparation)

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

( video )

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Seminar on the Mathematics of Reaction Networks

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This seminar series focuses on progress in mathematical theory for the study of reaction networks, mainly in biology and chemistry. The scope is broad and accommodates works arising from dynamical systems, stochastics, algebra, topology and beyond.

We aim at providing a common forum for sharing knowledge and encouraging discussion across subfields. In particular we aim at facilitating interactions between junior and established researchers. These considerations will be represented in the choice of invited speakers and we will strive to create an excellent, exciting and diverse schedule.

The seminar runs twice a month, typically on the 2nd and 4th Thursday of the month, at 17:00 Brussels time (observe that this webpage shows the schedule in your current time zone). Each session consists of two 25-minute talks followed by 5-minute questions. After the two talks, longer discussions will take place for those interested. To this end, we will use breakout rooms. For this to work well, you need to have the latest version of Zoom installed (version 5.3.0 or higher), and use the desktop client or mobile app (not supported on ChromeOS).

We look forward hearing about new work and meeting many of you over zoom! Many of the talks are recorded; to see the recording, from Past Talks, open details of the listed talk for a video link.

The organizers.

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