Information geometry of chemical reaction networks: Cramer-Rao bound and absolute sensitivity revisited
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916661998649344 |
|---|---|
| author | Loutchko, Dimitri Sughiyama, Yuki Kobayashi, Tetsuya J. |
| author_facet | Loutchko, Dimitri Sughiyama, Yuki Kobayashi, Tetsuya J. |
| contents | Information geometry is based on classical Legendre duality but allows to incorporate additional structure such as algebraic constraints and Bregman divergence functions. It is naturally suited, and has been successfully used, to describe the thermodynamics of chemical reaction networks (CRNs) based on the Legendre duality between concentration and potential spaces, where algebraic constraints are enforced by the stoichiometry. In this article, the Riemannian geometrical aspects of the theory are explored. It is shown that duality between concentration and potential spaces and the natural parametrizations of equilibrium subspace are isometries, which leads to a multivariate Cramer-Rao bound through the comparison of two Riemannian metric tensors.
In the subsequent part, the theory is applied to the recently introduced concept of absolute sensitivity. Using the Riemannian geometric tools, it is proven that the absolute sensitivity is a projection operator onto the tangent bundle of the equilibrium manifold. A linear algebraic characterization and explicit results on first order corrections to the thermodynamics of ideal solutions are provided. Finally, the theory is applied to the IDHKP-IDH glyoxylate bypass regulation system.
The novelty of the theory is that it is applicable to CRNs with non-ideal thermodynamical behavior, which are prevalent in highly crowded cellular environments due to various interactions between the chemicals. Indeed, the analyzed example shows remarkable behavior ranging from hypersensitivity to negative-self regulations. These are effects which usually require strongly nonlinear reaction kinetics. However, here, they are obtained by tuning thermodynamical interactions providing a complementary, and physically well-founded, viewpoint on such phenomena. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19384 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Information geometry of chemical reaction networks: Cramer-Rao bound and absolute sensitivity revisited Loutchko, Dimitri Sughiyama, Yuki Kobayashi, Tetsuya J. Molecular Networks Differential Geometry Dynamical Systems Biological Physics Classical Physics 80A30, 37C05, 37C25, 92C45, 53B12, 53B50, 62B11, 14M25 Information geometry is based on classical Legendre duality but allows to incorporate additional structure such as algebraic constraints and Bregman divergence functions. It is naturally suited, and has been successfully used, to describe the thermodynamics of chemical reaction networks (CRNs) based on the Legendre duality between concentration and potential spaces, where algebraic constraints are enforced by the stoichiometry. In this article, the Riemannian geometrical aspects of the theory are explored. It is shown that duality between concentration and potential spaces and the natural parametrizations of equilibrium subspace are isometries, which leads to a multivariate Cramer-Rao bound through the comparison of two Riemannian metric tensors. In the subsequent part, the theory is applied to the recently introduced concept of absolute sensitivity. Using the Riemannian geometric tools, it is proven that the absolute sensitivity is a projection operator onto the tangent bundle of the equilibrium manifold. A linear algebraic characterization and explicit results on first order corrections to the thermodynamics of ideal solutions are provided. Finally, the theory is applied to the IDHKP-IDH glyoxylate bypass regulation system. The novelty of the theory is that it is applicable to CRNs with non-ideal thermodynamical behavior, which are prevalent in highly crowded cellular environments due to various interactions between the chemicals. Indeed, the analyzed example shows remarkable behavior ranging from hypersensitivity to negative-self regulations. These are effects which usually require strongly nonlinear reaction kinetics. However, here, they are obtained by tuning thermodynamical interactions providing a complementary, and physically well-founded, viewpoint on such phenomena. |
| title | Information geometry of chemical reaction networks: Cramer-Rao bound and absolute sensitivity revisited |
| topic | Molecular Networks Differential Geometry Dynamical Systems Biological Physics Classical Physics 80A30, 37C05, 37C25, 92C45, 53B12, 53B50, 62B11, 14M25 |
| url | https://arxiv.org/abs/2503.19384 |