IIIT Hyderabad Studies Reveal How Reaction Networks Shape Living Systems

Ever wondered how mosquito populations explode in number after the rains, or why some diseases spread super-fast? Scientists use mathematical models to explain many of these natural, everyday phenomena. Prof. Abhishek Deshpande from the Center for Computational Natural Science and Bioinformatics at IIITH reveals more. 

Thirty years ago, a unique experiment reintroduced gray wolves into Yellowstone National Park. It was a deliberate attempt to restore the ecosystem, which had declined not just in woody plants but also in birds and led to an erosion in riverbanks. Scientists who investigated the matter discovered a population explosion in elk, a species that fed on these trees. Further analysis then revealed that the elk population had spiralled due to the slow extinction of the wolf species. It was thanks to mathematical modelling of the elk-wolf interaction that scientists were able to predict the future of the Yellowstone ecosystem. Essentially, they indicated that with more wolves there would be fewer elk, with fewer elk, there would be more trees, more birds, more plants near rivers, and so on – a prediction that rang true and led to a recovery in vegetation. This web of interconnected reactions is known as a reaction network. At IIITH, Prof. Abhishek Deshpande who is associated with the Center for Computational Natural Sciences and Bioinformatics has a keen interest in modelling interaction between species. “My research interests span dynamical systems, reaction networks, retroactivity and signal transduction,” he says, giving an overview of four applications where reaction networks can be used – dynamical systems, support vector machines, origin-of-life models and homeostasis.

Prof Abhishek Deshpande

Dynamical systems
One of Prof. Deshpande’s most recent works in this area is a research paper titled: “Realizations through Weakly Reversible Networks and the Globally Attracting Locus”, coauthored by his student Samay Kothari and Jiaxin Jin and published in the SIAM Journal on Applied Dynamical Systems. The researchers demonstrated how the dynamics of a family of reaction networks can be embedded into those of another family of networks. Examples include the Thomas-type models used to model the oxidation of uric acid by oxygen in the presence of the enzyme uricase. Another research paper titled, “Endotactic and strongly endotactic networks with infinitely many positive steady states” coauthored with Samay Kothari and published in the Journal of Mathematical Chemistry, explores the ability of “endotactic” networks to possess infinitely many steady states. 

Samay Kothari

Support Vector Machines
“Using chemistry to perform computation is an active area of research,” notes Prof Deshpande. In particular, applications include designing novel biochemical frameworks for implementing machine learning algorithms. The paper “Implementation of Support Vector Machines using Reaction Networks” coauthored with his student Amey Choudhary and Jiaxin Jin demonstrates how the dynamics of reaction networks can mimic Support Vector Machines (SVM). SVMs are powerful tools for data classification, leveraging VC theory to handle high-dimensional data and small datasets effectively. 

MS by Research student, Amey Choudhary’s focused research project on SVMs saw him bagging the IndiaAI fellowship, which is a Government of India initiative to boost talent by supporting UG, PG and PhD students engaged in AI research. The fellowship selects students whose projects aim to bridge the gap between theoretical knowledge and practical application.  

  

Amey Choudhary

Origin-of-Life Models
A mix of chemistry, math, and biology can also be used to explain “origin of life” models. Origin-of-life models assume that life began when molecules replicated themselves through autocatalytic interactions. In this line of research, Prof Deshpande and colleagues have developed tools where they analyze the structure of autocatalytic networks by studying their relative populations. In their paper titled “Autocatalytic recombination systems: A reaction network perspective”, which was published in Mathematical Biosciences they explore how to use techniques from reaction network theory to prove persistence and permanence for such networks.

Homeostasis

“There are several real-world applications of mathematical biology, and one of them includes the phenomenon of homeostasis – a process where organisms maintain a steady internal state despite changes in the external environment,” says Prof. Deshpande. It is how humans maintain their body temperature, blood sugar, blood pressure, and the concentration of ions in their bodily fluids. In their manuscript titled “Homeostasis and injectivity: a reaction network perspective”, published in the Journal of Mathematical Biology, they show that a network cannot exhibit homeostasis if a modified version of that network is “injective”. Further, they provide examples of reaction networks which can or cannot exhibit homeostasis by analyzing the injectivity of the homeostasis-associated reaction network.

According to Prof. Deshpande, mathematical biology and dynamical systems let us see the hidden patterns that guide living things – from cells to ecosystems – and turn that understanding into real solutions for medicine, conservation, and technology. “From mere observation of life, they help us truly understand how it works and how we can work with it.”