Dr. Sahaya Vijay Jeyaraj - Applied Mathematics & Chemical Reaction Networks

About Me

Dr. Sahaya Vijay Jeyaraj
Postdoctoral Researcher, NIMS

I am an interdisciplinary researcher with a strong background in applied mathematics, chemical kinetics, and chemical reaction networks. Currently, I am a postdoctoral researcher at the National Institute for Materials Science (NIMS), Japan, where I develop accurate mathematical models and analytical formulations to predict the properties and dynamics of complex, nonlinear chemical systems.

My doctoral research was in chemical graph theory, focusing on predicting the physicochemical properties of metamaterials and drug-related structures. The central contribution of that work was using regression analysis to evaluate a wide range of topological indices and identify those with the strongest predictive power for the physicochemical properties of several important classes of molecular structures.

Across both my doctoral and postdoctoral work, a single thread runs through everything: the analysis of chemical reaction networks. I am passionate about leveraging mathematical tools to gain deeper insight into chemical processes and to contribute to advances in materials science and related disciplines.

The greatest discoveries are made at the boundaries between disciplines, where different ways of thinking come together to reveal new understanding.

Research Interests

My current postdoctoral research concerns predicting the kinetic properties of chemical reaction networks in champion materials, using mathematical modelling based on ordinary differential equations (ODEs) and graph theory. Although the systems and fields differ, all of my projects rest on the same core framework: the analysis of chemical reaction networks.

Chemical Graph Theory

Topological indices and molecular descriptors for quantitative structure–property relationship (QSPR) analysis, entropy measures, and the physicochemical characterization of metamaterials and drug-related structures.

Molecular graph mapped to a property by regression — A molecule is treated as a graph of atoms (vertices) and bonds (edges); degree-based indices are regressed against measured properties to predict them.

Autocatalysis & the Origin of Life

Analyzing the amplification rate of autocatalysis in linear chemical reaction networks to understand what governs whether autocatalysis is amplified. This work is currently under review at Physical Review E.

Autocatalytic cycle and exponential growth curve — A species that catalyses its own formation (A→2A) feeds a loop; the network's amplification factor λ decides whether the population grows over time.

Mathematical & Computational Modelling

Developing analytical formulations and ODE-based models to predict the dynamics and stability of complex, nonlinear chemical systems across the origin of life, electrochemistry, and neuroscience.

ODE trajectories converging to a steady state — Reaction kinetics written as differential equations; trajectories from different starting points reveal the system's steady states and their stability.

Electrochemical Impedance Spectroscopy

Applying the reaction-network framework to electrochemistry: I derived a mathematical formula for the surface coverage in electrochemical impedance spectroscopy, and used it to obtain impedance spectra and Bode plots linked to the kinetic time scales of champion materials.

Nyquist impedance plot and equivalent circuit — Impedance Z(ω) traced in the complex plane as frequency varies; the arc's width encodes charge-transfer resistance and electrode surface coverage.

Synaptic Memory & the CaMKII Switch

Modelling the chemical reaction network underlying long-term memory storage - the autocatalytic CaMKII switch at the synapse - with ODE-based kinetics, to characterize the bistability and threshold conditions that decide whether a synaptic state persists or decays.

Bistable double-well potential with a threshold — Two stable states - memory stored (ON) or erased (OFF) - sit in separate wells; a signal must cross the threshold to flip the switch, so a memory that stays deep persists.

Scientific Computing & Open Tools

Building open scientific software, including PyTIE, a Python program for evaluating degree-based topological descriptors and molecular entropy, together with machine-learning approaches to the topological features of nanomaterials.

PyTIE computing descriptors from a molecular graph — Open Python tools (PyTIE) take a molecular graph as input and compute its topological descriptors and molecular entropy automatically, at scale.

Publications

Peer-reviewed research in mathematical modelling, topological analysis, molecular descriptors, and computational science.

16Publications

2023–26Active Years

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1. Kinetic Boundary between Autocatalysis and Diffusion in the Origin of Life

Sahaya Vijay Jeyaraj, Hirokazu Komatsu, Tomoharu Suda, Ryuhei Nakamuram, Hideshi Ooka

Chemrxiv(2026)

About Me

Research Interests

Chemical Graph Theory

Autocatalysis & the Origin of Life

Mathematical & Computational Modelling

Electrochemical Impedance Spectroscopy

Synaptic Memory & the CaMKII Switch

Scientific Computing & Open Tools

Publications

1. Kinetic Boundary between Autocatalysis and Diffusion in the Origin of Life

2. Anticancer Activity with Physical Property Analysis of Mollugo Cerviana (L.) Ser. Whole Plant Extract on Hepatocellular Carcinomic Cell Lines - HEPG2

3. Topological, Graph-Spectral Properties, NMR and ESR Spectral Patterns of Hydrogen-Bonded Nanosheets of Boric Acid

4. Machine Learning Approach on Topological Features of Bottom-up Synthesized Graphene Nanoribbons Using Valency-Based Descriptors

5. PyTIE: A Python Program for the Evaluation of Degree-Based Topological Descriptors and Molecular Entropy

6. Machine Learning Approach on Degree-Sum-Based Topological Indices of Bottom-up-Synthesized Graphene Nanoribbons

7. Graph-Theoretical Approach to Topological Features of Zeolitic Tetrahedral Imidazolate Framework-3

8. Efficient Generation of Specific Counting Polynomials and Its Subsequent Indices of Complex Boric Acid Structure

9. Exploring Neighborhood Topological Descriptors for QSPR Analysis and Entropy Measures of Some Anti-cancer Drugs

10. QSPR Modeling of Central Nervous System (CNS) Drug Activity Using Molecular Descriptors

11. Valency-Based Molecular Descriptor on Structural-Property Relationship of Ni Tetrathiafulvalene Tetrathionate

12. In Silico Rationalization of Piperidin-4-One Analogs as Anaplastic Lymphoma Kinase Inhibitors: DFT, Topological Descriptor, Molecular Docking and Pharmacological Feature Profiling

13. A Study on Efficient Technique for Generating Vertex-Based Topological Characterization of Boric Acid 2D Structure

14. Topological Properties and Entropy Calculations of Aluminophosphates

15. Computation of Wiener Descriptor for Melamine Cyanuric Acid Structure

16. Topological Study on Degree-Based Molecular Descriptors of Fullerene Cages

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