# DMS/NIGMS 2: Moment Kernel Machines for Decoding Complexity in Dynamic Biological Networks

> **NIH NIH R01** · WASHINGTON UNIVERSITY · 2024 · $415,134

## Abstract

Conducting an accurate yet simple mathematical description of large-scale dynamical networks, such as
biological networks, is an essential yet challenging step toward enabling design and control of such
complex systems. The extraordinary growth of data-rich biology further calls for discovery of transformative
mathematical techniques to facilitate data-driven research on dynamical systems. For example, daily
rhythms in physiology allow organisms to anticipate reliable environmental events and adapt to changing
environmental cues. The suprachiasmatic nucleus (SCN) generating these precise circadian oscillations
and adapting to environmental changes is comprised of thousands of circadian neurons in the brain. The
long-term goals of this research are to: 1) create a rigorous kernel method that generates a simple yet
accurate representation for modeling complex nonlinear dynamical processes; 2) leverage this method to
design interpretable and principled data-driven techniques for system control and learning of dynamic
networks; 3) resolve longstanding biological questions about deciphering the underlying dynamics of
coupled circadian clocks; and 4) identify enhanced environmental cues to produce desired behavior
patterns such as chronotype setting and sleep consolidation. This proposal aims to overcome the
significant mathematical challenges to solve important problems in circadian biology. In Aim 1, we will
establish the moment kernel machine (MKM) that generates lossless compression models equivalent to the
first-principles state-space models of dynamic network systems. In Aim 2, we will use the predictive power
of MKM modeling to design signals that create desired synchronization patterns in oscillator networks. In
Aim 3, we will demonstrate the versatility of the MKM technique with applications to circadian biology. This
will involve dynamic learning of the SCN gene expression from measurements; and learning and shaping
the output of SCN networks by designing dynamic light protocols for enforced biphasic sleep in young
animals and consolidation of sleep fragmentation in aged animals, and assigning phases of entrainment
(e.g., onset of daily activities) to animals of different genotypes and chronobiological properties. The
integration of novel mathematical and biological tools will provide insight and guidelines for the theory-
inspired experimental designs and lead to a comprehensive understanding of complex network behaviors
such as coupled circadian oscillators producing daily patterns of sleep and wake.

## Key facts

- **NIH application ID:** 11043486
- **Project number:** 1R01GM157609-01
- **Recipient organization:** WASHINGTON UNIVERSITY
- **Principal Investigator:** Jr-Shin Li
- **Activity code:** R01 (R01, R21, SBIR, etc.)
- **Funding institute:** NIH
- **Fiscal year:** 2024
- **Award amount:** $415,134
- **Award type:** 1
- **Project period:** 2024-09-13 → 2027-07-31

## Primary source

NIH RePORTER: https://reporter.nih.gov/project-details/11043486

## Citation

> US National Institutes of Health, RePORTER application 11043486, DMS/NIGMS 2: Moment Kernel Machines for Decoding Complexity in Dynamic Biological Networks (1R01GM157609-01). Retrieved via AI Analytics 2026-05-25 from https://api.ai-analytics.org/grant/nih/11043486. Licensed CC0.

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