Department of Mathematics
University of Michigan
Ann Arbor, MI 48109
East Hall, Room 1830
jptyler «at»
Research Interests

Molecular models of biological clocks 

Biological clocks generate rhythms with periods from seconds to months in many organisms and control many processes that are critical to the survival of the organism.  Many rhythms in biology are the result of rhythms in the mRNA and protein abundances at the cellular level that are then synchronized within the organism. To better understand biological clocks, mathematical and computational modeling is crucial as these tools provide directions for experimental procedures, test hypotheses within these models, and corroborate new biological revelations.  One main area of my research is using mathematical and computational techniques to understand how organisms generate these rhythms at the molecular level.      

Using Wearable Technologies in Health and Medicine 

Medicine is quickly moving to a personalized and precision paradigm that uses real-time information to inform healthcare decisions.   Wearable technologies provide a unique opportunity to monitor many physiological parameters continuously and passively.  With collaborators from the Michigan Medical School, we are developing computational methods to detect fevers earlier with continuous temperature measurements. 

With Danny Forger and other researchers from the University of Michigan, we are creating algorithms to measure circadian phase based on continuous heart rate measurements from Fitbit or other wearable devices.  We recently launched the app Social Rhythms that takes steps and heart rate data to track how a person's circadian rhythm changed in the time of social isolation due to Covid-19.

Discriminating Interactions in Oscillating Timecourse Data

Given accurate timecourse data of biological clocks, what can we infer about the interactions among the species?  With Jaekyoung Kim at KAIST, we are developing an algorithm that detects interactions among species in an oscillating timcourse data set under the assumption that all interactions are monotone.  We have a manuscript in preparation, so come back soon for code!       

Real-time, personalized medicine through wearable sensors and dynamic predictive modeling: a new paradigm for clinical medicine.
(with Sung Won Choi and Muneesh Tewari.)
Accepted to Current Opinion in Systems Biology.
Mathematical Modeling of Biological Clocks. Ph.D. Thesis, August 2019.
Revisiting a synthetic intracellular network that exhibits oscillations.
(with Anne Shiu and Jay Walton.)
arXiv:1808.00595 / DOI
Journal of Mathematical Biology, Vol. 78:2341-2368, 2018.