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# Welcome to __Receptors__


This [Jupyter Book](https://jupyterbook.org) explores how cell surface receptors can be modeled using [Sagemath](https://www.sagemath.org), a free open\-source mathematics software system (see [https://www.sagemath.org](https://www.sagemath.org)).

The focus is Markov chain models of receptors and symbolic algebraic calculations of equilibrium and steady\-state kinetic occupancy measures \(i.e., the probability of each state\), as opposed to numerical methods to calculate steady states or time\-dependent dynamics.

After an brief introductory tutorial, we illustrate an approach to **modeling conformational coupling of receptor dimers and higher\-order oligomers** that was introduced in the following two papers.

* Gregory Douglas Conradi Smith, **Allostery in oligomeric receptor models**, *Mathematical Medicine and Biology: A Journal of the IMA*, 37(3):313-333, 2020. [doi: 10.1093/imammb/dqz016](https://doi.org/10.1093/imammb/dqz016)

* Richard H. Hammack and Gregory D. Smith, **Cycle bases of reduced powers of graphs**, *ARS Mathematica Contemporanea*, 12(1):183–203, 2017. [doi: 10.26493/1855-3974.856.4d2](https://doi.org/10.26493/1855-3974.856.4d2)

Comments and suggestions are welcome!

[Greg Conradi Smith](https://gregconradismith.wordpress.com/)\
Professor and Associate Chair\
Department of [Applied Science](https://www.wm.edu/as/appliedscience/)\
Programs in [Neuroscience](https://www.wm.edu/as/neuroscience/) and [CAMS Mathematical Biology](https://www.wm.edu/as/cams/mathematical-biology/)\
[William & Mary](https://www.wm.edu/)

greg.conradi.smith@gmail.com\
[0000-0002-1054-6790](https://orcid.org/0000-0002-1054-6790)

Author of [Cellular Biophysics \& Modeling: a primer on the computational biology of excitable cells](https://www.cambridge.org/core/books/cellular-biophysics-and-modeling/0C728F4C44D89D8F3BA62E41A0D7336F). Cambridge University Press, 2019.

![Doodle](images/Doodle.png)

## Table of Contents

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