My research focuses on differential-equation based modeling to help understand and predict mechanisms of gene regulation underlying circadian rhythmicity, synaptic strengthening, and memory formation.

Day-night, or circadian, sleep and behavior rhythms seem to be driven by similar genetic oscillators in humans as in animals, insects, and even plants. Modeling suggests these oscillators all rely on a similar core negative feedback mechanism. However, input and output from the core and its modulation by other feedback loops differ greatly between humans and other organisms. Understanding these similarities and differences might help improve treatments for human sleep disorders.

Long-term strengthening of specific patterns of synaptic connections appears to be an essential component of the mechanism underlying memory storage in humans and other organisms. Furthermore, to maintain cell damage, a slow homeostatic mechanism must sense average neuronal activity and globally weaken or strengthen all synapses to maintain neuronal activity within a healthy range. Thus, strengthening of one pattern of synapses must be accompanied by weakening of nearby synapses. The above long-term changes are known to require transcriptional regulation. Most details are not yet known, but the qualitative roles of some key enzymes and genes are beginning to be understood. Mathematical modeling will be essential to develop a more comprehensive, predictive picture of how genes and proteins transduce brief stimuli into long-lasting memories and how these memories are preserved despite protein turnover and synaptic homeostasis mechanisms. Such understanding is likely to be important for improved treatment of memory disorders and learning disabilities.

I also maintain interest in modeling coupling between the electrical activity of excitable cells and intracellular metabolic and signaling pathways. For example, the rate of insulin secretion from pancreatic islets is tightly coupled to the level of blood glucose via the glycolytic pathway. I have been involved in a collaborative modeling effort to develop a more comprehensive picture of the glucose-insulin coupling, both in health and in the diabetic state. This effort could help in developing improved treatments for diabetes.

Research Information


A) Model of the roles of essential protein kinases in the induction of synaptic long-term potentiation (Smolen et al., 2006). Electrical stimuli activate influx of Ca2+ and elevate intracellular cyclic AMP (cAMP). These events activate convergent kinases that induce long-term potentiation (LTP), including CaM kinases II and IV, protein kinase A, and the MAP kinase cascade (Raf -> MAP kinase kinase -> MAP kinase). CaM kinase II, protein kinase A, and MAP kinase phosphorylate synaptic substrates to “tag” a synapse, enabling “capture” of newly made protein and synaptic strengthening. CaM kinase IV and MAP kinase phosphorylate transcription factors (TFs), inducing gene expression. Only upon synaptic tagging and gene induction does the synaptic weight W increase. B) Simulation of an experiment illustrating synaptic tagging (Frey and Morris, 1997). Synapse 1 is first electrically tetanized and tagged. Gene expression is activated (increased gene product level), and LTP occurs (increased W_tetanic). Then, a protein synthesis inhibitor shuts off gene product synthesis, after which synapse 2 is tetanized. Synapse 2 still gets tagged, because tagging requires kinase activation but not protein synthesis.  Synapse 2 undergoes LTP (increased W_tagged), by capturing gene product synthesized earlier due to tetanus of synapse 1.


Publication Information

  • Smolen P., Baxter D.A., and Byrne J.H. (2000) Mathematical modeling of gene networks. Neuron, 26: 567-580.
  • Smolen P., Baxter D.A., and Byrne J.H. (2002) A reduced model clarifies the role of feedback loops and time delays in the Drosophila circadian oscillator. Biophys. J. 83: 2349-2359.
  • Smolen P., Hardin P.E., Lo B.S., Baxter D.A., and Byrne J.H. (2004).  Simulation of Drosophila circadian oscillations, mutations, and light responses by a model with VRI, PDP-1, and CLK. Biophys. J. 86: 2786-2802.
  • Bertram R., Satin L., Zheng M., Smolen P., and Sherman A. (2004).  Calcium and glycolysis mediate multiple bursting modes in pancreatic islets.  Biophys. J. 87: 3074-3087.
  • Pettigrew D.B., Smolen P., Baxter D.A., and Byrne J.H. (2005). Dynamic properties of regulatory motifs associated with induction of three temporal domains of memory in Aplysia. J. Comput. Neurosci. 18: 163-181.
  • Smolen P., Baxter D.A., and Byrne J.H. (2006). A model of the roles of essential kinases in the induction and expression of late long-term potentiation. Biophys. J. 90: 2760-2765.
  • Smolen P., Baxter D.A., and Byrne J.H. (2008). Bistable MAP kinase activity, a plausible mechanism contributing to the maintenance of late long-term potentiation.  Am. J. Physiol. Cell Physiol. 294(2): C503-515
  • Smolen P., Baxter D.A., and Byrne J.H. (2009). Interlinked dual-time feedback loops can enhance robustness to stochasticity and persistence of memory. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(3 Pt 1): 031902.
  • Zhang Y., Smolen P., Baxter D.A., and Byrne J.H. (2010). The sensitivity of memory consolidation and reconsolidation to inhibitors of protein synthesis and kinases: computational analysis. Learn. Mem. 17: 428-439.