Skip to main content
From Discrete to Continuous and Back: Abstractions and Mesoscopic Phenomena in Cells
Departmental Papers (ESE)
  • Ádám M Halász, University of Pennsylvania
  • A. Agung Julius, University of Pennsylvania
  • George J Pappas, University of Pennsylvania
  • R. Vijay Kumar, University of Pennsylvania

We discuss the interplay between stochasticity and multistability in bio-molecular networks. The resulting cell-level stochastic behavior reflects the fundamentally discrete and random nature of the underlying molecular processes. These ideas are illustrated on the well studied example of the lac operon. We first describe the switching behavior predicted by a differential-equation based model and then show how cell-level stochastic behavior emerges. Finally we point out that the observed macroscopic behavior may not be enough to determine both the dynamic and stochastic parameters.

Document Type
Journal Article
Date of this Version
Copyright YEAR IEEE. Reprinted from Proceedings of the 9th International Workshop on Discrete Event Systems, pages 269-274.

This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
Citation Information
Ádám M Halász, A. Agung Julius, George J Pappas and R. Vijay Kumar. "From Discrete to Continuous and Back: Abstractions and Mesoscopic Phenomena in Cells" (2008)
Available at: