Bistable networks

Focusing on the first condition, the design of a bistable network requires the evaluation of the intermolecular association. 

Keywords Spin transition Coordination polymers Bistability Hofmann-like clathrates Supramolecular networks... 

G. Craciun, Y. Tang, and M. Feinberg, Understanding bistability in complex enzyme driven reaction networks. Proc. Natl. Acad. Sci. USA 103(23), 8697 8702 (2006). 

B. D. Agunda and B. L. Clarke, Bistability in chemical reaction networks Theory and application to the peroxidase reaction. J. Chem. Phys. 87(6), 3461 3469 (1987). 

Thermally or photochemically induced proton transfers represent bistable switching processes and are of interest for information storage. A lateral transfer of information on the surface of biological membranes is thought to occur by fast proton conduction through protonic networks [8.234]. 

Even though Eq. (5) is more realistic than Eq. (3) as a model for biological systems, this equation still is highly oversimplified. Yet this equation has remarkable mathematical properties that facilitate theoretical analysis. Moreover, there is an expectation, demonstrated in some simple examples like those discussed above, that the qualitative dynamics in the model system wiU be preserved in more realistic versions, for example when the discontinuous step functions are replaced by continuous sigmoidal functions [33, 34, 37]. As mentioned above, synthetic gene networks have been created that show some of the simple types of dynamical behavior found in our class of networks—in particular, bistability (two fixed points) [26] and oscillation in an inhibitory loop [27]. 

Single-cell experiments allow key parameters that define the dynamic properties of cellular signaling networks that are not available from cell population experiments to be extracted (e.g., Western blotting). Such parameters include delay time constants between signaling steps or bistability in the activation process. 

In the past few decades the technological possibilities and interests have boosted research in systems in highly restricted geometries in almost every field of physics — recently down to lengthscales close to or even below the molecular level. In the field of liquid crystals, the importance of electro-optical applications which incorporate ordered liquid materials [1-3] has focused the research on LC systems with high surface-to-volume ratio [4]. In order to provide mechanically stable applications, liquid crystals are dispersed in polymers, stabilized by a polymer network, fill the cavities in porous materials, etc. [5,6]. The major technological interest concerns the scattering, reflective and bistable displays, optical switches, and others. 

Predicting Dynamics and Bistability from Network Structure Alone... 

We should identify or classify classes of network structures that, from their structures alone, it is possible to tell whether they have the capacity to exhibit certain behavior. Given a biochemical reaction network, we can ask the following question Under which circumstances would this network exhibit phenomena like periodic oscillations and/or bistability For example, we would want to know the answer to this question when modeling the cell division cycle and circadian rhythm where periodic oscillations are required. For mass-action kinetics models, an extensive theoretical work already exists that answers this type of question for large classes of reaction networks. One such set of results is the deficiency theory.The deficiency 8 of a reaction... 

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