Multiple Internal States Research Articles

Hysteresis in a synthetic mammalian gene network

Bistable and hysteretic switches, enabling cells to adopt multiple internal expression states in response to a single external input signal, have a pivotal impact on biological systems, ranging from cell-fate decisions to cell-cycle control. We have designed a synthetic hysteretic mammalian transcription network. A positive feedback loop, consisting of a transgene and transactivator (TA) cotranscribed by TA's cognate promoter, is repressed by constitutive expression of a macrolide-dependent transcriptional silencer, whose activity is modulated by the macrolide antibiotic erythromycin. The antibiotic concentration, at which a quasi-discontinuous switch of transgene expression occurs, depends on the history of the synthetic transcription circuitry. If the network components are imbalanced, a graded rather than a quasi-discontinuous signal integration takes place. These findings are consistent with a mathematical model. Synthetic gene networks, which are able to emulate natural gene expression behavior, may foster progress in future gene therapy and tissue engineering initiatives.

Multistability in the lactose utilization network of Escherichia coli.

Multistability, the capacity to achieve multiple internal states in response to a single set of external inputs, is the defining characteristic of a switch. Biological switches are essential for the determination of cell fate in multicellular organisms, the regulation of cell-cycle oscillations during mitosis and the maintenance of epigenetic traits in microbes. The multistability of several natural and synthetic systems has been attributed to positive feedback loops in their regulatory networks. However, feedback alone does not guarantee multistability. The phase diagram of a multistable system, a concise description of internal states as key parameters are varied, reveals the conditions required to produce a functional switch. Here we present the phase diagram of the bistable lactose utilization network of Escherichia coli. We use this phase diagram, coupled with a mathematical model of the network, to quantitatively investigate processes such as sugar uptake and transcriptional regulation in vivo. We then show how the hysteretic response of the wild-type system can be converted to an ultrasensitive graded response. The phase diagram thus serves as a sensitive probe of molecular interactions and as a powerful tool for rational network design.

On the operational semantics of nondeterminism and divergence

An operational model of nondeterministic processes coupled with a novel theory of divergence is presented. The operational model represents internal nondeterminism without using explicit internal transitions. Here the notion of internal state effectively replaces the familiar notion of internal transition, giving rise to an alternative operational view of processes: the weak process. Roughly, a weak process is a collection of stable internal states together with a set of transitions each of which is defined from an internal state to another weak process. Internal nondeterminism arises from such refinement of processes into multiple internal states. A simple extension to the basic weak process model gives rise to an elaborate operational theory of divergence. According to this theory, the ability of a process to undertake an infinite internal computation which is pathological, or persistent, is distinguished from its ability to undertake an infinite internal computation which is not. Although applicable to process algebraic languages with an internal action construct, the resulting model is most suitable for supplying operational semantics to process algebras which express internal nondeterminism by an internal choice construct. The distinction between the two forms of divergence is in particular taken into account when the hiding construct of such a process algebra is assigned a weak process semantics.