Intracellular processes rarely work in isolation but continually interact with the rest of the cell. In microbes, for example, we now know that gene expression across the whole genome typically changes with growth rate. The mechanisms driving such global regulation, however, are not well understood. Here we consider three trade-offs that, because of limitations in levels of cellular energy, free ribosomes, and proteins, are faced by all living cells and we construct a mechanistic model that comprises these trade-offs. Our model couples gene expression with growth rate and growth rate with a growing population of cells. We show that the model recovers Monod's law for the growth of microbes and two other empirical relationships connecting growth rate to the mass fraction of ribosomes. Further, we can explain growth-related effects in dosage compensation by paralogs and predict host-circuit interactions in synthetic biology. Simulating competitions between strains, we find that the regulation of metabolic pathways may have evolved not to match expression of enzymes to levels of extracellular substrates in changing environments but rather to balance a trade-off between exploiting one type of nutrient over another. Although coarse-grained, the trade-offs that the model embodies are fundamental, and, as such, our modeling framework has potentially wide application, including in both biotechnology and medicine.systems biology | synthetic biology | mathematical cell model | host-circuit interactions | evolutionarily stable strategy I ntracellular processes rarely work in isolation but continually interact with the rest of the cell. Yet often we study cellular processes with the implicit assumption that the remainder of the cell can either be ignored or provides a constant, background environment. Work in both systems and synthetic biology is, however, showing that this assumption is weak, at best. In microbes, growth rate can affect the expression both of single genes (1, 2) and across the entire genome (3-6). Specific control by transcription factors seems to be complemented by global, unspecific regulation that reflects the physiological state of the cell (5-7). Correspondingly, progress in synthetic biology is limited by two-way interactions between synthetic circuits and the host cell that cannot be designed away (8, 9).These phenomena are thought to arise from trade-offs where commitment of a finite intracellular resource to one response necessarily reduces the commitment of that resource to another response. A trade-off in the allocation of ribosomes has been suggested to underlie global gene regulation (2, 5). Similarly, depletion of finite resources and competition for cellular processes is thought to explain the failure of some synthetic circuits (8). Such circuits "load" the host cell, which can induce physiological responses that further degrade the function of the circuit (10). Our understanding of such trade-offs, however, is mostly phenomenological.Here we take an alternative approach and ask what new insi...

A language of formal proteins, the ¢-calculus, is introduced. Interactions are modeled at the domain level, bonds are represented by means of shared names, and reactions are required to satisfy a causality requirement of mono-tonicity. An example of a simplified signalling pathway is introduced to illustrate how standard biological events can be expressed in our protein language. A more comprehensive example, the lactose operon, is also developed, bringing some confidence in the formalism considered as a modeling language. Then a finer-grained concurrent model, the £ ¤ ¢-calculus, is considered, where interactions have to be at most binary. We show how to embed the coarser-grained language in the latter, a property which we call self-assembly. Finally we show how the finer-grained language can itself be encoded in ¥-calculus, a standard foundational language for concurrency theory.

One obtains in this paper a process algebra RCCS, in the style of CCS, where processes can backtrack. Backtrack, just as plain forward computation, is seen as a synchronization and incurs no additional cost on the communication structure. It is shown that, given a past, a computation step can be taken back if and only if it leads to a causally equivalent past.

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