Unlimited multistability and Boolean logic in microbial signalling

Abstract

The ability to map environmental signals onto distinct internal physiological states or programmes is critical for single-celled microbes. A crucial systems dynamics feature underpinning such ability is multistability. While unlimited multistability is known to arise from multi-site phosphorylation seen in the signalling networks of eukaryotic cells, a similarly universal mechanism has not been identified in microbial signalling systems. These systems are generally known as two-component systems comprising histidine kinase (HK) receptors and response regulator proteins engaging in phosphotransfer reactions. We develop a mathematical framework for analysing microbial systems with multi-domain HK receptors known as hybrid and unorthodox HKs. We show that these systems embed a simple core network that exhibits multistability, thereby unveiling a novel biochemical mechanism for multistability. We further prove that sharing of downstream components allows a system with n multi-domain hybrid HKs to attain 3n steady states. We find that such systems, when sensing distinct signals, can readily implement Boolean logic functions on these signals. Using two experimentally studied examples of two-component systems implementing hybrid HKs, we show that bistability and implementation of logic functions are possible under biologically feasible reaction rates. Furthermore, we show that all sequenced microbial genomes contain significant numbers of hybrid and unorthodox HKs, and some genomes have a larger fraction of these proteins compared with regular HKs. Microbial cells are thus theoretically unbounded in mapping distinct environmental signals onto distinct physiological states and perform complex computations on them. These findings facilitate the understanding of natural two-component systems and allow their engineering through synthetic biology.

A Rhizobium radiobacter Histidine Kinase Can Employ Both Boolean AND and OR Logic Gates to Initiate Pathogenesis

“…Could the same result be achieved with two separate detectors? Recently, the principle of multicomponent sharing, so important in eukaryotic signaling, has been demonstrated among multidomain histidine kinases to achieve Boolean logic gate signaling . Unlike these systems that require multiple proteins, the single VirA protein of R. radiobacter provides this capability in a single protein and greatly simplifies the elements needed for pathogenesis.…”

“…Why would both strategiese xist?W hat might this signal information be, and why might it be complementary?C ould the same result be achievedw ith two separate detectors?R ecently,t he principle of multicomponent sharing, so important in eukaryotic signaling, has been demonstrated among multidomain histidine kinases to achieve Boolean logic gate signaling. [33] Unlike these systemst hat requirem ultiple proteins,t he single VirA protein of R. radiobacter provides this capabilityi nas ingle protein and greatly simplifies the elements needed for pathogenesis.T he ability to construct these AND/OR gates will now allow us to directly evaluatet he benefito ft hese logic gatesi n natural settings. And in as ynthetic sense, even without higher resolution structural models of the AND/ OR logic gates,t his singlep rotein antenna that can be engineeredt or esponds od ifferently to distinct small-molecule inputs might be but one example of am ore generalizable utility to regulate informational logic in synthetic biology.…”

Lower bounds for positive roots and regions of multistationarity in chemical reaction networks

“…Instead, our inequalities (1.4) give conditions on the total concentrations and the reaction rate constants for the ocurrence of multistationarity. In [21] necessary and sufficient conditions on all the parameters of the system for bistability are provided, with a treatment ad hoc using Sturm's Theorem.…”

Sign-sensitivities for reaction networks: an algebraic approach

“…Figure 1. (a) A simple network of a hybrid histidine kinase, taken from [17]. (b) Signsensitivities with respect to an increase of x 0 1 and x 0 5 .…”

“…For that, we consider a simple model of a hybrid histidine kinase from [17]. The network is depicted in Figure 1(a).…”