A biomolecular proportional integral controller based on feedback regulations of protein level and activity

Universal structural requirements for maximal robust perfect adaptation in biomolecular networks

Adaptation is a running theme in biology. It allows a living system to survive and thrive in the face of unpredictable environments by maintaining key physiological variables at their desired levels through tight regulation. When one such variable is maintained at a certain value at the steady state despite perturbations to a single input, this property is called robust perfect adaptation (RPA). Here we address and solve the fundamental problem of maximal RPA (maxRPA), whereby, for a designated output variable, RPA is achieved with respect to perturbations in virtually all network parameters. In particular, we show that the maxRPA property imposes certain structural constraints on the network. We then prove that these constraints are fully characterized by simple linear algebraic stoichiometric conditions which differ between deterministic and stochastic descriptions of the dynamics. We use our results to derive a new internal model principle (IMP) for biomolecular maxRPA networks, akin to the celebrated IMP in control theory. We exemplify our results through several known biological examples of robustly adapting networks and construct examples of such networks with the aid of our linear algebraic characterization. Our results reveal the universal requirements for maxRPA in all biological systems, and establish a foundation for studying adaptation in general biomolecular networks, with important implications for both systems and synthetic biology.

SIR-PID: A Proportional–Integral–Derivative Controller for COVID-19 Outbreak Containment

Ongoing social restrictions, including social distancing and lockdown, adopted by many countries to inhibit spread of the the COVID-19 epidemic, must attempt to find a trade-off between induced economic damage, healthcare system collapse, and the costs in terms of human lives. Applying and removing restrictions on a system with a given latency as represented by an epidemic outbreak (and formally comparable with mechanical inertia), may create critical instabilities, overshoots, and strong oscillations in the number of infected people around the desirable set-point, defined in a practical way as the maximum number of hospitalizations acceptable by a given healthcare system. A good understanding of the system reaction to any change of the input control variable can be reasonably achieved using a proportional–integral–derivative controller (PID), which is a widely used technique in various physics and technological applications. In this paper, this control theory to is proposed to be applied epidemiology, to understand the reaction of COVID-19 propagation to social restrictions and to reduce epidemic damages through the correct tuning of the containment policy. Regarding the synthesis of this interdisciplinary approach, the extended to the susceptible–infectious–recovered (SIR) model name “SIR-PID” is suggested.

Perfect adaptation in biology

A distinctive feature of many biological systems is their ability to adapt to persistent stimuli or disturbances that would otherwise drive them away from a desirable steady state. The resulting stasis enables organisms to function reliably while being subjected to very different external environments. This perspective concerns a stringent type of biological adaptation, robust perfect adaptation (RPA), that is resilient to certain network and parameter perturbations. As in engineered control systems, RPA requires that the regulating network satisfy certain structural constraints that cannot be avoided. We elucidate these ideas using biological examples from systems and synthetic biology. We then argue that understanding the structural constraints underlying RPA allows us to look past implementation details and offers a compelling means to unravel regulatory biological complexity.

Protein Activity Sensing in Bacteria in Regulating Metabolism and Motility

Bacteria have evolved complex sensing and signaling systems to react to their changing environments, most of which are present in all domains of life. Canonical bacterial sensing and signaling modules, such as membrane-bound ligand-binding receptors and kinases, are very well described. However, there are distinct sensing mechanisms in bacteria that are less studied. For instance, the sensing of internal or external cues can also be mediated by changes in protein conformation, which can either be implicated in enzymatic reactions, transport channel formation or other important cellular functions. These activities can then feed into pathways of characterized kinases, which translocate the information to the DNA or other response units. This type of bacterial sensory activity has previously been termed protein activity sensing. In this review, we highlight the recent findings about this non-canonical sensory mechanism, as well as its involvement in metabolic functions and bacterial motility. Additionally, we explore some of the specific proteins and protein-protein interactions that mediate protein activity sensing and their downstream effects. The complex sensory activities covered in this review are important for bacterial navigation and gene regulation in their dynamic environment, be it host-associated, in microbial communities or free-living.