Noise properties of adaptation-conferring biochemical control modules

A key goal of synthetic biology is to develop functional biochemical modules with network-independent properties. Antithetic integral feedback (AIF) is a recently developed control module in which two control species perfectly annihilate each other's biological activity. The AIF module confers robust perfect adaptation to the steady-state average level of a controlled intracellular component when subjected to sustained perturbations. Recent work has suggested that such robustness comes at the unavoidable price of increased stochastic fluctuations around average levels. We present theoretical results that support and quantify this trade-off for the commonly analyzed AIF variant in the idealized limit with perfect annihilation. However, we also show that this trade-off is a singular limit of the control module: Even minute deviations from perfect adaptation allow systems to achieve effective noise suppression as long as cells can pay the corresponding energetic cost. We further show that a variant of the AIF control module can achieve significant noise suppression even in the idealized limit with perfect adaptation. This atypical configuration may thus be preferable in synthetic biology applications.

DOPA Homeostasis by Dopamine: A Control-Theoretic View

Dopamine (DA) is an important signal mediator in the brain as well as in the periphery. The term "dopamine homeostasis" occasionally found in the literature refers to the fact that abnormal DA levels can be associated with a variety of neuropsychiatric disorders. An analysis of the negative feedback inhibition of tyrosine hydroxylase (TH) by DA indicates, with support from the experimental data, that the TH-DA negative feedback loop has developed to exhibit 3,4-dihydroxyphenylalanine (DOPA) homeostasis by using DA as a derepression regulator. DA levels generally decline when DOPA is removed, for example, by increased oxidative stress. Robust DOPA regulation by DA further implies that maximum vesicular DA levels are established, which appear necessary for a reliable translation of neural activity into a corresponding chemical transmitter signal. An uncontrolled continuous rise (windup) in DA occurs when Levodopa treatment exceeds a critical dose. Increased oxidative stress leads to the successive breakdown of DOPA homeostasis and to a corresponding reduction in DA levels. To keep DOPA regulation robust, the vesicular DA loading requires close to zero-order kinetics combined with a sufficiently high compensatory flux provided by TH. The protection of DOPA and DA due to a channeling complex is discussed.

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.

A hidden integral structure endows absolute concentration robust systems with resilience to dynamical concentration disturbances

Biochemical systems that express certain chemical species of interest at the same level at any positive steady state are called 'absolute concentration robust' (ACR). These species behave in a stable, predictable way, in the sense that their expression is robust with respect to sudden changes in the species concentration, provided that the system reaches a (potentially new) positive steady state. Such a property has been proven to be of importance in certain gene regulatory networks and signaling systems. In the present paper, we mathematically prove that a well-known class of ACR systems studied by Shinar and Feinberg in 2010 hides an internal integral structure. This structure confers these systems with a higher degree of robustness than was previously known. In particular, disturbances much more general than sudden changes in the species concentrations can be rejected, and robust perfect adaptation is achieved. Significantly, we show that these properties are maintained when the system is interconnected with other chemical reaction networks. This key feature enables the design of insulator devices that are able to buffer the loading effect from downstream systems-a crucial requirement for modular circuit design in synthetic biology. We further note that while the best performance of the insulators are achieved when these act at a faster timescale than the upstream module (as typically required), it is not necessary for them to act on a faster timescale than the downstream module in our construction.

Global shape of Toll activation is determined by wntD enhancer properties

Buffering variability in morphogen distribution is essential for reproducible patterning. A theoretically proposed class of mechanisms, termed "distal pinning," achieves robustness by combining local sensing of morphogen levels with global modulation of gradient spread. Here, we demonstrate a critical role for morphogen sensing by a gene enhancer, which ultimately determines the final global distribution of the morphogen and enables reproducible patterning. Specifically, we show that, while the pattern of Toll activation in the early Drosophila embryo is robust to gene dosage of its locally produced regulator, WntD, it is sensitive to a single-nucleotide change in the wntD enhancer. Thus, enhancer properties of locally produced WntD directly impinge on the global morphogen profile.

Need-based activation of ammonium uptake in Escherichia coli

The efficient sequestration of nutrients is vital for the growth and survival of microorganisms. Some nutrients, such as CO2 and NH3, are readily diffusible across the cell membrane. The large membrane permeability of these nutrients obviates the need of transporters when the ambient level is high. When the ambient level is low, however, maintaining a high intracellular nutrient level against passive back diffusion is both challenging and costly. Here, we study the delicate management of ammonium (NH4+/NH3) sequestration by E. coli cells using microfluidic chemostats. We find that as the ambient ammonium concentration is reduced, E. coli cells first maximize their ability to assimilate the gaseous NH3 diffusing into the cytoplasm and then abruptly activate ammonium transport. The onset of transport varies under different growth conditions, but always occurring just as needed to maintain growth. Quantitative modeling of known interactions reveals an integral feedback mechanism by which this need-based uptake strategy is implemented. This novel strategy ensures that the expensive cost of upholding the internal ammonium concentration against back diffusion is kept at a minimum.