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WIREs Syst Biol Med
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Implementation of integral feedback control in biological systems

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Integral control design ensures that a key variable in a system is tightly maintained within acceptable levels. This approach has been widely used in engineering systems to ensure offset free operation in the presence of perturbations. Several biological systems employ such an integral control design to regulate cellular processes. An integral control design motif requires a negative feedback and an integrating process in the network loop. This review describes several biological systems, ranging from bacteria to higher organisms in which the presence of integral control principle has been hypothesized. The review highlights that in addition to the negative feedback, occurrence of zero‐order kinetics in the process is a key element to realize the integral control strategy. Although the integral control motif is common to these systems, the mechanisms involved in achieving it are highly specific and can be incorporated at the level of signaling, metabolism, or at the phenotypic levels. WIREs Syst Biol Med 2015, 7:301–316. doi: 10.1002/wsbm.1307 This article is categorized under: Biological Mechanisms > Cell Signaling Analytical and Computational Methods > Dynamical Methods Physiology > Organismal Responses to Environment
Negative feedback loop motifs involving integral control action (left panel) and corresponding dynamic response (right panel). (a) and (b) represent the motif when the external cue E activates the signaling molecule A. (c) and (d) represent the motif when cue E represses the signaling molecule A. Pointed arrow indicates activation.
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Glucose homeostasis. (a) Blood glucose affects insulin effect positively and glucagon effect negatively. Insulin effect has a positive influence on uptake of the blood glucose from plasma to tissue and negative influence on glucagon. Glucagon effect has positive influence on tissue glucose and negative influence on insulin. (b) and (c) Negative feedback loop block diagram when the glucose input rate is increased and decreased in the system, respectively.
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Adaptation of neuron firing in the pre‐frontal cortex of brain. Comparison neuron C senses the stimulus S in terms of firing rate. Firing rate of memory neuron M is up‐regulated by both firing rate of comparison neuron C as well as an auto‐positive feedback loop. M acts negative only C.
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Integral action in maintaining ATP by the glycolysis and oxidative phosphorylation. (a): The network involves following components: (1) AMPK (2) Glycolytic Metabolites (3) Fructose Biphosphate FBP, a side product of glycolysis (4) flux toward oxidative phosphorylation and (5) other flux from glycolytic metabolite which do not contribute to oxidative phosphorylation. Interactions considered are (1) activation of AMPK by stimulus (2) conversion of glycolytic metabolite to FBP and its reversal reaction (3) Positive influence of F6BP on flux toward oxidative phosphorylation (4) regulation of AMPK due to oxidative phosphorylation. (b): The negative feedback motif involving AMPK, FBP, and conversion of FBP into other glycolytic metabolites.
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Blood Calcium Homeostasis: (a) The extracellular fluid ECF is shown as a continuous compartment in the figure. Bone, kidney, and intestine are shown as distinct compartments, capable of exchanging calcium with ECF. The other processes are (1) calcium absorption from diet (see intestine compartment) (2) calcium demand other than requirement for bone (represented as calcium demand) and (3) secretion and reabsorption (see calcium exchange of kidney with calcium secreted in the external space). The parathyroid gland is considered as a compartment that produces hormone PTH. The Ca in ECF is shown to have a negative effect on this production. The PTH is shown to positively regulate the uptake of calcium from bone. PTH also increases production of active vitamin D3 in the kidney, which in turn increases the calcium uptake from the external fluid (see kidney compartment). The active vitamin D3 also increases the uptake of calcium from the diet (see intestine compartment). The regulatory hormones PTH and active vitamin D3 are also subject to natural degradation. (b) Negative feedback motif involving plasma calcium, hormones PTH and DHCC.
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Chemotaxis in bacteria. (a) The signaling network manifesting perfect adaptation in chemotaxis of E.coli. Ligand (L) acts on the receptor to decrease its activity, phosphorylated CheB (CheBP) also decreases, which in turn lowers the demethylation of the receptor. On the other hand, CheR methylates the receptor at a constant rate. (b) Simplified network motif showing negative feedback loop block diagram.
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Nitrate homeostasis. (a) The homeostasis of nitrate in the cytosol of higher plants by regulation of efflux and influx proteins (i.e. EFT and IFT, respectively). Both IFT and EFT can take only two forms namely (1) activated (2) un‐activated (denoted by circle with ‘A’ and open circle, respectively). The nitrate is shown to be present in three compartments namely (1) external medium, (2) cytosol, and (3) storage (conversion to N02 is also considered as storage). The activated IFT is shown to catalyze the nitrate influx to cytosol, whereas activated EFT is shown to catalyze the efflux of nitrate from the cytosol. The cytosolic nitrate is shown to activate and deactivate EFT and IFT, respectively. (b) and (c) show simplified block diagram representations of the network during lower and higher demands for nitrate, respectively.
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Osmoadaptation of Yeast. (a) External osmotic pressure increases fluid efflux from the cell. This results in lowering of turgor pressure. The turgor pressure has a negative effect on Hog1PP activity. Hog1PP acts as a transcription factor for upregulaion of mRNA of glycerol synthesizing enzymes (E). The shunting of intracellular osmolyte glycerol is inhibited by Hog1PP. (b) Simplified block diagram representation of the osmoadaptation network
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Physiology > Organismal Responses to Environment
Biological Mechanisms > Cell Signaling
Analytical and Computational Methods > Dynamical Methods

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