Ultrasensitivity


In molecular biology, ultrasensitivity describes an output response that is more sensitive to stimulus change than the hyperbolic Michaelis-Menten response. Ultrasensitivity is one of the biochemical switches in the cell cycle and has been implicated in a number of important cellular events, including exiting G2 cell cycle arrests in Xenopus laevis oocytes, a stage to which the cell or organism would not want to return.
Ultrasensitivity is a cellular system which triggers entry into a different cellular state. Ultrasensitivity gives a small response to first input signal, but an increase in the input signal produces higher and higher levels of output. This acts to filter out noise, as small stimuli and threshold concentrations of the stimulus is necessary for the trigger which allows the system to get activated quickly. Ultrasensitive responses are represented by sigmoidal graphs, which resemble cooperativity. The quantification of ultrasensitivity is often performed approximately by the Hill equation:
Where Hill's coefficient may represent quantitative measure of ultrasensitive response.

Historical development

Zero-order ultrasensitivity was first described by Albert Goldbeter and Daniel Koshland, Jr in 1981 in a paper in the Proceedings of the National Academy of Sciences. They showed using mathematical modeling that modification of enzymes operating outside of first order kinetics required only small changes in the concentration of the effector to produce larger changes in the amount of modified protein. This amplification provided added sensitivity in biological control, and implicated the importance of this in many biological systems.
Many biological processes are binary, such as cell fate decisions, metabolic states, and signaling pathways. Ultrasensitivity is a switch that helps decision-making in such biological processes. For example, in apoptotic process, a model showed that a positive feedback of inhibition of caspase 3 and Casp9 by inhibitors of apoptosis can bring about ultrasensitivity. This positive feedback cooperates with Casp3-mediated feedback cleavage of Casp9 to generate irreversibility in caspase activation, which leads to cell apoptosis. Another model also showed similar but different positive feedback controls in Bcl-2 family proteins in apoptotic process.
Recently, Jeyeraman et al. have proposed that the phenomenon of ultrasensitivity may be further subdivided into three sub-regimes, separated by sharp stimulus threshold values: OFF, OFF-ON-OFF, and ON. Based on their model, they proposed that this sub-regime of ultrasensitivity, OFF-ON-OFF, is like a switch-like adaption which can be accomplished by coupling N phosphorylation–dephosphorylation cycles unidirectionally, without any explicit feedback loops.
Other recent work has emphasized that not only is the topology of networks important for creating ultrasensitivity responses, but that their composition strongly affects whether they will exhibit robust ultrasensitivity. Mathematical modeling suggests for a broad array of network topologies that a combination of enzymes and transcription factors tends to provide more robust ultrasensitivity than that seen in networks composed entirely of transcription factors or composed entirely of enzymes.

Mechanisms

Ultrasensitivity can be achieved through several mechanisms:
  1. Multistep mechanisms and multisite phosphorylation
  2. Buffering mechanisms or stoichiometric inhibitors
  3. Changes in localisation
  4. Saturation mechanisms
  5. Positive feedback
  6. Allovalency
  7. Non-Zero-Order Ultrasensitivity in Membrane Proteins
  8. Dissipative Allostery

    Multistep Mechanisms

Multipstep ultrasensitivity occurs when a single effector acts on several steps in a cascade. Successive cascade signals can result in higher levels of noise being introduced into the signal that can interfere with the final output. This is especially relevant for large cascades, such as the flagellar regulatory system in which the master regulator signal is transmitted through multiple intermediate regulators before activating transcription. Cascade ultrasensitivity can reduce noise and therefore require less input for activation. Additionally, multiple phosphorylation events are an example of ultrasensitivity. Recent modeling has shown that multiple phosphorylation sites on membrane proteins could serve to locally saturate enzyme activity. Proteins at the membrane are greatly reduced in mobility compared to those in the cytoplasm, this means that a membrane tethered enzyme acting upon a membrane protein will take longer to diffuse away. With the addition of multiple phosphorylation sites upon the membrane substrate, the enzyme can - by a combination of increased local concentration of enzyme and increased substrates - quickly reach saturation.

Buffering Mechanisms

Buffering Mechanisms such as molecular titration can generate ultrasensitivity. In vitro, this can be observed for the simple mechanism:
Where the monomeric form of A is active and it can be inactivated by binding B to form the heterodimer AB. When the concentration of is much greater than the Dissociation constant|, this system exhibits a threshold determined by the concentration of. At concentrations of , lower than, B acts as a buffer to free A and nearly all A will be found as AB. However, at the equivalence point, when ≈, can no longer buffer the increase in, so a small increase in causes a large increase in A. The strength of the ultrasensitivity of to changes in is determined by /. Ultrasensitivity occurs when this ratio is greater than one and is increased as the ratio increases. Above the equivalence point, and A are again linearly related.
In vivo, the synthesis of A and B as well as the degradation of all three components complicates generation of ultrasensitivity. If the synthesis rates of A and B are equal this system still exhibits ultrasensitivity at the equivalence point.
One example of a buffering mechanism is protein sequestration, which is a common mechanism found in signalling and regulatory networks. In 2009, Buchler and Cross constructed a synthetic genetic network that was regulated by protein sequestration of a transcriptional activator by a dominant-negative inhibitor. They showed that this system results in a flexibile ultrasensitive response in gene expression. It is flexible in that the degree of ultrasensitivity can be altered by changing expression levels of the dominant-negative inhibitor. Figure 1 in their article illustrates how an active transcription factor can be sequestered by an inhibitor into the inactive complex AB that is unable to bind DNA. This type of mechanism results in an "all-or-none" response, or ultransensitivy, when the concentration of the regulatory protein increases to the point of depleting the inhibitor. Robust buffering against a response exists below this concentration threshold, and when it is reached any small increase in input is amplified into a large change in output.

Changes in localization

Translocation

Signal transduction is regulated in various ways and one of the ways is translocation. Regulated translocation generates ultrasensitive response in mainly three ways:
  1. Regulated translocation increases the local concentration of the signaling protein. When concentration of the signaling protein is high enough to partially saturate the enzyme that inactivates it, ultrasensitive response is generated.
  2. Translocation of multiple components of the signaling cascade, where stimulus causes translocation of both signaling protein and its activator in the same subcellular compartment and thereby generates ultrasensitive response which increases speed and accuracy of the signal.
  3. Translocation to the compartment which contains stoichiometric inhibitors.
Translocation is one way of regulating signal transduction, and it can generate ultrasensitive switch-like responses or multistep-feedback loop mechanisms. A switch-like response will occur if translocation raises the local concentration of a signaling protein. For example, epidermal growth factor receptors can be internalized through clathrin-independent endocytosis and/or clathrin-dependent endocytosis in ligand concentration-dependent manner. The distribution of receptors into the two pathways was shown to be EGF concentration-dependent. In the presence of low concentrations of EGF, the receptor was exclusively internalized via CDE, whereas at high concentrations, receptors were equally distributed between CDE and CIE.

Saturation mechanisms (Zero-order ultrasensitivity)

Zero-order ultrasensitivity takes place under saturating conditions. For example, consider an enzymatic step with a kinase, phosphatase, and substrate. Steady state levels of the phosphorylated substrate have an ultrasensitive response when there is enough substrate to saturate all available kinases and phosphatases. Under these conditions, small changes in the ratio of kinase to phosphatase activity can dramatically change the number of phosphorylated substrate. This enhancement in sensitivity of steady state phosphorylated substrate to Km, or the ratio of kinase to phosphatase activity, is termed zero-order to distinguish it from the first order behavior described by Michaelis-Menten dynamics, wherein the steady state concentration responds in a more gradual fashion than the switch-like behavior exhibited in ultrasensitivity.
Using the notation from Goldbeter & Koshland, let W be a certain substrate protein and let W' be a covalently modified version of W. The conversion of W to W' is catalyzed by some enzyme E1 and the reverse conversion of W' to W is catalyzed by a second enzyme E2 according to following equations:
The concentrations of all necessary components are assumed to be constant and represented in the kinetic constants.
Using the chemical equations above, the reaction rate equations for each component are:
The total concentration of each component is given by:
The zero order mechanism assumes that the or. In other words, the system is in a Michaelis-Menten steady state, which means, to a good approximation, and are constant.
From these kinetic expressions one can solve for at steady state defining and
where and
When the is plotted against the molar ratio and it can be seen that the W to W' conversion occurs over a much smaller change in the ratio than it would under first order conditions, which is the telltale sign of ultrasensitivity.