GroEL Allostery Illuminated by a Relationship between the Hill Coefficient and the MWC Model

Gruber, Ranit; Mondal, Tridib; Horovitz, Amnon

doi:10.1016/j.bpj.2019.10.013

Cited by 10 publications

(11 citation statements)

References 27 publications

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“…The simulations were carried out using different values of L and constant values of c = 0.01 or c = 0.001 (Figure 1c,d). Values of c = 0.01 and L = 10 5 have been reported for hemoglobin, 13 but there is uncertainty in these values owing to a dependency between L and c in data fitting 14–16 . It may be seen that the value of the Hill coefficient is again found to decrease with an increasing value of α .…”

Section: Resultsmentioning

confidence: 92%

“…Values of c = 0.01 and L = 10 5 have been reported for hemoglobin, 13 but there is uncertainty in these values owing to a dependency between L and c in data fitting. [14][15][16] It may be seen that the value of the Hill coefficient is again found to decrease with an increasing value of α. The increase in the value of the Hill coefficient with increasing values of L for c = 0.001 (Figure 1c) and the converse for c = 0.01 (Figure 1d) is due to the bell-shaped dependence of the value of the Hill coefficient on L when ligand binding is not exclusively to the R state.…”

Section: Extending the Analysis For Higher Order Oligomers By Simulationmentioning

confidence: 90%

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Partitioning the Hill coefficient into contributions from ligand‐promoted conformational changes and subunit heterogeneity

Roy

Horovitz

2022

Protein Science

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Heterooligomers that undergo ligand‐promoted conformational changes are ubiquitous in nature and involved in many essential processes. Conformational switching often leads to positive cooperativity in ligand binding that is reflected in a Hill coefficient with a value greater than one. The subunits comprising heterooligomers can differ, however, in their affinity for the ligand. Such so‐called site heterogeneity results in apparent negative cooperativity that is reflected by a Hill coefficient with a value less than one. Consequently, positive cooperativity due to the ligand‐promoted allosteric switch can be masked, in cases of such heterooligomers, by apparent negative cooperativity owing to site heterogeneity. Here, we derived expressions for the Hill coefficient, in the case of a heterodimer, in which the contributions from the ligand‐promoted allosteric switch and site heterogeneity are separated. Using these equations and simulations for higher order oligomers, we show under which conditions site heterogeneity can significantly mask the extent of observed positive cooperativity.

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Section: Resultsmentioning

confidence: 92%

Section: Extending the Analysis For Higher Order Oligomers By Simulationmentioning

confidence: 90%

Partitioning the Hill coefficient into contributions from ligand‐promoted conformational changes and subunit heterogeneity

Roy

Horovitz

2022

Protein Science

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“…Thus, for any L , K R and K T values, nHMWC is unequivocally determined (Equation 5). A good approximation for n H (based on the [S] 0.5 expression of the true0Rfalse¯ conformational state function; Gruber et al, 2019) that is over 98% accurate across most of the range of L and c values is presented in Appendix 2.…”

Section: Resultsmentioning

confidence: 99%

“…As can be seen in true0Yfalse¯ MWC Equation 2 of the main text, under half- saturation condition (where true0Yfalse¯=1/2), [S] 0.5 is raised to a power of up to four and its explicit expression (obtained using the Mathematica software package) is long and complex. An approximation for [S] 0.5 may be obtained using the [S] 0.5 of the true0Rfalse¯ conformational state function (the fraction of R state as a function of substrate concentration), as described in Equation A2.2 below (Gruber et al, 2019). Plugging this expression into Equation A2.1 results in an explicit expression for nHMWC that depends on the MWC model parameters, as described by the long Equation A2.3, below.…”

Section: Hb Oxygen Ligation Is Reasonably Described By the Mwc Allostmentioning

confidence: 99%

Evolutionary and functional insights into the mechanism underlying body-size-related adaptation of mammalian hemoglobin

Rapp

Yifrach

2019

eLife

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Hemoglobin (Hb) represents a model protein to study molecular adaptation in vertebrates. Although both affinity and cooperativity of oxygen binding to Hb affect tissue oxygen delivery, only the former was thought to determine molecular adaptations of Hb. Here, we suggest that Hb affinity and cooperativity reflect evolutionary and physiological adaptions that optimized tissue oxygen delivery. To test this hypothesis, we derived the relationship between the Hill coefficient and the relative affinity and conformational changes parameters of the Monod-Wymann-Changeux allosteric model and graphed the ‘biophysical Hill landscape’ describing this relation. We found that mammalian Hb cooperativity values all reside on a ridge of maximum cooperativity along this landscape that allows for both gross- and fine-tuning of tissue oxygen unloading to meet the distinct metabolic requirements of mammalian tissues for oxygen. Our findings reveal the mechanism underlying body size-related adaptation of mammalian Hb. The generality and implications of our findings are discussed.

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“…On this point, however, it should be noted that Stefan et al [ 48 ] have shown how an extended MWC model such as the one developed here can be used in parameter estimation, and experimental methods to measure MWC parameters are constantly improving [ 49 – 51 ]. Another useful recent tool is a method developed by Gruber et al [ 52 ] which facilitates the determination of parameters in the MWC model, by finding a theoretical relationship between the Hill coefficient and model parameters.…”

Section: Discussionmentioning

confidence: 99%

Effect of magnitude and variability of energy of activation in multisite ultrasensitive biochemical processes

2020

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Protein activity is often regulated by ligand binding or by post-translational modifications such as phosphorylation. Moreover, proteins that are regulated in this way often contain multiple ligand binding sites or modification sites, which can operate to create an ultrasensitive dose response. Here, we consider the contribution of the individual modification/binding sites to the activation process, and how their individual values affect the ultrasensitive behavior of the overall system. We use a generalized Monod-Wyman-Changeux (MWC) model that allows for variable conformational free energy contributions from distinct sites, and associate a so-called activation parameter to each site. Our analysis shows that the ultrasensitivity generally increases as the conformational free energy contribution from one or more sites is strengthened. Furthermore, ultrasensitivity depends on the mean of the activation parameters and not on their variability. In some cases, we find that the best way to maximize ultrasensitivity is to make the contribution from all sites as strong as possible. These results provide insights into the performance objectives of multiple modification/binding sites and thus help gain a greater understanding of signaling and its role in diseases.

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GroEL Allostery Illuminated by a Relationship between the Hill Coefficient and the MWC Model

Cited by 10 publications

References 27 publications

Partitioning the Hill coefficient into contributions from ligand‐promoted conformational changes and subunit heterogeneity

Partitioning the Hill coefficient into contributions from ligand‐promoted conformational changes and subunit heterogeneity

Evolutionary and functional insights into the mechanism underlying body-size-related adaptation of mammalian hemoglobin

Effect of magnitude and variability of energy of activation in multisite ultrasensitive biochemical processes

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