A novel equation for cooperativity of the allosteric state function

Mathematical models describing oxygen binding by hemoglobin

Despite the fact that the investigation of the structural and functional properties of hemoglobin dates back more than 150 years, the topic has not lost its relevance today. The most important component of these studies is the development of mathematical models that formalize and generalize the mechanisms determining the cooperative binding of ligands based on data on the structural and functional state of the protein. In this work, we review the mathematical relationships describing oxygen binding by hemoglobin, ranging from the classical Hüfner, Hill, and Adair equations to the Szabo-Karplus and tertiary two-state mathematical models based on the Monod-Wyman-Changeux and Koshland-Némethy-Filmer concepts. The generality of the considered equations as mathematical functions, bearing in their basis a power dependence, is demonstrated. The problems and possible solutions related to approximation of experimental data by the oxygenation equations with correlated fitting parameters are noted. Attention is paid to empirical equations, extended versions of the Hill equation, where the coefficient of cooperation is modulated by Gauss and Lorentz distributions as functions of partial oxygen pressure.

Driving complex flow waveforms with a linear voice coil actuator

Oscillatory and pulsatile fluid flows for use in microfluidic applications were generated using a deformable chamber driven by a low cost linear voice coil actuator. Compliance in the fluidic system originating in the deformable chamber and the fluidic tubing produced a strong frequency dependence in the relationship between the system's input and the output flow rate. The effects of this frequency dependence were overcome by precise system calibration, enabling on-demand generation of sinusoidal oscillations in the fluid flow rate with a controlled amplitude in the range from 0.1 to over 1 ml/min across a frequency range from 0.1 Hz to 10 Hz. The calibration data further enabled the optimization of a multistage exponential smoothing model of the system that allowed the generation of arbitrary complex waveforms. This was demonstrated by combining flow modulation with a constant background flow generated by a syringe pump to mimic the pulsatile flow found in the human vascular system.

Biased Allostery

G-protein-coupled receptors (GPCRs) constitute a large group of integral membrane proteins that transduce extracellular signals from a wide range of agonists into targeted intracellular responses. Although the responses can vary depending on the category of G-proteins activated by a particular receptor, responses were also found to be triggered by interactions of the receptor with β-arrestins. It was subsequently discovered that for the same receptor molecule (e.g., the β-adrenergic receptor), some agonists have a propensity to specifically favor responses by G-proteins, others by β-arrestins, as has now been extensively studied. This feature of the GPCR system is known as biased agonism and is subject to various interpretations, including agonist-induced conformational change versus selective stabilization of preexisting active conformations. Here, we explore a complete allosteric framework for biased agonism based on alternative preexisting conformations that bind more strongly, but nonexclusively, either G-proteins or β-arrestins. The framework incorporates reciprocal effects among all interacting molecules. As a result, G-proteins and β-arrestins are in steric competition for binding to the cytoplasmic surface of either the G-protein-favoring or β-arrestin-favoring GPCR conformation. Moreover, through linkage relations, the strength of the interactions of G-proteins or β-arrestins with the corresponding active conformation potentiates the apparent affinity for the agonist, effectively equating these two proteins to allosteric modulators. The balance between response alternatives can also be influenced by the physiological concentrations of either G-proteins or β-arrestins, as well as by phosphorylation or interactions with positive or negative allosteric modulators. The nature of the interactions in the simulations presented suggests novel experimental tests to distinguish more fully among alternative mechanisms.