A Statistical Thermodynamic Model for Ligands Interacting With Ion Channels: Theoretical Model and Experimental Validation of the KCNQ2 Channel

The Hill function is the universal Hopfield barrier for sharpness of input-output responses

The Hill functions, ℋ h ( x ) = x h / 1 + x h , have been widely used in biology for over a century but, with the exception of ℋ 1 , they have had no justification other than as a convenient fit to empirical data. Here, we show that they are the universal limit for the sharpness of any input-output response arising from a Markov process model at thermodynamic equilibrium. Models may represent arbitrary molecular complexity, with multiple ligands, internal states, conformations, co-regulators, etc, under core assumptions that are detailed in the paper. The model output may be any linear combination of steady-state probabilities, with components other than the chosen input ligand held constant. This formulation generalises most of the responses in the literature. We use a coarse-graining method in the graph-theoretic linear framework to show that two sharpness measures for input-output responses fall within an effectively bounded region of the positive quadrant, Ω m ⊂ ℝ + 2 , for any equilibrium model with m input binding sites. Ω m exhibits a cusp which approaches, but never exceeds, the sharpness of ℋ m but the region and the cusp can be exceeded when models are taken away from thermodynamic equilibrium. Such fundamental thermodynamic limits are called Hopfield barriers and our results provide a biophysical justification for the Hill functions as the universal Hopfield barriers for sharpness. Our results also introduce an object, Ω m , whose structure may be of mathematical interest, and suggest the importance of characterising Hopfield barriers for other forms of cellular information processing.

Ligand activation mechanisms of human KCNQ2 channel

The human voltage-gated potassium channel KCNQ2/KCNQ3 carries the neuronal M-current, which helps to stabilize the membrane potential. KCNQ2 can be activated by analgesics and antiepileptic drugs but their activation mechanisms remain unclear. Here we report cryo-electron microscopy (cryo-EM) structures of human KCNQ2-CaM in complex with three activators, namely the antiepileptic drug cannabidiol (CBD), the lipid phosphatidylinositol 4,5-bisphosphate (PIP2), and HN37 (pynegabine), an antiepileptic drug in the clinical trial, in an either closed or open conformation. The activator-bound structures, along with electrophysiology analyses, reveal the binding modes of two CBD, one PIP2, and two HN37 molecules in each KCNQ2 subunit, and elucidate their activation mechanisms on the KCNQ2 channel. These structures may guide the development of antiepileptic drugs and analgesics that target KCNQ2.