scholarly journals Free-energy relationships in ion channels activated by voltage and ligand

2012 ◽  
Vol 141 (1) ◽  
pp. 11-28 ◽  
Author(s):  
Sandipan Chowdhury ◽  
Baron Chanda
Keyword(s):  
Free Energy ◽  
Ion Channels ◽  
Ligand Binding ◽  
Interaction Energy ◽  
Bk Channel ◽  
Direct Estimate ◽  
Voltage Dependent ◽  
Energy Relationships ◽  
Binding Curve ◽  
Binding Curves

Many ion channels are modulated by multiple stimuli, which allow them to integrate a variety of cellular signals and precisely respond to physiological needs. Understanding how these different signaling pathways interact has been a challenge in part because of the complexity of underlying models. In this study, we analyzed the energetic relationships in polymodal ion channels using linkage principles. We first show that in proteins dually modulated by voltage and ligand, the net free-energy change can be obtained by measuring the charge-voltage (Q-V) relationship in zero ligand condition and the ligand binding curve at highly depolarizing membrane voltages. Next, we show that the voltage-dependent changes in ligand occupancy of the protein can be directly obtained by measuring the Q-V curves at multiple ligand concentrations. When a single reference ligand binding curve is available, this relationship allows us to reconstruct ligand binding curves at different voltages. More significantly, we establish that the shift of the Q-V curve between zero and saturating ligand concentration is a direct estimate of the interaction energy between the ligand- and voltage-dependent pathway. These free-energy relationships were tested by numerical simulations of a detailed gating model of the BK channel. Furthermore, as a proof of principle, we estimate the interaction energy between the ligand binding and voltage-dependent pathways for HCN2 channels whose ligand binding curves at various voltages are available. These emerging principles will be useful for high-throughput mutagenesis studies aimed at identifying interaction pathways between various regulatory domains in a polymodal ion channel.

scholarly journals Estimating the voltage-dependent free energy change of ion channels using the median voltage for activation

2011 ◽  
Vol 139 (1) ◽  
pp. 3-17 ◽  
Author(s):  
Sandipan Chowdhury ◽  
Baron Chanda
Keyword(s):  
Free Energy ◽  
Ion Channels ◽  
Ion Channel ◽  
Free Energy Change ◽  
Energy Change ◽  
Displacement Curve ◽  
Charge Movement ◽  
Voltage Gated ◽  
State Process ◽  
Voltage Dependent

Voltage-gated ion channels are crucial for electrical activity and chemical signaling in a variety of cell types. Structure-activity studies involving electrophysiological characterization of mutants are widely used and allow us to quickly realize the energetic effects of a mutation by measuring macroscopic currents and fitting the observed voltage dependence of conductance to a Boltzmann equation. However, such an approach is somewhat limiting, principally because of the inherent assumption that the channel activation is a two-state process. In this analysis, we show that the area delineated by the gating charge displacement curve and its ordinate axis is related to the free energy of activation of a voltage-gated ion channel. We derive a parameter, the median voltage of charge transfer (Vm), which is proportional to this area, and prove that the chemical component of free energy change of a system can be obtained from the knowledge of Vm and the maximum number of charges transferred. Our method is not constrained by the number or connectivity of intermediate states and is applicable to instances in which the observed responses show a multiphasic behavior. We consider various models of ion channel gating with voltage-dependent steps, latent charge movement, inactivation, etc. and discuss the applicability of this approach in each case. Notably, our method estimates a net free energy change of approximately −14 kcal/mol associated with the full-scale activation of the Shaker potassium channel, in contrast to −2 to −3 kcal/mol estimated from a single Boltzmann fit. Our estimate of the net free energy change in the system is consistent with those derived from detailed kinetic models (Zagotta et al. 1994. J. Gen. Physiol. doi:10.1085/jgp.103.2.321). The median voltage method can reliably quantify the magnitude of free energy change associated with activation of a voltage-dependent system from macroscopic equilibrium measurements. This will be particularly useful in scanning mutagenesis experiments.

scholarly journals The structure of binding curves and practical identifiability of equilibrium ligand-binding parameters

2016 ◽  
Vol 149 (1) ◽  
pp. 121-147 ◽  
Author(s):  
Thomas R. Middendorf ◽  
Richard W. Aldrich
Keyword(s):  
Ligand Binding ◽  
Binding Sites ◽  
Association Constants ◽  
Binding Parameters ◽  
Parameter Identifiability ◽  
Binding Parameter ◽  
Binding Data ◽  
Binding Curve ◽  
Site Binding ◽  
Binding Curves

A critical but often overlooked question in the study of ligands binding to proteins is whether the parameters obtained from analyzing binding data are practically identifiable (PI), i.e., whether the estimates obtained from fitting models to noisy data are accurate and unique. Here we report a general approach to assess and understand binding parameter identifiability, which provides a toolkit to assist experimentalists in the design of binding studies and in the analysis of binding data. The partial fraction (PF) expansion technique is used to decompose binding curves for proteins with n ligand-binding sites exactly and uniquely into n components, each of which has the form of a one-site binding curve. The association constants of the PF component curves, being the roots of an n-th order polynomial, may be real or complex. We demonstrate a fundamental connection between binding parameter identifiability and the nature of these one-site association constants: all binding parameters are identifiable if the constants are all real and distinct; otherwise, at least some of the parameters are not identifiable. The theory is used to construct identifiability maps from which the practical identifiability of binding parameters for any two-, three-, or four-site binding curve can be assessed. Instructions for extending the method to generate identifiability maps for proteins with more than four binding sites are also given. Further analysis of the identifiability maps leads to the simple rule that the maximum number of structurally identifiable binding parameters (shown in the previous paper to be equal to n) will also be PI only if the binding curve line shape contains n resolved components.

scholarly journals A self-consistent approach for determining pairwise interactions that underlie channel activation

2014 ◽  
Vol 144 (5) ◽  
pp. 441-455 ◽  
Author(s):  
Sandipan Chowdhury ◽  
Benjamin M. Haehnel ◽  
Baron Chanda
Keyword(s):  
Free Energy ◽  
Ion Channels ◽  
Interaction Energy ◽  
Energy Of Activation ◽  
Interaction Energies ◽  
Channel Activation ◽  
Model Free ◽  
Pairwise Interactions ◽  
Free Energy Of Activation ◽  
Self Consistent

Signaling proteins such as ion channels largely exist in two functional forms, corresponding to the active and resting states, connected by multiple intermediates. Multiparametric kinetic models based on sophisticated electrophysiological experiments have been devised to identify molecular interactions of these conformational transitions. However, this approach is arduous and is not suitable for large-scale perturbation analysis of interaction pathways. Recently, we described a model-free method to obtain the net free energy of activation in voltage- and ligand-activated ion channels. Here we extend this approach to estimate pairwise interaction energies of side chains that contribute to gating transitions. Our approach, which we call generalized interaction-energy analysis (GIA), combines median voltage estimates obtained from charge-voltage curves with mutant cycle analysis to ascertain the strengths of pairwise interactions. We show that, for a system with an arbitrary gating scheme, the nonadditive contributions of amino acid pairs to the net free energy of activation can be computed in a self-consistent manner. Numerical analyses of sequential and allosteric models of channel activation also show that this approach can measure energetic nonadditivities even when perturbations affect multiple transitions. To demonstrate the experimental application of this method, we reevaluated the interaction energies of six previously described long-range interactors in the Shaker potassium channel. Our approach offers the ability to generate detailed interaction energy maps in voltage- and ligand-activated ion channels and can be extended to any force-driven system as long as associated “displacement” can be measured.

scholarly journals Free-Energy Relationships in Ion Channels Dually Activated by Voltage and Ligand

2013 ◽  
Vol 104 (2) ◽  
pp. 357a
Author(s):  
Sandipan Chowdhury ◽  
Baron Chanda
Keyword(s):  
Free Energy ◽  
Ion Channels ◽  
Energy Relationships

scholarly journals Mapping the energy landscape of protein–ligand binding via linear free energy relationships determined by protein NMR relaxation dispersion

2021 ◽  
Author(s):  
Olof Stenström ◽  
Carl Diehl ◽  
Kristofer Modig ◽  
Ulf J. Nilsson ◽  
Mikael Akke
Keyword(s):  
Free Energy ◽  
Ligand Binding ◽  
Energy Landscape ◽  
Protein Nmr ◽  
Nmr Relaxation ◽  
Binding Constants ◽  
Relaxation Dispersion ◽  
Linear Free Energy Relationships ◽  
Linear Free Energy ◽  
Energy Relationships

NMR relaxation dispersion experiments reveal linear free energy relationships relating the binding constants to the lifetimes of protein–ligand complexes, showing that the transition state is located close to the free state.

Automated, Accurate, and Scalable Relative Protein-Ligand Binding Free Energy Calculations using Lambda Dynamics

2020 ◽  
Author(s):  
E. Prabhu Raman ◽  
Thomas J. Paul ◽  
Ryan L. Hayes ◽  
Charles L. Brooks III
Keyword(s):  
Free Energy ◽  
Ligand Binding ◽  
Binding Affinity ◽  
Binding Free Energy ◽  
Computational Cost ◽  
Combinatorial Libraries ◽  
Free Energy Calculations ◽  
Lead Optimization ◽  
Efficient Estimation ◽  
Lead Compound

<p>Accurate predictions of changes to protein-ligand binding affinity in response to chemical modifications are of utility in small molecule lead optimization. Relative free energy perturbation (FEP) approaches are one of the most widely utilized for this goal, but involve significant computational cost, thus limiting their application to small sets of compounds. Lambda dynamics, also rigorously based on the principles of statistical mechanics, provides a more efficient alternative. In this paper, we describe the development of a workflow to setup, execute, and analyze Multi-Site Lambda Dynamics (MSLD) calculations run on GPUs with CHARMm implemented in BIOVIA Discovery Studio and Pipeline Pilot. The workflow establishes a framework for setting up simulation systems for exploratory screening of modifications to a lead compound, enabling the calculation of relative binding affinities of combinatorial libraries. To validate the workflow, a diverse dataset of congeneric ligands for seven proteins with experimental binding affinity data is examined. A protocol to automatically tailor fit biasing potentials iteratively to flatten the free energy landscape of any MSLD system is developed that enhances sampling and allows for efficient estimation of free energy differences. The protocol is first validated on a large number of ligand subsets that model diverse substituents, which shows accurate and reliable performance. The scalability of the workflow is also tested to screen more than a hundred ligands modeled in a single system, which also resulted in accurate predictions. With a cumulative sampling time of 150ns or less, the method results in average unsigned errors of under 1 kcal/mol in most cases for both small and large combinatorial libraries. For the multi-site systems examined, the method is estimated to be more than an order of magnitude more efficient than contemporary FEP applications. The results thus demonstrate the utility of the presented MSLD workflow to efficiently screen combinatorial libraries and explore chemical space around a lead compound, and thus are of utility in lead optimization.</p>

The Perturbed Free Energy Landscape: Linking Ligand Binding to Biomolecular Folding

ChemBioChem ◽  
2020 ◽  
Author(s):  
fareed aboul-ela ◽  
Abdallah S Abdelsatter ◽  
Youssef Mansour
Keyword(s):  
Free Energy ◽  
Ligand Binding ◽  
Energy Landscape ◽  
Free Energy Landscape
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