An exponential logarithmic measure of drug receptor binding and saturation

Arturo Tozzi

arxiv: 2605.16466 · v1 · pith:KX32BWILnew · submitted 2026-05-15 · 🧬 q-bio.OT

An exponential logarithmic measure of drug receptor binding and saturation

Arturo Tozzi This is my paper

Pith reviewed 2026-05-19 21:44 UTC · model grok-4.3

classification 🧬 q-bio.OT

keywords ligand-receptor bindingexponential logarithmic descriptorpharmacodynamicsoccupancy curvesdrug saturationfree energy relationsconcentration scaling

0 comments

The pith

Exponential logarithmic descriptor integrates binding affinity and concentration to reveal wider dynamic range in receptor saturation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces an exponential logarithmic descriptor (ELD) for ligand receptor binding that combines a logarithmic term based on free energy with an inverse exponential term based on concentration. This single quantity is designed to capture both the amplification from ligand availability and the constraints from thermodynamic binding. Through numerical simulations in various concentration regimes, the ELD shows a broader dynamic range than standard occupancy curves and asymmetric sensitivity especially at low concentrations and near saturation. The approach highlights the coexistence of exponential and logarithmic processes in these biological interactions and suggests uses in dose response analysis and pharmacodynamic tracking.

Core claim

We introduce an exponential logarithmic descriptor (ELD) that integrates ligand availability and thermodynamic binding propensity within a single quantity. The logarithmic component corresponds to a thermodynamic term derived from concentration dependent free energy relations, whereas the exponential component is represented through an inverse normalized concentration term corresponding to the reciprocal of the exponential occupancy factor emerging from Boltzmann type binding formulations. Numerical simulations spanning sub affinity, transition and saturating concentration regimes demonstrate that compared with conventional occupancy curves, ELD retained a broader dynamic range and revealed

What carries the argument

Exponential logarithmic descriptor (ELD), formed by integrating a logarithmic free-energy term from concentration-dependent relations with an inverse normalized exponential concentration term from Boltzmann-type occupancy.

If this is right

ELD may provide quantitative representation for biological systems in which exponential and logarithmic processes coexist across different scales.
Applications include characterization of dose response transitions and identification of subtherapeutic and saturating exposure states.
ELD enables comparison of compounds with different affinities and normalization across heterogeneous datasets.
Continuous tracking of pharmacodynamic regimes is possible during time dependent exposure.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

ELD could be applied to real-world experimental data to validate its advantage in detecting subtle changes at extreme concentrations.
Similar combined log-exp measures might be useful in other fields where scaling laws and saturation effects interact, such as enzyme kinetics or neural signaling.
Future work could derive the ELD from first principles rather than combining existing terms.

Load-bearing premise

That the specific combination of logarithmic free-energy term and inverse normalized exponential concentration term accurately represents the coexistence of amplification and constraint processes in ligand-receptor dynamics.

What would settle it

Comparing ELD and conventional occupancy on measured binding data from experiments at low and high ligand concentrations to see if ELD indeed shows less compression of variability.

Figures

Figures reproduced from arXiv: 2605.16466 by Arturo Tozzi.

**Figure 2.** Figure 2: Time-resolved dynamics of ligand exposure, receptor occupancy and exponential–logarithmic descriptor under different clearance conditions. Simulated pharmacokinetic profiles following a single dose are shown over 48 hours, with plasma ligand concentration expressed in nM for two clearance scenarios: standard elimination and reduced clearance. The upper-left panel displays concentration–time curves, includi… view at source ↗

read the original abstract

Ligand receptor interactions are commonly assessed through equilibrium occupancy and pharmacodynamic measures that describe binding and saturation by means of bounded response curves. Thermodynamic approaches relate binding affinity to logarithmic concentration scaling, while probabilistic descriptions of occupancy arise from exponential relations. We introduce an exponential logarithmic descriptor (ELD) that integrates ligand availability and thermodynamic binding propensity within a single quantity. The logarithmic component corresponds to a thermodynamic term derived from concentration dependent free energy relations, whereas the exponential component is represented through an inverse normalized concentration term corresponding to the reciprocal of the exponential occupancy factor emerging from Boltzmann type binding formulations. We explored ELD behavior through numerical simulations spanning sub affinity, transition and saturating concentration regimes under multiple affinity conditions and time dependent exposure profiles. Compared with conventional occupancy curves, ELD retained a broader dynamic range and revealed asymmetric sensitivity across concentration scales, particularly at low exposure and near saturation, where bounded occupancy measures progressively compress variability. The resulting behavior reflects the coexistence of amplification and constraint processes within ligand receptor dynamics. ELD may provide quantitative representation for biological systems in which exponential and logarithmic processes coexist across different scales. Potential applications include characterization of dose response transitions, identification of subtherapeutic and saturating exposure states, comparison of compounds with different affinities, normalization across heterogeneous datasets and continuous tracking of pharmacodynamic regimes during time dependent exposure.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper introduces an ELD that mixes a log free-energy term with an inverse exponential concentration term to claim broader dynamic range in binding curves, but the form is asserted rather than derived from mass-action or Boltzmann relations.

read the letter

The main takeaway is that this paper defines an exponential logarithmic descriptor (ELD) as a product of a thermodynamic log term and an inverse normalized exponential term, then uses numerical simulations to show it keeps more variability at low concentrations and near saturation than the standard occupancy equation. That behavior is presented as reflecting amplification and constraint in ligand-receptor dynamics. The simulations cover multiple affinity values and time-dependent profiles, which at least illustrates how the numbers play out across regimes. Credit for running those checks and for pointing out where bounded measures lose resolution. The work stays grounded in existing ideas from thermodynamics and probabilistic occupancy without claiming to replace them outright. The soft spot is the lack of any derivation showing why this exact combination must emerge from receptor binding equations instead of being selected to produce the wider range. The asymmetry and extended sensitivity could be artifacts of the reciprocal exponential choice rather than general features of the biology. There are no quantitative error metrics, no head-to-head statistical comparisons against baselines, and no experimental data to test the claim. The abstract frames it as an integration, but without the mechanistic link the advantages remain descriptive rather than predictive. This is aimed at quantitative pharmacologists or modelers who already work with dose-response curves and might want an alternative descriptor for asymmetric regimes or heterogeneous datasets. A reader could extract the simulation setup for their own checks, but they would have to supply the validation themselves. I would send it to peer review. The core idea is clear enough that referees could push for a proper derivation or falsifiable tests, and the simulations give them something concrete to evaluate.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes an exponential logarithmic descriptor (ELD) that combines a logarithmic free-energy term with an inverse normalized exponential concentration term to describe ligand-receptor binding and saturation. Through numerical simulations in sub-affinity, transition, and saturating regimes under various affinities and time-dependent exposures, the authors report that ELD maintains a broader dynamic range and shows asymmetric sensitivity at low and near-saturation concentrations compared to conventional occupancy θ = [L]/([L] + Kd), attributing this to coexisting amplification and constraint processes. Applications in dose-response characterization and pharmacodynamic tracking are discussed.

Significance. Should the ELD prove to have a solid mechanistic foundation and demonstrate predictive value in experimental settings, it could serve as a valuable metric for biological systems involving both exponential and logarithmic scaling, offering improved resolution in pharmacodynamic analyses where standard measures saturate. The numerical exploration highlights potential utility in identifying subtherapeutic and saturating states, though current evidence is limited to simulations of the descriptor itself.

major comments (2)

Abstract: The ELD is described as integrating a logarithmic thermodynamic term and an inverse normalized exponential concentration term, but no explicit functional form or derivation from mass-action or Boltzmann relations is given; this is central because the broader dynamic range and asymmetry may be artifacts of the chosen combination rather than general features of ligand-receptor dynamics.
Numerical simulations description: The abstract mentions numerical simulations spanning concentration regimes but provides no explicit equations for ELD, no quantitative results, error analysis, or baseline comparisons with standard occupancy, which undermines evaluation of the claimed retention of broader dynamic range and asymmetric sensitivity.

minor comments (2)

Abstract: Consider adding the mathematical expression for ELD early to clarify the proposed measure for readers.
Overall: Include citations to foundational receptor occupancy models (e.g., Hill-Langmuir) and thermodynamic binding literature to provide necessary context.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript proposing the exponential logarithmic descriptor (ELD). We address each major comment below and indicate the changes planned for the revised version.

read point-by-point responses

Referee: Abstract: The ELD is described as integrating a logarithmic thermodynamic term and an inverse normalized exponential concentration term, but no explicit functional form or derivation from mass-action or Boltzmann relations is given; this is central because the broader dynamic range and asymmetry may be artifacts of the chosen combination rather than general features of ligand-receptor dynamics.

Authors: We agree that an explicit functional form and derivation would strengthen the presentation. The ELD is constructed by multiplying the logarithmic free-energy term (derived from concentration-dependent binding affinity via ΔG = RT log([L]/Kd)) by the reciprocal of the normalized exponential occupancy factor (1 / (1 + exp(-[L]/Kd))), which arises directly from Boltzmann-type probabilistic weighting of bound and unbound states. In the revised manuscript we will state the closed-form expression explicitly in the abstract and add a short derivation subsection showing how the form follows from combining the mass-action equilibrium constant with the statistical-mechanical partition function for a two-state receptor. This will demonstrate that the reported dynamic-range and asymmetry properties are consequences of the coexisting amplification and saturation mechanisms rather than an arbitrary choice. revision: yes
Referee: Numerical simulations description: The abstract mentions numerical simulations spanning concentration regimes but provides no explicit equations for ELD, no quantitative results, error analysis, or baseline comparisons with standard occupancy, which undermines evaluation of the claimed retention of broader dynamic range and asymmetric sensitivity.

Authors: The body of the manuscript already contains the numerical exploration across sub-affinity, transition, and saturating regimes under multiple Kd values and time-dependent exposure profiles. To improve accessibility and allow direct evaluation, we will revise both the abstract and the results section to include (i) the explicit ELD equation, (ii) quantitative metrics such as the ratio of dynamic ranges and sensitivity slopes at low and near-saturation concentrations, (iii) standard-error estimates from repeated runs, and (iv) side-by-side plots and tabulated comparisons against the conventional occupancy θ = [L]/([L] + Kd). These additions will make the claimed advantages transparent without altering the underlying simulation framework. revision: yes

Circularity Check

1 steps flagged

ELD's broader dynamic range and asymmetric sensitivity reduce to the asserted log-plus-inverse-exp functional form by construction

specific steps

self definitional [Abstract]
"We introduce an exponential logarithmic descriptor (ELD) that integrates ligand availability and thermodynamic binding propensity within a single quantity. The logarithmic component corresponds to a thermodynamic term derived from concentration dependent free energy relations, whereas the exponential component is represented through an inverse normalized concentration term corresponding to the reciprocal of the exponential occupancy factor emerging from Boltzmann type binding formulations. We explored ELD behavior through numerical simulations spanning sub affinity, transition and saturating浓度"

ELD is constructed as the specific combination of log thermodynamic term plus inverse normalized exp concentration term. The paper then reports that simulations of this ELD yield broader dynamic range and asymmetric sensitivity at low and saturating concentrations. These properties are direct artifacts of the chosen functional form (log for thermodynamic scaling, inverse-exp for constraint) rather than derived from receptor binding equations, so the claimed advantages are equivalent to the definition of ELD.

full rationale

The paper defines ELD explicitly as the integration of a logarithmic free-energy term and an inverse normalized exponential concentration term, then demonstrates its 'broader dynamic range' and 'asymmetric sensitivity' solely through numerical simulations of that same asserted expression. No derivation from mass-action kinetics, Boltzmann occupancy, or free-energy relations is supplied to justify why this exact combination must be used; the reported advantages are therefore direct consequences of the chosen form rather than independent results. This constitutes self-definitional circularity in which the central claim reduces to the definition itself.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The proposal rests on standard domain assumptions about thermodynamic binding and Boltzmann occupancy while introducing ELD itself as the central new construct; no free parameters are explicitly fitted in the abstract.

axioms (2)

domain assumption Thermodynamic binding affinity relates to logarithmic concentration scaling via free energy relations
Stated as the basis for the logarithmic component of ELD.
domain assumption Occupancy follows exponential relations from Boltzmann-type probabilistic binding formulations
Stated as the basis for the exponential component of ELD.

invented entities (1)

Exponential Logarithmic Descriptor (ELD) no independent evidence
purpose: Single quantity integrating ligand availability and thermodynamic binding propensity
Newly defined measure whose properties are explored only via simulation; no independent falsifiable prediction is given.

pith-pipeline@v0.9.0 · 5753 in / 1495 out tokens · 55366 ms · 2026-05-19T21:44:06.918711+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The exponential–logarithmic descriptor was defined ... E(z) = 1/z − ln z ... built ad hoc and is not derived from a conservation law, variational principle or established physical observable.
IndisputableMonolith/Foundation/LogicAsFunctionalEquation.lean SatisfiesLawsOfLogic echoes

?

echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

The logarithmic component corresponds to a thermodynamic term ... exponential component is represented through an inverse normalized concentration term

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

22 extracted references · 22 canonical work pages · 1 internal anchor

[1]

A Free -Energy Landscape for the Glucagon -Like Peptide 1 Receptor GLP1R

Alhadeff, R., and A. Warshel. 2020. “A Free -Energy Landscape for the Glucagon -Like Peptide 1 Receptor GLP1R.” Proteins 88 (1): 127–134. https://doi.org/10.1002/prot.25777

work page doi:10.1002/prot.25777 2020
[2]

Binding Selectivity Analysis from Alchemical Receptor Hopping and Swapping Free Energy Calculations

Azimi, S., and E. Gallicchio. 2024. “Binding Selectivity Analysis from Alchemical Receptor Hopping and Swapping Free Energy Calculations.” Journal of Physical Chemistry B 128 (44): 10841 –10852. https://doi.org/10.1021/acs.jpcb.4c05732

work page doi:10.1021/acs.jpcb.4c05732 2024
[3]

Activation/Deactivation Free-Energy Profiles for the β2-Adrenergic Receptor: Ligand Modes of Action

Calderón, J. C., P. Ibrahim, D. Gobbo, F. L. Gervasio, and T. Clark. 2023. “Activation/Deactivation Free-Energy Profiles for the β2-Adrenergic Receptor: Ligand Modes of Action.” Journal of Chemical Information and Modeling 63 (20): 6332–6343. https://doi.org/10.1021/acs.jcim.3c00805

work page doi:10.1021/acs.jcim.3c00805 2023
[4]

Polymeric Immunoglobulin Receptor (pIgR) in Cancer

Chae, J., J. Choi, and J. Chung. 2023. “Polymeric Immunoglobulin Receptor (pIgR) in Cancer.” Journal of Cancer Research and Clinical Oncology 149 (19): 17683–17690. https://doi.org/10.1007/s00432-023-05335-4

work page doi:10.1007/s00432-023-05335-4 2023
[5]

Comparison of Receptor -Ligand Restraint Schemes for Alchemical Absolute Binding Free Energy Calculations

Clark, F., G. Robb, D. J. Cole, and J. Michel. 2023. “Comparison of Receptor -Ligand Restraint Schemes for Alchemical Absolute Binding Free Energy Calculations.” Journal of Chemical Theory and Computation 19 (12): 3686–3704. https://doi.org/10.1021/acs.jctc.3c00139

work page doi:10.1021/acs.jctc.3c00139 2023
[6]

Titration ELISA as a Method to Determine the Dissociation Constant of Receptor Ligand Interaction

Eble, J. A. 2018. “Titration ELISA as a Method to Determine the Dissociation Constant of Receptor Ligand Interaction.” Journal of Visualized Experiments 132: 57334. https://doi.org/10.3791/57334

work page doi:10.3791/57334 2018
[7]

Free-Energy Calculations for Bioisosteric Modifications of A3 Adenosine Receptor Antagonists

Jandova, Z., W. Jespers, E. Sotelo, H. Gutiérrez-de-Terán, and C. Oostenbrink. 2019. “Free-Energy Calculations for Bioisosteric Modifications of A3 Adenosine Receptor Antagonists.” International Journal of Molecular Sciences 20 (14): 3499. https://doi.org/10.3390/ijms20143499

work page doi:10.3390/ijms20143499 2019
[8]

In Vivo Receptor Occupancy in Rodents by LC -MS/MS

Jesudason, C. D., S. DuBois, M. Johnson, V . N. Barth, and A. B. Need. 2017. “In Vivo Receptor Occupancy in Rodents by LC -MS/MS.” In Assay Guidance Manual , edited by S. Markossian, A. Grossman, H. Baskir, M. Arkin, et al. Bethesda, MD: Eli Lilly & Company and the National Center for Advancing Translational Sciences

work page 2017
[9]

Synthesis, Molecular Docking, and Binding Gibbs Free Energy Calculation of β-Nitrostyrene Derivatives: Potential Inhibitors of SARS-CoV-2 3CL Protease

Jia, Z. J., X. W. Lan, K. Lu, X. Meng, W. J. Jing, S. R. Jia, K. Zhao, and Y . J. Dai. 2023. “Synthesis, Molecular Docking, and Binding Gibbs Free Energy Calculation of β-Nitrostyrene Derivatives: Potential Inhibitors of SARS-CoV-2 3CL Protease.” Journal of Molecular Structure 1284: 135409. https://doi.org/10.1016/j.molstruc.2023.135409

work page doi:10.1016/j.molstruc.2023.135409 2023
[10]

Integrative Genetic and Multi -Omics Analysis Reveals the Interleukin -6 Receptor’s Role in Recurrent Spontaneous Abortion

Ma, W., Z. Gu, Q. Lin, M. Cao, J. Zhong, X. Li, et al. 2025. “Integrative Genetic and Multi -Omics Analysis Reveals the Interleukin -6 Receptor’s Role in Recurrent Spontaneous Abortion.” Frontiers in Immunology 16: 1659251. https://doi.org/10.3389/fimmu.2025.1659251

work page doi:10.3389/fimmu.2025.1659251 2025
[11]

Psychedelic Effects of Psilocybin Correlate with Serotonin 2A Receptor Occupancy and Plasma Psilocin Levels

Madsen, M. K., P. M. Fisher, D. Burmester, A. Dyssegaard, D. S. Stenbæk, et al. 2019. “Psychedelic Effects of Psilocybin Correlate with Serotonin 2A Receptor Occupancy and Plasma Psilocin Levels.” Neuropsychopharmacology 44 (7): 1328–1334. https://doi.org/10.1038/s41386-019-0324-9

work page doi:10.1038/s41386-019-0324-9 2019
[12]

General Quasi-Equilibrium Multivalent Binding Model to Study Diverse and Complex Drug-Receptor Interactions of Biologics

Ng, C. M., and R. J. Bauer. 2024. “General Quasi-Equilibrium Multivalent Binding Model to Study Diverse and Complex Drug-Receptor Interactions of Biologics.” Journal of Pharmacokinetics and Pharmacodynamics 51 (6): 841–857. https://doi.org/10.1007/s10928-024-09936-5

work page doi:10.1007/s10928-024-09936-5 2024
[13]

All elementary functions from a single binary operator

Odrzywolek Andrzej. 2026. “All Elementary Functions from a Single Operator.” arXiv:2603.21852

work page internal anchor Pith review Pith/arXiv arXiv 2026
[14]

Methodological Uncertainties in Drug -Receptor Binding Free Energy Predictions Based on Classical Molecular Dynamics

Procacci, P. 2021. “Methodological Uncertainties in Drug -Receptor Binding Free Energy Predictions Based on Classical Molecular Dynamics.” Current Opinion in Structural Biology 67: 127 –134. https://doi.org/10.1016/j.sbi.2020.08.001

work page doi:10.1016/j.sbi.2020.08.001 2021
[15]

Non-Equilibrium Snapshots of Ligand Efficacy at the Mu -Opioid Receptor

Robertson, M. J., A. Modak, M. M. Papasergi -Scott, M. Hu, M. C. Peroto, et al . 2026. “Non-Equilibrium Snapshots of Ligand Efficacy at the Mu -Opioid Receptor.” Nature 652 (8110): 794 –802. https://doi.org/10.1038/s41586-025-10056-4. 10

work page doi:10.1038/s41586-025-10056-4 2026
[16]

Theory of Synergistic Effects: Hill-Type Response Surfaces as ‘Null-Interaction’ Models for Mixtures

Schindler, M. 2017. “Theory of Synergistic Effects: Hill-Type Response Surfaces as ‘Null-Interaction’ Models for Mixtures.” Theoretical Biology and Medical Modelling 14 (1): 15. https://doi.org/10.1186/s12976-017- 0060-y

work page doi:10.1186/s12976-017- 2017
[17]

Modeling Synergistic Effects by Using General Hill-Type Response Surfaces Describing Drug Interactions

Schindler, M. 2022. “Modeling Synergistic Effects by Using General Hill-Type Response Surfaces Describing Drug Interactions.” Scientific Reports 12 (1): 10524. https://doi.org/10.1038/s41598-022-13469-7

work page doi:10.1038/s41598-022-13469-7 2022
[18]

https://doi.org/10.1007/978-1- 4684-3384-5_11

Seibert, E., and T. S. Tracy. 2021. “Fundamentals of Enzyme Kinetics: Michaelis-Menten and Non-Michaelis- Type (Atypical) Enzyme Kinetics.” Methods in Molecular Biology 2342: 3–27. https://doi.org/10.1007/978-1- 0716-1554-6_1

work page doi:10.1007/978-1- 2021
[19]

Understanding Thyroid Hormone Receptor Function in Controlling Developmental Timing and Rate in Xenopus: A Journey from Biochemistry and Molecular Biology to Genetics

Shi, Y . B. 2026. “Understanding Thyroid Hormone Receptor Function in Controlling Developmental Timing and Rate in Xenopus: A Journey from Biochemistry and Molecular Biology to Genetics.” General and Comparative Endocrinology 380: 114927. https://doi.org/10.1016/j.ygcen.2026.114927

work page doi:10.1016/j.ygcen.2026.114927 2026
[20]

Antipsychotic Dose, Dopamine D2 Receptor Occupancy and Extrapyramidal Side -Effects: A Systematic Review and Dose -Response Meta -Analysis

Siafis, S., H. Wu, D. Wang, A. Burschinski, N. Nomura, H. Takeuchi, J. Schneider -Thoma, J. M. Davis, and S. Leucht. 2023. “Antipsychotic Dose, Dopamine D2 Receptor Occupancy and Extrapyramidal Side -Effects: A Systematic Review and Dose -Response Meta -Analysis.” Molecular Psychiatry 28 (8): 3267 –3277. https://doi.org/10.1038/s41380-023-02203-y

work page doi:10.1038/s41380-023-02203-y 2023
[21]

A Guide to the Michaelis-Menten Equation: Steady State and Beyond

Srinivasan, B. 2022. “A Guide to the Michaelis-Menten Equation: Steady State and Beyond.” FEBS Journal 289 (20): 6086–6098. https://doi.org/10.1111/febs.16124

work page doi:10.1111/febs.16124 2022
[22]

Steroid Receptor-Coregulator Transcriptional Complexes: New Insights from CryoEM

Yi, P., X. Yu, Z. Wang, and B. W. O’Malley. 2021. “Steroid Receptor-Coregulator Transcriptional Complexes: New Insights from CryoEM.” Essays in Biochemistry 65 (6): 857–866. https://doi.org/10.1042/EBC20210019

work page doi:10.1042/ebc20210019 2021

[1] [1]

A Free -Energy Landscape for the Glucagon -Like Peptide 1 Receptor GLP1R

Alhadeff, R., and A. Warshel. 2020. “A Free -Energy Landscape for the Glucagon -Like Peptide 1 Receptor GLP1R.” Proteins 88 (1): 127–134. https://doi.org/10.1002/prot.25777

work page doi:10.1002/prot.25777 2020

[2] [2]

Binding Selectivity Analysis from Alchemical Receptor Hopping and Swapping Free Energy Calculations

Azimi, S., and E. Gallicchio. 2024. “Binding Selectivity Analysis from Alchemical Receptor Hopping and Swapping Free Energy Calculations.” Journal of Physical Chemistry B 128 (44): 10841 –10852. https://doi.org/10.1021/acs.jpcb.4c05732

work page doi:10.1021/acs.jpcb.4c05732 2024

[3] [3]

Activation/Deactivation Free-Energy Profiles for the β2-Adrenergic Receptor: Ligand Modes of Action

Calderón, J. C., P. Ibrahim, D. Gobbo, F. L. Gervasio, and T. Clark. 2023. “Activation/Deactivation Free-Energy Profiles for the β2-Adrenergic Receptor: Ligand Modes of Action.” Journal of Chemical Information and Modeling 63 (20): 6332–6343. https://doi.org/10.1021/acs.jcim.3c00805

work page doi:10.1021/acs.jcim.3c00805 2023

[4] [4]

Polymeric Immunoglobulin Receptor (pIgR) in Cancer

Chae, J., J. Choi, and J. Chung. 2023. “Polymeric Immunoglobulin Receptor (pIgR) in Cancer.” Journal of Cancer Research and Clinical Oncology 149 (19): 17683–17690. https://doi.org/10.1007/s00432-023-05335-4

work page doi:10.1007/s00432-023-05335-4 2023

[5] [5]

Comparison of Receptor -Ligand Restraint Schemes for Alchemical Absolute Binding Free Energy Calculations

Clark, F., G. Robb, D. J. Cole, and J. Michel. 2023. “Comparison of Receptor -Ligand Restraint Schemes for Alchemical Absolute Binding Free Energy Calculations.” Journal of Chemical Theory and Computation 19 (12): 3686–3704. https://doi.org/10.1021/acs.jctc.3c00139

work page doi:10.1021/acs.jctc.3c00139 2023

[6] [6]

Titration ELISA as a Method to Determine the Dissociation Constant of Receptor Ligand Interaction

Eble, J. A. 2018. “Titration ELISA as a Method to Determine the Dissociation Constant of Receptor Ligand Interaction.” Journal of Visualized Experiments 132: 57334. https://doi.org/10.3791/57334

work page doi:10.3791/57334 2018

[7] [7]

Free-Energy Calculations for Bioisosteric Modifications of A3 Adenosine Receptor Antagonists

Jandova, Z., W. Jespers, E. Sotelo, H. Gutiérrez-de-Terán, and C. Oostenbrink. 2019. “Free-Energy Calculations for Bioisosteric Modifications of A3 Adenosine Receptor Antagonists.” International Journal of Molecular Sciences 20 (14): 3499. https://doi.org/10.3390/ijms20143499

work page doi:10.3390/ijms20143499 2019

[8] [8]

In Vivo Receptor Occupancy in Rodents by LC -MS/MS

Jesudason, C. D., S. DuBois, M. Johnson, V . N. Barth, and A. B. Need. 2017. “In Vivo Receptor Occupancy in Rodents by LC -MS/MS.” In Assay Guidance Manual , edited by S. Markossian, A. Grossman, H. Baskir, M. Arkin, et al. Bethesda, MD: Eli Lilly & Company and the National Center for Advancing Translational Sciences

work page 2017

[9] [9]

Synthesis, Molecular Docking, and Binding Gibbs Free Energy Calculation of β-Nitrostyrene Derivatives: Potential Inhibitors of SARS-CoV-2 3CL Protease

Jia, Z. J., X. W. Lan, K. Lu, X. Meng, W. J. Jing, S. R. Jia, K. Zhao, and Y . J. Dai. 2023. “Synthesis, Molecular Docking, and Binding Gibbs Free Energy Calculation of β-Nitrostyrene Derivatives: Potential Inhibitors of SARS-CoV-2 3CL Protease.” Journal of Molecular Structure 1284: 135409. https://doi.org/10.1016/j.molstruc.2023.135409

work page doi:10.1016/j.molstruc.2023.135409 2023

[10] [10]

Integrative Genetic and Multi -Omics Analysis Reveals the Interleukin -6 Receptor’s Role in Recurrent Spontaneous Abortion

Ma, W., Z. Gu, Q. Lin, M. Cao, J. Zhong, X. Li, et al. 2025. “Integrative Genetic and Multi -Omics Analysis Reveals the Interleukin -6 Receptor’s Role in Recurrent Spontaneous Abortion.” Frontiers in Immunology 16: 1659251. https://doi.org/10.3389/fimmu.2025.1659251

work page doi:10.3389/fimmu.2025.1659251 2025

[11] [11]

Psychedelic Effects of Psilocybin Correlate with Serotonin 2A Receptor Occupancy and Plasma Psilocin Levels

Madsen, M. K., P. M. Fisher, D. Burmester, A. Dyssegaard, D. S. Stenbæk, et al. 2019. “Psychedelic Effects of Psilocybin Correlate with Serotonin 2A Receptor Occupancy and Plasma Psilocin Levels.” Neuropsychopharmacology 44 (7): 1328–1334. https://doi.org/10.1038/s41386-019-0324-9

work page doi:10.1038/s41386-019-0324-9 2019

[12] [12]

General Quasi-Equilibrium Multivalent Binding Model to Study Diverse and Complex Drug-Receptor Interactions of Biologics

Ng, C. M., and R. J. Bauer. 2024. “General Quasi-Equilibrium Multivalent Binding Model to Study Diverse and Complex Drug-Receptor Interactions of Biologics.” Journal of Pharmacokinetics and Pharmacodynamics 51 (6): 841–857. https://doi.org/10.1007/s10928-024-09936-5

work page doi:10.1007/s10928-024-09936-5 2024

[13] [13]

All elementary functions from a single binary operator

Odrzywolek Andrzej. 2026. “All Elementary Functions from a Single Operator.” arXiv:2603.21852

work page internal anchor Pith review Pith/arXiv arXiv 2026

[14] [14]

Methodological Uncertainties in Drug -Receptor Binding Free Energy Predictions Based on Classical Molecular Dynamics

Procacci, P. 2021. “Methodological Uncertainties in Drug -Receptor Binding Free Energy Predictions Based on Classical Molecular Dynamics.” Current Opinion in Structural Biology 67: 127 –134. https://doi.org/10.1016/j.sbi.2020.08.001

work page doi:10.1016/j.sbi.2020.08.001 2021

[15] [15]

Non-Equilibrium Snapshots of Ligand Efficacy at the Mu -Opioid Receptor

Robertson, M. J., A. Modak, M. M. Papasergi -Scott, M. Hu, M. C. Peroto, et al . 2026. “Non-Equilibrium Snapshots of Ligand Efficacy at the Mu -Opioid Receptor.” Nature 652 (8110): 794 –802. https://doi.org/10.1038/s41586-025-10056-4. 10

work page doi:10.1038/s41586-025-10056-4 2026

[16] [16]

Theory of Synergistic Effects: Hill-Type Response Surfaces as ‘Null-Interaction’ Models for Mixtures

Schindler, M. 2017. “Theory of Synergistic Effects: Hill-Type Response Surfaces as ‘Null-Interaction’ Models for Mixtures.” Theoretical Biology and Medical Modelling 14 (1): 15. https://doi.org/10.1186/s12976-017- 0060-y

work page doi:10.1186/s12976-017- 2017

[17] [17]

Modeling Synergistic Effects by Using General Hill-Type Response Surfaces Describing Drug Interactions

Schindler, M. 2022. “Modeling Synergistic Effects by Using General Hill-Type Response Surfaces Describing Drug Interactions.” Scientific Reports 12 (1): 10524. https://doi.org/10.1038/s41598-022-13469-7

work page doi:10.1038/s41598-022-13469-7 2022

[18] [18]

https://doi.org/10.1007/978-1- 4684-3384-5_11

Seibert, E., and T. S. Tracy. 2021. “Fundamentals of Enzyme Kinetics: Michaelis-Menten and Non-Michaelis- Type (Atypical) Enzyme Kinetics.” Methods in Molecular Biology 2342: 3–27. https://doi.org/10.1007/978-1- 0716-1554-6_1

work page doi:10.1007/978-1- 2021

[19] [19]

Understanding Thyroid Hormone Receptor Function in Controlling Developmental Timing and Rate in Xenopus: A Journey from Biochemistry and Molecular Biology to Genetics

Shi, Y . B. 2026. “Understanding Thyroid Hormone Receptor Function in Controlling Developmental Timing and Rate in Xenopus: A Journey from Biochemistry and Molecular Biology to Genetics.” General and Comparative Endocrinology 380: 114927. https://doi.org/10.1016/j.ygcen.2026.114927

work page doi:10.1016/j.ygcen.2026.114927 2026

[20] [20]

Antipsychotic Dose, Dopamine D2 Receptor Occupancy and Extrapyramidal Side -Effects: A Systematic Review and Dose -Response Meta -Analysis

Siafis, S., H. Wu, D. Wang, A. Burschinski, N. Nomura, H. Takeuchi, J. Schneider -Thoma, J. M. Davis, and S. Leucht. 2023. “Antipsychotic Dose, Dopamine D2 Receptor Occupancy and Extrapyramidal Side -Effects: A Systematic Review and Dose -Response Meta -Analysis.” Molecular Psychiatry 28 (8): 3267 –3277. https://doi.org/10.1038/s41380-023-02203-y

work page doi:10.1038/s41380-023-02203-y 2023

[21] [21]

A Guide to the Michaelis-Menten Equation: Steady State and Beyond

Srinivasan, B. 2022. “A Guide to the Michaelis-Menten Equation: Steady State and Beyond.” FEBS Journal 289 (20): 6086–6098. https://doi.org/10.1111/febs.16124

work page doi:10.1111/febs.16124 2022

[22] [22]

Steroid Receptor-Coregulator Transcriptional Complexes: New Insights from CryoEM

Yi, P., X. Yu, Z. Wang, and B. W. O’Malley. 2021. “Steroid Receptor-Coregulator Transcriptional Complexes: New Insights from CryoEM.” Essays in Biochemistry 65 (6): 857–866. https://doi.org/10.1042/EBC20210019

work page doi:10.1042/ebc20210019 2021