Model-Based Virtual PK/PD Exploration and Machine Learning Approach to Define PK Drivers in Early Drug Discovery

While poor translatability of preclinical efficacy models can be responsible for clinical phase II failures, misdefinition of the optimal PK properties required to achieve therapeutic efficacy can also be a contributing factor. In the present work, the pharmacological dependency of PK end points in driving efficacy is demonstrated for six common pharmacological processes via model-based analysis. The analysis shows that the response is driven by multiple pharmacology-specific PK end points that change with how the response is defined. Moreover, the results demonstrate that the most important chemical structural features influencing response are specific to both target and downstream pharmacology, meaning the design and screening criteria must be defined uniquely for each target and corresponding pharmacology. The model-based virtual exploration of PK/PD relationships presented in this work offers one approach to identify target pharmacology-specific PK drivers and the associated potency-ADME space early in discovery to increase the probability of success and, ultimately, clinical attrition

Evaluation of the Role of Water in the H₂ Bond Formation by Ni(II)-Based Electrocatalysts

We investigate the role of water in the H–H bond formation by a family of nickel molecular catalysts that exhibit high rates for H₂ production in acetonitrile solvent. A key feature leading to the high reactivity is the Lewis acidity of the Ni­(II) center and pendant amines in the diphosphine ligand that function as Lewis bases, facilitating H–H bond formation or cleavage. Significant increases in the rate of H₂ production have been reported in the presence of added water. Our calculations show that molecular water can displace an acetonitrile solvent molecule in the first solvation shell of the metal. One or two water molecules can also participate in shuttling a proton that can combine with a metal hydride to form the H–H bond. However the participation of the water molecules does not lower the barrier to H–H bond formation. Thus these calculations suggest that the rate increase due to water in these electrocatalysts is not associated with the elementary step of H–H bond formation or cleavage but rather with the proton delivery steps. We attribute the higher barrier in the H–H bond formation in the presence of water to a decrease in direct interaction between the protic and hydridic hydrogen atoms forced by the water molecules

Computing Free Energy Landscapes: Application to Ni-based Electrocatalysts with Pendant Amines for H₂ Production and Oxidation

A general strategy is reported for the computational exploration of catalytic pathways of molecular catalysts. Our results are based on a set of linear free energy relationships derived from extensive electronic structure calculations that permit predicting the thermodynamics of intermediates, with accuracy comparable to experimental data. The approach is exemplified with the catalytic oxidation and production of H₂ by [Ni­(diphosphine)₂]²⁺ electrocatalysts with pendant amines incorporated in the second coordination sphere of the metal center. The analysis focuses upon prediction of thermodynamic properties including reduction potentials, hydride donor abilities, and p<i>K</i>_a values of both the protonated Ni center and the pendant amine. It is shown that all of these chemical properties can be estimated from the knowledge of only the two redox potentials for the Ni­(II)/Ni­(I) and Ni­(I)/Ni(0) couples of the nonprotonated complex, and the p<i>K</i>_a of the parent primary aminium ion. These three quantities are easily accessible either experimentally or theoretically. The proposed correlations reveal intimate details about the nature of the catalytic mechanism and its dependence on chemical structure and thermodynamic conditions such as applied external voltage and species concentration. This computational methodology is applied to the exploration of possible catalytic pathways, identifying low and high-energy intermediates and, consequently, possibly avoiding bottlenecks associated with undesirable intermediates in the catalytic reactions. We discuss how to optimize some of the critical reaction steps to favor catalytically more efficient intermediates. The results of this study highlight the substantial interplay between the various parameters characterizing the catalytic activity, and form the basis needed to optimize the performance of this class of catalysts

Hydrogen Production Using Nickel Electrocatalysts with Pendant Amines: Ligand Effects on Rates and Overpotentials

A Ni-based electrocatalyst for H₂ production, [Ni­(8P^Ph₂N^C₆H₄Br)₂]­(BF₄)₂, featuring eight-membered cyclic diphosphine ligands incorporating a single amine base, 1-<i>para</i>-bromophenyl-3,7-triphenyl-1-aza-3,7-diphosphacycloheptane (8P^Ph₂N^C₆H₄Br) has been synthesized and characterized. X-ray diffraction studies reveal that the cation of [Ni­(8P^Ph₂N^C₆H₄Br)₂(CH₃CN)]­(BF₄)₂ has a distorted trigonal bipyramidal geometry. In CH₃CN, [Ni­(8P^Ph₂N^C₆H₄Br)₂]²⁺ is an electrocatalyst for reduction of protons, and it has a maximum turnover frequency for H₂ production of 800 s^–1 with a 700 mV overpotential (at <i>E</i>_cat/2) when using [(DMF)­H]­OTf as the acid. Addition of H₂O to acidic CH₃CN solutions of [Ni­(8P^Ph₂N^C₆H₄Br)₂]²⁺ results in an increase in the turnover frequency for H₂ production to a maximum of 3300 s^–1 with an overpotential of 760 mV at <i>E</i>_cat/2. Computational studies carried out on [Ni­(8P^Ph₂N^C₆H₄Br)₂]²⁺ indicate the observed catalytic rate is limited by formation of nonproductive protonated isomers, diverting active catalyst from the catalytic cycle. The results of this research show that proton delivery from the exogenous acid to the correct position on the proton relay of the metal complex is essential for fast H₂ production

Ab Initio-Based Kinetic Modeling for the Design of Molecular Catalysts: The Case of H₂ Production Electrocatalysts

Design of fast, efficient electrocatalysts for energy production and energy utilization requires a systematic approach to predict and tune the energetics of reaction intermediates and the kinetic barriers between them as well as to tune reaction conditions (e.g., concentration of reactants, acidity of the reaction medium, and applied electric potential). Thermodynamics schemes based on the knowledge of p<i>K</i>_a values, hydride donor ability, redox potentials, and other relevant thermodynamic properties have been demonstrated to be very effective for exploring possible reaction pathways. We seek to identify high-energy intermediates, which may represent a catalytic bottleneck, and low-energy intermediates, which may represent a thermodynamic sink. In this study, working on a well-established Ni-based bioinspired electrocatalyst for H₂ production, we performed a detailed kinetic analysis of the catalytic pathways to assess the limitations of our current (standard state) thermodynamic analysis with respect to prediction of optimal catalyst performance. To this end, we developed a microkinetic model based on extensive ab initio simulations. The model was validated against available experimental data, and it reproduces remarkably well the observed turnover rate as a function of the acid concentration and catalytic conditions, providing valuable information on the main factors limiting catalysis. Using this kinetic analysis as a reference, we show that indeed a purely thermodynamic analysis of the possible reaction pathways provides us with valuable information, such as a qualitative picture of the species involved during catalysis, identification of the possible branching points, and the origin of the observed overpotential, which are critical insights for electrocatalyst design. However, a significant limitation of this approach is understanding how these insights relate to rate, which is an equally critical piece of information. Taking our analysis a step further, we show that the kinetic model can easily be extended to different catalytic conditions by using linear free energy relationships for activation barriers based on simple thermodynamics quantities, such as p<i>K</i>_a values. We also outline a possible procedure to extend it to other catalytic platforms, making it a general and effective way to design catalysts with improved performance

High Catalytic Rates for Hydrogen Production Using Nickel Electrocatalysts with Seven-Membered Cyclic Diphosphine Ligands Containing One Pendant Amine

A series of Ni-based electrocatalysts, [Ni­(7P^Ph₂N^C6H4X)₂]­(BF₄)₂, featuring seven-membered cyclic diphosphine ligands incorporating a single amine base, 1-<i>para</i>-X-phenyl-3,6-triphenyl-1-aza-3,6-diphosphacycloheptane (7P^Ph₂N^C6H4X, where X = OMe, Me, Br, Cl, or CF₃), have been synthesized and characterized. X-ray diffraction studies have established that the [Ni­(7P^Ph₂N^C6H4X)₂]²⁺ complexes have a square planar geometry, with bonds to four phosphorus atoms of the two bidentate diphosphine ligands. Each of the complexes is an efficient electrocatalyst for hydrogen production at the potential of the Ni­(II/I) couple, with turnover frequencies ranging from 2400 to 27 000 s^–1 with [(DMF)­H]⁺ in acetonitrile. Addition of water (up to 1.0 M) accelerates the catalysis, giving turnover frequencies ranging from 4100 to 96 000 s^–1. Computational studies carried out on the [Ni­(7P^Ph₂N^C6H4X)₂]²⁺ family indicate the catalytic rates reach a maximum when the electron-donating character of X results in the p<i>K</i>_a of the Ni­(I) protonated pendant amine matching that of the acid used for proton delivery. Additionally, the fast catalytic rates for hydrogen production by the [Ni­(7P^Ph₂N^C6H4X)₂]²⁺ family relative to the analogous [Ni­(P^Ph₂N^C6H4X₂)₂]²⁺ family are attributed to preferred formation of endo protonated isomers with respect to the metal center in the former, which is essential to attain suitable proximity to the reduced metal center to generate H₂. The results of this work highlight the importance of precise p<i>K</i>_a matching with the acid for proton delivery to obtain optimal rates of catalysis

High Catalytic Rates for Hydrogen Production Using Nickel Electrocatalysts with Seven-Membered Cyclic Diphosphine Ligands Containing One Pendant Amine

A series of Ni-based electrocatalysts, [Ni­(7P^Ph₂N^C6H4X)₂]­(BF₄)₂, featuring seven-membered cyclic diphosphine ligands incorporating a single amine base, 1-<i>para</i>-X-phenyl-3,6-triphenyl-1-aza-3,6-diphosphacycloheptane (7P^Ph₂N^C6H4X, where X = OMe, Me, Br, Cl, or CF₃), have been synthesized and characterized. X-ray diffraction studies have established that the [Ni­(7P^Ph₂N^C6H4X)₂]²⁺ complexes have a square planar geometry, with bonds to four phosphorus atoms of the two bidentate diphosphine ligands. Each of the complexes is an efficient electrocatalyst for hydrogen production at the potential of the Ni­(II/I) couple, with turnover frequencies ranging from 2400 to 27 000 s^–1 with [(DMF)­H]⁺ in acetonitrile. Addition of water (up to 1.0 M) accelerates the catalysis, giving turnover frequencies ranging from 4100 to 96 000 s^–1. Computational studies carried out on the [Ni­(7P^Ph₂N^C6H4X)₂]²⁺ family indicate the catalytic rates reach a maximum when the electron-donating character of X results in the p<i>K</i>_a of the Ni­(I) protonated pendant amine matching that of the acid used for proton delivery. Additionally, the fast catalytic rates for hydrogen production by the [Ni­(7P^Ph₂N^C6H4X)₂]²⁺ family relative to the analogous [Ni­(P^Ph₂N^C6H4X₂)₂]²⁺ family are attributed to preferred formation of endo protonated isomers with respect to the metal center in the former, which is essential to attain suitable proximity to the reduced metal center to generate H₂. The results of this work highlight the importance of precise p<i>K</i>_a matching with the acid for proton delivery to obtain optimal rates of catalysis

Incorporating Amino Acid Esters into Catalysts for Hydrogen Oxidation: Steric and Electronic Effects and the Role of Water as a Base

Four derivatives of a hydrogen oxidation catalyst, [Ni­(P^Cy₂N^Bn‑R₂)₂]²⁺ (Cy = cyclohexyl, Bn = benzyl, R = OMe, COOMe, CO-alanine-methyl ester, CO-phenylalanine-methyl ester), have been prepared to investigate steric and electronic effects on catalysis. Each complex was characterized spectroscopically and electrochemically, and thermodynamic data were determined. Crystal structures are also reported for the −OMe and −COOMe derivatives. All four catalysts were found to be active for H₂ oxidation. The methyl ester (R = COOMe) and amino acid ester containing complexes (R = CO-alanine-methyl ester or CO-phenylalanine-methyl ester) had rates slower (4 s^–1) than that of the parent complex (10 s^–1), in which R = H, which is consistent with the lower amine p<i>K</i>_a's and less favorable Δ<i>G</i>_H₂'s found for these electron-withdrawing substituents. Dynamic processes for the amino acid ester containing complexes were also investigated and found not to hinder catalysis. The electron-donating methyl ether derivative (R = OMe) was prepared to compare electronic effects and has a catalytic rate similar to that of the parent complex. In the course of these studies, it was found that water could act as a weak base for H₂ oxidation, although catalytic turnover requires a higher potential and utilizes a different sequence of catalytic steps than when using a base with a higher p<i>K</i>_a. Importantly, these catalysts provide a foundation upon which larger peptides can be attached to [Ni­(P^Cy₂N^Bn₂)₂]²⁺ hydrogen oxidation catalysts in order to more fully investigate and implement the effects of the outer coordination sphere

Incorporating Amino Acid Esters into Catalysts for Hydrogen Oxidation: Steric and Electronic Effects and the Role of Water as a Base

Four derivatives of a hydrogen oxidation catalyst, [Ni­(P^Cy₂N^Bn‑R₂)₂]²⁺ (Cy = cyclohexyl, Bn = benzyl, R = OMe, COOMe, CO-alanine-methyl ester, CO-phenylalanine-methyl ester), have been prepared to investigate steric and electronic effects on catalysis. Each complex was characterized spectroscopically and electrochemically, and thermodynamic data were determined. Crystal structures are also reported for the −OMe and −COOMe derivatives. All four catalysts were found to be active for H₂ oxidation. The methyl ester (R = COOMe) and amino acid ester containing complexes (R = CO-alanine-methyl ester or CO-phenylalanine-methyl ester) had rates slower (4 s^–1) than that of the parent complex (10 s^–1), in which R = H, which is consistent with the lower amine p<i>K</i>_a's and less favorable Δ<i>G</i>_H₂'s found for these electron-withdrawing substituents. Dynamic processes for the amino acid ester containing complexes were also investigated and found not to hinder catalysis. The electron-donating methyl ether derivative (R = OMe) was prepared to compare electronic effects and has a catalytic rate similar to that of the parent complex. In the course of these studies, it was found that water could act as a weak base for H₂ oxidation, although catalytic turnover requires a higher potential and utilizes a different sequence of catalytic steps than when using a base with a higher p<i>K</i>_a. Importantly, these catalysts provide a foundation upon which larger peptides can be attached to [Ni­(P^Cy₂N^Bn₂)₂]²⁺ hydrogen oxidation catalysts in order to more fully investigate and implement the effects of the outer coordination sphere

Incorporating Amino Acid Esters into Catalysts for Hydrogen Oxidation: Steric and Electronic Effects and the Role of Water as a Base

Four derivatives of a hydrogen oxidation catalyst, [Ni­(P^Cy₂N^Bn‑R₂)₂]²⁺ (Cy = cyclohexyl, Bn = benzyl, R = OMe, COOMe, CO-alanine-methyl ester, CO-phenylalanine-methyl ester), have been prepared to investigate steric and electronic effects on catalysis. Each complex was characterized spectroscopically and electrochemically, and thermodynamic data were determined. Crystal structures are also reported for the −OMe and −COOMe derivatives. All four catalysts were found to be active for H₂ oxidation. The methyl ester (R = COOMe) and amino acid ester containing complexes (R = CO-alanine-methyl ester or CO-phenylalanine-methyl ester) had rates slower (4 s^–1) than that of the parent complex (10 s^–1), in which R = H, which is consistent with the lower amine p<i>K</i>_a's and less favorable Δ<i>G</i>_H₂'s found for these electron-withdrawing substituents. Dynamic processes for the amino acid ester containing complexes were also investigated and found not to hinder catalysis. The electron-donating methyl ether derivative (R = OMe) was prepared to compare electronic effects and has a catalytic rate similar to that of the parent complex. In the course of these studies, it was found that water could act as a weak base for H₂ oxidation, although catalytic turnover requires a higher potential and utilizes a different sequence of catalytic steps than when using a base with a higher p<i>K</i>_a. Importantly, these catalysts provide a foundation upon which larger peptides can be attached to [Ni­(P^Cy₂N^Bn₂)₂]²⁺ hydrogen oxidation catalysts in order to more fully investigate and implement the effects of the outer coordination sphere