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Ali HS, Henchman RH. Energy-entropy multiscale cell correlation method to predict toluene-water log P in the SAMPL9 challenge. Phys Chem Chem Phys 2023; 25:27524-27531. [PMID: 37800345 DOI: 10.1039/d3cp03076h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/07/2023]
Abstract
The energy-entropy multiscale cell correlation (EE-MCC) method is used to calculate toluene-water log P values of 16 drug molecules in the SAMPL9 physical properties challenge. EE-MCC calculates the free energy, energy and entropy from molecular dynamics (MD) simulations of the water and toluene solutions. Specifically, MCC evaluates entropy by partitioning the system into cells of correlated atoms at multiple length scales and further partitioning the local coordinates into energy wells, yielding vibrational and topographical terms from the energy-well sizes and probabilities. The log P values calculated by EE-MCC using three 200 ns MD simulations have a mean average error of 0.82 and standard error of the mean of 0.97 versus experiment, which is comparable with the best methods entered in SAMPL9. The main contribution to log P is from energy. Less polar drugs have more favourable energies of transfer. The entropy of transfer consists of increased solute vibrational and conformational terms in toluene due to weaker interactions, fewer solute positions in the larger-molecule solvent, reduced water vibrational entropy, negligible change in toluene vibrational entropy, and gains in solvent orientational entropy. The solvent entropy contributions here may be slightly underestimated because software limitations and statistical fluctuations meant that only the first shell could be included while averaged over the whole solution. Nonetheless, such issues will be addressed in future software to offer a general method to calculate entropy directly from MD simulation and to provide molecular understanding or guide system design.
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Affiliation(s)
- Hafiz Saqib Ali
- Chemistry Research Laboratory, Department of Chemistry and the INEOS Oxford Institute for Antimicrobial Research, University of Oxford, 12 Mansfield Road, Oxford OX1 3TA, UK.
| | - Richard H Henchman
- Sydney Medical School, Faculty of Medicine and Health, University of Sydney, Sydney, Australia.
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Kalayan J, Chakravorty A, Warwicker J, Henchman RH. Total free energy analysis of fully hydrated proteins. Proteins 2023; 91:74-90. [PMID: 35964252 PMCID: PMC10087023 DOI: 10.1002/prot.26411] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2022] [Revised: 08/04/2022] [Accepted: 08/09/2022] [Indexed: 12/15/2022]
Abstract
The total free energy of a hydrated biomolecule and its corresponding decomposition of energy and entropy provides detailed information about regions of thermodynamic stability or instability. The free energies of four hydrated globular proteins with different net charges are calculated from a molecular dynamics simulation, with the energy coming from the system Hamiltonian and entropy using multiscale cell correlation. Water is found to be most stable around anionic residues, intermediate around cationic and polar residues, and least stable near hydrophobic residues, especially when more buried, with stability displaying moderate entropy-enthalpy compensation. Conversely, anionic residues in the proteins are energetically destabilized relative to singly solvated amino acids, while trends for other residues are less clear-cut. Almost all residues lose intraresidue entropy when in the protein, enthalpy changes are negative on average but may be positive or negative, and the resulting overall stability is moderate for some proteins and negligible for others. The free energy of water around single amino acids is found to closely match existing hydrophobicity scales. Regarding the effect of secondary structure, water is slightly more stable around loops, of intermediate stability around β strands and turns, and least stable around helices. An interesting asymmetry observed is that cationic residues stabilize a residue when bonded to its N-terminal side but destabilize it when on the C-terminal side, with a weaker reversed trend for anionic residues.
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Affiliation(s)
- Jas Kalayan
- Division of Pharmacy and Optometry, Faculty of Biology, Medicine and Health, University of Manchester, Manchester, UK
| | - Arghya Chakravorty
- Department of Chemistry and Biophysics, University of Michigan, Ann Arbor, Michigan, USA
| | - Jim Warwicker
- Manchester Institute of Biotechnology and School of Biological Sciences, Faculty of Biology, Medicine and Health, University of Manchester, Manchester, UK
| | - Richard H Henchman
- Sydney Medical School, Faculty of Medicine and Health, University of Sydney, Sydney, Australia
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Abstract
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Water is essential
for the structure, dynamics, energetics, and
thus the function of biomolecules. It is a formidable challenge to
elicit, in microscopic detail, the role of the solvation-related driving
forces of biomolecular processes, such as the enthalpy and entropy
contributions to the underlying free-energy landscape. In this Perspective,
we discuss recent developments and applications of computational methods
that provide a spatially resolved map of hydration thermodynamics
in biomolecular systems and thus yield atomic-level insights to guide
the interpretation of experimental observations. An emphasis is on
the challenge of quantifying the hydration entropy, which requires
characterization of both the motions of the biomolecules and of the
water molecules in their surrounding.
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Affiliation(s)
- Saumyak Mukherjee
- Theoretical Chemistry, Ruhr University Bochum, 44801 Bochum, Germany
| | - Lars V Schäfer
- Theoretical Chemistry, Ruhr University Bochum, 44801 Bochum, Germany
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Ali HS, Chakravorty A, Kalayan J, de Visser SP, Henchman RH. Energy-entropy method using multiscale cell correlation to calculate binding free energies in the SAMPL8 host-guest challenge. J Comput Aided Mol Des 2021; 35:911-921. [PMID: 34264476 PMCID: PMC8367938 DOI: 10.1007/s10822-021-00406-5] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2021] [Accepted: 06/22/2021] [Indexed: 11/29/2022]
Abstract
Free energy drives a wide range of molecular processes such as solvation, binding, chemical reactions and conformational change. Given the central importance of binding, a wide range of methods exist to calculate it, whether based on scoring functions, machine-learning, classical or electronic structure methods, alchemy, or explicit evaluation of energy and entropy. Here we present a new energy-entropy (EE) method to calculate the host-guest binding free energy directly from molecular dynamics (MD) simulation. Entropy is evaluated using Multiscale Cell Correlation (MCC) which uses force and torque covariance and contacts at two different length scales. The method is tested on a series of seven host-guest complexes in the SAMPL8 (Statistical Assessment of the Modeling of Proteins and Ligands) "Drugs of Abuse" Blind Challenge. The EE-MCC binding free energies are found to agree with experiment with an average error of 0.9 kcal mol-1. MCC makes clear the origin of the entropy changes, showing that the large loss of positional, orientational, and to a lesser extent conformational entropy of each binding guest is compensated for by a gain in orientational entropy of water released to bulk, combined with smaller decreases in vibrational entropy of the host, guest and contacting water.
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Affiliation(s)
- Hafiz Saqib Ali
- Manchester Institute of Biotechnology, The University of Manchester, 131 Princess Street, Manchester, M1 7DN, UK
- Department of Chemistry, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
| | - Arghya Chakravorty
- Department of Chemistry, University of Michigan, Ann Arbor, MI, 48109, USA
| | - Jas Kalayan
- Manchester Institute of Biotechnology, The University of Manchester, 131 Princess Street, Manchester, M1 7DN, UK
- Department of Chemistry, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
| | - Samuel P de Visser
- Manchester Institute of Biotechnology, The University of Manchester, 131 Princess Street, Manchester, M1 7DN, UK
- Department of Chemical Engineering and Analytical Science, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
| | - Richard H Henchman
- Manchester Institute of Biotechnology, The University of Manchester, 131 Princess Street, Manchester, M1 7DN, UK.
- Department of Chemistry, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK.
- Sydney Medical School, The University of Sydney, Sydney, NSW, 2006, Australia.
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Päslack C, Das CK, Schlitter J, Schäfer LV. Spectrally Resolved Estimation of Water Entropy in the Active Site of Human Carbonic Anhydrase II. J Chem Theory Comput 2021; 17:5409-5418. [PMID: 34259506 DOI: 10.1021/acs.jctc.1c00554] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A major challenge in understanding ligand binding to biomacromolecules lies in dissecting the underlying thermodynamic driving forces at the atomic level. Quantifying the contributions of water molecules is often especially demanding, although they can play important roles in biomolecular recognition and binding processes. One example is human carbonic anhydrase II, whose active site harbors a conserved network of structural water molecules that are essential for enzymatic catalysis. Inhibitor binding disrupts this water network and changes the hydrogen-bonding patterns in the active site. Here, we use atomistic molecular dynamics simulations to compute the absolute entropy of the individual water molecules confined in the active site of hCAII using a spectrally resolved estimation (SRE) approach. The entropy decrease of water molecules that remain in the active site upon binding of a dorzolamide inhibitor is caused by changes in hydrogen bonding and stiffening of the hydrogen-bonding network. Overall, this entropy decrease is overcompensated by the gain due to the release of three water molecules from the active site upon inhibitor binding. The spectral density calculations enable the assignment of the changes to certain vibrational modes. In addition, the range of applicability of the SRE approximation is systematically explored by exploiting the gradually changing degree of immobilization of water molecules as a function of the distance to a phospholipid bilayer surface, which defines an "entropy ruler". These results demonstrate the applicability of SRE to biomolecular solvation, and we expect it to become a useful method for entropy calculations in biomolecular systems.
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Affiliation(s)
| | - Chandan K Das
- Theoretical Chemistry, Ruhr University Bochum, D-44780 Bochum, Germany
| | | | - Lars V Schäfer
- Theoretical Chemistry, Ruhr University Bochum, D-44780 Bochum, Germany
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Falcioni F, Kalayan J, Henchman RH. Energy-entropy prediction of octanol-water logP of SAMPL7 N-acyl sulfonamide bioisosters. J Comput Aided Mol Des 2021; 35:831-840. [PMID: 34244906 PMCID: PMC8295089 DOI: 10.1007/s10822-021-00401-w] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2021] [Accepted: 06/17/2021] [Indexed: 12/23/2022]
Abstract
Partition coefficients quantify a molecule's distribution between two immiscible liquid phases. While there are many methods to compute them, there is not yet a method based on the free energy of each system in terms of energy and entropy, where entropy depends on the probability distribution of all quantum states of the system. Here we test a method in this class called Energy Entropy Multiscale Cell Correlation (EE-MCC) for the calculation of octanol-water logP values for 22 N-acyl sulfonamides in the SAMPL7 Physical Properties Challenge (Statistical Assessment of the Modelling of Proteins and Ligands). EE-MCC logP values have a mean error of 1.8 logP units versus experiment and a standard error of the mean of 1.0 logP units for three separate calculations. These errors are primarily due to getting sufficiently converged energies to give accurate differences of large numbers, particularly for the large-molecule solvent octanol. However, this is also an issue for entropy, and approximations in the force field and MCC theory also contribute to the error. Unique to MCC is that it explains the entropy contributions over all the degrees of freedom of all molecules in the system. A gain in orientational entropy of water is the main favourable entropic contribution, supported by small gains in solute vibrational and orientational entropy but offset by unfavourable changes in the orientational entropy of octanol, the vibrational entropy of both solvents, and the positional and conformational entropy of the solute.
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Affiliation(s)
- Fabio Falcioni
- Manchester Institute of Biotechnology, The University of Manchester, 131 Princess Street, Manchester, M1 7DN, UK.
- School of Chemistry, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK.
| | - Jas Kalayan
- Manchester Institute of Biotechnology, The University of Manchester, 131 Princess Street, Manchester, M1 7DN, UK
- School of Chemistry, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
| | - Richard H Henchman
- Manchester Institute of Biotechnology, The University of Manchester, 131 Princess Street, Manchester, M1 7DN, UK.
- School of Chemistry, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK.
- Sydney Medical School, The University of Sydney, Sydney, NSW, 2006, Australia.
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Kalayan J, Curtis RA, Warwicker J, Henchman RH. Thermodynamic Origin of Differential Excipient-Lysozyme Interactions. Front Mol Biosci 2021; 8:689400. [PMID: 34179093 PMCID: PMC8226134 DOI: 10.3389/fmolb.2021.689400] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2021] [Accepted: 05/25/2021] [Indexed: 01/15/2023] Open
Abstract
Understanding the intricate interplay of interactions between proteins, excipients, ions and water is important to achieve the effective purification and stable formulation of protein therapeutics. The free energy of lysozyme interacting with two kinds of polyanionic excipients, citrate and tripolyphosphate, together with sodium chloride and TRIS-buffer, are analysed in multiple-walker metadynamics simulations to understand why tripolyphosphate causes lysozyme to precipitate but citrate does not. The resulting multiscale decomposition of energy and entropy components for water, sodium chloride, excipients and lysozyme reveals that lysozyme is more stabilised by the interaction of tripolyphosphate with basic residues. This is accompanied by more sodium ions being released into solution from tripolyphosphate than for citrate, whilst the latter instead has more water molecules released into solution. Even though lysozyme aggregation is not directly probed in this study, these different mechanisms are suspected to drive the cross-linking between lysozyme molecules with vacant basic residues, ultimately leading to precipitation.
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Affiliation(s)
- Jas Kalayan
- Manchester Institute of Biotechnology, The University of Manchester, Manchester, United Kingdom.,Department of Chemistry, The University of Manchester, Manchester, United Kingdom
| | - Robin A Curtis
- Manchester Institute of Biotechnology, The University of Manchester, Manchester, United Kingdom.,Departments of Chemical Engineering and Analytical Science, The University of Manchester, Manchester, United Kingdom
| | - Jim Warwicker
- Manchester Institute of Biotechnology, The University of Manchester, Manchester, United Kingdom.,Division of Molecular and Cellular Function, School of Biological Sciences, Faculty of Biology, Medicine and Health, The University of Manchester, Manchester, United Kingdom
| | - Richard H Henchman
- Manchester Institute of Biotechnology, The University of Manchester, Manchester, United Kingdom.,Department of Chemistry, The University of Manchester, Manchester, United Kingdom.,Faculty of Medicine and Health, Sydney Medical School, The University of Sydney, Sydney, NSW, Australia
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Chakravorty A, Higham J, Henchman RH. Entropy of Proteins Using Multiscale Cell Correlation. J Chem Inf Model 2020; 60:5540-5551. [PMID: 32955869 DOI: 10.1021/acs.jcim.0c00611] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A new multiscale method is presented to calculate the entropy of proteins from molecular dynamics simulations. Termed Multiscale Cell Correlation (MCC), the method decomposes the protein into sets of rigid-body units based on their covalent-bond connectivity at three levels of hierarchy: molecule, residue, and united atom. It evaluates the vibrational and topographical entropy from forces, torques, and dihedrals at each level, taking into account correlations between sets of constituent units that together make up a larger unit at the coarser length scale. MCC gives entropies in close agreement with normal-mode analysis and smaller than those using quasiharmonic analysis as well as providing much faster convergence. Moreover, MCC provides an insightful decomposition of entropy at each length scale and for each type of amino acid according to their solvent exposure and whether they are terminal residues. While the residue entropy depends weakly on solvent exposure, there is greater variation in entropy components for larger, more polar amino acids, which have increased conformational entropy but reduced vibrational entropy with greater solvent exposure.
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Affiliation(s)
- Arghya Chakravorty
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Jonathan Higham
- MRC Human Genetics Unit, Institute of Genetics & Molecular Medicine, The University of Edinburgh, Western General Hospital, Crewe Road South, Edinburgh EH4 2XU, United Kingdom
| | - Richard H Henchman
- Manchester Institute of Biotechnology, The University of Manchester, 131 Princess Street, Manchester M1 7DN, United Kingdom.,Department of Chemistry, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
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Ali HS, Higham J, de Visser SP, Henchman RH. Comparison of Free-Energy Methods to Calculate the Barriers for the Nucleophilic Substitution of Alkyl Halides by Hydroxide. J Phys Chem B 2020; 124:6835-6842. [PMID: 32648760 DOI: 10.1021/acs.jpcb.0c02264] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
Calculating the free-energy barriers of liquid-phase chemical reactions with explicit solvent is a considerable challenge. Most studies use the energy and entropy of minimized single-point geometries of the reactants and transition state in implicit solvent using normal mode analysis (NMA). Explicit-solvent methods instead make use of the potential of mean force (PMF). Here, we propose a new energy-entropy (EE) method to calculate the Gibbs free energy of reactants and transition states in explicit solvent by combining quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations with multiscale cell correlation (MCC). We apply it to six nucleophilic substitution reactions of the hydroxide transfer to methyl and ethyl halides in water, where the halides are F, Cl, and Br. We compare EE-MCC Gibbs free energy barriers using two Hamiltonians, self-consistent charge density functional based tight-binding (SCC-DFTB) and B3LYP/6-31+G* density functional theory (DFT) with respective PMF values, EE-NMA values using B3LYP/6-31+G* and M06/6-31+G* DFT in implicit solvent and experimental values derived via transition state theory. The barriers using SCC-DFTB are found to agree well with the PMF and experiment and previous computational studies, being slightly higher but improving on the lower values obtained for the implicit solvent. Achieving convergence over many degrees of freedom remains a challenge for EE-MCC in explicit-solvent QM/MM systems, particularly for the more expensive B3LYP/6-31+G* and M06/6-31+G* DFT methods, but the insightful decomposition of entropy over all degrees of freedom should make EE-MCC a valuable tool for deepening the understanding of chemical reactions.
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Affiliation(s)
- Hafiz Saqib Ali
- Manchester Institute of Biotechnology, The University of Manchester, 131 Princess Street, Manchester M1 7DN, United Kingdom.,Department of Chemistry, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
| | - Jonathan Higham
- Manchester Institute of Biotechnology, The University of Manchester, 131 Princess Street, Manchester M1 7DN, United Kingdom.,Department of Chemistry, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom.,Institute of Genetics & Molecular Medicine, Western General Hospital, The University of Edinburgh, Crewe Road South, Edinburgh EH4 2XU, United Kingdom
| | - Sam P de Visser
- Manchester Institute of Biotechnology, The University of Manchester, 131 Princess Street, Manchester M1 7DN, United Kingdom.,Department of Chemical Engineering and Analytical Science, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
| | - Richard H Henchman
- Manchester Institute of Biotechnology, The University of Manchester, 131 Princess Street, Manchester M1 7DN, United Kingdom.,Department of Chemistry, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
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Ali HS, Higham J, Henchman RH. Entropy of Simulated Liquids Using Multiscale Cell Correlation. ENTROPY 2019; 21:e21080750. [PMID: 33267464 PMCID: PMC7515279 DOI: 10.3390/e21080750] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/29/2019] [Revised: 07/22/2019] [Accepted: 07/28/2019] [Indexed: 12/16/2022]
Abstract
Accurately calculating the entropy of liquids is an important goal, given that many processes take place in the liquid phase. Of almost equal importance is understanding the values obtained. However, there are few methods that can calculate the entropy of such systems, and fewer still to make sense of the values obtained. We present our multiscale cell correlation (MCC) method to calculate the entropy of liquids from molecular dynamics simulations. The method uses forces and torques at the molecule and united-atom levels and probability distributions of molecular coordinations and conformations. The main differences with previous work are the consistent treatment of the mean-field cell approximation to the approriate degrees of freedom, the separation of the force and torque covariance matrices, and the inclusion of conformation correlation for molecules with multiple dihedrals. MCC is applied to a broader set of 56 important industrial liquids modeled using the Generalized AMBER Force Field (GAFF) and Optimized Potentials for Liquid Simulations (OPLS) force fields with 1.14*CM1A charges. Unsigned errors versus experimental entropies are 8.7 J K - 1 mol - 1 for GAFF and 9.8 J K - 1 mol - 1 for OPLS. This is significantly better than the 2-Phase Thermodynamics method for the subset of molecules in common, which is the only other method that has been applied to such systems. MCC makes clear why the entropy has the value it does by providing a decomposition in terms of translational and rotational vibrational entropy and topographical entropy at the molecular and united-atom levels.
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Affiliation(s)
- Hafiz Saqib Ali
- Manchester Institute of Biotechnology, The University of Manchester, 131 Princess Street, Manchester M1 7DN, UK
- School of Chemistry, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Jonathan Higham
- Manchester Institute of Biotechnology, The University of Manchester, 131 Princess Street, Manchester M1 7DN, UK
- School of Chemistry, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Richard H. Henchman
- Manchester Institute of Biotechnology, The University of Manchester, 131 Princess Street, Manchester M1 7DN, UK
- School of Chemistry, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
- Correspondence: ; Tel.: +44-161-306-5194
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