Establishing the Canon: George Ripley and his Alchemical Sources

Abstract

George Ripley, Canon of Bridlington (ca. 1415 to ca. 1490) was one of England's most famous alchemists, whose alchemical opera attracted study and commentary throughout the sixteenth and seventeenth centuries, and were printed and translated both in England and abroad. Yet Ripley's frequently baffling texts have proved resistant to scholarly interpretation. This paper attempts to unravel some of Ripley's alchemical theories and practice, firstly by identifying his major sources, and secondly by gauging his response to these texts. For instance, although Ripley's interest in the corpus of alchemical texts pseudonymously attributed to Ramon Lull is well documented, it transpires that his best known work, the Compound of Alchemy, or Twelve Gates, is actually based not on a Lullian work, but on a Latin treatise that Ripley attributed to the little-known alchemist, Guido de Montanor. Further clues to Ripley's alchemical thought can be obtained by considering his handling of a potential conflict between his two authorities, Lull and Guido. The resulting insights into Ripley's alchemy provide an instrument for assessing which of Ripley's pseudoepigraphic works can be truly called "canonical".     

Stoicism and Alchemy in Late Antiquity: Zosimus and the Concept of Pneuma

At the beginning of the twentieth century, historians associated the alchemy of the third-century alchemist Zosimus of Panopolis with Platonism and Aristotelianism, explicating his theory of alchemical transmutation under the intellectual umbrella of these philosophical traditions. More recently, scholars of alchemy such as Christina Viano and William Newman have suggested a connection between Zosimean alchemy and Stoicism. Through a close reading of texts in Zosimus’s corpus, this paper posits a Stoic interpretation of several aspects of Zosimean alchemy, focusing on the concepts of pneuma and tension. For Zosimus, I argue, pneuma played a vital role in colouring metals, while tension conferred stability and cohesion upon metallic compounds. This interpretation suggests that Zosimus applied Stoic concepts to describe the alchemical process of tincturing metals.     

An Alchemist in Greenland: Hans Egede (1686–1758) and Alchemical Practice in the Colony of Hope

The article explores the practical and social circumstances of the alchemical experiments performed by the Norwegian priest and missionary Hans Egede (1686–1758) in the Colony of Hope in Greenland. Sources not previously used in connection with Egede’s alchemy are used to investigate in which ways his situation in the colony affected alchemical practice. A lack of fuel is found to have been a main obstacle which may have limited the number of experiments that Egede was able to perform in Greenland. At the same time, the area had natural resources that were useful to the alchemist, and Egede’s position as head of the colony gave access to resources that facilitated alchemical practice.     

Computing Alchemical Free Energy Differences with Hamiltonian Replica Exchange Molecular Dynamics (H-REMD) Simulations

Alchemical free energy calculations play a very important role in the field of molecular modeling. Efforts have been made to improve the accuracy and precision of those calculations. One of the efforts is to employ a Hamiltonian replica exchange molecular dynamics (H-REMD) method to enhance conformational sampling. In this paper, we demonstrated that HREMD method not only improves convergence in alchemical free energy calculations but also can be used to compute free energy differences directly via the Free Energy Perturbation (FEP)algorithm. We show a direct mapping between the H-REMD and the usual FEP equations, which are then used directly to compute free energies. The H-REMD alchemical free energy calculation (Replica exchange Free Energy Perturbation, REFEP) was tested on predicting the pK(a) value of the buried Asp26 in thioredoxin. We compare the results of REFEP with TI and regular FEP simulations. REFEP calculations converged faster than those from TI and regular FEP simulations. The final predicted pK(a) value from the H-REMD simulation was also very accurate, only 0.4 pK(a) unit above the experimental value. Utilizing the REFEP algorithm significantly improves conformational sampling, and this in turn improves the convergence of alchemical free energy simulations.     

Tinker‐OpenMM: Absolute and relative alchemical free energies using AMOEBA on GPUs

The capabilities of the polarizable force fields for alchemical free energy calculations have been limited by the high computational cost and complexity of the underlying potential energy functions. In this work, we present a GPU‐based general alchemical free energy simulation platform for polarizable potential AMOEBA. Tinker‐OpenMM, the OpenMM implementation of the AMOEBA simulation engine has been modified to enable both absolute and relative alchemical simulations on GPUs, which leads to a ∼200‐fold improvement in simulation speed over a single CPU core. We show that free energy values calculated using this platform agree with the results of Tinker simulations for the hydration of organic compounds and binding of host–guest systems within the statistical errors. In addition to absolute binding, we designed a relative alchemical approach for computing relative binding affinities of ligands to the same host, where a special path was applied to avoid numerical instability due to polarization between the different ligands that bind to the same site. This scheme is general and does not require ligands to have similar scaffolds. We show that relative hydration and binding free energy calculated using this approach match those computed from the absolute free energy approach. © 2017 Wiley Periodicals, Inc.     

Bad Chemistry: Basilisks and Women in Paracelsus and pseudo-Paracelsus

The basilisk of the pseudo-Paracelsian De natura rerum is the evil twin of the homunculus. Created from menstrual blood by artificial ectogenesis in an alchemical laboratory, the basilisk embodies the poisonous character traditionally ascribed to catamenial women, but magnified and concentrated by its mode of generation to the degree that it can kill by its glance alone. How does this remarkable thought experiment relate to other instances of the basilisk in the genuine and pseudonymous corpus of Paracelsus? The present paper outlines two primary uses which emerge repeatedly: first, in works other than De natura rerum, the basilisk is used by Paracelsus and his imitators as a means of explaining action at a distance, especially in the case of plague. Relying on a medieval association between the basilisk’s deadly gaze and the putative ability of menstruating women to damage mirrors, the genuine Paracelsus links contagious disease to the deleterious action of the female imagination. Second, because the basilisk was traditionally held to be the product of an unnatural birth, being born from an egg laid by a rooster and incubated by a toad, the Paracelsian corpus frequently invokes the monster as a model for unnatural generation in general.     

Synergistic approach to improve "alchemical" free energy calculation in rugged energy surface

The authors present an integrated approach to "alchemical" free energy simulation, which permits efficient calculation of the free energy difference on rugged energy surface. The method is designed to obtain efficient canonical sampling for rapid free energy convergence. The proposal is motivated by the insight that both the exchange efficiency in the presently designed dual-topology alchemical Hamiltonian replica exchange method (HREM), and the confidence of the free energy determination using the overlap histogramming method, depend on the same criterion, viz., the overlaps of the energy difference histograms between all pairs of neighboring states. Hence, integrating these two techniques can produce a joint solution to the problems of the free energy convergence and conformational sampling in the free energy simulations, in which lambda parameter plays two roles to simultaneously facilitate the conformational sampling and improve the phase space overlap for the free energy determination. Specifically, in contrast with other alchemical HREM based free energy simulation methods, the dual-topology approach can ensure robust conformational sampling. Due to these features (a synergistic solution to the free energy convergence and canonical sampling, and the improvement of the sampling efficiency with the dual-topology treatment), the present approach, as demonstrated in the model studies of the authors, is highly efficient in obtaining accurate free energy differences, especially for the systems with rough energy landscapes.     

BAR-based optimum adaptive steered MD for configurational sampling

The equilibrium and nonequilibrium adaptive alchemical free energy simulation methods optimum Bennett's acceptance ratio and optimum crooks' equation (OCE), based on the statistically optimal bidirectional reweighting estimator named Bennett's Acceptance Ratio or Crooks' equation, perform initial sampling in the staging alchemical transformation and then determine the importance rank of different states via the time-derivative of the variance. The method is proven to give speedups compared with the equal time rule. In the current work, we extend the time derivative of variance guided adaptive sampling method to the configurational space, falling in the term of steered MD (SMD). The SMD approach biasing physically meaningful collective variable (CV) such as one dihedral or one distance to pulling the system from one conformational state to another. By minimizing the variance of the free energy differences along the pathway in an optimized way, a new type of adaptive SMD (ASMD) is introduced. As exhibits in the alchemical case, this adaptive sampling method outperforms the traditional equal-time SMD in nonequilibrium stratification. Also, the method gives much more efficient calculation of potential of mean force than the selection criterion-based ASMD scheme, which is proven to be more efficient than traditional SMD. The OCE workflow is periodicity-of-CV dependent while ASMD is not. The performance is demonstrated in a dihedral flipping case and two distance pulling cases, accounting for periodic and nonperiodic CVs, respectively. © 2019 Wiley Periodicals, Inc.     

Descartes,Cardiac Heat,and Alchemy

René Descartes (1596–1650) insisted on a heat and light theory to explain cardiac movement, and used concepts such as distillation of the vital spirits, fermentation in the digestive process, and fermentation in the circulation of the blood. I argue that his theory of the body as a heat-exchange system was based on alchemical and natural philosophical notions of fire and light expounded by precursors and contemporaries who included Jean D'Espagnet, Jean Fernel, Jan Baptist van Helmont, and Andreas Libavius. Descartes endeavoured to mechanise their approaches, creating a theory in which fire and heat, a legacy from thermal explanations of physiology, were transformed into alchemical fire, and then into mechanistic or physicalist heat.     

Simulated scaling method for localized enhanced sampling and simultaneous "alchemical" free energy simulations: a general method for molecular mechanical, quantum mechanical, and quantum mechanical/molecular mechanical simulations

A potential scaling version of simulated tempering is presented to efficiently sample configuration space in a localized region. The present "simulated scaling" method is developed with a Wang-Landau type of updating scheme in order to quickly flatten the distributions in the scaling parameter lambdam space. This proposal is meaningful for a broad range of biophysical problems, in which localized sampling is required. Besides its superior capability and robustness in localized conformational sampling, this simulated scaling method can also naturally lead to efficient "alchemical" free energy predictions when dual-topology alchemical hybrid potential is applied; thereby simultaneously, both of the chemically and conformationally distinct portions of two end point chemical states can be efficiently sampled. As demonstrated in this work, the present method is also feasible for the quantum mechanical and quantum mechanical/molecular mechanical simulations.     

Large scale relative protein ligand binding affinities using non-equilibrium alchemy

Ligand binding affinity calculations based on molecular dynamics (MD) simulations and non-physical (alchemical) thermodynamic cycles have shown great promise for structure-based drug design. However, their broad uptake and impact is held back by the notoriously complex setup of the calculations. Only a few tools other than the free energy perturbation approach by Schrödinger Inc. (referred to as FEP+) currently enable end-to-end application. Here, we present for the first time an approach based on the open-source software pmx that allows to easily set up and run alchemical calculations for diverse sets of small molecules using the GROMACS MD engine. The method relies on theoretically rigorous non-equilibrium thermodynamic integration (TI) foundations, and its flexibility allows calculations with multiple force fields. In this study, results from the Amber and Charmm force fields were combined to yield a consensus outcome performing on par with the commercial FEP+ approach. A large dataset of 482 perturbations from 13 different protein–ligand datasets led to an average unsigned error (AUE) of 3.64 ± 0.14 kJ mol⁻¹, equivalent to Schrödinger''s FEP+ AUE of 3.66 ± 0.14 kJ mol⁻¹. For the first time, a setup is presented for overall high precision and high accuracy relative protein–ligand alchemical free energy calculations based on open-source software.

Relative ligand binding affinity calculations based on molecular dynamics (MD) simulations and non-physical (alchemical) thermodynamic cycles have shown great promise for structure-based drug design.     

Application of computer simulation free-energy methods to compute the free energy of micellization as a function of micelle composition. 2. Implementation

In this paper, the implementation of the CS-FE/MT model introduced in article 1 is discussed, and computer simulations are performed to evaluate the feasibility of the new theoretical approach. As discussed in article 1, making predictions of surfactant/solubilizate aqueous solution behavior using the CS-FE/MT model requires evaluation of DeltaDeltaG for multiple surfactant-to-solubilizate or surfactant-to-cosurfactant transformations. The central goal of this article is to evaluate the quantitative accuracy of the alchemical computer simulation method used in the CS-FE/MT modeling approach to predict DeltaDeltaG for a single surfactant-to-solubilizate or for a single surfactant-to-cosurfactant transformation. A hybrid single/dual topology approach was used to morph the ionic surfactant sodium dodecyl sulfate (SDS) into the ionic solubilizate ibuprofen (IBU), and a dual topology approach was used to morph the nonionic surfactant octyl glucoside (OG) into the nonionic solubilizate p-aminobenzoate (PAB). In addition, a single topology approach was used to morph the nonionic surfactant n-decyl dimethylphosphine oxide (C10PO) into the nonionic cosurfactant n-decyl methyl sulfoxide (C10SO), the nonionic surfactant octylsulfinyl ethanol (C8SE) into the nonionic cosurfactant decylsulfinyl ethanol (C10SE), and the nonionic surfactant n-decyl methyl sulfoxide (C10SO) into the nonionic cosurfactant n-octyl methyl sulfoxide (C8SO). Each DeltaDeltaG value was computed by using thermodynamic integration to determine the difference in free energy associated with (i) transforming a surfactant molecule of type A into a cosurfactant/solubilizate molecule of type B in a micellar environment (referred to as DeltaG2) and (ii) transforming a surfactant molecule of type A into a cosurfactant/solubilizate molecule of type B in aqueous solution (referred to as DeltaG1). CS-FE/MT model predictions of DeltaDeltaG for each alchemical transformation were made at a number of simulation conditions, including (i) different equilibration times at each value of the coupling parameter lambda, (ii) different data-gathering times at each lambda value, and (iii) simulation at a different number of lambda values. For the three surfactant-to-cosurfactant transformations considered here, the DeltaDeltaG values predicted by the CS-FE/MT model were compared with DeltaDeltaG values predicted by an accurate molecular thermodynamic (MT) model developed by fitting to experimental CMC data. Even after performing lengthy equilibration and data gathering at each lambda value, physically unrealistic values of DeltaDeltaG were predicted by the CS-FE/MT model for the transformations of SDS into IBU and of OG into PAB. However, more physically realistic DeltaDeltaG values were predicted for the transformation of C10PO into C10SO, and reasonable free-energy predictions were obtained for the transformations of C8SE into C10SE and C10SO into C8SO. Each of the surfactant-to-cosurfactant transformations considered here involved less extensive structural changes than the surfactant-to-solubilizate transformations. As computer power increases and as improvements are made to alchemical free-energy methods, it may become possible to apply the CS-FE/MT model to make accurate predictions of the free-energy changes associated with forming multicomponent surfactant and solubilizate micelles in aqueous solution where the chemical structures of the surfactants, cosurfactants, and solubilizates differ significantly.