Reaction path determination for quantum mechanical/molecular mechanical modeling of enzyme reactions by combining first order and second order "chain-of-replicas" methods

A two-step procedure for the determination of reaction paths in enzyme systems is presented. This procedure combines two chain-of-states methods: a quantum mechanical/molecular mechanical (QM/MM) implementation of the nudged elastic band (NEB) method and a second order parallel path optimizer method both recently developed in our laboratory. In the first step, a reaction path determination is performed with the NEB method, along with a restrained minimization procedure for the MM environment to obtain a first approximation to the reaction path. In the second step, the calculated path is refined with the parallel path optimizer method. By combining these two methods the reaction paths are determined accurately, and in addition, the number of path optimization iterations are significantly reduced. This procedure is tested by calculating both steps of the isomerization of 2-oxo-4-hexenedioate by 4-oxalocrotonate tautomerase, which have been previously determined by our group. The calculated paths agree with the previously reported results and we obtain a reduction of 45%-55% in the number of path optimization cycles.     

Optimization methods for finding minimum energy paths

A comparison of chain-of-states based methods for finding minimum energy pathways (MEPs) is presented. In each method, a set of images along an initial pathway between two local minima is relaxed to find a MEP. We compare the nudged elastic band (NEB), doubly nudged elastic band, string, and simplified string methods, each with a set of commonly used optimizers. Our results show that the NEB and string methods are essentially equivalent and the most efficient methods for finding MEPs when coupled with a suitable optimizer. The most efficient optimizer was found to be a form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno method in which the approximate inverse Hessian is constructed globally for all images along the path. The use of a climbing-image allows for finding the saddle point while representing the MEP with as few images as possible. If a highly accurate MEP is desired, it is found to be more efficient to descend from the saddle to the minima than to use a chain-of-states method with many images. Our results are based on a pairwise Morse potential to model rearrangements of a heptamer island on Pt(111), and plane-wave based density functional theory to model a rollover diffusion mechanism of a Pd tetramer on MgO(100) and dissociative adsorption and diffusion of oxygen on Au(111).     

Paths to which the nudged elastic band converges

A recent letter to the editor (Quapp and Bofill, J Comput Chem 2010, 31, 2526) claims that the nudged elastic band (NEB) method can converge toward gradient extremal paths and not to steepest descent paths, as has been assumed. Here, we show that the NEB does in fact converge to steepest descent paths and that the observed tendency for the NEB to approach gradient extremal paths was a consequence of implementation errors. We also note that while the NEB finds steepest descent paths, these are not necessarily minimum energy paths in the sense of being a set of points which are minima in the potential energy surface perpendicular to the path. An example is given where segments of steepest descent paths follow potential energy ridges.     

A comment to the nudged elastic band method

The minimum energy path (MEP) is an important reaction path concept of theoretical chemistry, and the nudged elastic band (NEB) method with its many facets is a central method to determine the MEP. We demonstrate in this comment that the NEB does not have to lead to a steepest descent pathway (as always assumed). In contrast, as long as it is used without spring forces, it can lead to a gradient extremal. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Exploring SCC-DFTB paths for mapping QM/MM reaction mechanisms

A new first-order procedure for locating transition structures (TS) that employs hybrid quantum mechanical/molecular mechanical (QM/MM) potentials has been developed. This new technique (RPATh+RESD) combines the replica path method (RPATh) and standard reaction coordinate driving (RCD) techniques in an approach that both efficiently determines reaction barriers and successfully eliminates two key weaknesses of RCD calculations (i.e., hysteresis/discontinuities in the path and the sequential nature of the RCD procedure). In addition, we have extended CHARMM's QM/MM reaction pathway methods, the RPATh and nudged elastic band (NEB) methods, to incorporate SCC-DFTB wave functions. This newly added functionality has been applied to the chorismate mutase-catalyzed interconversion of chorismate to prephenate, which is a key step in the shikimate pathway of bacteria, fungi, and other higher plants. The RPATh+RESD barrier height (DeltaE=5.7 kcal/mol) is in good agreement with previous results from full-energy surface mapping studies (Zhang, X.; Zhang, X.; Bruice, T. C. Biochemistry 2005, 44, 10443-10448). Full reaction paths were independently mapped with RPATh and NEB methods and showed good agreement with the final transition state from the RPATh+RESD "gold standard" and previous high-level QM/MM transition states (Woodcock, H. L.; Hodoscek, M.; Gilbert, T. B.; Gill, P. M. W.; Schaefer, H. F.; Brooks, B. R. J. Comput. Chem. 2007, 28, 1485-1502). The SCC-DFTB TS geometry most closely approximates the MP2/6-31+G(d) QM/MM result. However, the barrier height is underestimated and possibly points to an area for improvement in SCC-DFTB parametrization. In addition, the steepest descents (SD) minimizer for the NEB method was modified to uncouple the in-path and off-path degrees of freedom during the minimization, which significantly improved performance. The convergence behavior of the RPATh and NEB was examined for SCC-DFTB wave functions, and it was determined that, in general, both methods converge at about the same rate, although the techniques used for convergence may be different. For instance, RPATh can effectively use the adopted basis Newton-Raphson (ABNR) minimizer, where NEB seems to require a combination of SD and ABNR.     

A hybrid elastic band string algorithm for studies of enzymatic reactions

A common challenge in theoretical biophysics is the identification of a minimum energy path (MEP) for the rearrangement of a group of atoms from one stable configuration to another. The structure with maximum energy along the MEP approximates the transition state for the process and the energy profile itself permits estimation of the transition rates. In this work we describe a computationally efficient algorithm for the identification of minimum energy paths in complicated biosystems. The algorithm is a hybrid of the nudged elastic band (NEB) and string methods. It has been implemented in the pDynamo simulation program and tested by examining elementary steps in the reaction mechanisms of three enzymes: citrate synthase, RasGAP, and lactate dehydrogenase. Good agreement is found for the energies and geometries of the species along the reaction profiles calculated using the new algorithm and previous versions of the NEB and string techniques, and also those obtained by the common method of adiabatic exploration of the potential energy surface as a function of predefined reaction coordinates. Precisely refined structures of the saddle points along the paths may be subsequently obtained with the climbing image variant of the NEB algorithm. Directions in which the utility of the methods that we have implemented can be further improved are discussed.     

Simplex optimization of response-time-limited systems : A Study with a Spectrophotometric Determination of Aluminium and Mathematical Test Functions

A two-part modification to the standard simplex optimization is used to speed up the optimization of systems limited by response time. The modications are tested on a slow spectrophotometric procedure for aluminium, and on 2-, 3- and 5-parameter test functions. The modifications are shown to work for the aluminium method, with substantial time-savings, and to be statistically valid when used on the test functions. The best combination of the new modifications and the standard method are discussed.     

MALDI imaging mass spectrometry of β‐ and γ‐crystallins in the ocular lens

Lens crystallin proteins make up 90% of expressed proteins in the ocular lens and are primarily responsible for maintaining lens transparency and establishing the gradient of refractive index necessary for proper focusing of images onto the retina. Age‐related modifications to lens crystallins have been linked to insolubilization and cataractogenesis in human lenses. Matrix‐assisted laser desorption/ionization (MALDI) imaging mass spectrometry (IMS) has been shown to provide spatial maps of such age‐related modifications. Previous work demonstrated that, under standard protein IMS conditions, α‐crystallin signals dominated the mass spectrum and age‐related modifications to α‐crystallins could be mapped. In the current study, a new sample preparation method was optimized to allow imaging of β‐ and γ‐crystallins in ocular lens tissue. Acquired images showed that γ‐crystallins were localized predominately in the lens nucleus whereas β‐crystallins were primarily localized to the lens cortex. Age‐related modifications such as truncation, acetylation, and carbamylation were identified and spatially mapped. Protein identifications were determined by top‐down proteomics analysis of lens proteins extracted from tissue sections and analyzed by LC‐MS/MS with electron transfer dissociation. This new sample preparation method combined with the standard method allows the major lens crystallins to be mapped by MALDI IMS.     

Single‐ended transition state finding with the growing string method

Reaction path finding and transition state (TS) searching are important tasks in computational chemistry. Methods that seek to optimize an evenly distributed set of structures to represent a chemical reaction path are known as double‐ended string methods. Such methods can be highly reliable because the endpoints of the string are fixed, which effectively lowers the dimensionality of the reaction path search. String methods, however, require that the reactant and product structures are known beforehand, which limits their ability for systematic exploration of reactive steps. In this article, a single‐ended growing string method (GSM) is introduced which allows for reaction path searches starting from a single structure. The method works by sequentially adding nodes along coordinates that drive bonds, angles, and/or torsions to a desired reactive outcome. After the string is grown and an approximate reaction path through the TS is found, string optimization commences and the exact TS is located along with the reaction path. Fast convergence of the string is achieved through use of internal coordinates and eigenvector optimization schemes combined with Hessian estimates. Comparison to the double‐ended GSM shows that single‐ended method can be even more computationally efficient than the already rapid double‐ended method. Examples, including transition metal reactivity and a systematic, automated search for unknown reactivity, demonstrate the efficacy of the new method. This automated reaction search is able to find 165 reaction paths from 333 searches for the reaction of NH₃BH₃ and (LiH)₄, all without guidance from user intuition. © 2015 Wiley Periodicals, Inc.     

Reliable and efficient reaction path and transition state finding for surface reactions with the growing string method

The computational challenge of fast and reliable transition state and reaction path optimization requires new methodological strategies to maintain low cost, high accuracy, and systematic searching capabilities. The growing string method using internal coordinates has proven to be highly effective for the study of molecular, gas phase reactions, but difficulties in choosing a suitable coordinate system for periodic systems has prevented its use for surface chemistry. New developments are therefore needed, and presented herein, to handle surface reactions which include atoms with large coordination numbers that cannot be treated using standard internal coordinates. The double‐ended and single‐ended growing string methods are implemented using a hybrid coordinate system, then benchmarked for a test set of 43 elementary reactions occurring on surfaces. These results show that the growing string method is at least 45% faster than the widely used climbing image‐nudged elastic band method, which also fails to converge in several of the test cases. Additionally, the surface growing string method has a unique single‐ended search method which can move outward from an initial structure to find the intermediates, transition states, and reaction paths simultaneously. This powerful explorative feature of single ended‐growing string method is demonstrated to uncover, for the first time, the mechanism for atomic layer deposition of TiN on Cu(111) surface. This reaction is found to proceed through multiple hydrogen‐transfer and ligand‐exchange events, while formation of H‐bonds stabilizes intermediates of the reaction. Purging gaseous products out of the reaction environment is the driving force for these reactions. © 2017 Wiley Periodicals, Inc.     

Design and optimization of modified simplex methods

Four test functions are used to evaluate different modifications of the modified simplex method and to optimize the contraction, reflection and expansion parameters. The evaluation shows that some of the modifications and the optimization of the parameters result in a simplex method that has gained in convergence ability, with some improvement in speed.     

Visualization of the microtubules of glutaraldehyde-fixed cells by reflection-enhanced backscatter confocal microscopy.

Performing reflection-mode (backscatter-mode) confocal microscopy on cells growing on reflective substrates gives images that have improved contrast and are more easily interpreted than standard reflection-mode confocal micrographs (Keith et al., 1998). However, a number of factors degrade the quality of images taken with the highest-resolution microscope objectives in this technique. We here describe modifications to reflection-enhanced backscatter confocal microscopy that (partially) overcome these factors. With these modifications of the technique, it is possible to visualize structures the size-and refractility-of individual microtubules in intact cells. Additionally, we demonstrate that this technique, in common with fluorescence techniques such as standing wave widefield fluorescence microscopy and 4-Pi confocal microscopy, offers improved resolution in the Z-direction.     

Competitive adsorption of sodium dodecyl sulfate and polyethylene oxide at the air/water interface

Geoinspired synthetic chrysotile, which represents an ideal asbestos reference standard, has been utilized to investigate homomolecular exchange of bovine serum albumin (BSA), the major plasma protein, between the adsorbed and dissolved state at the interface between asbestos fibers and biological medium. FTIR spectroscopy has been used to quantify BSA structural modifications due to surface adhesion on chrysotile fibers as a function of the surface coating extent. Circular dichroism spectroscopy has been used to investigate the adsorption/desorption equilibrium through analysis of the BSA structural perturbations after protein desorption from chrysotile surface. Data results show clearly that in the solid state BSA modifications are driven by surface interaction with the substrate, following a bimodal adsorption evidenced by two different binding constants. On the other hand, BSA desorbed in solution is able to rearrange, in the lack of substrate, although keeping irreversible modifications with respect to the native species. The lack of regaining its native structure certainly affects albumin interaction with biological environment. The present investigation on the stoichiometric synthetic geoinspired chrysotile nanocrystals is the first approach toward a deeper attempt to use standard synthetic chrysotile reference samples in mimicking the behavior of asbestos fibers and allows to better understand their interaction with a biological environment.     

Global exploration of the energy landscape of solids on the ab initio level

Predicting which crystalline modifications can be present in a chemical system requires the global exploration of its energy landscape. Due to the large computational effort involved, in the past this search for sufficiently stable minima has been performed employing a variety of empirical potentials and cost functions followed by a local optimization on the ab initio level. However, this entails the risk of overlooking important modifications that are not modeled accurately using empirical potentials. In order to overcome this critical limitation, we develop an approach to employ ab initio energy functions during the global optimization phase of the structure prediction. As an example, we perform a global exploration of the landscape of LiF on the ab initio level and show that the relevant crystalline modifications are found during the search.     

Use of astronomy filters in fluorescence microscopy

Monochrome astronomy filters are well suited for use as excitation or suppression filters in fluorescence microscopy. Because of their particular optical design, such filters can be combined with standard halogen light sources for excitation in many fluorescent probes. In this "low energy excitation," photobleaching (fading) or other irritations of native specimens are avoided. Photomicrographs can be taken from living motile fluorescent specimens also with a flash so that fluorescence images can be created free from indistinctness caused by movement. Special filter cubes or dichroic mirrors are not needed for our method. By use of suitable astronomy filters, fluorescence microscopy can be carried out with standard laboratory microscopes equipped with condensers for bright-field (BF) and dark-field (DF) illumination in transmitted light. In BF excitation, the background brightness can be modulated in tiny steps up to dark or black. Moreover, standard industry microscopes fitted with a vertical illuminator for examinations of opaque probes in DF or BF illumination based on incident light (wafer inspections, for instance) can also be used for excitation in epi-illumination when adequate astronomy filters are inserted as excitatory and suppression filters in the illuminating and imaging light path. In all variants, transmission bands can be modulated by transmission shift.     

Determination of nebivolol hydrochloride and hydrochlorothiazide in tablets by first-order derivative spectrophotometry and liquid chromatography

Two simple and accurate methods for analysis of nebivolol hydrochloride (NEB) and hydrochlorothiazide (HCTZ) in their combined dosage forms were developed using first-order derivative spectrophotometry and reversed-phase liquid chromatography (LC). NEB and HCTZ in their combined dosage forms (tablets) were quantified using first-derivative responses at 294.6 and 334.6 nm in the spectra of their solutions in methanol. The calibration curves were linear in the concentration range of 8-40 microg/mL for NEB and 10-60 microg/mL for HCTZ. LC analysis was performed on a Phenomenex Gemini C18 column (250 x 4.6 mm id, 5 microm particle size) in the isocratic mode with 0.05 M potassium dihydrogen phosphate-acetonitrile-methanol (30 + 20 + 50, v/v/v; pH 4) mobile phase at a flow rate of 1 mL/min. Detection was made at 220 nm. Both of the drugs and the internal standard (ezetimibe) were well resolved with retention times of 5.1 min for NEB, 2.9 min for HCTZ, and 8.2 min for ezetimibe. The calibration curves were linear in the concentration range of 1-14 microg/mL for NEB and 0.3-28 microg/mL for HCTZ. Both methods were validated and found to be accurate, precise, and specific, and results were compared statistically. Developed methods were successfully applied for the estimation of NEB and HCTZ in their combined dosage forms.     

Preliminary attempt to follow the enthalpy of an enzymatic reaction by ab initio computations: Catalytic action of papain

A new theoretical approach to study the enthalpy variations occurring during an enzymatic reaction is presented. The structural modifications of the enzyme–substrate complex along the reaction path are distinguished as macro- and microdeformations. Macrodeformations, which concern primarily the approach of the substrate to the enzyme and the release of the reaction products and arise from nonbonded interactions, are treated with an empirical method for computing the energy of a macromolecule. Microdeformations, which are local displacements driven by variations of the electronic structure and its energy and involve only a limited portion of the complex, are treated with the ab initio SCF-LCAO-MO method. The reaction path is idealized as a sequence of major steps: at each step, first the empirical program REFINE is used to calculate the geometry of the system for that step, then the energy of an appropriate subsystem is computed ab initio with the program IBMOL, using the geometry provided by REFINE and applying small concerted atomic displacements. Thus along the entire reaction path one can obtain an energy profile computed with the ab initio method and compatible with the structure of the whole complex. This approach was applied here to the first steps of the reaction of proteolysis catalyzed by papain. The formation of an ion pair ImH⁺ …S^? between the side chains of residues His-159 and Cys-25 was examined in detail. The results show that the instability of the ion pair decreases by ? 11.5 kcal/mol when the interactions with residues Asn-175 and Ala- 160 are taken into account; the instability is further decreased by ?2 kcal/mol after a partial geometry optimization. The energies of the noncovalent enzyme–substrate complex and of the tetrahedral intermediate were computed, considering N-methyl acetamide (NMA) as model substrate and representing papain with the residues Cys-25, His-159, Gln-19, and Ala-160. The interaction energy of the noncovalent complex is -3.8 kcal/mol, compared to the value of +7.4 kcal/mol for the CH₃S^? -NMA complex. The tetrahedral intermediate is found to be less stable than the noncovalent complex by 27 and 38.5 kcal/mol, respectively, for the papain–NMA and the CH₃S^? -NMA systems. While these rather large energy differences are possibly due to the incorrect geometry of the tetrahedral intermediate and optimization of the structure is required, it appears that the interactions with the various protein residues represent a very important stabilization factor, which lowers the onthalpy variations during the reaction.     

Improvement of a cryogenic preconcentration unit for C2 - C6 hydrocarbons in ambient air at ppt levels

A previously described method for the quantitative analysis of C₂ - C₆ hydrocarbons in the ppt range based on cryogenic preconcentration has been improved further. Problems caused by condensation of O₂ and traces of water from the sample were overcome using a modified dyring procedure and a tandem preconcentration trap. In addition, the flow path through the unit was simplified further. Technical details are given. The reproducibility of both quantitative results and retention times was improved by these modifications. Typical standard deviations were in the order of 2% at the 200 ppt level.     

Application of the stepwise clustering method for efficient drawing of biopolymer structures

The reduction of drawing time is desirable in writing a complex molecular structure by use of a plotter. The stepwise clustering method is applied to find efficient drawing paths for six structures of protein and DNA molecules. All the optimization ratios of path lengths exceed 50%, while the necessary CPU times are of the order of 0.1 second. These results show the effectiveness of the method for molecular graphics. A summary of the algorithm and other possible applications are also discussed.