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Marciesky M, Aga DS, Bradley IM, Aich N, Ng C. Mechanisms and Opportunities for Rational In Silico Design of Enzymes to Degrade Per- and Polyfluoroalkyl Substances (PFAS). J Chem Inf Model 2023; 63:7299-7319. [PMID: 37981739 PMCID: PMC10716909 DOI: 10.1021/acs.jcim.3c01303] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2023] [Revised: 10/17/2023] [Accepted: 10/18/2023] [Indexed: 11/21/2023]
Abstract
Per and polyfluoroalkyl substances (PFAS) present a unique challenge to remediation techniques because their strong carbon-fluorine bonds make them difficult to degrade. This review explores the use of in silico enzymatic design as a potential PFAS degradation technique. The scope of the enzymes included is based on currently known PFAS degradation techniques, including chemical redox systems that have been studied for perfluorooctanesulfonic acid (PFOS) and perfluorooctanoic acid (PFOA) defluorination, such as those that incorporate hydrated electrons, sulfate, peroxide, and metal catalysts. Bioremediation techniques are also discussed, namely the laccase and horseradish peroxidase systems. The redox potential of known reactants and enzymatic radicals/metal-complexes are then considered and compared to potential enzymes for degrading PFAS. The molecular structure and reaction cycle of prospective enzymes are explored. Current knowledge and techniques of enzyme design, particularly radical-generating enzymes, and application are also discussed. Finally, potential routes for bioengineering enzymes to enable or enhance PFAS remediation are considered as well as the future outlook for computational exploration of enzymatic in situ bioremediation routes for these highly persistent and globally distributed contaminants.
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Affiliation(s)
- Melissa Marciesky
- Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15213, United States
| | - Diana S Aga
- Department of Chemistry, State University of New York at Buffalo, Buffalo, New York 14260, United States
| | - Ian M Bradley
- Department of Civil, Structural, and Environmental Engineering, State University of New York at Buffalo, Buffalo, New York 14228, United States
- Research and Education in Energy, Environmental and Water (RENEW) Institute, University at Buffalo, The State University of New York, Buffalo, New York 14260, United States
| | - Nirupam Aich
- Department of Civil and Environmental Engineering, University of Nebraska─Lincoln, Lincoln, Nebraska 68588-0531, United States
| | - Carla Ng
- Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15213, United States
- Department of Civil and Environmental Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States
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2
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Cabral L, Giovanella P, Pellizzer EP, Teramoto EH, Kiang CH, Sette LD. Microbial communities in petroleum-contaminated sites: Structure and metabolisms. CHEMOSPHERE 2022; 286:131752. [PMID: 34426136 DOI: 10.1016/j.chemosphere.2021.131752] [Citation(s) in RCA: 35] [Impact Index Per Article: 11.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2021] [Revised: 06/24/2021] [Accepted: 07/30/2021] [Indexed: 06/13/2023]
Abstract
Over recent decades, hydrocarbon concentrations have been augmented in soil and water, mainly derived from accidents or operations that input crude oil and petroleum into the environment. Different techniques for remediation have been proposed and used to mitigate oil contamination. Among the available environmental recovery approaches, bioremediation stands out since these hydrocarbon compounds can be used as growth substrates for microorganisms. In turn, microorganisms can play an important role with significant contributions to the stabilization of impacted areas. In this review, we present the current knowledge about responses from natural microbial communities (using DNA barcoding, multiomics, and functional gene markers) and bioremediation experiments (microcosm and mesocosm) conducted in the presence of petroleum and chemical dispersants in different samples, including soil, sediment, and water. Additionally, we present metabolic mechanisms for aerobic/anaerobic hydrocarbon degradation and alternative pathways, as well as a summary of studies showing functional genes and other mechanisms involved in petroleum biodegradation processes.
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Affiliation(s)
- Lucélia Cabral
- Laboratório de Micologia Ambiental e Industrial (LAMAI), Departamento de Biologia Geral e Aplicada, Instituto de Biociências, Universidade Estadual Paulista Júlio de Mesquita Filho (UNESP), Rio Claro, SP, Brazil
| | - Patricia Giovanella
- Laboratório de Micologia Ambiental e Industrial (LAMAI), Departamento de Biologia Geral e Aplicada, Instituto de Biociências, Universidade Estadual Paulista Júlio de Mesquita Filho (UNESP), Rio Claro, SP, Brazil; Centro de Estudos Ambientais (CEA), Instituto de Biociências, Universidade Estadual Paulista Júlio de Mesquita Filho (UNESP), Rio Claro, SP, Brazil
| | - Elisa Pais Pellizzer
- Laboratório de Micologia Ambiental e Industrial (LAMAI), Departamento de Biologia Geral e Aplicada, Instituto de Biociências, Universidade Estadual Paulista Júlio de Mesquita Filho (UNESP), Rio Claro, SP, Brazil
| | - Elias Hideo Teramoto
- Centro de Estudos Ambientais (CEA), Instituto de Biociências, Universidade Estadual Paulista Júlio de Mesquita Filho (UNESP), Rio Claro, SP, Brazil; Laboratório de Estudos de Bacias (LEBAC), Departamento de Geologia Aplicada, Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista Júlio de Mesquita Filho (UNESP), Rio Claro, SP, Brazil
| | - Chang Hung Kiang
- Centro de Estudos Ambientais (CEA), Instituto de Biociências, Universidade Estadual Paulista Júlio de Mesquita Filho (UNESP), Rio Claro, SP, Brazil; Laboratório de Estudos de Bacias (LEBAC), Departamento de Geologia Aplicada, Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista Júlio de Mesquita Filho (UNESP), Rio Claro, SP, Brazil
| | - Lara Durães Sette
- Laboratório de Micologia Ambiental e Industrial (LAMAI), Departamento de Biologia Geral e Aplicada, Instituto de Biociências, Universidade Estadual Paulista Júlio de Mesquita Filho (UNESP), Rio Claro, SP, Brazil; Centro de Estudos Ambientais (CEA), Instituto de Biociências, Universidade Estadual Paulista Júlio de Mesquita Filho (UNESP), Rio Claro, SP, Brazil.
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Theoretical study of the hydrogen abstraction reactions from substituted phenolic species. COMPUT THEOR CHEM 2021. [DOI: 10.1016/j.comptc.2020.113120] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
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Bharadwaj VS, Crowley MF, Peña MJ, Urbanowicz B, O'Neill M. Mechanism and Reaction Energy Landscape for Apiose Cross-Linking by Boric Acid in Rhamnogalacturonan II. J Phys Chem B 2020; 124:10117-10125. [PMID: 33112619 DOI: 10.1021/acs.jpcb.0c06920] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Rhamnogalacturonan II (RG-II)-the most complex polysaccharide known in nature-exists as a borate cross-linked dimer in the plant primary cell wall. Boric acid facilitates the formation of this cross-link on the apiosyl residues of RG-II's side chain A. Here, we detail the reaction mechanism for the cross-linking process with ab initio calculations coupled with transition state theory. We determine the formation of the first ester linkage to be the rate-limiting step of the mechanism. Our findings demonstrate that the regio- and stereospecific nature of subsequent steps in the reaction itinerary presents four distinct energetically plausible reaction pathways. This has significant implications for the overall structure of the cross-linked RG-II dimer assembly. Our transition state and reaction path analyses reveal key geometric insights that corroborate previous experimental hypotheses on borate ester formation reactions.
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Affiliation(s)
- Vivek S Bharadwaj
- Renewable Resources and Enabling Sciences Center, National Renewable Energy Laboratory, 15013 Denver West Parkway, Golden, Colorado 80401, United States
| | - Michael F Crowley
- Renewable Resources and Enabling Sciences Center, National Renewable Energy Laboratory, 15013 Denver West Parkway, Golden, Colorado 80401, United States
| | - Maria J Peña
- Complex Carbohydrate Research Center, University of Georgia, 315 Riverbend Road, Athens, Georgia 30602, United States
| | - Breeanna Urbanowicz
- Complex Carbohydrate Research Center, University of Georgia, 315 Riverbend Road, Athens, Georgia 30602, United States.,Department of Biochemistry and Molecular Biology, University of Georgia, 315 Riverbend Road, Athens, Georgia 30602, United States
| | - Malcolm O'Neill
- Complex Carbohydrate Research Center, University of Georgia, 315 Riverbend Road, Athens, Georgia 30602, United States
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Chemical Kinetics of Hydrogen Atom Abstraction from Propargyl Sites by Hydrogen and Hydroxy Radicals. Int J Mol Sci 2019; 20:ijms20133227. [PMID: 31262079 PMCID: PMC6650822 DOI: 10.3390/ijms20133227] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2019] [Revised: 06/26/2019] [Accepted: 06/27/2019] [Indexed: 01/02/2023] Open
Abstract
Hydrogen atom abstraction from propargyl C-H sites of alkynes plays a critical role in determining the reactivity of alkyne molecules and understanding the formation of soot precursors. This work reports a systematic theoretical study on the reaction mechanisms and rate constants for hydrogen abstraction reactions by hydrogen and hydroxy radicals from a series of alkyne molecules with different structural propargyl C-H atoms. Geometry optimizations and frequency calculations for all species are performed at M06-2X/cc-pVTZ level of theory and the hindered internal rotations are also treated at this level. The high-level W1BD and CCSD(T)/CBS theoretical calculations are used as a benchmark for a series of DFT calculations toward the selection of accurate DFT functionals for large reaction systems in this work. Based on the quantum chemistry calculations, rate constants are computed using the canonical transition state theory with tunneling correction and the treatment of internal rotations. The effects of the structure and reaction site on the energy barriers and rate constants are examined systematically. To the best of our knowledge, this work provides the first systematic study for one of the key initiation abstraction reactions for compounds containing propargyl hydrogen atoms.
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Nowak JA, Shrestha PM, Weber RJ, McKenna AM, Chen H, Coates JD, Goldstein AH. Comprehensive Analysis of Changes in Crude Oil Chemical Composition during Biosouring and Treatments. ENVIRONMENTAL SCIENCE & TECHNOLOGY 2018; 52:1290-1300. [PMID: 29320174 DOI: 10.1021/acs.est.7b05346] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Biosouring in crude oil reservoirs by sulfate-reducing microbial communities (SRCs) results in hydrogen sulfide production, precipitation of metal sulfide complexes, increased industrial costs of petroleum production, and exposure issues for personnel. Potential treatment strategies include nitrate or perchlorate injections into reservoirs. Gas chromatography with vacuum ultraviolet ionization and high-resolution time-of-flight mass spectrometry (GC-VUV-HTOF) and Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) combined with electrospray ionization were applied in this study to identify hydrocarbon degradation patterns and product formations in crude oil samples from biosoured, nitrate-treated, and perchlorate-treated bioreactor column experiments. Crude oil hydrocarbons were selectively transformed based on molecular weight and compound class in the biosouring control environment. Both the nitrate and the perchlorate treatments significantly reduced sulfide production; however, the nitrate treatment enhanced crude oil biotransformation, while the perchlorate treatment inhibited crude oil biotransformation. Nitrogen- and oxygen-containing biodegradation products, particularly with chemical formulas consistent with monocarboxylic and dicarboxylic acids containing 10-60 carbon atoms, were observed in the oil samples from both the souring control and the nitrate-treated columns but were not observed in the oil samples from the perchlorate-treated column. These results demonstrate that hydrocarbon degradation and product formation of crude oil can span hydrocarbon isomers and molecular weights up to C60 and double-bond equivalent classes ranging from straight-chain alkanes to polycyclic aromatic hydrocarbons. Our results also strongly suggest that perchlorate injections may provide a preferred strategy to treat biosouring through inhibition of biotransformation.
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Affiliation(s)
| | | | | | - Amy M McKenna
- National High Magnetic Field Laboratory, Florida State University , 1800 East Paul Dirac Drive, Tallahassee, Florida 32310-4005, United States
| | - Huan Chen
- National High Magnetic Field Laboratory, Florida State University , 1800 East Paul Dirac Drive, Tallahassee, Florida 32310-4005, United States
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Singh R, Guzman MS, Bose A. Anaerobic Oxidation of Ethane, Propane, and Butane by Marine Microbes: A Mini Review. Front Microbiol 2017; 8:2056. [PMID: 29109712 PMCID: PMC5660070 DOI: 10.3389/fmicb.2017.02056] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2017] [Accepted: 10/06/2017] [Indexed: 12/16/2022] Open
Abstract
The deep ocean and its sediments are a continuous source of non-methane short-chain alkanes (SCAs) including ethane, propane, and butane. Their high global warming potential, and contribution to local carbon and sulfur budgets has drawn significant scientific attention. Importantly, microbes can use gaseous alkanes and oxidize them to CO2, thus acting as effective biofilters. A relative decrease of these gases with a concomitant 13C enrichment of propane and n-butane in interstitial waters vs. the source suggests microbial anaerobic oxidation. The reported uncoupling of sulfate-reduction (SR) from anaerobic methane oxidation supports their microbial consumption. To date, strain BuS5 isolated from the sediments of Guaymas Basin, Gulf of California, is the only pure culture that can anaerobically degrade propane and n-butane. This organism belongs to a metabolically diverse cluster within the Deltaproteobacteria called Desulfosarcina/Desulfococcus. Other phylotypes involved in gaseous alkane degradation were identified based on stable-isotope labeling and fluorescence in-situ hybridization. A novel syntrophic association of the archaeal genus, Candidatus Syntrophoarchaeum, and a thermophilic SR bacterium, HotSeep-1 was recently discovered from the Guaymas basin, Gulf of California that can anaerobically oxidize n-butane. Strikingly, metagenomic data and the draft genomes of ca. Syntrophoarchaeum suggest that this organism uses a novel mechanism for n-butane oxidation, distinct from the well-established fumarate addition mechanism. These recent findings indicate that a lot remains to be understood about our understanding of anaerobic SCA degradation. This mini-review summarizes our current understanding of microbial anaerobic SCA degradation, and provides an outlook for future research.
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Affiliation(s)
- Rajesh Singh
- Department of Biology, Washington University in St. Louis, St. Louis, MO, United States
| | - Michael S Guzman
- Department of Biology, Washington University in St. Louis, St. Louis, MO, United States
| | - Arpita Bose
- Department of Biology, Washington University in St. Louis, St. Louis, MO, United States
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Urbanowicz BR, Bharadwaj VS, Alahuhta M, Peña MJ, Lunin VV, Bomble YJ, Wang S, Yang JY, Tuomivaara ST, Himmel ME, Moremen KW, York WS, Crowley MF. Structural, mutagenic and in silico studies of xyloglucan fucosylation in Arabidopsis thaliana suggest a water-mediated mechanism. THE PLANT JOURNAL : FOR CELL AND MOLECULAR BIOLOGY 2017; 91:931-949. [PMID: 28670741 PMCID: PMC5735850 DOI: 10.1111/tpj.13628] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2017] [Revised: 06/21/2017] [Accepted: 06/22/2017] [Indexed: 05/17/2023]
Abstract
The mechanistic underpinnings of the complex process of plant polysaccharide biosynthesis are poorly understood, largely because of the resistance of glycosyltransferase (GT) enzymes to structural characterization. In Arabidopsis thaliana, a glycosyl transferase family 37 (GT37) fucosyltransferase 1 (AtFUT1) catalyzes the regiospecific transfer of terminal 1,2-fucosyl residues to xyloglucan side chains - a key step in the biosynthesis of fucosylated sidechains of galactoxyloglucan. We unravel the mechanistic basis for fucosylation by AtFUT1 with a multipronged approach involving protein expression, X-ray crystallography, mutagenesis experiments and molecular simulations. Mammalian cell culture expressions enable the sufficient production of the enzyme for X-ray crystallography, which reveals the structural architecture of AtFUT1 in complex with bound donor and acceptor substrate analogs. The lack of an appropriately positioned active site residue as a catalytic base leads us to propose an atypical water-mediated fucosylation mechanism facilitated by an H-bonded network, which is corroborated by mutagenesis experiments as well as detailed atomistic simulations.
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Affiliation(s)
- Breeanna R. Urbanowicz
- Complex Carbohydrate Research Center, University of Georgia, 315 Riverbend Road, Athens, GA 30602, USA
| | - Vivek S. Bharadwaj
- Biosciences Division, National Renewable Energy Laboratory, Golden, Colorado 80401, USA
| | - Markus Alahuhta
- Biosciences Division, National Renewable Energy Laboratory, Golden, Colorado 80401, USA
| | - Maria J. Peña
- Complex Carbohydrate Research Center, University of Georgia, 315 Riverbend Road, Athens, GA 30602, USA
| | - Vladimir V. Lunin
- Biosciences Division, National Renewable Energy Laboratory, Golden, Colorado 80401, USA
| | - Yannick J. Bomble
- Biosciences Division, National Renewable Energy Laboratory, Golden, Colorado 80401, USA
| | - Shuo Wang
- Complex Carbohydrate Research Center, University of Georgia, 315 Riverbend Road, Athens, GA 30602, USA
| | - Jeong-Yeh Yang
- Complex Carbohydrate Research Center, University of Georgia, 315 Riverbend Road, Athens, GA 30602, USA
| | - Sami T. Tuomivaara
- Complex Carbohydrate Research Center, University of Georgia, 315 Riverbend Road, Athens, GA 30602, USA
| | - Michael E. Himmel
- Biosciences Division, National Renewable Energy Laboratory, Golden, Colorado 80401, USA
| | - Kelley W. Moremen
- Complex Carbohydrate Research Center, University of Georgia, 315 Riverbend Road, Athens, GA 30602, USA
| | - William S. York
- Complex Carbohydrate Research Center, University of Georgia, 315 Riverbend Road, Athens, GA 30602, USA
| | - Michael F. Crowley
- Biosciences Division, National Renewable Energy Laboratory, Golden, Colorado 80401, USA
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Modeling of the Reaction Mechanism of Enzymatic Radical C-C Coupling by Benzylsuccinate Synthase. Int J Mol Sci 2016; 17:514. [PMID: 27070573 PMCID: PMC4848970 DOI: 10.3390/ijms17040514] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2016] [Revised: 03/15/2016] [Accepted: 03/24/2016] [Indexed: 11/16/2022] Open
Abstract
Molecular modeling techniques and density functional theory calculations were performed to study the mechanism of enzymatic radical C–C coupling catalyzed by benzylsuccinate synthase (BSS). BSS has been identified as a glycyl radical enzyme that catalyzes the enantiospecific fumarate addition to toluene initiating its anaerobic metabolism in the denitrifying bacterium Thauera aromatica, and this reaction represents the general mechanism of toluene degradation in all known anaerobic degraders. In this work docking calculations, classical molecular dynamics (MD) simulations, and DFT+D2 cluster modeling was employed to address the following questions: (i) What mechanistic details of the BSS reaction yield the most probable molecular model? (ii) What is the molecular basis of enantiospecificity of BSS? (iii) Is the proposed mechanism consistent with experimental observations, such as an inversion of the stereochemistry of the benzylic protons, syn addition of toluene to fumarate, exclusive production of (R)-benzylsuccinate as a product and a kinetic isotope effect (KIE) ranging between 2 and 4? The quantum mechanics (QM) modeling confirms that the previously proposed hypothetical mechanism is the most probable among several variants considered, although C–H activation and not C–C coupling turns out to be the rate limiting step. The enantiospecificity of the enzyme seems to be enforced by a thermodynamic preference for binding of fumarate in the pro(R) orientation and reverse preference of benzyl radical attack on fumarate in pro(S) pathway which results with prohibitively high energy barrier of the radical quenching. Finally, the proposed mechanism agrees with most of the experimental observations, although the calculated intrinsic KIE from the model (6.5) is still higher than the experimentally observed values (4.0) which suggests that both C–H activation and radical quenching may jointly be involved in the kinetic control of the reaction.
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Bharadwaj VS, Eagan NM, Wang NM, Liberatore MW, Maupin CM. Molecular Simulations of Fatty-Acid Methyl Esters and Representative Biodiesel Mixtures. Chemphyschem 2015; 16:2810-2817. [DOI: 10.1002/cphc.201500453] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2015] [Revised: 07/15/2015] [Indexed: 11/11/2022]
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Funk MA, Marsh ENG, Drennan CL. Substrate-bound structures of benzylsuccinate synthase reveal how toluene is activated in anaerobic hydrocarbon degradation. J Biol Chem 2015. [PMID: 26224635 DOI: 10.1074/jbc.m115.670737] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022] Open
Abstract
Various bacteria perform anaerobic degradation of small hydrocarbons as a source of energy and cellular carbon. To activate non-reactive hydrocarbons such as toluene, enzymes conjugate these molecules to fumarate in a radical-catalyzed, C-C bond-forming reaction. We have determined x-ray crystal structures of the glycyl radical enzyme that catalyzes the addition of toluene to fumarate, benzylsuccinate synthase (BSS), in two oligomeric states with fumarate alone or with both substrates. We find that fumarate is secured at the bottom of a long active site cavity with toluene bound directly above it. The two substrates adopt orientations that appear ideal for radical-mediated C-C bond formation; the methyl group of toluene is positioned between fumarate and a cysteine that forms a thiyl radical during catalysis, which is in turn adjacent to the glycine that serves as a radical storage residue. Toluene is held in place by fumarate on one face and tight packing by hydrophobic residues on the other face and sides. These hydrophobic residues appear to become ordered, thus encapsulating toluene, only in the presence of BSSβ, a small protein subunit that forms a tight complex with BSSα, the catalytic subunit. Enzymes related to BSS are able to metabolize a wide range of hydrocarbons through attachment to fumarate. Using our structures as a guide, we have constructed homology models of several of these "X-succinate synthases" and determined conservation patterns that will be useful in understanding the basis for catalysis and specificity in this family of enzymes.
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Affiliation(s)
| | - E Neil G Marsh
- the Department of Chemistry and Biological Chemistry, University of Michigan, Ann Arbor, Michigan 48109
| | - Catherine L Drennan
- From the Departments of Chemistry and Biology and the Howard Hughes Medical Institute, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 and
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