1
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Phan TM, Schmit JD. Conformational entropy limits the transition from nucleation to elongation in amyloid aggregation. Biophys J 2022; 121:2931-2939. [PMID: 35778843 PMCID: PMC9388551 DOI: 10.1016/j.bpj.2022.06.031] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2022] [Revised: 06/11/2022] [Accepted: 06/17/2022] [Indexed: 11/30/2022] Open
Abstract
The formation of β-sheet rich amyloid fibrils in Alzheimer's disease and other neurodegenerative disorders is limited by a slow nucleation event. To understand the initial formation of β-sheets from disordered peptides, we used all-atom simulations to parameterize a lattice model that treats each amino acid as a binary variable with β and non-β states. We show that translational and conformational entropy give the nascent β-sheet an anisotropic surface tension which can be used to describe the nucleus with two-dimensional Classical Nucleation Theory. Since translational entropy depends on concentration, the aspect ratio of the critical β-sheet changes with protein concentration. Our model explains the transition from the nucleation phase to elongation as the point where the β-sheet core becomes large enough to overcome the conformational entropy cost to straighten the terminal molecule. At this point the β-strands in the nucleus spontaneously elongate, which results in a larger binding surface to capture new molecules. These results suggest that nucleation is relatively insensitive to sequence differences in co-aggregation experiments because the nucleus only involves a small portion of the peptide.
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Affiliation(s)
- Tien M Phan
- Department of Physics, Kansas State University, Manhattan, KS 66506, USA
| | - Jeremy D Schmit
- Department of Physics, Kansas State University, Manhattan, KS 66506, USA.
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2
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Tang X, Han W. Multiscale Exploration of Concentration-Dependent Amyloid-β(16-21) Amyloid Nucleation. J Phys Chem Lett 2022; 13:5009-5016. [PMID: 35649244 DOI: 10.1021/acs.jpclett.2c00685] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Atomic descriptions of peptide aggregation nucleation remain lacking due to the difficulty of exploring complex configurational spaces on long time scales. To elucidate this process, we develop a multiscale approach combining a metadynamics-based method with cluster statistical mechanics to derive concentration-dependent free energy surfaces of nucleation at near-atomic resolution. A kinetic transition network of nucleation is then constructed and employed to systematically explore nucleation pathways and kinetics through stochastic simulations. This approach is applied to describe Aβ16-21 amyloid nucleation, revealing a two-step mechanism involving disordered aggregates at millimolar concentration, and an unexpected mechanism at submillimolar concentrations that exhibits kinetics reminiscent of classical nucleation but atypical pathways involving growing clusters with structured cores wrapped by disordered surface. When this atypical mechanism is operative, critical nucleus size can be reflected by the nucleation reaction order. Collectively, our approach paves the way for a more quantitative and detailed understanding of peptide aggregation nucleation.
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Affiliation(s)
- Xuan Tang
- State Key Laboratory of Chemical Oncogenomics, Guangdong Provincial Key Laboratory of Chemical Genomics, School of Chemical Biology and Biotechnology, Peking University Shenzhen Graduate School, Shenzhen, 518055, China
| | - Wei Han
- State Key Laboratory of Chemical Oncogenomics, Guangdong Provincial Key Laboratory of Chemical Genomics, School of Chemical Biology and Biotechnology, Peking University Shenzhen Graduate School, Shenzhen, 518055, China
- Institute of Chemical Biology, Shenzhen Bay Laboratory, Shenzhen, 518132, China
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3
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Cai X, Han W. Development of a Hybrid-Resolution Force Field for Peptide Self-Assembly Simulations: Optimizing Peptide-Peptide and Peptide-Solvent Interactions. J Chem Inf Model 2022; 62:2744-2760. [PMID: 35561002 DOI: 10.1021/acs.jcim.2c00066] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Atomic descriptions of peptide self-assembly are crucial to an understanding of disease-related peptide aggregation and the design of peptide-assembled materials. Obtaining these descriptions through computer simulation is challenging because current force fields, which were not designed for this process and are often unable to describe correctly peptide self-assembly behavior and the sequence dependence. Here, we developed a framework using dipeptide aggregation as a model system to improve force fields for simulations of self-assembly. Aggregation-related structural properties were designed and used to guide the optimization of peptide-peptide and peptide-solvent interactions. With this framework, we developed a self-assembly force field, termed PACE-ASM, by reoptimizing a hybrid-resolution force field that was originally developed for folding simulation. With its applicability in folding simulations, the new PACE was used to simulate the self-assembly of two disease-related short peptides, Aβ16-21 and PHF6, into β-sheet-rich cross-β amyloids. These simulations reproduced the crystal structures of Aβ16-21 and PHF6 amyloids at near-atomic resolution and captured the difference in packing orientations between the two sequences, a task which is challenging even with all-atom force fields. Apart from cross-β amyloids, the self-assembly of emerging helix-rich cross-α amyloids by another peptide PSMα3 can also be correctly described with the new PACE, manifesting the versatility of the force field. We demonstrated that the ability of the PACE-ASM to model peptide self-assembly is based largely on its improved description of peptide-peptide and peptide-solvent interactions. This was achieved with our optimization framework that can readily identify and address the deficiency in describing these interactions.
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Affiliation(s)
- Xiang Cai
- State Key Laboratory of Chemical Oncogenomics, Guangdong Provincial Key Laboratory of Chemical Genomics, School of Chemical Biology and Biotechnology, Peking University Shenzhen Graduate School, Shenzhen 518055, China
| | - Wei Han
- State Key Laboratory of Chemical Oncogenomics, Guangdong Provincial Key Laboratory of Chemical Genomics, School of Chemical Biology and Biotechnology, Peking University Shenzhen Graduate School, Shenzhen 518055, China.,Institute of Chemical Biology, Shenzhen Bay Laboratory, Shenzhen 518132, China
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4
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Stuij S, Rouwhorst J, Jonas HJ, Ruffino N, Gong Z, Sacanna S, Bolhuis PG, Schall P. Revealing Polymerization Kinetics with Colloidal Dipatch Particles. PHYSICAL REVIEW LETTERS 2021; 127:108001. [PMID: 34533362 DOI: 10.1103/physrevlett.127.108001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2021] [Revised: 07/05/2021] [Accepted: 07/20/2021] [Indexed: 06/13/2023]
Abstract
Limited-valency colloidal particles can self-assemble into polymeric structures analogous to molecules. While their structural equilibrium properties have attracted wide attention, insight into their dynamics has proven challenging. Here, we investigate the polymerization dynamics of semiflexible polymers in 2D by direct observation of assembling divalent particles, bonded by critical Casimir forces. The reversible critical Casimir force creates living polymerization conditions with tunable chain dissociation, association, and bending rigidity. We find that unlike dilute polymers that show exponential size distributions in excellent agreement with Flory theory, concentrated samples exhibit arrest of rotational and translational diffusion due to a continuous isotropic-to-nematic transition in 2D, slowing down the growth kinetics. These effects are circumvented by the addition of higher-valency particles, cross linking the polymers into networks. Our results connecting polymer flexibility, polymer interactions, and the peculiar isotropic-nematic transition in 2D offer insight into the polymerization processes of synthetic two-dimensional polymers and biopolymers at membranes and interfaces.
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Affiliation(s)
- Simon Stuij
- Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - Joep Rouwhorst
- Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - Hannah J Jonas
- van 't Hoff Institute for Molecular Sciences, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - Nicola Ruffino
- Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - Zhe Gong
- Molecular Design Institute, Department of Chemistry, New York University, New York, New York 10003-6688, USA
| | - Stefanno Sacanna
- Molecular Design Institute, Department of Chemistry, New York University, New York, New York 10003-6688, USA
| | - Peter G Bolhuis
- van 't Hoff Institute for Molecular Sciences, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - Peter Schall
- Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
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5
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Yang J, Agnihotri MV, Huseby CJ, Kuret J, Singer SJ. A theoretical study of polymorphism in VQIVYK fibrils. Biophys J 2021; 120:1396-1416. [PMID: 33571490 DOI: 10.1016/j.bpj.2021.01.032] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2020] [Revised: 01/07/2021] [Accepted: 01/11/2021] [Indexed: 02/06/2023] Open
Abstract
The VQIVYK fragment from the Tau protein, also known as PHF6, is essential for aggregation of Tau into neurofibrillary lesions associated with neurodegenerative diseases. VQIVYK itself forms amyloid fibrils composed of paired β-sheets. Therefore, the full Tau protein and VQIVYK fibrils have been intensively investigated. A central issue in these studies is polymorphism, the ability of a protein to fold into more than one structure. Using all-atom molecular simulations, we generate five stable polymorphs of VQIVYK fibrils, establish their relative free energy with umbrella sampling methods, and identify the side chain interactions that provide stability. The two most stable polymorphs, which have nearly equal free energy, are formed by interdigitation of the mostly hydrophobic VIY "face" sides of the β-sheets. Another stable polymorph is formed by interdigitation of the QVK "back" sides. When we turn to examine structures from cryo-electron microscopy experiments on Tau filaments taken from diseased patients or generated in vitro, we find that the pattern of side chain interactions found in the two most stable face-to-face as well as the back-to-back polymorphs are recapitulated in amyloid structures of the full protein. Thus, our studies suggest that the interactions stabilizing PHF6 fibrils explain the amyloidogenicity of the VQIVYK motif within the full Tau protein and provide justification for the use of VQIVYK fibrils as a test bed for the design of molecules that identify or inhibit amyloid structures.
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Affiliation(s)
- Jaehoon Yang
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio
| | - Mithila V Agnihotri
- Interdisciplinary Biophysics Graduate Program, The Ohio State University, Columbus, Ohio
| | - Carol J Huseby
- Interdisciplinary Biophysics Graduate Program, The Ohio State University, Columbus, Ohio
| | - Jeff Kuret
- Interdisciplinary Biophysics Graduate Program, The Ohio State University, Columbus, Ohio; Department of Biological Chemistry and Pharmacology, The Ohio State University, Columbus, Ohio.
| | - Sherwin J Singer
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio; Interdisciplinary Biophysics Graduate Program, The Ohio State University, Columbus, Ohio.
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6
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Gaughran SK, Rickman JM, Haaga J, Gunton JD. Monte Carlo simulations of patch models with applications to soft matter. SOFT MATTER 2020; 16:8628-8638. [PMID: 32844865 DOI: 10.1039/d0sm01110j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Patch models have been employed to describe anisotropic interactions in disparate soft matter systems. In this work, we present a unified study of a patch model to explore particle self-assembly in both monodisperse and polydisperse systems, with applications to both proteins and colloids. In the first case, we obtained a temperature-density phase diagram for a model of the protein polyglutamine from Monte Carlo simulations. These simulations evinced clusters in the gas phase and, via a comparison with the corresponding coarse-grained PLUM model for this system, we verified that dense clustering in the gas phase falls into the supersaturation region of the saturation curve. In the second case, we have investigated the effect of size polydispersity on the phase behavior of binary colloidal mixtures. It was found that the width of gas-liquid phase coexistence increases with increasing polydispersity and that, in addition to the aforementioned particle clustering, small particles decorate patches on large particles, thereby creating large-particle bridges. Our aim is to compare and contrast self-assembly in these two prototypical systems.
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Affiliation(s)
- S K Gaughran
- Department of Physics, Lehigh University, Bethlehem, PA 18015, USA.
| | - J M Rickman
- Department of Physics, Lehigh University, Bethlehem, PA 18015, USA. and Department of Materials Science and Engineering, Lehigh University, Bethlehem, PA 18015, USA
| | - J Haaga
- Department of Physics, Lehigh University, Bethlehem, PA 18015, USA.
| | - J D Gunton
- Department of Physics, Lehigh University, Bethlehem, PA 18015, USA.
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7
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Hussain S, Haji-Akbari A. Studying rare events using forward-flux sampling: Recent breakthroughs and future outlook. J Chem Phys 2020; 152:060901. [DOI: 10.1063/1.5127780] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Sarwar Hussain
- Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520, USA
| | - Amir Haji-Akbari
- Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520, USA
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8
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Le Ferrand H, Duchamp M, Gabryelczyk B, Cai H, Miserez A. Time-Resolved Observations of Liquid–Liquid Phase Separation at the Nanoscale Using in Situ Liquid Transmission Electron Microscopy. J Am Chem Soc 2019; 141:7202-7210. [DOI: 10.1021/jacs.9b03083] [Citation(s) in RCA: 44] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Hortense Le Ferrand
- Biological and Biomimetic Material Laboratory and Center for Biomimetic Sensor Science, School of Materials Science and Engineering, Nanyang Technological University (NTU), 50 Nanyang Avenue, Singapore 637553
| | - Martial Duchamp
- Laboratory for in Situ & Operando Electron Nanoscopy, School of Materials Science and Engineering, Nanyang Technological University (NTU), 50 Nanyang Avenue, Singapore 637371
| | - Bartosz Gabryelczyk
- Biological and Biomimetic Material Laboratory and Center for Biomimetic Sensor Science, School of Materials Science and Engineering, Nanyang Technological University (NTU), 50 Nanyang Avenue, Singapore 637553
| | - Hao Cai
- Biological and Biomimetic Material Laboratory and Center for Biomimetic Sensor Science, School of Materials Science and Engineering, Nanyang Technological University (NTU), 50 Nanyang Avenue, Singapore 637553
| | - Ali Miserez
- Biological and Biomimetic Material Laboratory and Center for Biomimetic Sensor Science, School of Materials Science and Engineering, Nanyang Technological University (NTU), 50 Nanyang Avenue, Singapore 637553
- School of Biological Sciences, Nanyang Technological University (NTU), 60 Nanyang Drive, Singapore 637551
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9
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Haaga J, Gunton JD, Buckles CN, Rickman JM. Early stage aggregation of a coarse-grained model of polyglutamine. J Chem Phys 2018; 148:045106. [DOI: 10.1063/1.5010888] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Affiliation(s)
- Jason Haaga
- Department of Physics, Lehigh University, Bethlehem, Pennsylvania 18015, USA
| | - J. D. Gunton
- Department of Physics, Lehigh University, Bethlehem, Pennsylvania 18015, USA
| | - C. Nadia Buckles
- Department of Physics and Astronomy, University of Oklahoma, Norman, Oklahoma 73019, USA
| | - J. M. Rickman
- Department of Materials Science and Engineering and Department of Physics, Lehigh University, Bethlehem, Pennsylvania 18015, USA
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10
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Safari MS, Byington MC, Conrad JC, Vekilov PG. Polymorphism of Lysozyme Condensates. J Phys Chem B 2017; 121:9091-9101. [DOI: 10.1021/acs.jpcb.7b05425] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Mohammad S. Safari
- Department
of Chemical and Biomolecular Engineering, University of Houston, 4726 Calhoun Road, Houston, Texas 77204-4004, United States
| | - Michael C. Byington
- Department
of Chemical and Biomolecular Engineering, University of Houston, 4726 Calhoun Road, Houston, Texas 77204-4004, United States
| | - Jacinta C. Conrad
- Department
of Chemical and Biomolecular Engineering, University of Houston, 4726 Calhoun Road, Houston, Texas 77204-4004, United States
| | - Peter G. Vekilov
- Department
of Chemical and Biomolecular Engineering, University of Houston, 4726 Calhoun Road, Houston, Texas 77204-4004, United States
- Department
of Chemistry, University of Houston, 3585 Cullen Blvd., Houston, Texas 77204-5003, United States
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11
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Smit FX, Luiken JA, Bolhuis PG. Primary Fibril Nucleation of Aggregation Prone Tau Fragments PHF6 and PHF6. J Phys Chem B 2016; 121:3250-3261. [PMID: 27776213 DOI: 10.1021/acs.jpcb.6b07045] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We performed replica exchange molecular dynamics and forward flux sampling simulations of hexapeptide VQIINK and VQIVYK systems, also known as, respectively, fragments PHF6* and PHF6 from the tau protein. Being a part of the microtubule binding region, these fragments are known to be aggregation prone, and at least one of them is a prerequisite for fibril formation of the tau protein. Using a coarse-grained force field, we establish the phase behavior of both fragments, and investigate the nucleation kinetics for the conversion into a β-sheet fibril. As the conversion is, in principle, a reversible process, we predict the rate constants for both the fibril formation and melting, and examine the corresponding mechanisms. Our simulations indicate that, while both fragments form disordered aggregates, only PHF6 is able to form β-sheet fibrils. This observation provides a possible explanation for the lack of available steric zipper crystal structures for PHF6*.
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Affiliation(s)
- Florent X Smit
- van't Hoff Institute for Molecular Sciences, University of Amsterdam , PO Box 94157, 1090 GD Amsterdam, The Netherlands
| | - Jurriaan A Luiken
- van't Hoff Institute for Molecular Sciences, University of Amsterdam , PO Box 94157, 1090 GD Amsterdam, The Netherlands
| | - Peter G Bolhuis
- van't Hoff Institute for Molecular Sciences, University of Amsterdam , PO Box 94157, 1090 GD Amsterdam, The Netherlands
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12
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Ilie IM, den Otter WK, Briels WJ. A coarse grained protein model with internal degrees of freedom. Application to α-synuclein aggregation. J Chem Phys 2016; 144:085103. [DOI: 10.1063/1.4942115] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Affiliation(s)
- Ioana M. Ilie
- Computational Chemical Physics, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands
- MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Wouter K. den Otter
- Computational Chemical Physics, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands
- MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
- Multi Scale Mechanics, Faculty of Engineering Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Wim J. Briels
- Computational Chemical Physics, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands
- MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
- Forschungszentrum Jülich, ICS, D-52425 Jülich, Germany
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13
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Vorontsova MA, Chan HY, Lubchenko V, Vekilov PG. Lack of Dependence of the Sizes of the Mesoscopic Protein Clusters on Electrostatics. Biophys J 2015; 109:1959-68. [PMID: 26536272 PMCID: PMC4643268 DOI: 10.1016/j.bpj.2015.09.025] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2015] [Revised: 09/15/2015] [Accepted: 09/21/2015] [Indexed: 12/21/2022] Open
Abstract
Protein-rich clusters of steady submicron size and narrow size distribution exist in protein solutions in apparent violation of the classical laws of phase equilibrium. Even though they contain a minor fraction of the total protein, evidence suggests that they may serve as essential precursors for the nucleation of ordered solids such as crystals, sickle-cell hemoglobin polymers, and amyloid fibrils. The cluster formation mechanism remains elusive. We use the highly basic protein lysozyme at nearly neutral and lower pH as a model and explore the response of the cluster population to the electrostatic forces, which govern numerous biophysical phenomena, including crystallization and fibrillization. We tune the strength of intermolecular electrostatic forces by varying the solution ionic strength I and pH and find that despite the weaker repulsion at higher I and pH, the cluster size remains constant. Cluster responses to the presence of urea and ethanol demonstrate that cluster formation is controlled by hydrophobic interactions between the peptide backbones, exposed to the solvent after partial protein unfolding that may lead to transient protein oligomers. These findings reveal that the mechanism of the mesoscopic clusters is fundamentally different from those underlying the two main classes of ordered protein solid phases, crystals and amyloid fibrils, and partial unfolding of the protein chain may play a significant role.
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Affiliation(s)
- Maria A Vorontsova
- Department of Chemical and Biomolecular Engineering, University of Houston, Houston, Texas
| | - Ho Yin Chan
- Department of Physics, University of Houston, Houston, Texas
| | - Vassiliy Lubchenko
- Department of Physics, University of Houston, Houston, Texas; Department of Chemistry, University of Houston, Houston, Texas
| | - Peter G Vekilov
- Department of Chemical and Biomolecular Engineering, University of Houston, Houston, Texas; Department of Chemistry, University of Houston, Houston, Texas.
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14
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Luiken JA, Bolhuis PG. Primary Nucleation Kinetics of Short Fibril-Forming Amyloidogenic Peptides. J Phys Chem B 2015; 119:12568-79. [DOI: 10.1021/acs.jpcb.5b05799] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Jurriaan A. Luiken
- van ’t
Hoff Institute
for Molecular Sciences, University of Amsterdam, P.O. Box 94157, 1090 GD Amsterdam, Netherlands
| | - Peter G. Bolhuis
- van ’t
Hoff Institute
for Molecular Sciences, University of Amsterdam, P.O. Box 94157, 1090 GD Amsterdam, Netherlands
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