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Bowles RK, Harrowell P. Influence on crystal nucleation of an order-disorder transition among the subcritical clusters. Phys Rev E 2022; 105:L062602. [PMID: 35854518 DOI: 10.1103/physreve.105.l062602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2021] [Accepted: 05/31/2022] [Indexed: 06/15/2023]
Abstract
Studies of nucleation generally focus on the properties of the critical cluster, but the presence of defects within the crystal lattice means that the population of nuclei necessarily evolve through a distribution of precritical clusters with varying degrees of structural disorder on their way to forming a growing stable crystal. To investigate the role precritical clusters play in nucleation, we develop a simple thermodynamic model for crystal nucleation in terms of cluster size and the degree of cluster order that allows us to alter the work of forming the precritical clusters without affecting the properties of the critical cluster. The steady state and transient nucleation behavior of the system are then studied numerically, for different microscopic ordering kinetics. We find that the model exhibits a generic order-disorder transition in the precritical clusters. Independent of the types of ordering kinetics, increasing the accessibility of disordered precritical clusters decreases both the steady state nucleation rate and the nucleation lag time. Furthermore, the interplay between the free-energy surface and the microscopic ordering kinetics leads to three distinct nucleation pathways.
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Affiliation(s)
- Richard K Bowles
- Department of Chemistry, University of Saskatchewan, Saskatoon, SK, Canada S7H 0H1
- Centre for Quantum Topology and its Applications (quanTA), University of Saskatchewan, SK, Canada S7N 5E6
| | - Peter Harrowell
- School of Chemistry, University of Sydney, New South Wales 2006, Australia
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2
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Eaton D, Saika-Voivod I, Bowles RK, Poole PH. Free energy surface of two-step nucleation. J Chem Phys 2021; 154:234507. [PMID: 34241260 DOI: 10.1063/5.0055877] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
We test the theoretical free energy surface (FES) for two-step nucleation (TSN) proposed by Iwamatsu [J. Chem. Phys. 134, 164508 (2011)] by comparing the predictions of the theory to numerical results for the FES recently reported from Monte Carlo simulations of TSN in a simple lattice system [James et al., J. Chem. Phys. 150, 074501 (2019)]. No adjustable parameters are used to make this comparison. That is, all the parameters of the theory are evaluated directly for the model system, yielding a predicted FES, which we then compare to the FES obtained from simulations. We find that the theoretical FES successfully predicts the numerically evaluated FES over a range of thermodynamic conditions that spans distinct regimes of behavior associated with TSN. All the qualitative features of the FES are captured by the theory, and the quantitative comparison is also very good. Our results demonstrate that Iwamatsu's extension of classical nucleation theory provides an excellent framework for understanding the thermodynamics of TSN.
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Affiliation(s)
- Dean Eaton
- Department of Physics, St. Francis Xavier University, Antigonish, Nova Scotia B2G 2W5, Canada
| | - Ivan Saika-Voivod
- Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John's, Newfoundland A1B 3X7, Canada
| | - Richard K Bowles
- Department of Chemistry, University of Saskatchewan, Saskatoon, Saskatchewan 57N 5C9, Canada
| | - Peter H Poole
- Department of Physics, St. Francis Xavier University, Antigonish, Nova Scotia B2G 2W5, Canada
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3
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James D, Beairsto S, Hartt C, Zavalov O, Saika-Voivod I, Bowles RK, Poole PH. Phase transitions in fluctuations and their role in two-step nucleation. J Chem Phys 2019; 150:074501. [DOI: 10.1063/1.5057429] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Daniella James
- Department of Physics, St. Francis Xavier University, Antigonish, Nova Scotia B2G 2W5, Canada
| | - Seamus Beairsto
- Department of Physics, St. Francis Xavier University, Antigonish, Nova Scotia B2G 2W5, Canada
| | - Carmen Hartt
- Department of Physics, St. Francis Xavier University, Antigonish, Nova Scotia B2G 2W5, Canada
| | - Oleksandr Zavalov
- Department of Physics, St. Francis Xavier University, Antigonish, Nova Scotia B2G 2W5, Canada
| | - Ivan Saika-Voivod
- Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John’s, Newfoundland A1B 3X7, Canada
| | - Richard K. Bowles
- Department of Chemistry, University of Saskatchewan, Saskatoon, Saskatchewan 57N 5C9, Canada
| | - Peter H. Poole
- Department of Physics, St. Francis Xavier University, Antigonish, Nova Scotia B2G 2W5, Canada
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4
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Zhang F. Nonclassical nucleation pathways in protein crystallization. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:443002. [PMID: 28984274 DOI: 10.1088/1361-648x/aa8253] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Classical nucleation theory (CNT), which was established about 90 years ago, has been very successful in many research fields, and continues to be the most commonly used theory in describing the nucleation process. For a fluid-to-solid phase transition, CNT states that the solute molecules in a supersaturated solution reversibly form small clusters. Once the cluster size reaches a critical value, it becomes thermodynamically stable and favored for further growth. One of the most important assumptions of CNT is that the nucleation process is described by one reaction coordinate and all order parameters proceed simultaneously. Recent studies in experiments, computer simulations and theory have revealed nonclassical features in the early stage of nucleation. In particular, the decoupling of order parameters involved during a fluid-to-solid transition leads to the so-called two-step nucleation mechanism, in which a metastable intermediate phase (MIP) exists between the initial supersaturated solution and the final crystals. Depending on the exact free energy landscapes, the MIPs can be a high density liquid phase, mesoscopic clusters, or a pre-ordered state. In this review, we focus on the studies of nonclassical pathways in protein crystallization and discuss the applications of the various scenarios of two-step nucleation theory. In particular, we focus on protein solutions in the presence of multivalent salts, which serve as a model protein system to study the nucleation pathways. We wish to point out the unique features of proteins as model systems for further studies.
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Affiliation(s)
- Fajun Zhang
- Universität Tübingen, Institut für Angewandte Physik, Auf der Morgenstelle 10, 72076 Tübingen, Germany
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5
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Abstract
We present a theoretical model for the nucleation of amyloid fibrils. In our model we use helix-coil theory to describe the equilibrium between a soluble native state and an aggregation-prone unfolded state. We then extend the theory to include oligomers with β-sheet cores and calculate the free energy of these states using estimates for the energies of H-bonds, steric zipper interactions, and the conformational entropy cost of forming secondary structure. We find that states with fewer than ~10 β-strands are unstable relative to the dissociated state and three β-strands is the highest free energy state. We then use a modified version of Classical Nucleation Theory to compute the nucleation rate of fibrils from a supersaturated solution of monomers, dimers, and trimers. The nucleation rate has a non-monotonic dependence on denaturant concentration reflecting the competing effects of destabilizing the fibril and increasing the concentration of unfolded monomers. We estimate heterogeneous nucleation rates and discuss the application of our model to secondary nucleation.
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Affiliation(s)
- Lingyun Zhang
- Department of Physics, Kansas State University, Manhattan, KS 66506, USA
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Jeremy D Schmit
- Department of Physics, Kansas State University, Manhattan, KS 66506, USA
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6
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Lifanov Y, Vorselaars B, Quigley D. Nucleation barrier reconstruction via the seeding method in a lattice model with competing nucleation pathways. J Chem Phys 2016; 145:211912. [DOI: 10.1063/1.4962216] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Affiliation(s)
- Yuri Lifanov
- Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Bart Vorselaars
- School of Mathematics and Physics, University of Lincoln, Lincolnshire LN6 7TS, United Kingdom
| | - David Quigley
- Department of Physics and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom
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7
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Singh RS, Bagchi B. Correlation between thermodynamic anomalies and pathways of ice nucleation in supercooled water. J Chem Phys 2015; 140:164503. [PMID: 24784283 DOI: 10.1063/1.4871388] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
The well-known classical nucleation theory (CNT) for the free energy barrier towards formation of a nucleus of critical size of the new stable phase within the parent metastable phase fails to take into account the influence of other metastable phases having density/order intermediate between the parent metastable phase and the final stable phase. This lacuna can be more serious than capillary approximation or spherical shape assumption made in CNT. This issue is particularly significant in ice nucleation because liquid water shows rich phase diagram consisting of two (high and low density) liquid phases in supercooled state. The explanations of thermodynamic and dynamic anomalies of supercooled water often invoke the possible influence of a liquid-liquid transition between two metastable liquid phases. To investigate both the role of thermodynamic anomalies and presence of distinct metastable liquid phases in supercooled water on ice nucleation, we employ density functional theoretical approach to find nucleation free energy barrier in different regions of phase diagram. The theory makes a number of striking predictions, such as a dramatic lowering of nucleation barrier due to presence of a metastable intermediate phase and crossover in the dependence of free energy barrier on temperature near liquid-liquid critical point. These predictions can be tested by computer simulations as well as by controlled experiments.
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Affiliation(s)
- Rakesh S Singh
- Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India
| | - Biman Bagchi
- Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India
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8
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Observing classical nucleation theory at work by monitoring phase transitions with molecular precision. Nat Commun 2014; 5:5598. [PMID: 25465441 PMCID: PMC4268696 DOI: 10.1038/ncomms6598] [Citation(s) in RCA: 80] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2014] [Accepted: 10/17/2014] [Indexed: 01/09/2023] Open
Abstract
It is widely accepted that many phase transitions do not follow nucleation pathways as envisaged by the classical nucleation theory. Many substances can traverse intermediate states before arriving at the stable phase. The apparent ubiquity of multi-step nucleation has made the inverse question relevant: does multistep nucleation always dominate single-step pathways? Here we provide an explicit example of the classical nucleation mechanism for a system known to exhibit the characteristics of multi-step nucleation. Molecular resolution atomic force microscopy imaging of the two-dimensional nucleation of the protein glucose isomerase demonstrates that the interior of subcritical clusters is in the same state as the crystalline bulk phase. Our data show that despite having all the characteristics typically associated with rich phase behaviour, glucose isomerase 2D crystals are formed classically. These observations illustrate the resurfacing importance of the classical nucleation theory by re-validating some of the key assumptions that have been recently questioned. Many nanoscale systems can form ordered microphases through non-classical multistep nucleation. Here, the authors report that glucose isomerase, which is known to exhibit the characteristics of multi-step nucleation in 3D, nucleates along the pathway predicted by classical nucleation theory in 2D.
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9
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Roosen-Runge F, Zhang F, Schreiber F, Roth R. Ion-activated attractive patches as a mechanism for controlled protein interactions. Sci Rep 2014; 4:7016. [PMID: 25388788 PMCID: PMC5382698 DOI: 10.1038/srep07016] [Citation(s) in RCA: 75] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2014] [Accepted: 10/20/2014] [Indexed: 12/04/2022] Open
Abstract
The understanding of protein interactions to control phase and nucleation behavior of protein solutions is an important challenge for soft matter, biological and medical research. Here, we present ion bridges of multivalent cations between proteins as an ion-activated mechanism for patchy interaction that is directly supported by experimental findings in protein crystals. A deep understanding of experimentally observed phenomena in protein solutions--including charge reversal, reentrant condensation, metastable liquid-liquid phase separation, cluster formation and different pathways of crystallization--is gained by an analytic model that directly displays parameter dependencies and physical connections. The direct connection between experiment and theory provides a conceptual framework for future experimental, computational and theoretical research on topics such as rational design of phase behavior and crystallization pathways on the basis of the statistical physics of patchy particles.
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Affiliation(s)
- Felix Roosen-Runge
- Institut für Angewandte Physik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
- Institut Laue-Langevin, 71 avenue des Martyrs, 38042 Grenoble, France
| | - Fajun Zhang
- Institut für Angewandte Physik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
| | - Frank Schreiber
- Institut für Angewandte Physik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
| | - Roland Roth
- Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
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10
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Abstract
Crystalline bacterial cell surface layers (S-layers) represent the outermost cell envelope component in a broad range of bacteria and archaea. They are monomolecular arrays composed of a single protein or glycoprotein species and represent the simplest biological membranes developed during evolution. They are highly porous protein mesh works with unit cell sizes in the range of 3 to 30 nm, and pore sizes of 2 to 8 nm. S-layers are usually 5 to 20 nm thick (in archaea, up to 70 nm). S-layer proteins are one of the most abundant biopolymers on earth. One of their key features, and the focus of this review, is the intrinsic capability of isolated native and recombinant S-layer proteins to form self-assembled mono- or double layers in suspension, at solid supports, the air-water interface, planar lipid films, liposomes, nanocapsules, and nanoparticles. The reassembly is entropy-driven and a fascinating example of matrix assembly following a multistage, non-classical pathway in which the process of S-layer protein folding is directly linked with assembly into extended clusters. Moreover, basic research on the structure, synthesis, genetics, assembly, and function of S-layer proteins laid the foundation for their application in novel approaches in biotechnology, biomimetics, synthetic biology, and nanotechnology.
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Affiliation(s)
- Dietmar Pum
- Institute of Biophysics, Department of Nanobiotechnology, University of Natural Resources and Life Sciences, Vienna, Muthgasse 11, 1190 Vienna, Austria
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11
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Agarwal V, Peters B. Solute Precipitate Nucleation: A Review of Theory and Simulation Advances. ADVANCES IN CHEMICAL PHYSICS 2014. [DOI: 10.1002/9781118755815.ch03] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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12
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Role of clusters in nonclassical nucleation and growth of protein crystals. Proc Natl Acad Sci U S A 2014; 111:E546-53. [PMID: 24449867 DOI: 10.1073/pnas.1309320111] [Citation(s) in RCA: 140] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The development of multistep nucleation theory has spurred on experimentalists to find intermediate metastable states that are relevant to the solidification pathway of the molecule under interest. A great deal of studies focused on characterizing the so-called "precritical clusters" that may arise in the precipitation process. However, in macromolecular systems, the role that these clusters might play in the nucleation process and in the second stage of the precipitation process, i.e., growth, remains to a great extent unknown. Therefore, using biological macromolecules as a model system, we have studied the mesoscopic intermediate, the solid end state, and the relationship that exists between them. We present experimental evidence that these clusters are liquid-like and stable with respect to the parent liquid and metastable compared with the emerging crystalline phase. The presence of these clusters in the bulk liquid is associated with a nonclassical mechanism of crystal growth and can trigger a self-purifying cascade of impurity-poisoned crystal surfaces. These observations demonstrate that there exists a nontrivial connection between the growth of the macroscopic crystalline phase and the mesoscopic intermediate which should not be ignored. On the other hand, our experimental data also show that clusters existing in protein solutions can significantly increase the nucleation rate and therefore play a relevant role in the nucleation process.
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13
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Bingham RJ, Rizzi LG, Cabriolu R, Auer S. Communication: Non-monotonic supersaturation dependence of the nucleus size of crystals with anisotropically interacting molecules. J Chem Phys 2013; 139:241101. [DOI: 10.1063/1.4861044] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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14
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Hedges LO, Whitelam S. Limit of validity of Ostwald's rule of stages in a statistical mechanical model of crystallization. J Chem Phys 2011; 135:164902. [DOI: 10.1063/1.3655358] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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15
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Peters B. On the coupling between slow diffusion transport and barrier crossing in nucleation. J Chem Phys 2011; 135:044107. [DOI: 10.1063/1.3613674] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
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16
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Jacobson LC, Molinero V. Can Amorphous Nuclei Grow Crystalline Clathrates? The Size and Crystallinity of Critical Clathrate Nuclei. J Am Chem Soc 2011; 133:6458-63. [DOI: 10.1021/ja201403q] [Citation(s) in RCA: 133] [Impact Index Per Article: 10.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Liam C. Jacobson
- Department of Chemistry, University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112-0850, United States
| | - Valeria Molinero
- Department of Chemistry, University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112-0850, United States
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17
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Jacobson LC, Hujo W, Molinero V. Nucleation pathways of clathrate hydrates: effect of guest size and solubility. J Phys Chem B 2011; 114:13796-807. [PMID: 20931990 DOI: 10.1021/jp107269q] [Citation(s) in RCA: 110] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Understanding the microscopic mechanism of nucleation of clathrate hydrates is important for their use in hydrogen storage, CO(2) sequestration, storage and transport of natural gas, and the prevention of the formation of hydrate plugs in oil and gas pipelines. These applications involve hydrate guests of varied sizes and solubility in water that form different hydrate crystal structures. Nevertheless, molecular studies of the mechanism of nucleation of hydrates have focused on the single class of small hydrophobic guests that stabilize the sI crystal. In this work, we use molecular dynamics simulations with a very efficient coarse-grained model to elucidate the mechanisms of nucleation of clathrate hydrates of four model guests that span a 2 orders of magnitude range in solubility in water and that encompass sizes which stabilize each one a different hydrate structure (sI and sII, with and without occupancy of the dodecahedral cages). We find that the overall mechanism of clathrate nucleation is similar for all guests and involves a first step of formation of blobs, dense clusters of solvent-separated guest molecules that are the birthplace of the clathrate cages. Blobs of hydrophobic guests are rarer and longer-lived than those for soluble guests. For each guest, we find multiple competing channels to form the critical nuclei, filled dodecahedral (5(12)) cages, empty 5(12) cages, and a variety of filled large (5(12)6(n) with n = 2, 3, and 4) clathrate cages. Formation of empty dodecahedra is an important nucleation channel for all but the smallest guest. The empty 5(12) cages are stabilized by the presence of guests from the blob in their first solvation shell. Under conditions of high supercooling, the structure of the critical and subcritical nuclei is mainly determined by the size of the guest and does not reflect the cage composition or ordering of the stable or metastable clathrate crystals.
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Affiliation(s)
- Liam C Jacobson
- Department of Chemistry, University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112-0850, USA
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18
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Miller WL, Cacciuto A. Exploiting classical nucleation theory for reverse self-assembly. J Chem Phys 2010; 133:234108. [DOI: 10.1063/1.3524307] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Stannard A, Blunt MO, Beton PH, Garrahan JP. Entropically stabilized growth of a two-dimensional random tiling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:041109. [PMID: 21230240 DOI: 10.1103/physreve.82.041109] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2010] [Revised: 05/19/2010] [Indexed: 05/30/2023]
Abstract
The assembly of molecular networks into structures such as random tilings and glasses has recently been demonstrated for a number of two-dimensional systems. These structures are dynamically arrested on experimental time scales, so the critical regime in their formation is that of initial growth. Here, we identify a transition from energetic to entropic stabilization in the nucleation and growth of a molecular rhombus tiling. Calculations based on a lattice-gas model show that clustering of topological defects and the formation of faceted boundaries followed by a slow relaxation to equilibrium occur under conditions of energetic stabilization. We also identify an entropically stabilized regime in which the system grows directly into an equilibrium configuration without the need for further relaxation. Our results provide a methodology for identifying equilibrium and nonequilibrium randomness in the growth of molecular tilings, and we demonstrate that equilibrium spatial statistics are compatible with exponentially slow dynamical behavior.
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Affiliation(s)
- Andrew Stannard
- School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
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20
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Whitelam S. Control of pathways and yields of protein crystallization through the interplay of nonspecific and specific attractions. PHYSICAL REVIEW LETTERS 2010; 105:088102. [PMID: 20868132 DOI: 10.1103/physrevlett.105.088102] [Citation(s) in RCA: 64] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2010] [Indexed: 05/29/2023]
Abstract
We use computer simulation to study crystal-forming model proteins equipped with interactions that are both orientationally specific and nonspecific. Distinct dynamical pathways of crystal formation can be selected by tuning the strengths of these interactions. When the nonspecific interaction is strong, liquidlike clustering can precede crystallization; when it is weak, growth can proceed via ordered nuclei. Crystal yields are in certain parameter regimes enhanced by the nonspecific interaction, even though it promotes association without local crystalline order. Our results suggest that equipping nanoscale components with weak nonspecific interactions (such as depletion attractions) can alter both their dynamical pathway of assembly and optimize the yield of the resulting material.
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Affiliation(s)
- Stephen Whitelam
- Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA.
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