Statistical theory of nucleation in the presence of uncharacterized impurities

Proc. Natl. Acad. Sci. U.S.A.

2006

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239

295

The determination of high-resolution structures of proteins requires crystals of suitable quality. Because of the new impetus given to structural biology by structural genomics͞proteomics, the problem of crystallizing proteins is becoming increasingly acute. There is therefore an urgent requirement for the development of new efficient methods to aid crystal growth. Nucleation is the crucial step that determines the entire crystallization process. Hence, the holy grail is to design a ''universal nucleant,'' a substrate that induces the nucleation of crystals of any protein. We report a theory for nucleation on disordered porous media and its experimental testing and validation using a mesoporous bioactive gelglass. This material induced the crystallization of the largest number of proteins ever crystallized using a single nucleant. The combination of the model and the experimental results opens up the scope for the rational design of nucleants, leading to alternative means of controlling crystallization.protein crystallization ͉ phase diagram ͉ microbatch ͉ vapor diffusion T he study of the nucleation and growth of protein crystals is one of the most important and underdeveloped areas of structural biology. Crystallization has always been, and still remains, a very difficult task, often referred to as the ''bottleneck'' of structure determination. The ability to control the nucleation phase is pivotal in the quest to overcome the bottleneck of protein crystallization (1).Protein crystals are grown from supersaturated aqueous solutions. Homogeneous nucleation takes place in the bulk of the solution, when the supersaturation is high enough for the free-energy barrier to nucleus formation to be overcome. Heterogeneous nucleation is caused by the presence in the solution of solid material, which can be an already formed crystal of the molecule to be crystallized (a ''seed'' crystal) or a different type of solid substance that has nucleation-inducing properties (a ''nucleant''). It can occur even when the supersaturation is not sufficient for homogeneous nucleation, in what is called the metastable zone of conditions (2).Because growth in the metastable zone affords kinetic advantages that often lead to larger and better-ordered crystals than those grown at higher supersaturations, an aim of protein crystallizers is to be able to induce heterogeneous nucleation (2). Thus, a search for a ''universal nucleant'' has been ongoing for 2 decades (e.g., refs. 2-4). Such a nucleant could enhance the chances of any single trial producing crystalline material.In 1988, McPherson and Shlichta (3) introduced the idea of controlling nucleation using mineral substrates as epitaxial nucleants for protein crystallization. This initiative has been pursued over the past 17 years by employing a variety of substrates (e.g., refs. 2 and 4-7), but none have proved to be generally applicable as nucleants.More recently, Chayen et al. (8) proposed the idea of using a porous substrate containing pore sizes that are comparable with the size of ...

“…In this case, there will be significant variation between nominally identical samples of the porous medium. The statistics of this variability is dealt with in more detail elsewhere (13).…”

Section: [3]mentioning

confidence: 99%

Experiment and theory for heterogeneous nucleation of protein crystals in a porous medium

Chayen

Saridakis

Proc. Natl. Acad. Sci. U.S.A.

2006

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239

295

“…These clusters were around a few tens of lysozyme As these clusters form irreversibly via a random process they are an example of what in statistical physics is known as quenched disorder. See [10,4] for previous work on the effect of quenched disorder on nucleation. The microgel particles of Diao et al [6] are another example.…”

mentioning

confidence: 99%

Non-self-averaging nucleation rate due to quenched disorder

J. Phys.: Condens. Matter

2011

We study the nucleation of a new thermodynamic phase in the presence of quenched disorder. The quenched disorder is a generic model of both impurities and disordered porous media; both are known to have large effects on nucleation. We find that the nucleation rate is non-self-averaging. This is in a simple Ising model with clusters of quenched spins. We also show that non-self-averaging behaviour is straightforward to detect in experiments, and may be rather common.

“…Also, there are simple models for variability in which assumption 3 is seen to be satisfied. 11,26 Extreme value statistics…”

Section: Modelmentioning

confidence: 99%

“…8,[15][16][17][18][19][20][21][22][23] Then, simply by chance one crystallising droplet may have a particularly good nucleation site and so nucleation is fast, whereas another droplet does not, and so nucleation is much slower. 11 Here I introduce a simple model, and show how to estimate the variation with droplet volume, of the typical time until nucleation occurs. I show that it is related to the variability in the nucleation sites, and that this variability can be estimated from experiments.…”

Section: Introductionmentioning

confidence: 99%

“…[1][2][3][4][5][6][7] When I say that the nucleation rate does not exist, I mean that the rate is far from the thermodynamic limit. 11 Properties of a crystallising droplet, such as the heat capacity, viscosity, etc, are in the thermodynamic limit. 12 These properties do not vary from one sample at the same concentration and temperature, to another.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Estimation of the Scaling of the Nucleation Time with Volume When the Nucleation Rate Does Not Exist

Crystal Growth & Design

2013

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Recent experimental [Diao et al., J. Am. Chem. Soc. 2011 133, 3756.] and simulation results [Sear, J. Phys. Cond. Matt. 2012 24, 052205.] are not consistent with a nucleation rate that is in the thermodynamic limit. This has consequences, if the rate is not in the thermodynamic limit, the time for nucleation will not necessarily scale as one over system size.Here, I show how to analyse data for nucleation times to test for the existence of a well defined nucleation rate. I also show how to estimate the scaling of the nucleation time with the number of nucleation sites. The prediction is that the farther the system is from the thermodynamic limit, the more rapidly the nucleation time varies with system size. To make this prediction, I use extreme-value statistics. I also show how nucleation data can be analysed to extract information on the heterogeneity in the surfaces nucleation is occurring on.