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The effect of sequence on the conformational stability of a model heteropolymer in explicit water
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10.1063/1.2909974
/content/aip/journal/jcp/128/17/10.1063/1.2909974
http://aip.metastore.ingenta.com/content/aip/journal/jcp/128/17/10.1063/1.2909974

Figures

Image of FIG. 1.
FIG. 1.

Phase diagram of Staphylococcal nuclease from a combination of Fourier transform infrared spectroscopy, small angle X-ray scattering, and differential scanning calorimetry experiments. Adapted with permission (Ref. 1).

Image of FIG. 2.
FIG. 2.

Schematic of the model protein and water. The black circles are hydrophobic (H) monomers, the gray circles are polar (P) monomers, and the lines connecting them are covalent bonds. The white circles are water molecules, and the four arms on each water molecule are the hydrogen bonding arms. Examples of each of the four types of bonding arms are shown, along with the variables which count their number: bulk bonding arm pairs , hydrophobic bonding arm pairs , polar bonding arm pairs , and unpaired bonding arms . This figure shows a portion of the whole system and, in practice, a much larger box is used to prevent the protein from interacting with itself across the periodic boundary.

Image of FIG. 3.
FIG. 3.

The phase diagram of a 16-mer heteropolymer denoted 16.4, with sequence , for parameter values of , , , , . The inner line marks the region within which the probability of observing the native state is 60% or greater. In the same way, the other lines mark the regions within which the native state probabilities are greater than 50% (bold), 40%, 30%, 20%, and 10% (outermost).

Image of FIG. 4.
FIG. 4.

Representative configurations for sequence 16.4 in the (a) native state, (b) cold-denatured state, and (c) thermally denatured ensemble of states.

Image of FIG. 5.
FIG. 5.

Contour of 50% native state probability for sequence 16.4 with temperature and pressure converted into dimensional quantities using and for parameter values , , , , .

Image of FIG. 6.
FIG. 6.

Contours of 50% native state probability for sequence 16.4 for varying values of the enthalpic bonus . The other model parameters remained constant at , , , and .

Image of FIG. 7.
FIG. 7.

Contours of 50% native state probability for sequence 16.4 for varying values of the relative entropic penalty for hydrogen bonding around hydrophobic monomers. The parameter values used were and changing . To maintain the same bulk water thermodynamics, the total number of water orientations increases so that the fraction of bonding orientations for a pair of bonding arms [i.e., ] is kept constant at 0.1. The other model parameters remained constant at , .

Image of FIG. 8.
FIG. 8.

Distributions of the range of thermal stability of randomly generated sequences for four different sets of sizes and H composition: (a) 16-mers at 37.5%, (b) 16-mers at 50%, (c) 16-mers at 62.5%, and (d) 20-mers at 50%. The number of sequences with thermal stability in the interval in dimensionless units is shown by the height of the bar marked 0.01. The left axis shows the total number of sequences in each interval of thermal stability, while the right axis shows that number relative to the total number of simulated sequences in that set. The model parameters values are , , , , and .

Image of FIG. 9.
FIG. 9.

Distributions of the pressure stability of randomly generated sequences for four different sets of sizes and H composition: (a) 16-mers at 37.5%, (b) 16-mers at 50%, (c) 16-mers at 62.5%, and (d) 20-mers at 50%. The model parameter values are , , , , and .

Image of FIG. 10.
FIG. 10.

Distributions of the range of thermal stability of randomly generated sequences for four different sets of sizes and H composition: (a) 16-mers at 37.5%, (b) 16-mers at 50%, (c) 16-mers at 62.5%, and (d) 20-mers at 50%. The model parameter values are , , , , and .

Image of FIG. 11.
FIG. 11.

Directed evolution of initial sequence through four generations of mutation and selection for optimal pressure stability. The black circles are the best mutants at each generation that are used for subsequent rounds of mutation, and the line shows the improvement in pressure stability of the selected sequence. The empty circles show the pressure stability of the other mutants not selected at each generation for comparison with the best mutant.

Tables

Generic image for table
Table I.

Example 16-mer and 20-mer sequences with their thermal stability , pressure stability , and aggregate stability given in dimensionless units for model parameters , , , , and . The ranks listed next to each stability measure are the position of that sequence when ranked among sequences of the same size and composition in order of most stable to least stable for that stability measure.

Generic image for table
Table II.

Average values of the properties of large sets of simulated sequences for model parameters , , , , and . %H is the percent hydrophobicity of the set of sequences.

Generic image for table
Table III.

Statistically significant patterns between two and five monomers in length from the set of very stable 16-mers with 50% composition. The frequent patterns appear more often than expected by random chance in the top 10% most stable simulated sequences, while the infrequent patterns appear less often than expected by random chance.

Generic image for table
Table IV.

Statistically significant patterns from the set of very stable 16-mers with 37.5% composition.

Generic image for table
Table V.

Statistically significant patterns from the set of very stable 16-mers with 62.5% composition.

Generic image for table
Table VI.

Statistically significant patterns from the set of very stable 20-mers with 50% composition.

Generic image for table
Table VII.

Results of four generations of directed evolution beginning with an unstable initial 16-mer of 50% composition, for parameters , , , , and . The sequence, percent hydrophobicity (%H), and properties of the best mutant at each generation are given below. Three different selection criteria were used to determine the best mutant at each generation: the cold denaturation temperature , the thermal denaturation temperature , and the maximum stable pressure . After two generations of mutations selecting for , none of the mutants improved upon the previous generation’s best sequence.

Generic image for table
Table VIII.

Results of four generations of directed evolution beginning with an unstable 20-mer of 50% composition, for parameters , , , , and . The selection for , and proceeded along identical paths. After three generations, none of the subsequent mutations improved protein stability for any of the metrics.

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/content/aip/journal/jcp/128/17/10.1063/1.2909974
2008-05-01
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The effect of sequence on the conformational stability of a model heteropolymer in explicit water
http://aip.metastore.ingenta.com/content/aip/journal/jcp/128/17/10.1063/1.2909974
10.1063/1.2909974
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