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Order statistics inference for describing topological coupling and mechanical symmetry breaking in multidomain proteins
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10.1063/1.4816104
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Affiliations:
1 Department of Chemistry, University of Massachusetts, Lowell, Massachusetts 01854, USA
2 Moscow Institute of Physics and Technology, Moscow Region, 141700 Russia
3 Department of Mathematical Sciences, University of Massachusetts, Lowell, Massachusetts 01854, USA
a) Author to whom correspondence should be addressed. Electronic mail: Valeri_Barsegov@uml.edu. Telephone: 978-934-3661. Fax: 978-934-3013.
J. Chem. Phys. 139, 121913 (2013)
/content/aip/journal/jcp/139/12/10.1063/1.4816104
http://aip.metastore.ingenta.com/content/aip/journal/jcp/139/12/10.1063/1.4816104

## Figures

FIG. 1.

Schematic representation of the native structure of dimer , formed by the C-terminal to N-terminal connected all-β-sheet domains (PDB code: 1PIN). The first domain, denoted as , is shown in blue, the second domain, denoted as , is shown in red, and the two-residue linker is shown in yellow color. In pulling simulations, the constant force is applied to the C-terminus of domain in the direction coinsiding with the end-to-end vector of dimer ; the N-terminus of domain is constrained. Structural analysis of unfolding trajectories revealed that the force unfolding transitions from the native folded state () to the unfolded state () in each domain occur in a single step, . Shown are the two possible scenarios. In the first pathway (left), unfolds first (1st unfolding time ) and unfolds second (2-nd unfolding time ). In the second pathway (right), unfolds second ( ) and unfolds first ( ).

FIG. 2.

The time-evolution of the end-to-end distance of the dimer (see Fig. ), , under the influence of constant pulling force of = 100 pN (panel (a)) and = 160 pN (panel (b)). Shown in different color are a few representative trajectories. The unfolding transitions in are reflected in the stepwise increases in , which occur at the 1st unfolding time (unfolding of or ), and 2nd unfolding time (unfolding of or ). These transitions are magnified in for each force value for just one simulation run.

FIG. 3.

The “parent unfolding times” , = 1, 2, for the dimer of domains and connected by the two-residue linker (panels (a) − (f)) and four-residue linker (panels (g) − (l)). Shown are the histogram-based estimates of the pdf's of unfolding times for the first domain ( , blue bars) and for the second domain ( , red bars), obtained directly from the simulation output. These are compared with the theoretical curves of the same quantities obtained by applying Order statistics inference (black and purple curves) for = 80 pN (panels (a), (b) and (g), (h)), = 120 pN (panels (c), (d) and (i), (j)), and = 160 pN (panels (e), (f) and (k), (l)).

FIG. 4.

The “time-ordered unfolding times” , = 1, 2 for the dimer (two-residue linker). The data are represented by the histogram-based estimates of the pdf's of the 1st unfolding time ( ) and 2nd unfolding time ( ) compared for = 80 pN (panels (a) and (b)), = 120 pN (panels (c) and (d)), and = 160 pN (panels (e) and (f)).

FIG. 5.

The “parent unfolding times” , = 1, 2, and 3, for the trimer of domains connected by linkers of two residues. Compared are the histogram-based estimates of the parent pdf's of unfolding times for the first domain ( , blue bars), second domain ( , red bars), and third domain ( , green bars), obtained directly from the simulation output generated for = 100 pN (panels (a), (b), and (c)), = 140 pN (panels (d), (e), and (f)), and = 160 pN (panels (g), (h), and (i)).

## Tables

Table I.

Statistical measures of the parent unfolding times for the first domain ( ), and second domain ( ), connected in the dimer by the two-residue linker: the average unfolding times and , the standard deviations and , the skewness of the distributions and , the Pearson correlation coefficient , and Spearman rank correlation coefficient . The estimates of these measures (except for ), obtained directly from the simulation output, are compared with the estimates obtained by applying Order statistics inference (shown in parentheses).

Table II.

Same quantities as in Table but for the dimer of domains connected by the linker of four residues.

Table III.

The Pearson correlation coefficients, , , and , and the Spearman rank correlation coefficients, , , and , quantifying the degree of pairwise correlations (dependence) of the parent unfolding times ( = 1, 2, 3) for the first domain ( ), second domain ( ), and third domain ( ). These measures are obtained by performing a statistical analysis of the simulation output for the trimer of domains connected by the linkers of two residues.

/content/aip/journal/jcp/139/12/10.1063/1.4816104
2013-07-29
2014-04-25

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