Optimal evaluation of single-molecule force spectroscopy experiments

Abstract

The forced rupture of single chemical bonds under external load is addressed. A general framework is put forward to optimally utilize the experimentally observed rupture force data for estimating the parameters of a theoretical model. As an application, we explore to what extent a distinction between several recently proposed models is feasible on the basis of realistic experimental data sets.

Single-molecule force spectroscopy: Practical limitations beyond Bell’s model

“…Fig. 3 shows the results for 10000 repetitions of a computer experiment, each sampling N = 400 rupture forces f according to (29) with experimentally realistic parameter values α 0 = 0.1 pN −1 and λ 0 = −5. Since twodimensional distributions are difficult to compare graphically, we focus on the marginal distributions.…”

“…3. The systematic bias of the estimate for λ can be traced back to fitting a Gaussian, which is symmetric about its maximum, to an asymmetric "true" distribution (29) [35], while the suboptimal variance of the estimate for both λ and α signals that quite some information is lost by only considering the most probable rupture forces f * . Hence, the maximum likelihood estimate represents a substantial improvement compared to the so far "standard method" of data evaluation in this field.…”

“…The proceeding consists in simply maximizing (12) with respect to µ [29,30]; usually, this has to be done numerically. For any given f and v the corresponding set of parameters µ * = µ * (f , v) is called the maximum likelihood estimate.…”

“…The rupture force density (29) is conditioned on µ = (λ, α), and v. As usual, we assume that the pulling velocity v is known exactly for each measurement, and similarly for the elasticity κ appearing on the right hand side of (29). The remaining model parameters to be estimated from a given set of rupture forces f = {f i } N i=1 measured at pulling velocities {v β } Z β=1 with relative frequencies ρ β are therefore µ = (λ, α).…”

“…This introduces some specific functional form for the escape rate (1) involving several parameters, which are then determined by fitting the experimental data. In the present work, we describe the application of the maximum likelihood approach [29,30] as a tool to deduce the model parameters. We show that this method is superior to any other approach that may be used for this purpose.…”