Open source platform for the execution and analysis of
mechanical refolding experiments
Daniel Aioanei1∗, Marco Brucale1and Bruno Samor´ ı1
1Department of Biochemistry ‘G.Moruzzi’, University of Bologna, Via Irnerio 48, 40126 Bologna,
Motivation: Single-molecule force spectroscoy (SMFS) has facili-
tated the experimental investigation of biomolecular force-coupled
kinetics, from which the kinetics at zero force can be extrapolated
via explicit theoretical models. The atomic force microscope (AFM)
in particular is routinely used to study protein unfolding kinetics, but
only rarely protein folding kinetics. The discrepancy arises because
mechanical protein refolding studies are more technically challenging.
Results: We developed software that can drive and analyse mechani-
cal refolding experiments when used with the commercial AFM setup
“Picoforce AFM”, Bruker (previously Digital Instruments). We expect
the software to be easily adaptable to other AFM setups. We also
developed an improved method for the statistical characterisation of
protein folding kinetics, and implemented it into an AFM-independent
Availability: Software and documentation are available at
http://code.google.com/p/refolding under Apache License 2.0.
Biochemical reactions commonly proceed via large conformational
changes, resulting in a well defined mechanical reaction coordinate
on which they can be monitored. Since force is a determinant fac-
tor in the rate of such reactions, single-molecule force spectroscopy
(SMFS) emerged as an invaluable tool in their investigation under
mechanical tension (Kumar and Li, 2010; Bustamante et al., 2004).
Thanks to its remarkable ability to stretch and monitor one mole-
cule at a time, SMFS seeks to achieve the long-standing goal of
mapping the energy landscape of biomolecules (e.g. proteins, RNA)
on a well defined reaction coordinate, even for proteins which show
irreversiblethermal orchemical unfolding(Jollymoreand Li,2010).
In particular, protein folding kinetics can be studied at the single
molecule level using the atomic force microscope (AFM). To this
end protein modules can be first unfolded and subsequently allo-
wed to refold while subjected to a “force-clamp” (Garcia-Manyes
et al., 2009b, 2007; Fernandez and Li, 2004), or they can be directly
observed to refold at fixed extension via “lock-in force spectros-
copy” (Garcia-Manyes et al., 2009a). Such techniques depend on
recent technological advances implemented in custom-built AFMs
with very limited availability. Alternatively, the AFM can be used in
the more traditional “velocity-clamp” mode to drive protein modu-
les to fold under mechanical tension via the “double-pulse protocol”
∗to whom correspondence should be addressed
(see Suplementary Data). Shortly, the distance between the base of
the cantilever and the surface, rather than the stretching force, is
maintained constant for some amount of time allowing previously
unfolded protein modules to refold (Cao and Li, 2007; Bullard et al.,
2006; Carrion-Vazquez et al., 1999).
Despite the widespread availability of AFM instrumentation sup-
porting the velocity-clamp mode of operation, single molecule fol-
ding kinetics studies remain rather scarce in the scientific literature,
likely due to the unavailability of mandatory software technology.
We fill this gap by making such software freely available. To vali-
date our software we studied the folding kinetics of protein GB1
(Cao et al., 2006) and obtained a kinetics characterisation similar to
the previously published one (Cao and Li, 2007).
Our software contains three main components:
1. An automated procedure for driving refolding experiments
through Nanoscope v6 software, in conjunction with Picoforce
AFM and Nanoscope IIIa controller, Bruker. For each execu-
tion of the double-pulse protocol, our software instructs the
Nanoscope software to execute a “Nanoscope script” and cap-
ture a “Nanoscope strip chart”. Importantly, the actual bending
of the cantilever is detected from the strip chart file and the
starting position is adjusted accordingly for the next double-
pulse so as to counterbalance accumulating drift (Oberhauser
et al., 2001). Section 1 in Supplementary Data contains more
information on the implemented double-pulse protocol.
2. Offline tools for automated peak identification, force measu-
rements, Worm-like chain (Bustamante et al., 1994) fits and
data filtering. Tools are also included for manually improving
the results of some of the automated tasks such as zero-force
baseline and contact point identification.
3. A standalone, AFM-independent offline procedure for the sta-
tistical characterisation of protein folding kinetics from mecha-
nical refolding experiments with homomeric polyproteins,
based on the analytical model of Section 3.1.
Associate Editor: Prof. Anna Tramontano
© The Author (2010). Published by Oxford University Press. All rights reserved. For Permissions, please email: email@example.com
Bioinformatics Advance Access published December 1, 2010
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Maximum likelihood estimation of folding kinetic
We adopt Bell’s approximation (Walcott, 2008; Bell, 1978) to Kramers’
reaction-rate theory (H¨ anggi et al., 1990), which describes the force-
dependent folding rate as kf(F) = k0
is the Boltzmann constant, T is the temperature in Kelvin, k0
taneous folding rate and ∆xfis the folding distance. We aim to extract the
last two mentioned parameters from refolding experiments.
Traditionally data was collected in a few fixed configurations, where a
configuration is defined by the amount of time allowed for refolding and the
inferred force at the start of the waiting period. It was therefore assumed that
the same configuration can be reproduced exactly multiple times, ignoring
any variation between double-pulse protocol executions. It was also assumed
that the residual force remains constant during the waiting time (Cao and
Li, 2007; Carrion-Vazquez et al., 1999), ignoring the fact that it increases
after each folding event. Furthermore, it was assumed that the total number
of modules that could refold is limited by the extension during the waiting
period (Cao and Li, 2007), breaking the assumption of the ideal spring can-
tilever. The mean and standard deviation of the refolding ratio would then be
computed for each configuration and then fitted to an exponential formula
based on Bell’s equation or to Monte-Carlo simulations based on it, ignoring
the fact that such summary statistics are not sufficient (Lehmann and Casella,
1998), i.e., they do not capture all possible information about the parameters.
We overcome all the above limitations by introducing a Maximum Like-
lihood estimation procedure. Shortly, the stretching force is computed by
solving the WLC cubic equation (Aioanei et al., 2009), and the likelihood
function is computed as the product of the probability to observe the actual
number of folding events for each double-pulse protocol execution. The
maximum likelihood is then located over a grid of (k0
and estimation errors are computed by case resampling (see Section 2 in
fexp[−F∆xf/(KbT)], where Kb
fis the spon-
3.2 Folding kinetics of protein GB1
We estimated the kinetic parameters of protein GB1 in buffer Tris/HCl (10
mM, pH 7.5) by performing mechanical refolding experiments with homo-
meric polyproteins (GB1)8and (GB1)16(see Section 3 in Supplementary
Data for experimental data statistics). A sample trace can be seen in Figure 1.
We obtained the kinetic parameters ∆xf
tics characterisation is roughly compatible with previously published values
of ∆xf= 2.1 nm and k0
= 2.53 ± 0.12 nm and
f= 500 ± 85s−1, errors representing one standard deviation. Our kine-
f= 720 ± 120s−1(Cao and Li, 2007).
Mechanical refolding experiments can be performed with typical
commercial velocity-clamp AFM instrumentation, and we provide
an out-of-the-box software solution for performing and analysing
such experiments in conjunction with Picoforce AFM, Bruker. We
expect our software to be easily adaptable to other AFM setups. In
fact since the analytical model of Section 3.1 is not specific to a
particular AFM, its implementation can already be used with refol-
ding data obtained with any other AFM. Furthermore, we developed
all the software in the Java and Python programming languages to
ensure its portability across all major operating systems.
We thank Prof. Hongbin Li, University of British Columbia, Van-
couver, Canada for kindly providing the (GB1)8 plasmid, Dr.
Fig. 1. (Colour online) A force-extension trace according to the double-
pulse protocol with the homomeric polyprotein (GB1)16. The lower curve
represents the protein fetching phase, during which the polyprotein attached
nonspecifically to the cantilever and then a total of 15 modules have been
subsequently unfolded. The higher curve is shifted by 260 pN just for dis-
play purposes, and it represents the phase where the same molecule is pulled
for the second time. Note that only 15 out of the 16 modules could have
refolded, since one module was not unfolded during the fetching phase. The
vertical dashed line represents the piezo position during the waiting time-
lapse relative to the resting position of the cantilever tip, and its numerical
value is shown together with the length of the time-lapse at the top of the
figure. Each WLC fit is shown redundantly shifted higher for display pur-
poses. The contour length at the start of the waiting time-lapse (before any
refolding) is indicated in the bottom-right position.
Isabella Tessari and Prof. Luigi Bubacco, University of Padova,
Italy for providing the (GB1)16construct.
Funding: This work was supported by Ministero dellUniversit´ a e
della Ricerca Fondo per gli Investimenti della Ricerca di Base
(MIUR FIRB) RBNE03PX83/001; MIUR FIRB Progetto NG-lab
(G.U. 29/07/05 n.175); Progetti di Ricerca di Interesse Nazionale
(PRIN) 2008 (Prot. 2008KZ3E5).
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