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as the average a-b-score of the set of c-dihedral angles

: i A A}.

For our analysis of the cAPB peptide conformations we will

use the sets A

= {1,2,8} and A

= {3,4,5,6}, where 1 denotes

alanine, 2 cysteine and so on (cf. Fig. 1). Thus, H

 H

ELO

)

reﬂects the structure of the peptide in the vicinity of the

chromophore and H

 H

ELO

) the structure within

the core of the peptide moiety. Note, that we have omitted

the residue 7 (glycine) in A

because of its high ﬂexibility.

Free energy maps

The conformational coordinates H

and H

introduced above

were used for characterizing the conformational ensembles of

cis and trans cAPB by free energy maps G(H

). To compute

these maps the rectangle [1, 1]  [1, 1] was divided into

20  20 bins and statistics over the HELO scores encountered

in the REST simulations yielded bin-counts m(H

). Up to

an arbitrary constant, the free energy is given by G(H

) =

k

T ln[m(H

)/M

max

], where M

max

is the maximal bin-count.

Note that this choice for G guarantees that the minimum of G

is zero. Because empty bins in the histogram density estimate

would lead to inﬁnite free energies, an upper energy cutoﬀ

max

= k

Tln(1/M

max

) was introduced and G was set to

max

at all empty bins. A nearest neighbor smoothing was

applied before generating contour plots of G(H

Proton distances

To compare the equilibrium ensembles computed by our REST

simulations with the well-known NMR distance restraints

derived from NOEs of the cis and trans isomers of cAPB,

we have calculated proton–proton interaction distances

from proton–proton distances r

sampled by the simula-

tions. Because a NOE is caused by a dipole–dipole inter-

action, we have calculated the interaction distances d

by the

prescription

,t) = (hr

6

,t]

)

1/6

. (7)

Here, hi

,t]

denotes the average over the simulation time

interval [t

,t] with t > t

. For chemically equivalent protons

,. . .,i

} the geometrical center was used to compute the

distance r

to proton j. In analogy to the well known root

mean square deviation, we introduce the root mean square

violation (RMSV)

RMSVðt

; tÞ ¼

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

jMj

ðijÞ2M

max½0; d

ðt

; tÞ  d

exp



; ð8Þ

by which a simulation result violates the NOE distance

restraints.

Here, M is the set of all proton pairs (ij), for

which distances d

exp

were experimentally determined, and |M|

is the number of these distances. Note that the ESI contains a

section explaining the properties and particularly the tempera-

ture dependence of the RMSV.

Experimental methods

Sample preparation

The cAPB peptides were prepared as described in ref. 26. The

sample was dissolved in dimethylsulfoxide (DMSO) from

Merck (Darmstadt, Germany) at a concentration of about

7 mM. In the time resolved pump probe experiments the sample

was circulated through home made ﬂow cells (pathlength 0.1 mm)

with CaF

windows. This closed cycle system ensures the exchange

of the illuminated sample volume between consecutive excitation

laser pulses.

Stationary IR spectroscopy

Steady state absorption spectra were recorded using a Fourier

transform infrared (FTIR) spectrometer IFS66 from Bruker

(Ettlingen, Germany). No indications for sample degradation

were found from stationary FTIR spectroscopy during the

measurements. The trans-azo conformation is the thermally

stable form of cAPB. At room temperature the cAPB molecules

reach the trans-azo conformation at a timescale of some days.

As a consequence, dark adapted molecules (yielding a con-

centration of about 100% trans isomers) were used for the

study of the trans ensemble of cAPB. For the investigation of

the cis ensemble the sample was converted to the cis-azo

conformation by continuous UV illumination of the trans

pp*-absorption band with the light of a HgXe arc lamp

emitting around 370 nm (LOT, Darmstadt, Germany). The

lamp was equipped with ﬁlters from Schott (UG11, WG320,

GG375). Taking the extinction coeﬃcients for the cis and trans

isomers into account one can estimate that about 90% of all

molecules were in the cis form during the measurements.

Femtosecond IR spectroscopy

The structural dynamics of the cis to trans reaction have been

investigated by time resolved UV pump IR probe spectro-

scopy. A detailed description of the experimental setup is given

in ref. 66. In brief, we used the pump and probe technique

with single pulses from a Ti-sapphire laser-ampliﬁer system

operated at 1 kHz. Second harmonic generation was used for

excitation at 404 nm with an energy of about 2 mJ. In order to

reduce excessive nonlinearities induced by the intense excita-

tion pulses the duration of the pump pulses was increased by a

quartz rod (15 cm) in front of the sample. The pump pulses

had a duration of about 700 fs and were focused to a spot size

of about 150 mm (FWHM) at the sample position. The IR

probe pulses were generated using a two stage BBO optical

Fig. 2 The a-b-scoring function h

elo

(c).

6208 | Phys. Chem. Chem. Phys., 2010, 12, 6204–6218 This journal is

c

the Owner Societies 2010

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