Biomedical Engineering Reference
In-Depth Information
Considering for example the two main constituents of muscle (i.e., myosin and actin), the α-helices
present in G-actin display an orientational dispersion preventing SHG, while myosin is endowed with
some extraordinarily long α-helices highly aligned, especially in the tail portion. Clearly, a single pro-
tein would produce too low an intensity of SHG to be detected. Thus, a third level of structural orga-
nization is required in which SHG-emitting proteins are arranged with a symmetry allowing further
summation of the signal up to a detectable level. These considerations provide basis of interpreta-
tion for the experimental observation of SHG only in specific samples such as collagen and myosin in
muscle.
The identification of the C-N peptide bond as the main HRS emitter in proteins allows applying the
theory described in Section 5.3 for probing protein structural conformation through SPA measure-
ments. In the case of proteins characterized by sequence repeats with amino acids containing methylene
groups (e.g., proline), this additional element of resonance should be considered (Rocha-Mendoza et al.,
2007). For example, in collagen (rich of the -ProHypGly- repeat), the second-order susceptibility arises
mainly from peptide groups in the backbone (Deniset-Besseau et al., 2009), but also from the symmetric
stretch of the methylene groups in the side chain. Analysis of collagen SPA data showed that the helical
pitch angle estimated including methylene groups resonance more closely agrees (Su et al., 2011) with
the known pitch angle of 45.3°. The analysis of large conformational changes in a protein (see the next
section), on the other hand, can be satisfactorily conducted with the simplified assumption of all HRS
emitters residing within the amide group.
5.7 Probing Protein Structural conformation
Knowledge of the atomic structure of a protein allows placing all its HRS emitters in space so that
the bulk second-order susceptible tensor (χ
(2)
) can be calculated using Equation 5.7. According to the
previous section, we can assume that all C-N HRS emitters (Figure 5.14a) have the same nonlinear
hyperpolarizability tensor, characterized by β
y
′
y
′
y
′
as the only nonzero component in the
x
′
y
′
z
′ molecu-
lar reference system. Since all biological samples capable of SHG emission are characterized by a cylin-
drically symmetric distribution of their protein constituents, the theoretical framework developed in
Section 5.3 can be used to experimentally extract structural information in terms of the factor γ from
SPA data (see Equation 5.14). On the other hand, γ can also be calculated from the computed χ
(2)
derived
from an atomic model of the protein conformation (see Equations 5.7 and 5.15), so that one can calculate
(a)
(b)
(d)
(e)
1E17
1E16
N
C
1E15
N
S1
1E14
C
(c)
S2
LMM
FIgurE 5.14
Structural modeling. (a) Example of location of two C-N HRSs in α-helix. (b) Atomic structure of an
actin monomer in ribbon representation. (c) Atomic structure of myosin molecule with light meromyosin (LMM),
S2 and the S1 globular head shown. (d) Model of the nine-myosin motif which repeats along the thick filament. The
figure shows S1, S2, and only a small segment of LMM, with the fiber axis oriented vertically. (e) Computed SHG
intensities. The relative contributions of actin and myosin were calculated modeling the acto-myosin array inside the
excitation volume. The
I
SHG
ratio between full and S1-less myosin is 1.11.
