2.2 Holographic Study of Structural and Functional Characteristics …
121
the theoretical assumption of academician A. S. Davydov (Institute of Theoretical Physics, Kiev) about the existence of solitons that allows understanding and
explaining the process of muscle contraction. The soliton mechanism was demonstrated very convincing in work (A. S. Davydov “Solitons, Bioenergetics, and the
Mechanism of Muscle Contraction”, Institute of Theoretical Physics, Academy of
Sciences of the Ukrainian S. S. R., Kiev, USSR. Int. J. of Quantum Chemistry. 1979.
Vol. 16. P. 5–17).
However, let us consider the main known principles of functioning of the contractile apparatus. The nerve fiber contractile apparatus, as a rule, consists of ~10
4
consequently connected identical elements—sarcomeres, each of them contains 10
6
thick and thin filaments. The force developed by the sarcomeres at a constant length
is proportional to the number of bridges in the overlap area of the thick and thin
filaments.
Closed bridges are the source of the muscle contractile force. From discreteness
of acceptors and their filaments incompressibility, it follows that while contracting
every bridge must work cyclically: close, develop moving force at a certain interval of
the muscle relative movement and then open, but closing and opening of the myosin
bridge cannot be considered as elementary chemical acts. It can be assumed that
in an excited muscle each of these processes is characterized by the effective rate
constant, which depends on the relative position of myosin and actin active centers.
This allows applying the kinetic approach to describe muscle contractions [343]. The
force recorded at both ends of the muscle fiber is equal to the force developed in any
half of any sarcomere. The rate of fiber shortening v = 2 Nυ, where N is the number
of sarcomeres, and υ is the rate of thick and thin filaments relative movement. The
myosin bridges function independently. That means that bridge opening is subjected
to monomolecular kinetics. Under steric limitations, only a free active center can be
situated near a free bridge, so bridge closing is also subjected to the monomolecular kinetics. Mathematical formulations of muscle contraction are presented in the
work [344].
One of the important concepts in researching biological mobility problems is also
cross-striated muscle structure studying.
Using optical microscopy for this purpose appeared to be impossible because
focusing conditions alter under large deformation amplitudes during contraction.
Moreover, the light microscope spatial resolution is not enough, as the size of the
structural elements of this object is commensurable to the length of the light wave.
A muscle fiber is a cylinder with the diameter of about 50–100 μm. Most of its
volume is filled with myofibrillas which are longitudinal structures with the diameter
of 1–2 μm. In the myofibrillas from the adjacent Z plates, two systems of thin
filaments move toward each other. Periodical recurrence of such a structure provides
fiber cross-striation. In this case, the muscle fiber can be considered as a diffraction
grating with the period equal to the length of the sarcomere. The general absorption
of the muscle in the visible part of the spectrum does not exceed 1.4 × 10
−4 for 1 μm
of the fiber thickness, and differences in structural elements absorption will be lower
than 10 that makes it possible to neglect the contribution of the proper absorption
to diffraction grating creation. Nevertheless, the muscle fiber cannot be considered
121
the theoretical assumption of academician A. S. Davydov (Institute of Theoretical Physics, Kiev) about the existence of solitons that allows understanding and
explaining the process of muscle contraction. The soliton mechanism was demonstrated very convincing in work (A. S. Davydov “Solitons, Bioenergetics, and the
Mechanism of Muscle Contraction”, Institute of Theoretical Physics, Academy of
Sciences of the Ukrainian S. S. R., Kiev, USSR. Int. J. of Quantum Chemistry. 1979.
Vol. 16. P. 5–17).
However, let us consider the main known principles of functioning of the contractile apparatus. The nerve fiber contractile apparatus, as a rule, consists of ~10
4
consequently connected identical elements—sarcomeres, each of them contains 10
6
thick and thin filaments. The force developed by the sarcomeres at a constant length
is proportional to the number of bridges in the overlap area of the thick and thin
filaments.
Closed bridges are the source of the muscle contractile force. From discreteness
of acceptors and their filaments incompressibility, it follows that while contracting
every bridge must work cyclically: close, develop moving force at a certain interval of
the muscle relative movement and then open, but closing and opening of the myosin
bridge cannot be considered as elementary chemical acts. It can be assumed that
in an excited muscle each of these processes is characterized by the effective rate
constant, which depends on the relative position of myosin and actin active centers.
This allows applying the kinetic approach to describe muscle contractions [343]. The
force recorded at both ends of the muscle fiber is equal to the force developed in any
half of any sarcomere. The rate of fiber shortening v = 2 Nυ, where N is the number
of sarcomeres, and υ is the rate of thick and thin filaments relative movement. The
myosin bridges function independently. That means that bridge opening is subjected
to monomolecular kinetics. Under steric limitations, only a free active center can be
situated near a free bridge, so bridge closing is also subjected to the monomolecular kinetics. Mathematical formulations of muscle contraction are presented in the
work [344].
One of the important concepts in researching biological mobility problems is also
cross-striated muscle structure studying.
Using optical microscopy for this purpose appeared to be impossible because
focusing conditions alter under large deformation amplitudes during contraction.
Moreover, the light microscope spatial resolution is not enough, as the size of the
structural elements of this object is commensurable to the length of the light wave.
A muscle fiber is a cylinder with the diameter of about 50–100 μm. Most of its
volume is filled with myofibrillas which are longitudinal structures with the diameter
of 1–2 μm. In the myofibrillas from the adjacent Z plates, two systems of thin
filaments move toward each other. Periodical recurrence of such a structure provides
fiber cross-striation. In this case, the muscle fiber can be considered as a diffraction
grating with the period equal to the length of the sarcomere. The general absorption
of the muscle in the visible part of the spectrum does not exceed 1.4 × 10
−4 for 1 μm
of the fiber thickness, and differences in structural elements absorption will be lower
than 10 that makes it possible to neglect the contribution of the proper absorption
to diffraction grating creation. Nevertheless, the muscle fiber cannot be considered