the distance between the bead center and the focal point [28, 29]. Thus, the restoring
force, F, has characteristics of a spring: F ¼ kx, where k and x is the stiffness (spring
constant) and the amount of the shift of the sphere. Hence, if one can measure k and
x, one will know the magnitude of the force exerted on the sphere. Theoretical
calculations of the stiffness have been presented [28–31] and an example of the
experimental method to estimate the stiffness is given in Fig. 3.25.
With the above feature, the optical trapping technique has been widely used to
measure, for example, the force developed by a single motor force or protrusive
force of the cell edge (ie., lamellipodium). By utilizing infra-red laser beam, one can
manipulate intracellular objects, because the cell membrane is relatively transparent
to the infra-red laser beam [32]. Another advantage is that if the light is split by a
polarization beam splitter and each light is focused at two different focal points
separately, one can hold two objects at each focal point. The ability to separately
change the direction of the beam by two independent reflecting mirrors will enable
further applications. Some applications of the optical trapping are presented in
Chap. 7.
3.10 Outlook of Molecular Dynamics
Nobel Prizes in Chemistry for 2013 were awarded to Martin Karplus, Michael Levitt
and Arieh Warshel [33] for the development of multiscale models for complex
chemical systems. Chemists used to create models of molecules using plastic balls
and sticks. Today, the modelling is carried out in computers. In the 1970s, Martin
Karplus, Michael Levitt and Arieh Warshel laid the foundation for the powerful
programs that are used to understand and predict chemical processes. Computer
models mirroring real life have become crucial for most advances made in chemistry
today. For instance, in simulations of how a drug couples to its target protein in the
body, the computer performs quantum theoretical calculations on those atoms in the
target protein that interact with the drug. Today the computer is just as important a
tool for chemists as the test tube. Simulations are so realistic that they predict the
outcome of traditional experiments.
⁄
ä
Fig. 3.25 (continued) Panel D, an example of the plot of ρ(R). Panel E, the potential of the trap and
the trap stiffness deduced from ρ(R), assuming that the density distribution obeyed the Boltzmann
distribution. In fact, the potential was approximated with quadratic function of R (x in the figure),
which implied the force exerted on the trapped bead was indeed spring-like (force is calculated from
the product of the stiffness of the trap and R). In this instance the stiffness was deduced to be
~0.01 pN/nm
3.10 Outlook of Molecular Dynamics
57
force, F, has characteristics of a spring: F ¼ kx, where k and x is the stiffness (spring
constant) and the amount of the shift of the sphere. Hence, if one can measure k and
x, one will know the magnitude of the force exerted on the sphere. Theoretical
calculations of the stiffness have been presented [28–31] and an example of the
experimental method to estimate the stiffness is given in Fig. 3.25.
With the above feature, the optical trapping technique has been widely used to
measure, for example, the force developed by a single motor force or protrusive
force of the cell edge (ie., lamellipodium). By utilizing infra-red laser beam, one can
manipulate intracellular objects, because the cell membrane is relatively transparent
to the infra-red laser beam [32]. Another advantage is that if the light is split by a
polarization beam splitter and each light is focused at two different focal points
separately, one can hold two objects at each focal point. The ability to separately
change the direction of the beam by two independent reflecting mirrors will enable
further applications. Some applications of the optical trapping are presented in
Chap. 7.
3.10 Outlook of Molecular Dynamics
Nobel Prizes in Chemistry for 2013 were awarded to Martin Karplus, Michael Levitt
and Arieh Warshel [33] for the development of multiscale models for complex
chemical systems. Chemists used to create models of molecules using plastic balls
and sticks. Today, the modelling is carried out in computers. In the 1970s, Martin
Karplus, Michael Levitt and Arieh Warshel laid the foundation for the powerful
programs that are used to understand and predict chemical processes. Computer
models mirroring real life have become crucial for most advances made in chemistry
today. For instance, in simulations of how a drug couples to its target protein in the
body, the computer performs quantum theoretical calculations on those atoms in the
target protein that interact with the drug. Today the computer is just as important a
tool for chemists as the test tube. Simulations are so realistic that they predict the
outcome of traditional experiments.
⁄
ä
Fig. 3.25 (continued) Panel D, an example of the plot of ρ(R). Panel E, the potential of the trap and
the trap stiffness deduced from ρ(R), assuming that the density distribution obeyed the Boltzmann
distribution. In fact, the potential was approximated with quadratic function of R (x in the figure),
which implied the force exerted on the trapped bead was indeed spring-like (force is calculated from
the product of the stiffness of the trap and R). In this instance the stiffness was deduced to be
~0.01 pN/nm
3.10 Outlook of Molecular Dynamics
57