Chemist’s speech and his book “Networks of Interacting Machines”

Prof. Mikhailov is a chemist. He went to my nstitute to give a talk how to design a molecular machine. Since Nano-technology is booming and now people know lots of new knowledge how to make new material in the nanoscale. However, it is still almost a dream for the most researchers to design artificial molecules which will work exactly like a functioning protein. So it becomes almost a holy grail for many physicists, chemists and nano-engineers to make artificial molecule machines. Prof. Mikhailov is an active researcher in this field and he has some new ideas about this issue. (he will be the International Solvay Chair in Chemistry 2009). He published a book about “Networks of Interacting Machines”, in which some simple models are used to demonstrate some results which are not intuitive at all.

Fig.1 Book of interacting machine

Design principal of molecular machines

The essential task of biophysics is to explain the life process from the first principle of chemistry and physics. As the molecular machines to perform various functions in the life process, proteins play an important role in life. If we can understand proteins well, then we are almost nearly reaching some important goals of understanding life. With the development of new technology of the microscopy of the dynamics of single molecule[1, 2], people can see clearly the conformation relaxation of single-molecular motor triggered by binding with ligand and departing from it later. For example, after a macromolecule with a catalytic site (blue ball) is binding with a ligand (red ball), it begins to bend its upper component due to the electrostatic or hydrophobic force. When the ligand finally touches the catalytic site, it is converted into some new molecules and released into the environment. The macromolecule returns to its balanced state through conformation relaxation, see Fig. 2. This process can go on for ever, and the macromolecule can perform certain tasks (for example, walking on the microtubule like Myosin or Kinesin) as long as there are enough ATP in the solution nearby. To understand how the chemical energy is converted to mechanical energy and how efficient this molecular machine is for a tiny motor in this scale, we need to build a non-equilibrium physical model of the macromolecule to understand this process. Also we could apply the principles which we find in the bio-molecules to the design of artificial molecular machines.

Fig. 2 The process of the conformation relaxation of single-molecular motor triggered by binding with ligand

Modeling dynamics of molecular motors with coarse-grain model

However, since the proteins usually have about 200-300 amino acids and its conformation relaxation is in the time scale of mini-seconds, it is totally impossible to build a molecular dynamics models in the atom-level to obtain the protein dynamics in this time scale. Because MD models can usually simulate the process in the time scale of pico- or nanoseconds. A coarse-scale model is adequate to give us slow motion dynamics which is relevant to the biological functions of the macromolecule. Togashi and Mikhailov used an elastic network model to compute the dynamics of an artificial molecular machine⁵. The working circle of a molecular motor triggered by binding and detaching with ligand is shown in following Fig. 3.

Fig. 3 Working circle of a molecular machine

In their paper, they also show that any random force perturbation of the real molecular motors will rapidly converge to a unique trajectory of conformation relaxation to back to the equilibrium state. While the randomly connected structure will have messy trajectories which lead to several sub-equilibrium state.

Fig. 4 Converged trajectory for real molecular motors and non-converged trajectories for random molecular structures

Questions unanswered for molecular machine design

Supposing the ligand is ATP and the protein is Myosin, this process is to convert the chemical energy of ATP to the mechanical energy to drive the myosin to walk on the microtubule³. We also assume the system is in the solution with constant room temperature. Because this process is far away from the equilibrium, the work done by the myosin will be influenced by the loading scheme of the macromolecule. We should ask the questions:

• The conformation change caused by macromolecules binding with ligand is nonlinear, large deformation. Linear elastic network model is not applicable. A new type of model need to be developed.

• From this model we should understand how the chemical energy is converted to kinetic energy in the circle: Ligand binding → deformation → chemical reaction → detachment → relaxation.

• We also should do some theoretical analysis: Is there relationship between the molecular structures and its maximum power output? For the real molecular motors, such as Myosin, does it achieve its maximum power?

• What’s the influence of thermal noise in environment upon the molecular machine? What’s the hydrodynamic influence upon the molecular machine?

• Most important of all, some experiments should be done to measure:

• - Deformation of the Macromolecules-ligand complex. Does it agree with theoretical prediction?

• - Molecule motor efficiency. We need to compare it with theoretical Prediction as well.

Reference:

¹ Eddy Arnold and Stefan G. Sara_anos. Molecular biology: An hiv secret uncovered. Nature, 453:169_170, May 2008.

² Giovanna Ghirlanda. Computational biochemistry: Old enzymes, new tricks. Nature, 453:164_166, May 2008.

³ Frank Julicher, Armand Ajdari, and Jacques Prost. Modeling molecular

motors. Reviews of Modern Physics, 69:1269, October 1997.

⁴ Udo Seifert. Entropy production along a stochastic trajectory and an integral Fluctuation theorem. Physical Review Letters, 95:040602_4, July 2005.

⁵ Yuichi Togashi and Alexander S. Mikhailov. Nonlinear relaxation dynamics in elastic networks and design principles of molecular machines. Proceedings of the National Academy of Sciences, 104:8697_8702, May 2007.