Proteomics/Protein Separations - Centrifugation/SOME FUNDAMANTAL PHYSICAL AND MATHEMATICAL CONCEPTS

1. Some fundamental physical and mathematical concepts
2. Centrifugal fractionation of tissues and cells: Basic approaches and instrumentation
3. Density gradient centrifugation: Preparing gradients and measuring density
4. Density Gradient centrifuation: Rate and isopynic separations of particles

Some fundamental physical and mathematical concepts

[1] "Molecular Biology Techniques Centrifugation"

• Gravity

It was Galileo Galilei (1564-1642) who first systematically and scientifically investigated gravity as a natural phenomenon. The gravitational acceleration constant is customarily assigned the symbol "g" and for simplicity taken to be 980 cm/sec sec. Newton showed that the force acting on a body undergoing constant acceleration is equal to the product of its mass and its acceleration that is,

         F = ma       // Force F = mass x acceleration

• Centrifugal Force

Consider an object P of mass m moving in a horizontal circular path at a constant speed (i.e, at a specific number of revolutions per unit of time and at a fixed distance x from the axis of rotation. Although the speed is constant, the direction of movement is continuously changing. Since velocity is defined in terms of the direction of motion, and this direction is changing, the velocity is continuously changing and the object is said to manifest constant acceleration. To restrict the movement to a circular path, a force must be exerted in a horizontal plane toward the axis of rotation. In the absence of such a force, the object would move off along a tangent to the circle. The force called the "centrifugal force" can be given as the same equation.

      F=ma.

• Relative Sedimentation Rate

Relative Centrifugal Force--gFORCE

Usually , the value cited for the force applied to a suspension of particles during the centrifugation is a relative one, that is to say it is compared with the force that the earth's gravity would have on the same particles.It is called relative centrifugal force (RCF)

      RCF = F centrifugation / F gravity 

CORIOLIS FORCE: In addition to centrifugal force, particles in suspension ( and the body of suspending fluid itself) within a spinning rotor are subjected to Coriolis force

The Coroilis force which results from the inertia of the liquid and the suspended particles, is a small force directed at the right angles to both the axis of rotation clockwise, the force acts to deflect particles in a counterclockwise direction (and vice versa). Under nearly all experiment conditions, the coroilis force is very small in comparison with the inertial force, its effects are magnified when the rotor's speed changes (e.g during acceleration and deceleration).

While the centrifugal force acts to accelerate a particle away from the axis of rotation, the radially sedimenting particle is also subjected to additional forces including frictional force, the force of buoyancy and gravitational force. Frictional Forces, Force of Buoyancy.

• The Sedimentation Coefficient

Sedimentation Coefficients of some biological particles differ greatly.The parameters determining sedimentation rate fall into three major categories:

(1) the physical conditions of centrifugation

(2) the nature of the suspending medium.

(3) the properties of the suspending medium( i.e its density and viscosity)

• Diffusion

Diffusion is the bulk movement of solute molecules or particles from a region of higher concentration to a region of lower concentration. Such a movement occurs as a consequence of random molecular motion or Brownian movement. Since the sedimentation of suspended particles is in effect a means of concentrating the particles, it is opposed by diffusion.