Sedimentation for determining molecular weight of macromolecules

Process of sedimentation with mechanism of action and mathematical derivations, different methods for separation of macromolecules by sedimentation, viscometry vs sedimentation

1. SEDIMENTATION BY : SHUBHANGI SURI B.tech student SMVD university, J&K

2. CONTENTS INTRODUCTION Macromolecules Characterization of macromolecules Various methods for determining molecular weight. Sedimentation or ultracentrifugation DISCUSSION Sedimentation basics Basic principle Mechanism of action Two methods of sedimentation Sedimentation velocity method Sedimentation equilibrium method CONCLUSION Sedimentation vs viscometry

3. INTRODUCTION

4. MACROMOLECULES Giant molecules. Large number of atoms are linked by covalent bonds. Term “macromolecules” was introduced by German Chemist Herman Staudinger and further significant contributions were made by P.J.Flory . Examples of macromolecules are proteins, starch etc.

5. CHARACTERIZATION OF MACROMOLECULES As these are made up of very minute atoms or molecules, so characterization of macromolecules is very difficult or rather impossible directly. No doubt, they form true solution, but large sized particles start settling down due to gravity, though very slowly. By using appropriate variant of technique, the molecular weight, density, shape etc. of macromolecule can be detected. For determining molecular mass, the various methods are:

6. SEDIMENTATION OR ULTRACENTRIFUGATION Macromolecules are almost insensitive to gravitational settling. So gravitational settling will be useless for separation or characterisation of macromolecules. By increasing gravitational potential energy by high speed rotation, characterization will be possible and the particles in solution sediment faster. i.e. Ultracentrifugation. Gravitational force + Centrifugal force. Applications range from collection and separation of cells, organelles, and molecules to study of molecular weight of macromolecules.

7. DISCUSSION

8. Sedimentation is tendency for particles in suspension to settle out of the fluid in which they are entrained and come to rest against a barrier. Due to motion of particles through the fluid in response to forces acting on them. Even a small molecules supply a sufficiently strong force to produce significant sedimentation. It is different from settling, as settling is falling of suspended particles through the liquid but sedimentation is termination of settling process. Svedberg and Nicols employed centrifuge first time. SEDIMENTATION BASICS

9. BASIC PRINCIPLE An object moving in a circle at a steady angular velocity will experience a force, directed outwards .

10. MECHANISM OF ACTION Particles are made to move by centrifugal force and distribution in concentration of particles along the length of centrifuge tube is determined at one or more times. A measurement made while the molecules are moving along the centrifugal axis called sedimentation velocity determination and the result is a sedimentation coefficient , that will give information about molecular weight and shape of particle. Also at sedimentation equilibrium density and composition can also be determined.

11. TWO METHODS

12. SEDIMENTATION VELOCITY METHOD Principle – Rate of sedimentation depends upon the size of particles. Mathematical derivation For any sedimenting particle, 2 forces act on it— i . Gravitational force, downwards = 4 [(d-d’)g  r 3 ]/3 ii. Oppositional frictional force = 6  rv where r=radius, d=density & v= velocity of sedimentation of particle, d’=density of solvent, g=acceleration due to gravity, =coefficient of viscosity of medium.

13. SEDIMENTATION VELOCITY METHOD Equating both forces , we get V=[2r 2 g(d-d’)]/9  ..........(1) If the level at a distance x from top travels dx distance in time interval dt , then velocity of sedimentation = dx / dt =V dx = { [2r 2 g(d-d’)]/9 } dt Integrating both sides within proper limits, i.e. L.H.S from x 2 to x 1 and R.H.S from t 2 to t 1 , we get

14. SEDIMENTATION VELOCITY METHOD dx ={[2r 2 g(d-d’)]/9  }  dt x 2 - x 1 =[2r 2 g(d-d’)(t 2 - t 1 )] /9  .........(2) Thus by knowing value of d and d’ and by measuring the distances x1 and x2 at two different times t1 and t2, r (radius) can be determined. Then we have mass of particle, m=(4 r 3 d)/3

15. SEDIMENTATION VELOCITY METHOD And molecular mass of macromolecule =N o m where N o is Avogadro number. This formula was not applicable unless suspended particles are large. So , Svedberg , who invented centrifuge overcome the problem by replacing g with acceleration due to centrifugal field given by , a=  2 x

16. SEDIMENTATION VELOCITY METHOD Hence , dx = { [2r 2 (d-d’)  2 x] /9 } dt dx /x= { [2r 2 (d-d’)  2 ] /9 } dt Integrating as before within same limits, we get Ln ( x 2 /x 1 ) = [2r 2 (d-d’)  2 (t 2 - t 1 )] /9  Using this equation molecular mass can be determined as before.

17. SEDIMENTATION EQUILIBRIUM METHOD Principle – When the solution is whirled for sufficiently long time in an ultracentrifuge, a stage is reached when the concentrations at different levels of solution become constant, known as “ sedimentation equilibrium.“ Mathematical derivation At sedimentation equilibrium, Rate of sedimentation=Rate of back diffusion

18. SEDIMENTATION EQUILIBRIUM METHOD If C1 and C2 are the concentrations at the two levels at distances x1 and x2 respectively, then Ln (C2/C1)={M  2 (d-d’) (x 2 2 - x1 2 )}/2RTd Where M=molecular weight of macromolecule, R= gas constant , T= absolute temperature. Thus by determining C1 & C2 at two levels x2 & x1 in the settling cell at sedimentation equilibrium, M can be easily calculated.

19. CONCLUSION

20. SEDIMENTATION VS VISCOMETRY By Sedimentation – sedimentation average molecular weight equivalent to mass average molecular weight. By Viscometry – viscosity average molecular weight equivalent to number average molecular weight.

21. THANK YOU