THEORY Basic Principles Rotation of an object about a central axis generates a centrifugal force upon the object. If the object in ques- tion is a molecule or particle of molecular weight M, then (S-1) centrifugal force = Mu?x where w is the angular velocity in radians/second (rad/sec) and x is the axis of rotation (ie., radial dis- tance from the center of rotation). Equation 5-1 dic- tates that the larger the molecule, or the faster the centrifugation, or the larger the axis of rotation, the greater the centrifugal force and the rate of molecular or particle sedimentation. ‘The considerations of Equation 5-1 hold through- out all media. However, biochemical experiments usu- ally are conducted with soluble systems. Two forces significantly counteract the centrifugal forces on solu- bilized molecules or particles. First, molecules or par- ticles must displace the solution media into which they sediment. Equation 5-2 Centrifugation (5-2) buoyant force = Mu?xVp describes this displacement or buoyant force. The symbol V is partial specific volume of the molecules or particles (i.e.,cc of solution volume increase caused by addition of 1 g of solute), p is the density of the solu- tion, and the other terms are as above. Equation 5-2 dictates that the higher the partial specific volume of the solute in question or the greater the density of the fluid being centrifuged, the slower the rate of molecu- lar or particle sedimentation. Second, dissolved or suspended molecules or particles generate friction as they migrate through the solution. Equation 5-3 (5-3) frictional force = iE) depicts this relationship where fis the frictional coeffi- cient unique to the molecule or particle in question and dx/dt is the rate of sedimentation expressed as change in the axis of rotation with time. Equations 5-1 to 5-3 can be used to derive a prac- tical relationship between the rate of sedimentation (dx/dt) and the molecular or particle weight (M). Asedimenting molecule ot particle moves faster and faster in a centrifugal field until the centrifugal force equals the counteracting buoyant and frictional force (Equation 5-4). centrifugal _ buoyant force force frictional Ge] force This occurs because the frictional force increases with increased rate of sedimentation, whereas centrifugal force and bouyant force are constant for any mole- cule and rotor speed. In practice, this balancing of forces occurs quickly with the result that a molecule sediments at a constant rate, (dx/dt) Substituting Equations 5-1 to 5-3 into Equation 5-4 and rearranging, you obtain Equations 5-5 to 5-7. (5-5) Mex = MutxVo + Ae ) (5-6) M(-Vp)otx = A) oe “am (1 ) If you define a new term, a sedimentation coefliccat, 5, a8 5 = (dx/dt)/u*x, substitution of this definition into Equation 5-7 yields Equation 5-8 SV) (5-8 = oy (1-Wo) The frictional coefficient, f, can be evaluated through an experimentally determined diffusion con- stant, D, where: \ absolute constant)( temperature} _ RT 5.9) D = \onstant/\temperature]_ AT © frictional coefficient =f or Substitution of Equation 5-9 into Equation 5-8 yields: (5-10) a DU-Vp) Equation 5-10 is the basis for velocity sedimentation analysis, in which the rate of sedimentation, expressed as the sedimentation coefficient, s, is used to evaluate the molecular weight, M, of the molecule or particle in question. Sedimentation coefficient, 5, units for biological macromolecules fall between 1 and 500 x 10-"? sec. Biochemists avoid the awkward unit of 10"? seconds by defining one Svedberg unit, or Svedberg (depicted by an S) as 1 x 10-! seconds. Thus single proteins have Svedberg values of 1-20 §, large nucleic acid molecules have Svedberg values of 4-100 S, and still larger subcellular particles have S values of 30-500 S. Centrifuge Applications Biochemists use two basic types of centrifuges: ana- lytical centrifuges and preparative scale centrifuges. Analytical centrifuges or analytical ultracentrifuges (the prefix ultra implies faster speeds and higher centrifugal forces) only work with small (<1 ml) sam- ples of dissolved or suspended solutes. Such centri- fuges also employ elaborate optical systems to analyze the progress of solutes during the centrifugation run, These analytical centrifuge applications are very sig- nificant to biochemists; for example, the applications of Equation 5-10 to determine molecular weights usually employ analytical ultracentrifuges. However, such sophisticated centrifugal applications are beyond the mission or capacity of an introductory course. In contrast, preparative scale centrifuges are cap- able of working with larger samples (10-2,000 ml). Preparative scale centrifuges also lack optical systems to analyze samples during the centrifugation run. Preparative scale centrifuges are necessary for many of the biochemical isolations or applications of this text; consequently, an understanding of their basic applications is fundamental to this course. Preparative Scale Velocity Sedimentation Centrifu- gation. Velocity sedimentation is the centrifuge appli- cation used most frequently in biochemistry. Usually this procedure employs a fixed-angle rotor operating at a given speed for a defined time (Figure 5-1). The practical considerations of fixed-angle rotor velocity sedimentation follow the principles of Equa- tions 5-1 to $-3. Each rotor type has a fixed potential axis of rotation dictated by the centrifuge tube holes in the rotor. Biochemists define the centrifugal force obtainable at any speed (i., rpm or w) in terms of the axis of rotation (i.¢., x) at the center of the angled centrifuge tubes. This leads to the “times gravity” con- vention in which the centrifugal force on a molecule or particle in the center of a tube in a given fixed-angle rotor rotating at a given rpm expressed as a relative centrifugal force in terms of gravity, such as 10,000 x gravity or 10,000 g. Tables relating speeds of rotors with relative centrifugal forces or times gravity valuesFill tubes two-thirds full Place equal weighted, paired tubes in rotor FIGURE 5-1 Velocity sedimentation in a preparative scale fixed angle rotor for the center of the centrifuge tubes are available for all centrifuges. Thus, use of the times gravity conven- tion facilitates adaptation of rotor speeds and times to match the centrifugal or gravity forces used by others with different rotors or centrifuges. All fixed-angle rotors also carry a designated maxi- mum speed rating, Operation of rotors at speeds in ex- cess of these designated maxima can result in “rotor ex- plosion” (i.e., disintegration) with possible great harm 10 the centrifuge and people nearby. Last, preparative 10,000 x g supernate Centrituge at 10,000 x g for 10 min Decant —> Ficune 5-2 Differential centrifugation. Cover rotor with id > | aD Decant with precipitate ‘on lower side of tube Centrifuge at specified rpm for specified time scale centrifuges may contain a constant temperature refrigeration system to minimize loss of biological ac- tivity and reduce disruptive convective effects caused by temperature differentials. The higher-speed pre- parative ultracentrifuges also usually employ vacuum systems that minimize air friction in the rotor chamber and resultant temperature fluctuations. Fixed-angle rotors are frequently used in a kind of preparative scale velocity sedimentation called differ- ential centrifugation. Figure 5-2 depicts the process on 30,000 x g supernate or $-30 Centrifuge at 30,000 x g for 30 min Decant aea sample containing suspended particles of two sizes. As can be seen, successive centrifugations at increas- ing speeds or gravity forces resolve different sus- pended materials or particles from each other and from a supernatant fraction. Supernatant fractions obtained after specific centrifugation are frequently ‘abbreviated with the prefix S, which refers to the supernate obtained after a certain 1,000 times gravity centrifugation. Thus, the supernate obtained after the 30,000 X g centrifugation of Figure 5-2 is a $-30 frac- tion, and so forth. (Note: Do not confuse the prefix S Use gradient former to make gradient Centrifuge at desired rpm for desired time CoS a SS a “eames a symbol of superate fractions with the S symbol of Svedberg values, which appears after a number.) Differential centrifugation will readily fractionate or resolve different subcellular particles of cells from each other. Table 5-1 depicts a generalized pattern of differential centrifugation for the resolution of cellular and subcellular fractions from tissue or cellular homogenates. ‘The final 100,000 x g supernate (S-100) fraction therefore generally represents the truly soluble frac- tion containing soluble proteins and small molecules. Layer sample on top of gradient = a Place sample in a swinging bucket Attach swinging bucket to rotor ee, FIGURE 5-3 Use af swinging bucket rotors in gradient centrifugation,ABLE 5-1 eneralized centrifugation conditions to sediment specitic ells or particles (consider in terms of successive ‘entrifugations at listed increasing g forces.) Jentrifugation conditions Fractions sedimented 1000 x g, § min 4000 x g, 10 min Most eucaryotic cells, Chloroplasts Most eucaryotic cell debris Most cell nuclei Mitochondria Bacteria Lysosomes Most bacterial cell debris Ribosomes and polysomes 18,000 x g, 20 min 30,000 x g, 30 min 00,000 x g, 3 hrs Table 5-1 lists both the relative centrifugal forces ind the times required to sediment the various cellu- ar components. That is, sedimentation involves an nterrelationship of both g force (ie., rpm) and time. fyou know the specificrpm for a given rotor to obtain utequired or specified g force for a specified time, you van use equation 5-11 new time] ( ‘0 determine an equivalent (yet possibly more con- venient) longer time at a lower g force, or a shorter $-11) fa sraaiel time ead 2 ( Centrifugal force Different samples nitial sediment reterogenous at varied sample layered rates on gradient FIGURE 5-4 Steps of density gradient sedimentation. time ata higher g force. Note that Equation 5-11 holds for rotors with specified axes of rotation. Thus, Equa- tion 5-1] may not be used to interrelate time and rpm between different rotor types. Gradient Centrifugation. Most preparative centri- fuges will accommodate one or more different swing- ing bucket rotors for use in gradient centrifugations. Figure 5-3 illustrates the basic principles of swinging bucket rotors. Swinging bucket rotors can be used in two ways during gradient centrifugation: in density gradient sedimentation and in equilibrium density gradient centrifugation. Let’s consider each application in turn. Density gradient sedimentation is a form of velocity sedimentation. First the sample is layered on top of a linear or exponential gradient of dissolved inert organic material, such as sucrose or glycerol. The inert gradient agent both stabilizes the fluid environment of the centrifuge tube and facilitates sharp resolution of zones of the centrifuge fluid in the tubes after the centrifugation. Thus, as seen in Figure 5-4, a hetero- gencous band of molecules or particles of different sizes sediments into the gradient following the rules of sedimentation velocity. After resolution within the gradient, the increasing density of the gradient fluid Puncture and drain tube from bottom (the gradient assures serial fractionation) Puncture tube, Resolution s of samples displace sample at end of out the top by pumping in dense sucrose mm centrifugation Dense sucroseSample einer = layered 2 conto ; gradient of Spin Sample migrating to its own density Dispensed throughout Sample gradient accumulated. at its density in the salt gradient FIGURE 5-5 Equilibrium density gradient centrifugation. facilitates the fractionation, so that each layer is re- solved free of the less dense fluid above or the more dense fluid below. This method is very useful in pre- parative procedures, and it also can be used to deter- mine molecular weights of soluble enzymes or proteins (see Martin and Ames, 1961). Equilibrium density gradient centrifugation differs from density gradient sedimentation in two ways. First, equilibrium density gradient centrifugations employ denser salts solutions, (e.g., cesium chloride) that have densities spanning those of the biological molecules to be resolved. Second, the sample under- goes lengthy centrifugation so that the dissolved so- lutes accumulate at their own equilibrium densities within the salt gradient as a result of the sedimenting centrifugal force and the counteracting buoyant den- sity of the higher salt solution (Figure 5-5). This process is called isopycnic centrifugation. Such a reso- lution can be an analytical tool: for example, DNAs accumulate at densities of ~1.7 g/ml, whereas RNAs accumulate at densities of ~1.9 g/ml. Further, such equilibrium density gradient centrifugation may be performed in a preparative scale centrifuge (as in Figure 5-5) or it may be performed in an analytical ultracentrifuge (see Meselson and Stahl, 1958). -6-EXPERIMENT ON CENTRIFUGATION EXPERIMENTAL PROCEDURES Materials Fresh spinach (Spinacia oleracea) leaves Cold isolation buffer (=0.3 M sorbitol; 0.1 M Tris-Cl. pH 7.8: § mM MgCl; 10 mM NaCl) Blender Beaker Funnel Glass rod Cheesecloth Centrifuge tubes (4 tubes of 50 mL: 4 tubes of 10 mL) Balance Centrifuge Ice Paint brush Graduated cylinder of 10 mL Parafilm Acetone (90 %) Spectrophotometer Spectrophotometer cuvettes Procedure for isolation and concentration measurement of chlorophyll 1) Weigh out 40 gr of fresh spinach (Spinacia oleracea) leaves from which the major veins have been removed. 2) Tear the leaves into smal] pieces and place them in a blender with 200 mL of cold isolation buffer. 3) Blend the mixture at low speed for 10 seconds. Use a glass rod to push any tissue pieces down the sides of the jar into the solution. and blend for 10 more seconds. 4) Filter the homogenate through 8 layers of cheesecloth into a beaker. Add approximately 40 mL of filtrate to each of four centrifuge tubes (30 mL), making sure they are balanced (¥ 0.1 gn). 5) Centrifuge at 4°C for 5 minutes at 1000xe, 6) Decant and discard the supernatant from all 4 tubes. Add 0.5 mL of cold isolation buffer each tube and gently resuspend the chloroplasts with a paint brush 7) Store the centrifuge tube on ice, away from bright light. 8) Add 0.05 mL (=50 iL) of the chloroplast suspension to a clean glass conical centrifuge tube, ape9) Use a graduated cylinder to measure out 7.5 mL. of 90% acetone, add to the centrifuge tube, cover tightly with Parafilm and invert several times to dissolve the chlorophyll. A flocculent precipitate of protein should be visible. 10) Remove the protein by centrifuging for 2 minutes at about $00xg. The protein should form a pellet at the bottom of the tube. Pour the supernatant (acetone extract) into a clean tube and discard the tube containing the pellet. 11) Pour some of the supernatant into a clean spectrophotometer cuvette. Read absorbance of your sample at 652 nm using a blank of 90% acetone. If the absorbance reading is greater than 1.5, dilute your sample with 90% acetone until its absorbance below 1.5. Record how much additional acetone was added. 12) Use the equation below to determine the concentration of chlorophyll in your chloroplast sample: Chlorophyll (mg/mL) = absorbance x total vol.(mL,) of acetone used x 0.029 vol.(mL) of suspention used IMPORTANT NOTE: Clean cuvettes and tubes and other lab items before leaving the laboratory.