Selection of th e Optimum Fraction

This section d escrib es two possible methods of determ ining an optimum fractio n based on e ith e r a co n stan t yield or purification factor, since e ith e r of th e se param eters may be more im portant.

purification fac to r for a given yield. The algorithm s ta r ts with th e yield line (eg. FE on fig u re 4.2) a t zero on th e total protein axis and th e end of th e tie line is a t th e point of th e c u rv e giving th e d esired yield. The purification fac to r for th is fractio n is calculated. The yield line is th en moved by an increm ent in th e total protein co -o rd in ate and th e purification fac to r recalculated. This process is rep eated until th e set yield can no longer be reached. The optimum fractio n will be th e fraction with th e h ig h est purification factor.

If yield is to be maximised th en th e purification facto r may be se t a t a c o n stan t value and th e maximum yield obtainable from th e fractionation c u rv e determ ined. This is c arried o u t by s ta rtin g a t th e origin and extending a tie -lin e with a g rad ie n t equivalent to th e purification factor se t to th e maximum total protein co -o rd in ate (ie. th e rig h t-m o st position). Where th is tie -lin e cro sses th e fractionation c u rv e co rresp o n d s to th e end point of a fractio n with th e desired purification factor. I t is possible th a t more th a n one fraction could exist which has th e same purification facto r. This is shown in fig u re 4.4. Here th re e possible fractio n s exist with th e same purification factor - one larg e fractio n which may be sp lit into two su b -fra c tio n s both with th e same purification factor. Although th e fractio n of p ro d u ct protein to total protein will be equivalent for th e se th re e frac tio n s th e actual composition of contam inating components will be d ifferen t. The fractio n with th e la rg e s t yield will clearly be a combination of th e two su b -fra ctio n s, b u t th is may not n ecessarily be th e most d esirab le fraction.

Having calculated th e yield for one s ta rtin g point th e tie-lin e is th en moved along th e total protein axis by a se t increm ent and th e process rep eated . The yield is calculated fo r each fractio n and th e optimum fractio n is defined as th e fractio n which gives th e h ig h est p ro d u ctiv ity for th e p re s e t purification factor.

The selection of th e optimum fractio n from th e fractio n atio n -co n cen tratio n diagram (or th e combination of two dimensional diagram s d escribed in section 4.1.3) may be c arried out in a similar way as fo r th e fractionation c u rv e (ie. e ith e r a purification facto r o r a p ro d u ctiv ity may be set) b u t since an additional param eter has been in troduced an e x tra optimisation c rite rio n m ust be introduced. This additional optim isation criterio n will e ith e r be a volume or a concentration limit which will affect both th e yield and volume param eters to g e th e r (since concentration is calculated from th e p ro d u c t yield and fractio n volume). Since it is likely th a t co n cen tratio n changes will be th e least im portant th e selection of th e

optimum frac tio n should u se concentration as th e least im portant param eter. T here should however be a concentration or volume th resh o ld , ie. a minimum (ie. a maximum volume) should be defined.

The ra n g e of possible fractio n s may be described by a volume shown in fig u re 4.5. The axes re p re s e n t th e volume of th e fraction, th e yield of th e fractio n and th e p u rity of th e pro d u ct. The volume axis will ru n from zero to th e total elution volume of th e sep aratio n and th e p u rity axis will ru n from zero to 100%. The yield axis will ru n from zero to th e maximum possible yield. The cuboid shape indicates th a t a t certain regions, ie. tow ards a c o rn e r of th e cube few er possible solutions exist with com parable c h a ra c te ristic s. This is as would be expected since th e co rn e rs re p re s e n t th e extreme conditions, ie. combinations of extrem es of two p aram eters sim ultaneously. Towards th e c e n tre of th e cube more p otential solutions exist which may be seen by th e g re a te r size of th e cube a t th is point. This shows th a t if more th an one param eter is co n strain ed to a h ig h er value th en th e potential num ber of fractio n s with th e se c h a ra c te ristic s is relativ ely small. C onstraints which may be imposed on th e quality and n a tu re of th e p ro d u ct fraction may also be added to th e fractionation diagram as shown in fig u re 4.5 (planes indicated by th e dotted lines). By plotting each of th e fractio n s which can be obtained th is diagram may be used as an aid in th e selection of th e b e st fractio n . Generally co rn er A is th e most desirable position and frac tio n s which lie closest to th is location should be selected as it c o rre sp o n d s to a combination of maximum p u rity and yield b u t minimum volume. The lea st optimum position is diam etrically opposite (corner B) which c o rre sp o n d s to a high volume, and low yield and p u rity .

The rela tiv e im portance of each of th e param eters volume, yield, and p u rity will depend upon th e aim and position of th e sep aratio n in a sequence. The n e a re r th e beginning of a sep aratio n th e more im portant is th e yield and th e less im portant is th e p u rity as th e yield in early pu rificatio n s te p s will affect th e overall efficiency of th e sep aratio n sequence. The p u rity may be gained in following ste p s b u t again a t th e expense of yield. The ran g e of volumes of th e fractio n th a t would be accep tab le is d ep en d en t upon th e ty p e of u n it operations which follow. Unit o p eratio n s which may typically follow an ion exchange chrom atographic sep aratio n a re gel filtratio n , freeze d ry in g , and u ltra filtratio n . All of th e se will be affected by v ariatio n s in th e volume of th e p ro d u c t frac tio n of th e preceding step . Of th e u n it operations listed gel filtra tio n is p a rticu la rly sen sitiv e to in creases in p ro d u ct fractio n volume

since th e capacity of a gel filtratio n column will be rig id ly fixed. If th e product fraction in creases above th e column capacity th en th is will req u ire an o th er ru n to se p ara te th e excess volume since it cannot simply be added to th e sta n d ard loading w ithout significantly affecting th e perform ance of th e separation. This would in crease th e processing time greatly - in excess of th e proportional in crease in processing volume. Similarly red u ctio n in process volumes a t th e end of a downstream process sequence is also im portant in term s of minimizing su b seq u en t loads on finishing operations such as free ze -d ry in g .

4.2 Effects of deconvolution accu racy on th e fractio n c u rv e

As described in section 2.2.5 and 2.2.2 th e accuracy of deconvolution will have an effect upon th e accu racy to which peak a re as a re determ ined. Since fractio n s a re su b seq u en tly selected using th e peak a re as as a basis, th e deconvolution accuracy will have an im portant effect upon th e actual p u rity and amount of p ro d u ct th a t is contained within th e fraction selected. The consequences of deconvolution accuracy on su b seq u e n t fraction selection and th e re s u lta n t fractionation diagram s a re discussed in th e following section.

As described in c h ap ter two sev erely overlapping peaks and overlapping peaks with g rea tly differing h eig h ts cause th e g re a te s t e rr o r s in th e determ ination of peak functions by deconvolution. From a stu d y of th e fractionation diagram s of th e te s t chrom atograms examined in c h ap ter 2 th e areas of th e fractionation c u rv e s which a re su b je c t to th e g re a te s t e rro r a re caused by th e same a re as of th e chromatogram which prove th e most problem atic in deconvolution, ie. th o se a re as of th e chromatogram which consist of more th an one peak function - p articu la rly where one peak is much taller th an th e o th er. In general th e maximum yield is found co rrectly as is th e maximum purification factor, th e main exception to th is is where a small cen tral p ro d u ct peak is overlapped by relativ ely tall contam inant peaks. This is because th e cen tral peak in th e model chromatogram may be su b je c t to excessive fro n tin g and tailing th u s causing th e area of th e peak to be la rg e r th an in reality .

The initial and final cu rv ed regions of th e diagram a re th e a re as most su scep tib le to e rr o r as th ey co rresp o n d to areas of th e chromatogram consisting of two or more component peaks (see fig u re 4.6).

Two example fractionation diagram s a re shown in fig u re s 4.6 and 4.7 th e f ir s t is for a chromatogram with a high d eg ree of overlap w hilst th e

second is for a chromatogram with relativ ely low overlap (both have similar peak heights). As can be seen th e c u rv e for th e second chromatogram has been more accu rately determ ined. The f ir s t was not deconvoluted satisfacto rily (see c h a p te r 2).