Use of Multivariate Statistical Analysis in the Modelling of Chromatographic Processes

Transcription

1 Use of Multivariate Statistical Analysis in the Modelling of Chromatograhic Processes Simon Edwards-Parton 1, Nigel itchener-hooker 1, Nina hornhill 2, Daniel Bracewell 1, John Lidell 3 Abstract his aer rooses a method currently under develoment that uses a combination of Princial Comonent Analysis (PCA) modelling and grahical reresentation techniques to raidly develo and otimise chromatograhic searations. PCA is used to extract key characteristics from a searation and modelling is then based on the relationshis of these characteristics. In the roosed method a set of lab exeriments are analysed by PCA to define the key characteristics and the relationshis and further runs are generated from this. Utilising PCA and a small set of large scale runs the modelled data can then be scaled u to the larger scale. he data is analysed using grahical techniques to quickly identify oerating conditions offering the best comromise between yield and urity and the otimum oerating conditions are chosen from this. he PCA modelling allows for a large number of otential oerating conditions to be generated in a small time frame using limited lab time and material and the use Analysis of the data using the grahical techniques can be used to raidly highlight the otimum oerating conditions. Introduction Chromatograhic searations are widely used in the bioharmaceuticals industry due to the high degree of urification ossible using a series of chromatograhy stes. Regulatory authorities often require a minimum of two such searation stes be emloyed in the manufacture of rotein based harmaceuticals (Walsh, 1998). A range of techniques exist to develo and otimise chromatograhy searation stages. here is a comromise inherent in all of these methods. he greater time sent in develoment the greater the otential yield from each stage and the overall system. On the other hand additional time sent may reduce the sales eriod under atent rotection. his aer introduces a method for analysis of chromatograhic searations using a combination of modelling using Princial Comonent Analysis (PCA) and grahical reresentation methods. ogether these allow for raid develoment and otimisation of the chromatograhic searation. he first stage uses rocess modelling based on PCA to cature key searation characteristics from lab scale data and subsequently to exand the data and to scale the data to a larger scale of oeration. he second stage of the rocess involves the use of grahical techniques to reduce the comlexity of the data analysis through conversion to a format that enable the comromises between degree of urification and yield of the roduct to be seen. hese techniques highlight small but imortant differences in searations that are difficult to observe from the original data chromatograms. he method has the otential to generate a large number of runs and then aly raid analysis to find the otimum run based on requirements of urification, yield and robustness of the searation at the chosen rocess conditions. In this aer a samle chromatograhic rocess in which three rocess variables may be altered is examined. A set of exeriments is carried out at small lab scale chosen as art of a 4x4x5 results matrix. he remainder of this matrix is then modelled using PCA. Finally a small set of runs are carried out at large scale and PCA modelling is used to extraolate the small lab scale results to the larger scale. In this way a large data set of runs can be generated with limited lab time and material usage. he data can then be raidly analysed using grahical techniques to find the otimum rocess conditions based on yield and urification criteria. he next section details the basis of PCA and its alication to modelling chromatograhic searations. his is followed by a section that describes the grahical reresentation techniques. he final section describes the combined system using the above techniques and outlines the benefits of the roosed methodology. 1 Advance Centre for Biochmemical Engineering, Deartment of Biochemcial Engineering, UCL, London, UK 2 Deartment of Electronic and Electrical Engineering, UCL, London, UK 3 Avecia Biologics, Billingham, UK

2 Princial Comonent Analysis (PCA) his section gives a brief introduction to PCA, its alications and the imortance of data rerocessing rior to PCA. he second art of the section covers the alication of PCA to chromatograhy modelling and secific re-rocessing of chromatograhic data. PCA heory PCA was develoed as a tool be used in the analysis of large amounts of data by reducing the number of variables used to characterise the data by establishing relationshis between the original variables (Wold and Sjostrom 1998). PCA has been alied across a range of areas including sychology, biology and chemistry and has reviously been used as an analysis tool for chromatograhy. PCA works by identifying a series of key characteristics of a multivariate data set, called rincial comonents. Analysis of the relationshi between the rincial comonents can then used to increase understanding of the data. Multivariate data consists of observations or exeriments on several different variables. Data for rocessing is reresented as a n x matrix of n observations for each of the variables, giving an n x matrix, X. he secific formulation for chromatograhic PCA will be discussed shortly. When alied to matrix X, PCA creates a new smaller set of variables from the data that catures as much variance in the original variable set as ossible. he new variables are called rincial comonents, with the first comonent caturing the most variance and each following comonent caturing the largest amount of residual variance. Figure 1 shows a samle data set with 100 observations and three variables X, Y and Z. As can be seen the oints line u on a lane so in this case the PCA will adjust itself to the axis of this lane with the first comonent assuming the axis that catures the most variance, the second comonent will cature the next lower variance axis. he rincial comonents are orthogonal to each other, as with traditional co-ordinate axis. Z Y X Figure 1 Samle dataset where PCA is alied. he number of variables has been reduced from three to two with the first comonent caturing the most variance and the second comonent caturing the remaining. Each rincial comonent is made u of two column vectors, the scores vector, t i, and the loadings vector i. he loadings vector translates the original data axis to those of the rincial comonent, while the scores show how much of each observation is measured based on the new rojected axis.

3 o cature all of the variance from a data set the number of comonents will equal the number of variables (n). his is shown in Equation 1, where all the variance is catured by a series of rincial comonents resented in a decreasing variance format. X = t1 1 + t t Equation 1 In Equation 1 the lower rincial comonents only reresent a small amount of the variance of X, and tend to reflect slight changes in the data set often related to errors or background noise. An alternative is to reresent the system without the inclusion of these comonents, Equation 2 shows a system characterised by two rincial comonents. X = t 1 + t E 1 Equation 2 where E is the remaining variance attributed to error or random noise in the data. Data Pre-Processing o obtain the maximum insight from PCA the data must be adjusted rior to analysis. A range of methods can be used although mean centring of the data is recommended for all cases. Mean centring of the data entails calculation of the mean for each variable then deducting this from the variable values for each observation. his has the effect of focusing uon the deviations from the mean and therefore investigating variance from the mean data rather than the data as a whole. his imroves the level of resolution achieved and reduces the number of rincial comonents needed to characterise a system. Peak Alignment When PCA is alied to a series of chromatograhic eaks it has been found that the analysis imroves when the matching eaks for each run are aligned, Pate et al (1998). his is due to the way that PCA comares the measurements for each run. In the case where the eaks are aligned the comarison between oints is based on the same offset from the eak centre. his allows the PCA to analyse better the eak shae. In the case where the eaks are offset the analysis for the eak shae is hindered as one eak centre is comared to the offset from the eak centre for another run. his requires the PCA also to formulate a series of rincial comonents to account for the change in eak osition, increasing the number of comonents and the comlexity of the interaction between scores. Previous alication of PCA for analysis of chromatograhy (Malmquist and Danielsson, 1994) has used dynamic adjustment of the axis, where the time or volume axis is stretched or comacted to align the eaks. Although successful for analysis, reversal after modelling is comlex. he method roosed in this aer searates the chromatogram into its individual eak comonents then aligns each eak individually by altering each eaks centre osition to the mean for that eak across the set of runs. Peak searation is achieved using the Gaussian equation to define the shae of each individual eaks. Various standard rograms can be used to give the otimum Gaussian shaes of each comonent, such as the FIYK curve fitting software (Marcin Wojdyr, Poland) Princial Comonent Analysis Modelling PCA has reviously been used in conjunction with chromatograhy to aid in roduct analysis (Malmquist and Danielsson, 1994) and was alied by Pate et al. (1998, 1999 and 2004) for the modelling of chromatograhy. he model roosed in this aer is based on that of Pate but exands its use to rovide a caacity for modelling additional runs at the same scale and for more comlex searations using curve fitting techniques to model comonent eaks. he basic aroach is to use a small set of exerimental runs to generate the redictive basis for the modelling of further runs. When alied to a set of chromatograhy runs the observations, n, relates to the runs, while the variables,, refer to the measured absorbance at a secific time or volume throughut. PCA aims to condense the reresentation of each run from the measured absorbencies to a much smaller set of rincial comonents. hese rincial comonents can then be calculated and converted back to the original variable set, the absorbencies. Figure 2 shows an examle of a mean chromatogram and the loadings for a single eak system. he mean chromatogram (Fig 2a) gives the basic outline of the system. he PCA loadings are adjustments that can be alied to the eak and will alter its shae. he first comonent added to the centred array will increase eak height and narrow the eak (Fig 2b), while the second comonent reduces the eak height while widening the eak (Fig 2c). By adding a certain amount of each comonent to the mean chromatogram a range of chromatograms can be modelled. he scores for each run define how much of each comonent loading it is necessary to add to the mean chromatogram.

4 Figure 2 Examle of PCA alied to a single eak. (a) shows the mean data, (b) gives the first rincial comonent loadings, (c) shows the second rincial comonent loadings. he model uses the comarison of scores at two rocess values. Figure 3 shows a samle set of exerimental runs for a model. In this case flow is the rocess value and a series of runs are carried out at two different flow rates for varying salt gradients. he sets of data corresonding to the two flow rates have PCA alied searately. he scores for the aired runs at the two different flow rates can then be used to define a relationshi between the scores at the different flow rates. So for examle the scores for the run at an eight column volumes salt gradient at the lower flow rate can then be used to generate the corresonding scores at the higher flow rate. he generated scores can be combined with the known loadings at the higher flow rate and added to the mean chromatogram at the higher flow rate to obtain a modelled run for the 8 column volumes salt gradient and at the higher flow rate. Salt Gradient 5cv Modelled 11cv 14cv Flow 1cv.min -1 Paired Runs Salt Gradient 5cv 8cv 11cv 14cv Flow 0.5cv.min1-1 Figure 3 Samle data used in Princial Comonent Modelling. Paired runs at 5, 11 and 14 column volume salt gradient are used to initialise the model based on the Princial Comonent scores. he score at the lower flow rate for the 8 column volumes salt gradient can then be used to generate the matching run at the higher flow rate. he variable the model is alied across, i.e. flow as shown in Figure 3, can be a rocess variable such as loading, salt gradient or H, or a system variable such as column bed height. he relationshi between the scores at the two variable values does not have to be between the same rincial comonents. For examle the first comonent may correlate best to the second comonent at the other flow rate. he scores across all comonents must therefore be tested to define the otimum relationshis between the scores. his can be done through calculation of the correlation

5 coefficient for each airing of scores and selecting the combinations that gives the greatest overall correlation coefficient. o obtain the correct eak location as well as shae the value for the eak alignment can be generated in the same way as the PCA scores to allow the model to redict accurately the eak osition as well as the eak shae. As can be seen in the examle above with the requirement of one unaired run for each modelled run lus additional initialisation runs the best ratio of modelled runs to exerimental runs achievable is just below one to one. o obtain the maximum use from the PCA modelling multile iterations are carried out using the revious stages modelling result as art of the initialisation ste for the following stage. his roduces a much higher ratio of modelled runs to exerimental runs than if PCA was alied as one ste using just the exerimental runs. Additional Data Modelling In many cases data such as key rocess contaminants like endotoxin and rdna, are required in addition to the raw chromatograhic data. his allows for a more detailed analysis of the searation. his kind of additional data can be aended to chromatogram data after time adjustment but rior to centring of the data. his more comlete set of data will then be analysed by PCA and relationshis between eak shae and these variables are defined. his data can then be extracted after the reverse centring oeration but rior to the time adjustment. In the case of scale-u the data may not be resent at both scales, as small scale lab exeriments may be such that insufficient material is available to rovide for assays as well as chromatograhic searation data. he model will therefore relate the eak shaes at the smaller scales to the additional data and eak shaes at the larger scale. Model Workflow Figure 4 shows a reresentation of the model workflow. he flow starts with a series of exeriments, from which the individual eak rofiles are calculated and then aligned. he mean eak is then deducted from each eak rofile to give the variance for each eak from the mean. he data then has PCA alied and the aired scores are used to define relationshis at different rocess values. Unaired runs are then used to generate additional scores. hese modelled scores are recombined with the loadings to give the variance from the mean chromatogram for the modelled runs. he mean chromatogram is added to give the eak shae and the time adjusted value is then generated similar to the scores and the eak location adjusted to this value. o give the modelled comonent eaks, these can then be converted to concentration rofiles, or recombined to allow viewing of the absortion chromatogram.

6 Lab Scale Exeriments Absortion Chromatograms Conversion o Individual Peaks ime Alignment Mean Centring Of Data PC1 Loadings Large Scores Large Scores PC1 Loadings E1 PC1 Scores Small Scores Small Scores PC1 Scores Combined With Mean Peaks o Obtain Peak Shae Reversal of PCA to Generate Centred Data Generation of PCA Scores for additional runs Comarison and Model Initialisation of PCA Scores PCA of Data Large imes Large imes Small imes Small imes Correlation For ime Adjust Values Modelling of ime Adjust Values Reverse ime Adjust Peaks Figure 4 Workflow for Princial Comonent Analysis Modelling. Grahical Reresentation At this stage of the methodology a large data set of chromatograhic runs has been generated. he next set in the method uses grahical techniques analyse the data to obtain the otimum rocess variables based on secifications on yield and degree of urification. he techniques exlored are a series of grahical reresentations of chromatograhic searations (Ngiam et al. 2002). his section introduces the basis of these so-called fractionation and maximum urification versus yield diagrams, describes their uses and methods of creation. Fractionation Diagrams A fractionation diagram is a grahical reresentation that shows the change in the total amount of rotein during chromatograhic searation eluted versus the amount of target rotein eluted. his reresentation has the effect of reducing the multile eak chromatogram to a single oerating curve. o roduce the fractionation diagram the concentrations of the comonents of the searation must first be known either using an on-line assay, if one is available, or by using the corresonding off-line data. he chromatogram is then fractionated into N stes with equal width on a time or volume basis. For each interval a time t is defined as 1 t = t + t Equation 3 2 m ( ) I II where t I is the lower time limit and t II is the uer time limit. hese can then be used to calculate the total fractional mass eluted as well as the fractional mass of roduct eluted.

7 Fractional mass of material eluted, X Equation 4 Fractional mass of roduct eluted, Y Equation 5 A samle diagram is shown in Figure 5. = = Cumulative mass of otal mass of Cumulative mass of otal mass of material eluted at time t material eluted at time t =! roduct eluted at time t roduct eluted at time t =! Figure 5 Samle fractionation diagram. he x-axis shows the change in total amount of comonent eluted, in this case rotein, and the y-axis shows the total amount of target comonent eluted. he steeness of the curve shows the degree of searation that can be achieved, the steeer the curve the more target roduct is being eluted relative to the total rotein, and therefore a higher degree of urity is being achieved. he amount of material eluted on the y-axis shows the yield that can be achieved at this level of urification. Maximum Purification Factor versus Yield Diagrams he maximum urification versus yield diagram is a rogression from the fractionation diagram that shows the maximum degree of urification for each value of the yield. he urification factor is defined as the ratio between the final urity of the load roduct after urification comared to the reurification samle. PF = Final Purity Intial Purity & M = $ $ % M (2) (2) ' M ' M (1) (1) #!!" & M $ % M 0 s #! " Equation 6 M s is the total amount of roduct and M 0 is the total amount of the target comonent. Subscrits P and S reresent the amount of roduct comonent and samle, resectively. Suerscrits (1) and (2) are the oints of the starting and end collection times, resectively. Rearrangement gives

8 (2) (1) & M # ' M & M PF = $! $ $ % M 0 ' M 0!" % M M / M s and / M 0 where (2) S M ' M (1) s #! " M P resectively define the x-axis and y-axis from the fractionation Equation 7 diagram. Equation 7 can therefore be seen as the gradient on the fractionation diagram between any two cut oints on the chromatogram. Calculation of the PF and the yield for every combination of two oints from the fractionation diagram rovides a range of urification factors for each yield. he maximum urification for each yield can then be calculated to calculate the maximum urification factor versus yield diagram. Figure 6 shows a tyical maximum urification factor versus yield diagram. Such a diagram may be used to highlight the comromise between the extent of urification against the yield achieved by the searation. Once the maximum urification factor and yield have been selected from the curve the cut oints that corresond to these values can be found by tracing back through the above rocess to obtain the cut oints on the time axis. Figure 6 Samle Maximum Purification versus Yield diagram showing three searations. Searation 3 offers the lowest overall urification, Searation 2 offers higher urification at higher yields, Searation 1 offers higher urification at lower yields. When used to aid in comaring effects of changing rocess variables, multile searations are lotted on the same diagram to highlight the differences between searations. In the case of Figure 6, searation 3 offers the lowest urification for any yield, while searation 2 offers a better urification for the high yields but at lower yields searation 1 offers better urification factors. By comaring the curves obtained with slight changes in rocess variables the effect of small alterations in oerating conditions on the extent of urification and yield can be demonstrated. his allows for investigations into the robustness of a system. Princial Comonent Analysis and Grahical Reresentation echnique his section describes the combined method using rincial comonent analysis modelling and diagrammatical reresentations, highlighting the advantages of this aroach and ossible alications. o show a ossible alication of this method a matrix of runs based on changing three variables will be used. he otential of exeriments matrix is of size 4x4x5. Figure 7 shows the chromatograhy

9 searation design and otimisation system. wenty-two runs are required, eighteen small scale runs are carried out. By using several stages of PCA modelling these are extracted to generate a resulting array of 80 runs. At the larger scale other data such as levels of endotoxin and rdna removal may be available. his is not usually available at the smaller scale due to limitations on the material needed for such of assays. he large scale runs are then aired with the smaller scale runs to initialise the scaleu model, the unaired small scale runs are then modelled u to the large scale. he resultant large data set can then be analysed using the maximum urification versus yields diagrams to select the otimum combination of oerating conditions. From there the cut oints to obtain the best urification for the chosen yield may be selected. Small Lab Scale Exeriments 18 Runs Exansion PCA Modelling 80 Runs Large Lab Scale Exeriments 4 Runs Scale U PCA Modelling 80 Runs Maximum Purification versus Yield Diagrams Fractionation Diagrams Figure 7 Workflow combining Princial Comonent Analysis modelling and grahical reresentation techniques. A series of 18 small scale lab runs are combined with a set of 4 large scale runs to obtain information on 80 runs at large scale. his data is then analysed using the grahical techniques to define the otimum oerating conditions for the searation. he use of PCA modelling for the exansion of limited data sets and scale u modelling makes the best use of this technique, enabling a small amount of time and material usage on the lab based exeriments to yield a valuable rediction of a large number of runs at large scale. Small scale runs have traditionally been of limited use for design and otimisation due to the roblem of taking fractions for further analysis and the imact of extra-column effects altering the shae of the chromatogram in comarison to runs obtained at a larger scale. PCA modelling allows for the generation of the fractionation data as art of scale u modelling and rovides for the removal of the effects of extra column effects such as mixing in ie work. he method generates a large amount of data. Alication of the grahical techniques and additional data on contaminants from the large scale trials can be used to raidly exclude searations based on the following criteria: 1) Product requirements: remove searations that do not meet the minimum roduct secifications such as maximum endotoxin levels. 2) Remove searations that fail to achieve a minimum maximum urification. In the case of Figure 6 Searation 1 can be excluded as it offers a low urification at all yields comared to the other runs. 3) Selection is then based on the comromise between degree of urification and yield. his allows for selection of the otimum oerating conditions and the cut oints to achieve the chosen yield and urification. Conclusion his aer rooses an alternative to lab based rocess design and otimisation of chromatograhic searations. It uses Princial Comonent Analysis (PCA) modelling to obtain a large result set in a small time frame and using a selected sub-set of small scale lab runs and a targeted grou of large

10 scale runs. his has the effect of reducing the amount of materials needed comared to conventional aroaches and increases the amount of data available. Grahical reresentation techniques are used as an efficient way to reresent key comromises between yield and degree of urification. hey, in effect, reduce the comlexity of the data while highlighting imortant factors related to the searation. his allows for detailed analysis of large data sets in a short eriod. he combination of the above methods allows for more detailed analysis of chromatograhy searation for otimisation and oeration while keeing to the strict timelines required for rocess develoment. References Walsh, G (1998), Bioharmaceuticals: Biochemistry and Biotechnology, Wiley, Chichester, UK Wold, S.; Sjostrom, M (1998), Chemometrics, resent and future success. Chem. and Intel. Lab. Sys., 44, 3-14 Malmquist G, Danielsson R (1994), Alignment of Chromatograhic Profiles for Princial Comonent Analysis: a rerequisite for finger rinting methods. J. Chrom. A, 687, (1998) Pre-Processing of chromatograhic data for rincial comonent analysis. Bioroc. Eng., 19, Pate, M. E.; hornhill, N. F.; Chandwani, R. M.; Hoare, M.; itchener-hooker, N. J. (1999) he use of rincial comonent analysis for the modelling of high erformance liquid chromatograhy. Bioroc. Eng., 21 (4), Pate, M. E.; hornhill, N. F.; Chandwani, R. M.; Hoare, M.; itchener-hooker, N. J. Pate, M. E.; urner K..; hornhill, N. F.; itchener-hooker, N. J. (2004) Princial Comonent Analysis of Nonlinear Chromatograhy. Bioroc. Eng., 20, Ngiam, S. H, Zhou Y.H., urner M.K., itchener-hooker N.J., (2001) Grahical Frameworks For Facilitating he Study of Chromatograhic Searations, J. Chrom. A,