In preparative and industrial chromatography, the current viewpoint is that the dynamic binding capacity governs the process economy, and increased dynamic binding capacity and column utilization are achieved at the expense of productivity. The dynamic binding capacity in chromatography increases with residence time until it reaches a plateau, whereas productivity has an optimum.
Trang 1Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/chroma
Touraj Eslamia, b, Martin Steinbergerc, Christian Csizmaziaa, Alois Jungbauera, d, ∗,
Nico Lingga, d, ∗
a Department of Biotechnology, Institute of Bioprocess Science and Engineering, University of Natural Resources and Life Sciences, Vienna, Muthgasse 18,
Vienna A-1190, Austria
b Evon GmbH, Wollsdorf 154, A-8181St., Ruprecht an der Raab, Austria
c Institute of Automation and Control, Graz University of Technology, Inffeldgasse 21b, Graz A-8010, Austria
d Austrian Centre of Industrial Biotechnology, Muthgasse 18, Vienna A-1190, Austria
a r t i c l e i n f o
Article history:
Received 13 June 2022
Revised 3 August 2022
Accepted 12 August 2022
Available online 13 August 2022
Keywords:
MPC
Protein A
Linear driving force model
Mechanistic model
Linearization
EKF
a b s t r a c t
Inpreparativeandindustrialchromatography,thecurrentviewpointisthatthedynamicbinding capac-ity governsthe processeconomy, and increased dynamicbinding capacityand column utilization are achievedattheexpenseofproductivity.Thedynamicbindingcapacityinchromatographyincreaseswith residencetimeuntilitreachesaplateau,whereasproductivityhasanoptimum.Therefore,theloading stepofachromatographicprocessisabalancingactbetweenproductivity,columnutilization,andbuffer consumption.Thisworkpresentsanonlineoptimizationapproachforcapturechromatographythat em-ploysaresidencetimegradientduringtheloadingsteptoimprovethetraditionaltrade-off between pro-ductivityandresinutilization.TheapproachusestheextendedKalmanfilterasasoftsensorforproduct concentrationinthesystemandamodelpredictivecontrollertoaccomplishonlineoptimizationusing theporediffusionmodelasasimplemechanisticmodel.Whenasoftsensorfortheproductisplaced beforeandafterthecolumn,themodelpredictivecontrollercanforecasttheoptimalconditionto max-imizeproductivityandresinutilization.Thecontrollercanalsoaccountforvaryingfeedconcentrations Thisstudy examinedthe robustnessas thefeed concentration variedwithinarangeof50% The on-lineoptimizationwasdemonstratedwithtwomodelsystems:purificationofamonoclonalantibodyby proteinAaffinity andlysozymebycation-exchange chromatography.Using thepresentedoptimization strategywith acontrollersaves upto43% ofthe bufferand increasesthe productivitytogetherwith resinutilizationinasimilarrangeasamulti-columncontinuouscounter-currentloadingprocess
© 2022TheAuthor(s).PublishedbyElsevierB.V ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/)
1 Introduction
The prevailing view in preparative and industrial chromatogra-
phy used to capture a biomolecule from a feedstock is that the
dynamic binding capacity governs the process economy, and in-
creased dynamic binding capacity and column utilization are ob-
tained at the expense of productivity The dynamic binding ca-
pacity in column chromatography increases with increasing resi-
dence time until it approaches a plateau, whereas productivity has
an optimum and the column utilization remains low Therefore,
∗ Corresponding authors at: Department of Biotechnology, Institute of Bioprocess
Science and Engineering, University of Natural Resources and Life Sciences, Vienna,
Muthgasse 18, Vienna A-1190, Austria
E-mail addresses: alois.jungbauer@boku.ac.at (A Jungbauer),
nico.lingg@boku.ac.at (N Lingg)
the loading step of a chromatographic process requires a balancing act between productivity, buffer consumption, and resin utilization [ 1, 2]
The column utilization, productivity, and buffer consum ption are interrelated, and higher column utilization leads to a decrease
in the buffer consumption and productivity [3] The column uti- lization and throughput can be optimized by employing strate- gies of counter-current loading with two or more columns [4–8] Two main categories of approaches have been studied for optimiz- ing the loading The first approach, called off-line optimization [9– 11], applies a model-based optimizer to analyze the system’s be- havior under different conditions to anticipate the optimal setting, and the obtained solution is validated experimentally In the sec- ond approach, called online optimization, the system is evaluated and optimized at each time increment of the process to fulfill the requirements [12–14] In this technique, the optimizer uses recent
https://doi.org/10.1016/j.chroma.2022.463420
0021-9673/© 2022 The Author(s) Published by Elsevier B.V This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )
Trang 2measurements and considers all quality constraints and limitations,
then it generates a new control command at each iteration to di-
rect the process to the optimal operating point [15–19]
Ghose et al [20] used the off-line optimization methodology
and presented a dual-flow-rate strategy for the loading phase They
discovered that the productivity and resin utilization rate improve
by loading the column at a low residence time and then increasing
it to a higher level They used a model-based optimizer to eval-
uate the best switching time between the initial and final resi-
dence times This strategy was expanded recently [ 11, 21] by intro-
ducing the multi-flow-rate approach, which applies multiple opti-
mization techniques to successfully improve the productivity while
maintaining resin utilization at a high level However, it is worth
noting that off-line optimization suffers from reduced robustness
through experimental errors, since it requires a thorough under-
standing of the dynamics of the system Additionally, due to the
nature of off-line optimization, the system cannot cope with any
change in the process conditions or any unforeseen disturbance
Therefore, it may lead to suboptimal results and require iterative
optimization
Model predictive control (MPC) has become a prominent non-
linear control strategy for online optimization over the last two
decades [ 15, 22–25], and it incorporates concepts from systems
theory, system identification, and optimization [26] Compared to
commonly employed controllers, such as PID controllers, MPC is an
advanced control method that effectively deals with nonlinearities,
constraints, and uncertainties [ 12, 27] Moreover, MPC can control
systems that cannot be controlled by conventional feedback con-
trollers [28] The main goal of MPC is to estimate a future trajec-
tory of the process in the control horizon window to optimize the
system’s future behavior [29] Complimentary reviews on the ad-
vantages and principles of MPC, either linear or nonlinear, are pro-
vided by Qin and Bagwell [30–32]
In this work, the MPC controller is built on a computationally
efficient mechanistic model, linear driving force with a pore diffu-
sion model [33], to anticipate the adsorption in the column Since
this model is highly nonlinear, a linear approximation of the sys-
tem that corresponds to the general equation with the same be-
havior is required to enable use within linear MPC Various meth-
ods for linearization can be found in the open literature, including
piecewise linearization [34] to transform the model into multiple
linear parts Another robust technique is to approximate the linear
format of the system with Taylor expansion at each timing cycle
at a steady-state point [14] The current work uses successive lin-
earization to approximate the linear model at each operating point
Toward this end, the extended Kaman filter (EKF) as a soft sen-
sor is used to adaptively estimate the state of the column at the
operating point The EKF incorporates the information embedded
in the local models into a global description of the nonlinear dy-
namics and performs state estimation by tracking transition online
[ 34, 35]
We have expanded our previous study [11]by utilizing a MPC
and an EKF to optimize the experiments in batch mode [36–39]
We assessed the performance of the controller by IgG capture with
protein A and lysozyme with cation exchange resin Our objective
of applying such a strategy is to exploit the maximum benefits of
the process by increasing productivity and resin utilization, regard-
less of any potential discrepancy between the experimental data
and the corresponding model The MPC requires an additional sen-
sor for product concentration, which can be a simple UV sensor in
the case of pure material or a soft sensor for crude material [40–
42] Additionally, we examined the process performance under an
extreme change of concentration at the inlet of the column and in
the presence of white noise Therefore, at each time step, the con-
troller employs integrated real-time data with the process model
to predict the future dynamics of the system over a finite predic-
tion horizon ( N p) The MPC generates a sequence of control inputs over a finite control horizon ( N c) to fulfill the process objectives It
is worth mentioning that the first element of this sequence will be applied to the system at each time step In this way, the controller requires limited prior knowledge to optimize the process, such as
an approximation of porosity and the adsorption isotherm There are advantages when using this strategy; primarily, the system can cope with the aging of the adsorbent, since the Kalman filter can provide a good approximation of the system at each timing step This will also reduce lab work requirements, since the number of characterization experiments would be limited in scope [43]
2 Process control via model predictive control
This section presents the mathematical model that describes the system at each timing cycle We first describe the basics of the principle of mass transfer into the column, then we explain the implementation of the model predictive controller in detail
2.1 Mathematical modeling of the process
The mass transfer into the column chromatography was pre- dicted using an empirical approximation model known as the lin- ear driving force (LDF) model, given by Eqs.(1)and (2)[33] This model considers the movement of solute molecules in the column due to convection and axial dispersion Moreover, the overall ef- fective mass transfer coefficient is calculated using pore diffusion
to account for the intraparticle mass transfer resistance, shown by
Eq.(3) The Langmuir isotherm has been used to relate the average product concentration in the solid phase, q, to the average concen- tration in the mobile phase, C, as given by Eq.(4)
∂C
∂t = D ax∂2C
∂z 2 −εf A
∂C
∂z −(1−εc)
∂q
∂t =K
¯q− q
(2)
K =15D e
r 2
p
C F
q max
(3)
¯q=k eq q max C
where t and z are the process time and the position along the column, respectively; D ax is the axial diffusion; A is the column cross-sectional area; ε and εc are the total porosity and interpar- ticle porosity, respectively; f is the volumetric flow rate; K is the overall mass transfer coefficient obtained from the pore diffusion model; q and ¯q represent the average concentration in the sta-
tionary phase and the adsorption isotherm, respectively; D e and p
are the effective diffusivity of the protein solution and the resin particle radius, respectively; C F is the feed concentration at the in- let of the column; q max is the maximum column capacity; and k eq
is the Langmuir equilibrium constant It is important to mention that the pore diffusion is the primary controlling mechanism for protein liquid chromatography; therefore, the effect of axial disper- sion is neglected (D e =0 ) in our work [33] We successfully imple- mented this model in our prior work to approximate the general adsorption of protein with different types of resin [11]
The mass transfer Eq.(1) is a partial differential equation To solve this equation numerically, the method of lines (MOL) was used to discretize the column in the space domain using N g grid points [44] As a result, a set of N gordinary differential equations is generated to approximate the mass transfer into the column Addi- tionally, the backward Euler method is used to discretize the con- vection term, given by Eq.(5)[44]
∂C
∂z =C i − C i−1
z , i =1, 2, , N g−1 (5)
Trang 3C t(z =0)=C F (6)
∂C
∂z
z=L
Where z is the distance between two consecutive grid points,
and L is the axial length of the column Eqs.(6)and (7)describe
the Dirichlet and Neumann boundary conditions at the column’s
inlet and outlet Eq.(6)states that the concentration at the inlet of
the column is equal to the concentration of the stock solution C F,
and Eq.(7)indicates that the concentration change at the outlet is
independent of time Moreover, Eq.(8)is the initial condition and
indicates that the column is empty at the beginning of the process
This work examines three economic factors in the process, in-
cluding the resin utilization RU, productivity P r, and buffer con-
sumption BC:
RU = DBC 10%
V10%
0 (C F − C)dv
V (1−ε ) q max
(9)
t load10%+t rest
BC = V bu f f er
DBC 10%
(11) where t load
10%is the time required to reach 10% of the breakthrough
curve during the loading phase, and t rest and V bu f f er respectively
indicate the total time duration and the total volume of buffer con-
sumed in the washing, eluting, cleaning in place (CIP), and column
regeneration phases
2.2 Control approach
There are numerous ways to apply a model predictive control
framework to a system with linear and nonlinear equations This
work uses a discrete-time state-space representation of the model,
which is a well-established technique with MPC [28]
In general, all the time-dependent ordinary differential equa-
tions can be expressed in the compact form shown in Eq (12),
where the time derivative of the states, x NL ∈ R n, is dependent on
the value of the states and other independent variables:
dx NL
where x NL is the vector of states, u NL ∈R N u is the control input
vector, and θ are unknown parameters The output of the system
is given by y NL ∈R N y Eq.(12)is called the state differential equa-
tion, and Eq.(13)is the output function that is measured from the
sensory system [45]
In this work, f is the nonlinear function corresponding to
Eqs (1)–(4) The vector of states, x, contains c and q
x NL =c
q
The control input, u, is scalar (N u = 1 )and represents the flow rate,
and θ is the system noise The concentration of the product at the
outlet of the column ( C i=N g) is y and is scalar The system repre-
sented by Eqs.(12)and (13)is converted into a linearized discrete-
time form, as shown in the following sections
2.2.1 Linearization
In the state-space model, the process model can be formulated
as a function of states (x) and control input (u)[46]
dx
dt = A c x (t )+B c u (t )+D c w (t ) (14)
where A c ∈ R n ×n, B c ∈ R n ×m, and C c ∈ R r ×n are linearized matrices
related to states, the control input, and the output Eqs (12)and (13) in the linear differential equation format In this work, the feed concentration ( C F), which is the boundary condition at the in- let, is considered to be variable in time; therefore, another term,
w(t), is added to Eq.(14)to handle this variation Accordingly, D∈
R n ×n is a matrix resulting from the linearization of Eq. (12)with
respect to this variation
We use the first-order Taylor expansion to linearize the sys- tem’s model To achieve this, each point is considered to be a vari- ation around the linearizing point [47]:
where x Lin, y Lin, u Lin, and w Lin correspond to the values of the in- ternal states, measurement at the outlet, control variable, and con- centration at the inlet at the linearizing point, respectively, and x,
y, u, and w are the related variation variables The nonlinear for- mat of the aforementioned variables is indicated by the subscript
NL Consequently, based on the Taylor expansion, the linearized form of the model at each timing cycle can be represented as in Eqs.(14)and (15)
A c, B c, and D care the Jacobian matrices of the state function f
( Eq (12)) with respect to states x, control input u, and the con- centration at the inlet C F, respectively Accordingly, the matrix C cis the Jacobian matrix of the output function g (Eq.(12)) with respect
to x
A c=
⎡
⎢
⎣
∂ f1
∂ x1 · · · ∂ f1
∂ x n x
.. ...
∂ f n x
∂ x1 · · · ∂ f n x
∂ x n x
⎤
⎥
In brief, A ccan be expressed as A c = ∂ f
∂ x Similarly, B c = ∂ f
∂ u , D c =
∂ f
∂ w, and C c = ∂ g
∂ x
It should be noted that adsorption into the column does not reach the steady-state point; therefore, successive linearization around the operating point instead of the steady-state point is ap- plied in this study
2.2.2 Time discretization
The equations obtained from linearization are in a continuous- time domain Thus, in order to use the linearized equations in the discrete model predictive control framework, they must be trans- formed to the discrete time domain:
where k is the iteration index The system matrices in the discrete- time domain are given by A d =e A c T s , B d =A−1c (e A c T s − I)B c , D d =
A−1c (e A c T s − I)D c, and C d =C c These matrices are obtained by con- sidering the sampling time constant, T s, and applying the zero- order hold sampling technique [14]
3
Trang 4Fig 1 The extended Kalman filter (EKF) layout
2.2.3 Extended Kalman filter
A dynamic approximation of a nonlinear system Eqs.(12) and
(13)in the presence of additive noise can be formulated as in [36]:
ˆ
ˆ
y k=G
ˆ
x k
where x and y are the extended Kalman filter estimations of inter-
nal states and inputs Function F depends on the previous states
x k−1 and control input u k−1, and function G is the measurement
function related to the current state Also, μk−1 and vkare white
noise terms with zero mean and covariance matrices Q and R, cor-
responding to the model and measurement errors, respectively
In general, the dynamic estimation of a nonlinear system
Eqs.(12)and (13)with the Kalman filter algorithm consists of two
stages: prediction and correction First, the states and covariance
matrix are predicted at the prediction stage, based on the mea-
surement and the model at the previous iteration (k-1):
ˆ
x p k= F
ˆ
x u
k−1, u k−1
(22)
The variable P k pis the predicted matrix of error covariance, and
f j ,k−1 is the Jacobian matrix of F at the previous iteration (k-1)
Then, these values are corrected at the correction step to minimize
the covariance of the estimation At this stage, the Kalman gain is
generated based on the calculated prediction of the error covari-
ance matrix and the measurement noise to correct the predicted
states:
˜
y ek f ,k= y k − G
ˆ
x k p
(24)
K k=P k p H T
j ,k−1
R +H j,k−1 P k p H T
j ,k−1
−1
(25) ˆ
x u
k= x ˆk p+K k y ˜ek f ,k (26)
P k u=
I − K k H j ,k−1
where y ek f ,kis the measurement residual and is equal to the differ-
ence between the actual measurement, y k, and the output estima-
tion, G(x k p); matrix K k is the Kalman filter gain; x u
k is the optimal local estimation of states at the current step; and P u
k is the covari- ance of the estimation error for the next timing cycle This calcula-
tion sequence is repeated for each timing cycle, with the previous
estimated states and covariance as the input The related flowchart
is shown in Fig.1 The major difference between the extended and
the classical Kalman filter is the use of the Jacobian for lineariza- tion Thus, this set of equations can also be applied to the classical Kalman filter in linear systems
2.2.4 Model predictive controller (MPC)
MPC consists of two main parts Initially, it predicts the system based on the model formulation and then commences optimiza- tion using the obtained prediction MPC optimizes the system by finding a control input sequence ( u k) over a finite control horizon (N c) that minimizes the cost function over a prediction horizon (N p) In general, the prediction horizon is larger than the control horizon (N p ≥ Nc) This sequence of prediction and optimization recurs at each iteration to ensure the objectives and constraints are fulfilled
The linear time-invariant (LTI) prediction of the system over the prediction horizon is formed on the linearized state-space equation Eqs.(18) and (19) However, it is common to replace the control input with its incremental change, letting u k= u k−1+ u k, u k+1=
u k+u k+1 =u k−1 +u k +u k+1, resulting in the following: ˆ
ˆ
x k+2= A x ˆk+1+Bu k+1+Dw k=A
A x ˆk+Bu k−1+B u k+Dw k
+B (u k−1+u k+u k+1)+Dw k = A 2x k+(A +I )Bu k−1
+(A +I )B u k+B u k+1+(A +I )Dw k (29) and so forth, until the Np-th prediction is reached for the whole prediction horizon Then, as a result, Eq.(29)can be rewritten as ˆ
x k+N p= A N p x k+
A N p−1+· · · +A +I
B u k−1
+
N c
j=1
A N p − j+· · · +A +I
B u k+j−1
+
A N p−1+· · · +A +I
˜
The newly represented variable y k+N p is the predicted output
at the end of the prediction horizon N p Additionally, u k+j−1 in- cludes the variation in flow rate over the control horizon N c, con- sidering the flow rate at the last timing cycle, u k−1 The unknown ( u k+j−1) is found by an optimizer locating the optimum point of the process and fulfilling the constraints
2.2.5 Derivation of a convex cost function for online optimization
Since the flow rate has a significant impact on the economics
of the process, and any variation will significantly influence the
Trang 5breakthrough curve [11], the flow rate is considered to be the ma-
nipulated variable in this work Furthermore, as mentioned earlier,
the aim is to maximize productivity Pr ( Eq.(10)) and resin utiliza-
tion RU (Eq.(9)) Thus, a combination of productivity and resin uti-
lization is considered in the cost function to be maximized at each
timing cycle ( Eq.(32))
In the present study, the cost function is defined based on the
normalized value of resin utilization and productivity, given by
Eqs.(33)and (34):
RU norm= RU − RU min
RU max − RU min
(33)
P r norm= P r − P r min
where P min and RU max are the minimum productivity and maxi-
mum resin utilization at the lowest flow rate (LB) bound, respec-
tively Similarly, P max and RU min refer to the maximum productiv-
ity and the minimum resin utilization at the highest bound of the
flow rate (HB)
The combination of productivity and resin utilization ( Eq.(32))
results in a concave function; therefore, its negative sign is con-
sidered for the optimization In addition, to penalize any abrupt
changes in the control input sequence and to ensure a smooth
breakthrough curve at the outlet, an additional term is included
in the cost function to weight the u over the control horizon N c
Costfunction: J =−w Ru RU norm − w Pr P r norm+
N c
i=1
u T R u
(35) Decisionboundaries: DV B =[DV B Lb , DV B Hb] (36)
where RR N p ×N pis a positive definite weighting matrix for the vec-
tor u, and w Ru and w Pr are the weighting parameters for pri-
oritizing resin utilization and productivity ( w Ru +w Pr =1 ) R kept
constant, while w Ru and w Pr are changed according to the experi-
ment priorities
DVB refers to the boundaries of the decision variable ( Eq.(35)),
and DV B Lband DV B Hbrefer to the minimum and maximum admis-
sible flow rates (LB and HB)
3 Materials and methods
3.1 Experimental setup
Lysozyme was purchased from Sigma-Aldrich (St Gallen,
Switzerland) Polyclonal IgG was a kind gift from Octapharma (Vi-
enna, Austria)
A prepacked 1 mL cation exchange column with Toyopearl SP
650 M resin from Tosoh corporation (Sursee, Switzerland) was
used for the lysozyme experiment The diameter and length of the
column are 0.8 and 2 cm, respectively In this category of experi-
ments, the column was equilibrated with 5 CV of 20 mM sodium
phosphate buffer and eluted by 5 CV of 1 M sodium chloride,
where both were at pH 7, and the flow rate was set to 5 mL/min
Clean in place (CIP) was performed by 1 CV of 1 M sodium hy-
droxide solution with 10 min residence time A stock solution of
1.43 g/l lysozyme was used in these experiments
Experiments with IgG were conducted by a 1.26 mL column
with MabSelect PrismA protein A chromatography resin (Cytiva,
Sweden) The diameter and length of the column were 1 cm
Fig 2 Schematic depiction of chromatography workstation
and 1.6 cm, respectively The equilibration, elution, wash, and CIP buffers are the same as those used in Eslami et al [11]
An Äkta Avant 25 (Cytiva, Sweden) chromatography workstation was used for these experiments System pump-B was used to in- ject the sample, and two UV sensors at 280 nm were used to mea- sure the protein concentration at the inlet and outlet of the column ( Fig.2)
3.2 Process control
All the experiments in this work were performed with the Äkta Avant 25 workstation To perform the online optimization, a cen- tral supervisory control and data acquisition (SCADA) system is required to capture the online data and control the system ac- cordingly [48] Unicorn, the software that shipped with Äkta, was not usable for online optimization Therefore, we used XAMControl (Evon GmbH, Austria) software for this aim XAMControl is com- posed of management, SCADA, and field levels At the management level, the operator has the ability to monitor the online/historical data and control the operating stations through the graphical user interface (GUI) This graphical user interface is connected to the field level, including the actuating and sensory systems via the SCADA system
The key aspect of XAMControl is its compatibility and con- nectivity with the SCADA system, since all the standard commu- nication protocols (including OPC UA/DA, TCP) are well defined within the software Furthermore, since XAMControl is based on the PLC and C# programming languages, it is capable of communi- cating with different programming languages such as MATLAB and Python As a result, a world of optimization methods that have al- ready been established can be applied [ 11, 14, 49] Here, the Äkta Avant 25 was controlled by XAMControl via the OPC DA communi- cation protocol
4 Results and discussion
It has been shown that flow-rate gradients during the load- ing phase is a strategy for overcoming the trade-off between pro- ductivity and resin utilization [11] However, this approach re- quires a large number of experiments to determine the conditions where productivity and resin utilization are beyond the maximum achieved by constant loading velocity Therefore, our controller was tested for two different cases, lysozyme and antibodies, either with constant feed or varying feed concentration
This work obtained q max, D e, and k eq by fitting the experimen- tal data at constant residence time with the simulation data, ex- cept the porosity values were acquired from an experiment with
Trang 6Table 1
Model parameters for the cation exchange and affinity chromatography experiments
L ( cm ) ε c ε k eq ( ml/mg ) D e r p ( μ m ) C F ( g/ml ) q max ( g/ml )
Fig 3 Comparison of lysozyme loading at constant residence time with the model
predictive controller (MPC); breakthrough curves in the (A) time and (B) volume
domain, respectively The solid lines with filled symbols represent breakthrough
curves, and the dash-dotted lines represent the related flow rates with hollow sym-
bols The black lines correspond to the breakthrough curves at the highest and low-
est constant flow rates (HB and LB levels) The fuchsia line is the breakthrough
curve with the highest productivity at a constant flow rate (OPT CONST) The red,
blue, and green solid lines represent the breakthrough curves with MPC
a pulse injection of acetone and blue dextran The obtained values
from the fitting and the porosity values are reported in Table1
4.1 Online optimization in cation exchange chromatography
To compare the outcome of the online optimization with the
conventional strategy, 10 experiments were conducted with a con-
stant loading flow rate to cover a wide range of residence times,
from 0.1 to 10 min corresponding to the flow rate from 10 to
1 mL/min Productivity and resin utilization were determined at
10% of the breakthrough curve ( Fig.3) to fully define the relation-
ship between these factors when using a constant flow rate dur-
ing loading The productivity was plotted versus resin utilization in
Fig.4 This is the base case for what is achievable with a constant
flow rate during the loading phase
Three experiments with changing flow rate on a cation ex-
changer were conducted, using the MPC to optimize the load-
Fig 4 Productivity versus resin utilization of loading of lysozyme on CEX resin
Blue circles are the experimental data at constant residence time, and the square symbol indicates the process at maximum productivity with constant flow rate (OPT CONST) The upward-pointing triangle sign indicates the MPC-1 experiment The di- amond and the asterisk represent the MPC-2 and MPC-3 experiments, respectively
Table 2
Weighting factors for resin utilization and pro- ductivity
Number of experiments
Weighting factors
w Ru w Pr
ing of lysozyme Productivity and resin utilization were differently weighted according to the factors in Table 2 The loading condi- tions were entirely controlled except for the starting condition, which was derived from the maximum delta pressure over the col- umn Moreover, at the lowest flow rate (LB), the resin utilization
by constant flow rate is at a maximum, equaling 93% Therefore, MPC optimizes the process based on the model and the measure- ments at each sampling time ( T s =5 seconds) by updating the flow rate between the HB and LB levels Prediction and control horizons are set at 2 and 0.5 min ( N p = 24 T s and N c = 6 T s) The choice of sampling time in practice is dependent on the calculation capac- ity of the operating computer and the dynamics of the process to
be controlled This means that the sampling time has to capture the main dynamics of the process In our case, a sampling time of
5 is used since it is the minimal possible sampling time that can
be used in our specific experimental setup to solve the optimiza- tion problem Moreover, the longer sampling time will change the sensitivity of the closed feedback loop since less inter-sample be- havior is considered and the actuating signals are sparser in the underlying optimization problem
4.1.1 Constant feed concentration
One chromatographic run was conducted at the highest pos- sible flow rate (10 mL/min) so that the maximum pressure drop (HB) was not exceeded This is the first boundary condition for the
Trang 7Fig 5 Buffer consum ption com parison of the breakthrough curves at a constant
residence time with online optimizer MPC The black and purple bars describe the
experiments at the constant flow rate, the purple bar shows the experiment at the
OPT condition, and the black bars are the experiments at the highest and lowest
flow rates (HB and LB) The red, blue, and green bars are related to the experiments
with the online optimizer MPC
MPC The lowest flow rate (LB) was chosen (1 mL/min) to reach
the highest resin utilization possible; in our case, this was 93%
Therefore, MPC optimizes the process by calculating a new flow
rate from the [LB, HB] interval at each timing cycle by solving the
optimization problem at Eqs.(35)and (36), with the three sets of
weighting factors from Table2
The resin utilization for the high and low flow rates are 40.5%
and 93.9%, while the productivity is 1.06 and 1.02 mg min−1.mL−1,
respectively In the experiments with constant flow rate, the pro-
ductivity is maximized where the resin utilization is 68% (OPT
CONST in Fig.4)
It is noteworthy that the performance and sensitivity of the MPC controller are heavily dependent on the choice of prediction and control horizons In general, longer horizons offer significant performance benefits [ 50, 51], because the future (predicted) sys- tem behavior is included in the solution of the underlying opti- mization problem A longer prediction horizon will increase the performance considerably, while the length of the control horizon yields to more flexibility in the solution finding due to the larger number of optimization variables [50] Therefore, increasing these constants will improve the performance of the controller but will increase the computational effort drastically and can cause an in- tractable computational task The used prediction model gives an upper limit for the prediction horizon Since any model is an ap- proximation for describing the main dynamics of the process, pre- diction errors will increase with larger horizons Thus, a balance has to be found for the actually implemented horizons In this work, N pand N care defined based on the offline simulations The experiments with MPC resulted in resin utilization of 48.8%, 83.8%, and 90% and productivity of 1.30, 1.66, and 1.6
mg min−1.mL−1 for MPC-1 to MPC-3, respectively ( Fig 4) Accord-
ingly, when the resin utilization is weighted equal or higher than the productivity, the MPC results in higher productivity and resin utilization than the optimal condition at constant loading (OPT CONST) With the highest weight of resin utilization, we could reach 90% resin utilization where the productivity is still higher than the experiment at a constant flow rate with the optimal condition In addition, the buffer consumption is reduced by 44%
at MPC-3 experiment compared to the OPT CONST experiment ( Fig 5) This indicates that our MPC strategy can achieve simi- lar productivity and resin utilization compared to a multi-column counter-current loading strategy [52]
4.1.2 Variable feed concentration
Four experiments with the MPC-2 settings were performed
to handle the concentration change at the column inlet
Fig 6 Online optimization of four experiments with variable feed concentration, each row represents an individual experiment in time and volume domain, at the left and
right column, respectively The red dashed lines with triangle symbols represent the concentration of the product at the inlet of the column The solid black lines are the concentration at the outlet of the column The dotted blue line indicates the flow rate of each experiment
7
Trang 8( Figs 6 and 3) The protein solution is injected from the system
pump-B line, and the equilibration buffer from system pump-A
was added to the inlet flow by a random percentage during the
loading phase Accordingly, the concentration at the inlet started
from zero and then increased to the maximum level ( C / C f=1 );
at this point, the concentration varied randomly by changing
the percentage of buffer-B and its step length Additionally,
two UV monitors measured the inlet and outlet concentrations
continuously before and after the column, as shown in Fig.2
In these experiments, the concentration at the inlet between
two successive iterations was considered to be constant by MPC
Furthermore, the resin utilization was calculated for 60% of the
breakthrough instead of 10%, allowing a more prolonged observa-
tion Naturally, when the breakthrough has appeared, it will be-
come sharper as the inlet concentration increases Therefore, as
demonstrated in Fig 6, the controller instantly reduced the flow
rate to save on resin utilization when the inlet concentration has
reached the maximum level
In addition, in Experiment (1), the flow rate reduction rate was
higher than in the other experiments, since the inlet concentration
was maintained at the highest value for a longer duration Note
that the maximum column capacity was considered to be constant
Our approach can accommodate changes in binding capacity over
time, e.g through fouling or ligand degradation [53], since we ac-
count for the discrepancy between the actual data and the mathe-
matical model and mitigate this at each timing step Such a control
strategy can be used to automate prolonged continuous processes
when feed concentrations are not constant Although, if the feed
material is crude, a soft sensor at the inlet is required to measure
the amount of target protein to be used within the MPC controller,
as demonstrated by others [ 34, 39–41] Additionally, the ability to
vary the flow rate while maximizing productivity and resin utiliza-
tion can be used to correct a mismatch of flow rates between unit
operations or to adjust the volume in surge tanks after pauses Fi-
nally, this demonstrates that the MPC controller is able to derive
optimal process conditions, even if the input parameter of the feed
concentration is highly variable and that this transient behavior
does not lead to instability of the controller
4.2 Online optimization in affinity chromatography
The loading of IgG on a high-capacity resin, Mabselect PrismA,
was used to assess the performance of the controller in affinity
chromatography Here, the weighting factors for productivity and
resin utilization in the cost function ( w Ru and w Pr) are the same
as those in the experiments with cation exchange chromatography
( Table2) However, to validate the repeatability of the results, we
performed triple experiments for each weighting factor; the related
breakthrough curves can be found in the supplementary material
Two experiments at constant flow rate, HB and LB, together
with three experiments with the model predictive controller, were
performed The results are shown in Fig.7 The highest and low-
est flow-rate bounds are equal to 2 and 0.5 mL/min, respectively
These flow-rates result in vastly different breakthrough curves as
shown in Fig 7 It is essential to note that IgG-3 does not bind
to this resin, and the polyclonal IgG is a combination of IgG-1, 2,
3, and 4; therefore, IgG-3 leaves the column immediately, which
causes a small breakthrough at the beginning of each experiment
As a result, this immediate breakthrough has to be deducted, as
done previously [54]
The breakthrough at the highest flow rate emerges after ap-
proximately 4 min, and this results in low resin utilization and
productivity However, the experiment at the lowest flow rate leads
to a process with high resin utilization and limited productivity
The following phases, including washing, elution, CIP, and regener-
Fig 7 Experimental comparison of loading IgG at constant flow rate with the
breakthroughs with online optimizer MPC Results are shown in the (a) time and (b) volume domains Solid lines with filled symbols represent the breakthrough curves, and the dash-dotted lines with hollow symbols are the related flow rates The black lines are the breakthrough curves at the highest and lowest constant flow rates (HB and LB levels) The fuchsia line with the square symbols represents the break- through curve with the highest productivity at a constant flow rate (OPT CONST) The red, blue, and green solid lines represent the breakthrough curves with MPC
ation, are performed in 25 min Accordingly, the resin utilization and productivity at the HB and LB levels are equal to 23.2% and 0.68 mg min−1.mL−1resin, and 66.5% and 0.53 mg min−1.mL−1resin,
respectively The results related to the HB and LB levels are shown
in Fig.8with the same notation
Similarly, to compare productivity and resin utilization, three more experiments at constant flow rates of 1, 0.2, and 0.1 mL/min are performed (the resulting breakthrough curves can be found in the supplementary material) According to the conducted experi- ments at a constant flow rate, the maximum productivity is 0.71
mg min−1.mL−1 resin and is gained at 1 mL/min; this experiment
is marked by the OPT CONST sign and indicated by the filled pur- ple square in Fig.8 Similar to the experiments with lysozyme, we achieved a higher resin utilization and productivity compared to the optimal condition with constant flow rate (OPT CONST), while reducing the buffer consumption by 30% ( Fig.9) Therefore, we can conclude that the MPC strategy exceeds the performance of classi- cal chromatography at a constant flow rate
It is important to emphasize that the model predictive con- troller (MPC) requires online monitoring of the product concentra- tion in the outlet In addition, the MPC was limited to optimizing the system in real time at the interval of the LB and HB levels; thus, a higher resin utilization level can be reached by decreasing the lowest flow rate level The choice of the highest bound for the
Trang 9Fig 8 Productivity versus resin utilization in affinity chromatography The blue cir-
cles are related to the experiments at a constant flow rate The filled purple square
is the peak of the curvature (OPT CONST) The red pluses, blue pentagrams, and
green asterisks correspond to MPC-1, MPC-2, and MPC-3, respectively
Fig 9 Comparison of buffer consumption for three experiments at a constant flow
rate with the MPC controller and three weighting factors in the cost function The
black bars are related to the experiment at the highest and lowest flow rates, HB
and LB levels The purple bar is related to the experiment at the optimal productiv-
ity at a constant flow rate (OPT CONST) Experiments with MPC are shown by red,
blue, and green bars, indicating MPC-1, MPC-2, and MPC-3, respectively
flow rate, HB, depends on pressure considerations for the column,
while the lowest flow rate level is driven by the required resin uti-
lization and the breakthrough curve profile
5 Conclusion
Based on the experimental results with the model predictive
controller, we conclude that a higher level of productivity and resin
utilization has been achieved compared to the optimal condition
at a constant flow rate With the proposed control framework, it
would also be possible to react to a decreasing resin capacity over
time, either due to fouling or ligand degradation Furthermore,
such a control mechanism can be used to automate bioprocesses in
order to account for varying feed concentrations or flow rate mis-
matches between unit operations The system can maintain resin
utilization at high productivity and reduces the buffer consump-
tion, similar to a counter-current loading strategy but with less
hardware complexity
Declaration of Competing Interest
The authors declare that they have no known competing finan- cial interests or personal relationships that could have appeared to influence the work reported in this paper
CRediT authorship contribution statement Touraj Eslami: Methodology, Software, Investigation, Writing – original draft, Visualization Martin Steinberger: Methodology,
Writing – review & editing, Conceptualization Christian Csiz- mazia: Investigation, Writing – review & editing Alois Jungbauer:
Conceptualization, Resources, Writing – review & editing, Supervi- sion, Funding acquisition Nico Lingg: Conceptualization, Method- ology, Investigation, Writing – review & editing, Supervision
Acknowledgments
This work has received funding from the European Union’s Horizon 2020 Research and Innovation Program under the Marie Skłodowska-Curie grant agreement No 812909 CODOBIO, within the MSCA-ITN framework
The COMET center: acib: Next Generation Bioproduction is funded by BMK, BMDW, SFG, Standortagentur Tirol, Government
of Lower Austria und Vienna Business Agency in the framework
of COMET Competence Centers for Excellent Technologies The COMET-Funding Program is managed by the Austrian Research Pro- motion Agency FFG
Supplementary materials
Supplementary material associated with this article can be found, in the online version, at doi: 10.1016/j.chroma.2022.463420
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