The conventional solution-phase method currently employed for the production of Antibody-drug Conjugates (ADC) has certain drawbacks, which makes production inefficient and cost extensive process. In this study, we developed a rigorous cost model for an intensified solid-phase production method utilizing a packed bed resin column to carry out all the steps involved in the production of ADC, at an industrial scale. The aim of this study was to find a suitable operating region (column length and feed velocity) to minimize the cost of ADC production. Simulation results showed that productivity was maximum when the process was operated at a linear velocity ranging between 120-140 cm/hr and unit cost of ADC production was minimum when column length was 60 cm and operated at 100 cm/hr. We found that production cost is highly dependent on monoclonal antibody (mAb) cost, followed by cytotoxic drug as being the second-highest contributor to the overall production cost.
Authors: Anirudh Gairola, Ahmad K. Hilaly*, M. Nazmul Karim [Author Information]
*Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, Texas 778843-3122 | Corresponding Author: Ahmad K. Hilaly; E-mail: [email protected]. Phone: +1979-458-0090
Key terms: ADC, cost modeling, simulation, solid-phase production, process intensification
Published In: ADC Review| Journal of Antibody-drug Conjugates
How to cite:
Gairola A, Hilaly AK*, Karim MN. Modeling and Optimization of Antibody-drug Conjugate Production Using Process Intensified Solid Phase Method – J. ADC. February 17, 2020. DOI: 10.14229/jadc.2020.02.001
Antibody-drug conjugates (ADCs) are the proteinaceous novel therapeutic drug molecules that are being used extensively in cancer therapy recently. The antigen-specific property of monoclonal antibodies makes ADCs more precise in their actions as they only target tumors expressing a particular surface antigen. This gives ADCs an upper hand over conventional chemotherapy cytotoxic drug molecules, which have a high tendency to affect healthy cells because of a lack of specificity. Monoclonal antibodies are the best-suited molecules to impart specificity to cytotoxins since they have a very high affinity for antigens which are expressed on the surface of cancerous cells.
An ADC consist of three major components: 1) Antibody, 2) Linker and 3) Cytotoxin (payload). Each part plays either a direct or an auxiliary role in killing the cancerous cells. As mentioned above, the antibody provides specificity to otherwise nonspecific cytotoxin. In addition, the linker plays an important role in conjugating the payload to the antibody and makes sure that it does not affect any healthy cell. The cytotoxic payload is the lethal component in the ADC and plays a direct role in killing cancerous cells. The mechanism by which ADCs kill cells depends on the class of cytotoxins used.
The current trend for ADC production is to utilize a batch mode homogenous system consisting of solution-phase to carry out modification and conjugation of antibodies and payload. The solution phase methods are not very efficient as they generate a large amount of waste and are susceptible to ADC aggregation during the synthesis. 
ADC production begins with a modification of antibodies to make them amenable for payload conjugation. The most common modification is to partially reduce the disulfide bonds present in the antibodies. Reduction of disulfide bond results in the formation of a free thiol group which plays an integral role in conjugation chemistry as it provides reactive ends on an antibody. Tris(2-carboxyethyl) phosphine (TCEP) is the most commonly used reducing agent used for this step.  According to stoichiometry, one mole of TCEP reduces one disulfide bond thereby creating two free thiol groups.
One of the critical parameters which are used to assess ADCs is the drug-to-antibody ratio (DAR) as it determines its potency and therapeutic index.  DAR value is highly dependent on the reduction step. DAR value is directly proportional to the amount of TCEP used since more amount of reducing agents will create more active thiol groups which will then act as a site for payload conjugation. Hence, controlling this step is important for the overall quality of ADCs. Reduction step is followed by a washing step, where an excess of reducing agent is removed from the solution to prevent an undesirable reduction of antibodies. For the solution-phase method, this step often becomes a bottleneck as it is quite time-consuming. After the excess reducing agent has been removed, linker-coupled drug molecules are added to the solution. During this step, an active thiol group on antibodies reacts with drug moiety to bind payload to the antibody. The major drawback for carrying out this reaction in the solution-phase is that it results in aggregation of ADCs as conjugation significantly increases overall hydrophobicity. 
Most of the payloads used for conjugation are hydrophobic in nature and tend to aggregate. Gandhi et al., showed that the hydrophobic drug payload on an ADC significantly reduced the repulsive inter protein interactions when compared to the unconjugated antibody under formulation buffer conditions (pH 6.0). Attaching hydrophobic drug and linker moieties onto the antibody lowered the thermal and colloidal stabilities and increased the propensity to aggregate for ADCs. In 2019, Gandhi et al., found that the application of agitation has the tendency to induce aggregation in lysine based ADCs. In large scale homogenous production of ADC, mixing is an essential part of the reduction and conjugation step. This might initiate unwanted aggregation during production.
To maintain homogeneity of the batch, the aggregates are further separated using hydrophobic interaction chromatography (HIC)  or filtration units. This leads to an overall decrease in productivity and an increase in the cost of production. Additionally, product degradation takes place when multiple columns are used for the separation of aggregates. Monoclonal antibodies are expensive. Therefore, it necessary to minimize the loss of material through undesired side reactions and physiochemical interactions such as aggregation. Adding more unit operations to remove aggregated ADCs results in loss of product. The new classes of cytotoxins such as duocarmycins, pyrollebenzodiazepene (PBDD-) dimers, and alpha amanitins, are even more hydrophobic than their predecessor cytotoxin. Hence, it is imperative to develop a novel method for ADC production which minimizes the aggregation of ADCs in the solution.
In the last few years, there has been a substantial number of peer-reviewed research articles championing the application of site-specific conjugation to reduce the ADC heterogeneity, instability and efficacy. In 2016 Puthenveetil et al., put forward the efficacy of the solid-phase method in synthesizing site-specific conjugated ADCs for high throughput screening. They successfully employed a solid-phase synthesis method by using protein A/L based beads and generated site-specific ADCs, dual-labeled, site-specific antibody and Fab conjugates. The solid-phase method has been shown to be versatile because of its compatibility with various conjugation functional handles such as maleimides, halocetamides, copper-free click substrates, and transglutaminase substrate.  Owing to the interest developing in the application of solid-phase ADC synthesis method for a high throughput screening procedure, there have been studies where researchers have compared solution phase-based ADCs with solid-phase ADCs. ADCs are complex engineered biomolecules. Before the new method is adopted it is important to assess the effect of change in the production method. Arlotta et al (2018)., did in-depth characterization analysis of differences between solution phase and solid phase method for ADC synthesis by employing LC/MS for determining DAR distribution, DSC & DLS to investigate the thermal stability, Raman spectroscopy to detect changes in tertiary structure and ITC for measuring binding attributes. Their characterization study revealed nominal differences in drug distribution, which did not impart significant differences in structure or function. This characterization study by Arlotta et al., further curbs the apprehension regarding the application of the solid-phase synthesis method.
The method adopted so far to carry out the solid-phase synthesis method is to immobilize mAb on a solid support which is dispersed in solution. In patent (WO 2016/067013 A1), David John et al., demonstrated that ADC can also be produced by first binding mAb on a laboratory scale affinity resin packed column and subsequently carrying out mAb modification (partial reduction) and conjugation reaction in the same column. They reported that, for the same DAR value of 2.4, ADC produced by solid-phase method had 50% less aggregation than that produced by the solid-phase method. For this study, they used trastuzumab (mAb) and vcMMAE (Monomethyl Auristatin E, cytotoxin with valine-citrulline (vc-) linker).
In their work, David John et al. (2016) focused solely on the experimental front of the method and did not attempt to develop a mathematical model that can predict and simulate solid-phase production of ADCs. In this work, we have presented a rigorous mathematical model that simulates the production of ADCs using an intensified solid-phase production process. We believe this simulation model will be useful for accelerating process development and the commercialization of this novel method. Process intensification, which can be obtained by carrying out all the production steps within a single packed column, is an effective method to reduce capital and operating expenses. This work investigated the process intensification of ADC production by using an affinity resin column and conducting multistep reactions in the same column.
The aim of this study is to optimize the ADC production process by finding the operating region that minimizes the annual cost of production per unit quantity of ADC produced. This was accomplished by predicting the CAPEX (capital expenditure) and OPEX (operating expenditure) involved in an intensified production process. The optimized ADC production process can be coupled directly with the mAb production process in order to achieve plant-wide optimization.
Process Intensification (PI) is a subfield of chemical engineering in which the conventional and existing technologies are taken as a reference, and are subsequently modified to achieve drastic improvements in the efficiency of chemical and biochemical processes by developing innovative, often radically new types of equipment, processes, and their operation.
Miniaturization of the plant or integration of reaction and separation within one zone of the apparatus, have become a trademark of Process Intensification. In ADC production, process intensification can be obtained by coupling mAb reduction and payload conjugation step in the one-unit operation. One way to achieve it is to bind mAb on solid support and subsequently modify it to form ADCs. In our work, we have built a cost model for a solid phase ADC production method extending the experimental work done by David John et al. (2016).
The intensified solid-phase production method has the potential to significantly decrease the capital cost involved by combining mAb reduction and payload conjugation step in a single packed bed reactor, unlike traditional homogenous phase production which utilizes different tank reactors to carry out mAb reduction and payload conjugation. Less number of equipment also translates to decreased cost of maintenance and less complicated operation. Since the homogenous phase has more steps, it has higher CAPEX than an intensified process. This aspect of the intensified solid-phase process makes it even more attractive. A typical traditional ADC production method would include 7 to 8 storage tanks, two stirred tank reactors and 3 membrane filtration processes. Whereas the intensified process would have one packed bed reactor, one membrane filtration process and 8 storage tanks. Let’s consider a traditional ADC manufacturing plant capable of processing 5000 Liters of volume per batch. SuperPro Designer™ has a good database of equipment costs and related installation and maintenance costs. We Calculated the CAPEX of a traditional plant by using the cost data from the SuperPro Designer™ database. The CAPEX of traditional ADC manufacturing plant was US $ 2,558,400.00 Whereas the CAPEX of the intensified process involving 120 cm wide and 60 cm tall packed bed reactor was US $ 1,008,850.00 CAPEX of the traditional process is approximately 2.5 times more than that of an intensified solid process.
This novel approach also reduces the space required for production by reducing the number of equipment. Apart from saving space, the intensified process will also reduce the amount of waste generated during the production process (John et al). The traditional ADC manufacturing process requires extra diafiltration steps to exchange buffer in order to carry out the reduction and conjugation step. The intensified solid-phase process does not require the extra time to conduct diafiltration steps since the mAbs are bound to the solid support and all the modifications which take place are heterogeneous in nature, and the buffer/modification reagents simply washes the column. In large scale manufacturing, the amount of solution to be processed can easily reach 5,000 liters. For example, let us assume 5,000 liters of the solution is to be processed for the buffer exchange process, in a homogenous ADC production method. Assuming that the membrane area is 20 m2 and flux is maintained at 50 L m-2 hr-1 at a retention factor of 0.999, it will take 15 hours and 15,000 liters of the buffer. This can be easily calculated using standard diafiltration equations for formulation time and the amount of buffer required. A conventional process will contain at least three buffer exchange processes, one each after reduction and conjugation step and final exchange to formulation buffer. This translates to 45,000 liters of buffer volume. Assuming that buffer cost is US $ 0.0311 per ml, the addition of each diafiltration step would add US $ 466,500.00 to the operational cost per batch. Filtration processes are known to cause some product loss and if the solution to be processed is low in protein concentration then adsorption losses cannot be ignored.  The filter membrane area can be increased to decrease the processing time but that will increase the product loss, especially if the solution has a low concentration of mAb.  Therefore, increasing the number of filtration steps will further amplify the product loss. The intensified production process just involves one formulation step which involves the filtration process. Few researchers have also exploited TFF as an alternative to the chromatographic methods to remove aggregates after the conjugation steps. TFF might supersede the chromatographic method for aggregate removal, but when compared with the intensified process which does not need aggregate removal step, it simply adds to the process cost. On the other hand, using a chromatographic method for ADC purification will be an even more cost extensive process.
The homogenous phase method uses tank reactors to carry out reduction and conjugation steps. The rate of reaction will be more in a homogenous phase than in a heterogeneous phase. If the effectiveness factor packed bed reactor is 0.8, the reduction and conjugation steps in a homogenous phase method would be 1.25 times faster. But the fact that homogenous phase methods are usually constrained by the concentration of mAb that can be processed. To minimize the aggregation in the process, mAb concentration of 1 mg/ml is used for the production.  Whereas, the intensified solid-phase method can process more concentrated mAb solutions. Therefore, more amount of mAb can be processed in the intensified process for a given volume of a mAb solution.
Capturing the mAb in solid support also improves the final product by decreasing the ADC aggregation. Therefore, we believe that the intensified solid-phase method would be a great alternative to the conventional production method.
As mentioned above, the process begins with capturing mAbs on an affinity column. It is essential to have a reliable model that can simulate the capture step because these steps govern the amount of mAbs which will be subsequently processed during the reduction and conjugation step. Affinity chromatography is a complex process and involves transport phenomena and mass transfer occurring in tandem. There are many ways to model the capturing step. Previously, authors have developed breakthrough models by simplifying the column dynamics by assuming local equilibrium in the system. This assumption often may not be true and hence predicts a breakthrough profile that is sharper than the actual breakthrough curve obtained experimentally. This is because the local equilibrium assumption does not account for mass transfer resistance within the resin particle or in the liquid film surrounding the particle and therefore falsely predicts a breakthrough profile with a narrower mass transfer zone. 
Models that account for the concentration gradient within resin particle or liquid film generally provide a more accurate prediction of breakthrough profiles. Ozdural et al., 13 developed a mathematical model that incorporated the non-equilibrium nature of the process and assumed non-linear isotherm. The model is governed by solid diffusion within the particle as a mode of intraparticle transport.
The mathematical model developed by Ozdural et a.,l considered that single component adsorption takes place from a flowing liquid stream in a packed bed chromatographic column (inside radius = cm, bed height = L cm, bed void fraction = ε) of spherical adsorbent particles (radius = cm) under isothermal conditions. The change of interstitial velocity of the liquid stream, v (cm/s), and the liquid concentration gradients in the radial direction of the bed were considered to be negligible. A constant surface (solid) diffusivity, (cm2/s) was used. Non-equilibrium conditions existed between the adsorbent particle and the liquid in the void fraction of the packed-bed chromatographic adsorption column. It was assumed that the non-linear equilibrium data can be represented by the Langmuir equation. The model was based on a dual resistance model combining external mass transfer and intra-particle transport by solid (surface) diffusion and assumed a parabolic concentration profile within the particle.
Mass transfer of adsorbate from liquid to the solid phase can be depicted by Linear Driving Force (LDF) model.
Here, Bi is the Biot number, qs is the solid phase concentration at the adsorbent surface, qav is the average solid phase concentration, and c is the liquid phase concentration. According to Langmuir isotherm, we have
From equation (1) and (2), we have,
The variable can be evaluated using the quadratic formula.
The transport equation governing the system can be described as,
The mass transfer equation can be described as
The concentration profile c(x,t) can be obtained by simultaneously solving (4) and (5), which forms a system of two coupled partial differential equations(PDEs), under the following initial and boundary conditions.
The capture step is followed by a washing step to remove any unbound antibodies and impurities from the column. The column is washed with 10 mM Tris/2mM EDTA at pH 7.5 buffer.1 Washing is performed at a linear velocity ranging between 100 cm/hr to 120 cm/hr.
After the column has been washed, a reducing agent is added to partially reduce the interchain disulfide bonds present in the mAbs. Controlling this step is crucial for ADC production because it determines the number of active sites for cytotoxin conjugation, which directly affects the DAR value and therapeutic efficacy. The reduction of interchain disulfides yields free thiols that react with the linker drug complex (vcMMAE), under the thiol-maleimide reaction mechanism.
Many reducing reagents, such as dithiothreitol (DTT), tris(2-carboxyethyl) phosphine (TCEP), aminoethanethiol etc., have been cited in the literature which has been already employed for partially reducing mAbs.  Stoichiometric loading of a reducing agent plays a vital role in determining the DAR value of the ADC. TCEP is a better option for reducing bound antibodies because it is a thiol free reducing agent hence does not react with maleimides, unlike DTT which is a thiol based reducing agent.
By the general stoichiometry, one mole of TCEP reduces one disulfide bond and creates two free thiol groups.
To achieve an average DAR value of 4, ideally on an average 4 conjugation sites (free thiol group) must be developed after partial reduction. Therefore, 2 moles of TCEP is required to create 4 conjugation sites.
But it has been noticed that in the actual reduction process excess of TCEP is used. Michael M.C Sun et al., (2005), used about 2.75 molar equivalent of TCEP to achieve an average DAR value of 4, whereas David John et al., (2016) used 2.24 molar equivalent of TCEP to achieve DAR value of 3.8. 
The excess of TCEP required can be accounted for the presence of interchain trisulfide bonds instead of disulfide bonds.  In the presence of trisulfide bond, it is first converted into a disulfide bond, which subsequently is converted in to free thiol group. Researchers have already studied and modeled the reduction of interchain trisulfides into disulfides bonds, on mAbs bound to the affinity column. The excess amount of TECP required is directly related to the number of trisulfide bonds present in mAbs. Generally, 25%-30% excess is the norm. To maintain sufficient contact time, David et al., used an external recycling loop.
After the mAbs have been partially reduced, the column is washed with 10 mM Tris/2mM EDTA at pH 7.5 buffer, at a linear velocity of 120 cm/hr. The linker drug complex (vcMMAE) is added to the column, where it reacts with the free thiol group present in the cysteine residue of mAbs. The conjugation reaction is based on the thiol-maleimide mechanism. Similar to the reduction step, the amount of drug complex added will control the DAR value. If excess drug complex is used for the conjugation reaction, a high average DAR value will be obtained which might decrease the therapeutic efficacy. As per the stoichiometry, one free thiol group must react with the drug complex. Hence, if on an average a mAb contains 4 conjugation sites, 4 moles of drug complex must be used per mole of mAb to achieve desired DAR value. Similar to the reduction step, David et al., used a recycle loop to maintain sufficient contact time. 
To achieve desired DAR value, researchers have previously used Drug to free thiol molar ratio of 1.1 or Drug to mAB molar ratio of 5.  The general conjugation reaction can be described as:
Here α is vcMMAE.
MMAE is an antineoplastic and antimitotic drug which is cytotoxic even in picomolar concentration. Owing to the high ultra-potency and cytotoxicity, the excess drug complex must be quenched from the column before eluting the ADCs. The same concept which is used for conjugation reaction is utilized for quenching excess drug complex. The excess drug is reacted with cysteine or cysteine-containing molecules such as N-acetyl cysteine (NAC). The thiol present in cysteine reacts with maleimide moiety of the drug linker complex, thereby capping it and rendering it less toxic. The amount of quencher is generally added in excess with quencher to drug ratio 2.Here again recycle loop is used for the solid-phase production method.
This step is quite similar to chromatography elution where bound proteins are desorbed from the resin support by modifying ionic strength. David John et al (2016) used 0.1 M glycine, pH 3 and collected the conjugates into 2% v/v of 1M tris(hydroxymethyl) aminoethane (TRIS) to neutralize them.
After the ADCs have been eluted and neutralized, it is suspended in a more stable buffer for formulation purposes. The formulation buffer increases the stability of ADC product. The buffer is exchanged using a cross-flow filtration module conducted in diafiltration mode. The formulation buffer’s composition consists of 5 mM Histidine, 50mM Trehalose and 0.01% Tween 20.1
Calculation of reagents and resin required for production
The mAb binding step is simulated by MATLAB™ R2018a, where equations (4) and (5) are solved by using a finite difference method under initial and boundary conditions described in equations (6), (7) and (8). The finite-difference model converts the PDEs into a set of linear algebraic equations which can be then solved by MATLAB.
Space is discretized using the central difference formula, whereas time is discretized using backward difference formula.
Therefore, in order to render the system of coupled PDEs into a system of linear algebraic equations, the following transformations are used
(1) Spatial discretization:
(2) Temporal discretization:
In the above discretization, i and j are space and temporal indices. Δx and Δt are unit increments in space and time respectively.
To apply the method of finite difference, the column is divided into N equidistant segments. Therefore, in a column, we will have N+1 nodes. Similarly, simulation time is divided into K equally spaced points, consisting of K+1 nodes. The final concentration profile will be a matrix of [K+1, N+1] dimension. For each time node j, we will have a set of N+1 linear algebraic equations of the following form: Ax=B.
Here A is the stiffness matrix and B is the forcing function matrix. The concentration profile is then evaluated by performing a Gauss elimination method at each time node j, in order to solve for concentration at each space node i at any given time.
Space and temporal nodes are bound by the following constraint:
Concentration profile generated by solving the set of algebraic equations can be used to calculate various useful parameters that can be used to assess the efficacy of the binding step.
Length of unused bed (LUB) is a parameter that represents the fraction of unused bed after a breakthrough point has been reached. Breakthrough point is generally considered to be a point when the effluent concentration reaches 5%-10% of the initial inlet concentration.
It is desirable to have a low value of LUB. Low LUB value signifies that resin material is being used efficiently to capture mAbs. LUB is a function of velocity, bed length, isotherm parameters, etc.
For practical purposes, LUB can be calculated from the following equation.
Here is the time required to reach a breakthrough and is the time required to reach 50% of initial inlet concentration.
It is also important to estimate the pressure drop across the column as the reagents flow through the packed bed. The packed bed can maintain its integrity when the pressure drop is below a certain threshold value. The pressure drop can be estimated using Ergun’s equation (1952).
Here, Δρ is the pressure drop, L is column length, μ is fluid viscosity, is linear velocity, is void fraction of packed bed, r is the particle radius and ρ is the fluid density. In the case of laminar flow, the first term dominates the equation and the equation reduces to Kozeny-Carman equation (1927).
The total amount of mAb bound until breakthrough time tb is an important parameter which reflects the efficacy of the binding step. Like LUB, the amount of mAb bound is a function of column length, velocity and isotherm parameters. Predicting the amount of mAb captured is important because the required quantity of reducing agent, drug linker complex and quencher directly depend on mAb bound on the column.
The amount of mAb bound can be calculated by mass balance.
Here, V = Flow rate (ml/s), Co = Inlet concentration (mg/ml) and C (t) represents concentration profile of the effluent stream.
After the amount of mAb bound on resin has been predicted, the amount of reducing agent, drug linker complex and quencher can be predicted by the aforementioned general stoichiometry.
If the amount of mAb captured is M moles,
The amount of resin, washing buffer and eluent required for one production cycle can be determined from column dimensions.
Where the column volume is the product of column length and area of cross-section. The amount of formulating buffer required depends on the time of formulation (tƒ), the trans-membrane flux of diafiltration and membrane area.
The cost of production consists of CAPEX (capital expenditure) and OPEX (operating expenditure). The CAPEX includes the cost of equipment, cost of instrumentation, piping, and installation. The OPEX consist of the cost of raw materials, resin and reagents, cost of utilities, cost of labor and cost of maintenance. All the cost items were estimated on an annual basis.
Annual capital cost is defined as:
Here COE is the depreciated cost of equipment, COC is the depreciated cost of column, COI is the depreciated cost of instrumentation, COV is the deprecated cost of tanks, COD is the cost of diafiltration unit (tanks and frames (CTF), pipes and valves (CPV), instrumentation & control components (CIC) and miscellaneous components (CMI)). COPI is the depreciated cost of piping and COIN is the annual cost of installation. The depreciated cost of CAPEX items, apart from COIN, depends on the lifecycle of the item. COIN is estimated by using the following relation:
In 2000, Sandeep Sethi and Mark Wiesner  gave the empirical formula to estimate the capital cost of a membrane filtration unit.
Annual operation cost or OPEX can be defined as
Here, COR is the annual cost of raw material, COP is the annual cost of pumping, COM is the annual cost of maintenance and COL is the annual cost of labor.
Annual Cost of raw material (COR) can be defined as:
Here, cycle refers to the number of annual cycles of production. The cycle is defined as the total time taken to complete all the steps. Resin lifecycle is the number of cycles after which the resin needs to be replaced. The unit cost is per unit weight of the reagents required except for the unit cost of resin and buffer which are expressed in terms of per unit volume. The weight of reagents required was calculated by multiplying the number of moles with the molecular weight of the respective reagents.
The cost of pumping was estimated by calculating the pressure drop across the column and converting it into hydraulic power.
Here, P is the power required, Δp is the pressure drop across the column and ƒ is the volumetric flow rate.
Annual Cost of Pumping (COP) was defined as:
Here, tcy is the number of hours pump was used per cycle of production, cu is the cost of electricity per KWH.
As a rule of thumb, COM was taken as 10% of COE. The value of COL depends on the number of operators per shift and their average annual salary.
To estimate the number of cycles in one year, it is imperative to calculate the amount of time it takes to complete one production cycle (tcy). It was defined as the sum of time to complete binding, washing, reducing, conjugating, quenching and eluting and formulating the final product. It is expressed as:
The time required to wash column (tw) and elute (tel) the final product was calculated based on the volumetric flow rate and amount of reagents required in these steps. David John et al (2016)., used 2 hours for reduction and 1 hour of reaction time for the conjugation step, where the reagents were being recirculated continuously using a reservoir-pump combination at a linear velocity of 120 cm/hr. Additionally, the reservoir volume was maintained at 50% of that of the column. The number of recirculation cycles on an average was 50 for the reduction step and 25 for the conjugation step and 8 for quenching.
For practical purposes, the time required for reduction (tre), conjugation (tco) and elution steps were scaled up by keeping the number of recycles constant for each reaction step for a particular length and varying linearly with velocity u.
The final expression for tcy can be written as:
Here, td is the downtime and is assumed to be 10% of operation time. The term tƒ is the formulation time and is a function of permeation flux, membrane area and volume to be filtered.
Simulation and Results
To get the optimal operating condition, the binding step was simulated for a range of combinatorial values of column length (ranging from 20 cm to 60 cm) and linear velocity (ranging from 100 cm/hr to 700 cm/hr) of the inlet feed. The amount of mAb captured, breakthrough time, LUB and cost of production were calculated for each combination of length and velocity. The diameter was taken twice the column length for simulation, which is normally seen in industrial applications.
The following parameters were used for simulation:
|Particle diameter||100 µm|
|Bed Height||20-60 cm|
|Column I.D||40-120 cm|
|Flux||50 L/(m2. hr)|
Table 1.0 Simulation Parameters.
The film mass transfer coefficient and axial dispersion (Kƒ and Da) were calculated using empirical relations. For evaluation of Kƒ correlation given by Wilson and Geankoplis  for mass transfer of liquids in packed beds was used where Sherwood number (Sh = 2rKƒ/D) is correlated with Reynolds number (Re = 2rup/μ) and Schmidt number (Sc = μ/pD). For calculation of Da, Peclet number (Pe = 2rv/Da) versus Reynolds number correlation was used. 
The binding step was simulated using solid diffusivity (Ds) value of 0.48×10-9 cm2/s and since the feed is dilute, viscosity and density of water are used for simulation.
For cost function estimation, the following unit cost values are used:
|mAb||$ 50 per gm|
|Resin||$ 13.32 per ml|
|TCEP||$ 34 per gm|
|Buffer||$ 0.0311 per ml|
|Drug||$ 700 per gm|
|Quencher||$ 0.811 per gm|
|Eluent||$ 4 per kg|
|Histidine||$ 4 per kg|
|Trehalose||$ 2 per kg|
|Tween 20||$ 2 per Kg|
|Electricity cost||$ 0.05 per KWH|
Table 2.0 Consumable Unit Cost
For CAPEX estimation following under-appreciated values are used for the column which is 60 cm long and has a diameter of 120 cm. For estimation of CAPEX for other column dimensions, the following relation is used:
|Column||US $ 150,000.00|
|Piping||US $ 100,000.00|
|Tanks||US $ 400,000.00|
|Instrumentation||US $ 150,000.00|
Table 3.0 Capital Cost
The life cycle of resin is assumed to be 60 cycles, after which it needs to be replenished. The CAPEX items are depreciated linearly over a span of 10 years.
The simulation of the mAb binding step can be optimized at the process development scale, using small columns and then scaling up the column for industrial application.
Figure 4.0 elicits how the feed velocity affects the binding of mAb on the affinity resin. It is apparent from the figure that on increasing the velocity the breakthrough point is reached much earlier and the profile has a much broader mass transfer zone (MTZ). Whereas at the lower velocity the profile breakthroughs later and has a narrower mass transfer zone. This simulation at a laboratory scale can help in calculating the LUB which remains unaffected when the column is scaled up at an industrial scale.
To find suitable operating parameters, it is necessary to simulate the binding step for a range of bed lengths and velocities.
A profile with narrower MTZ translates to better utilization of resin bed and lower LUB whereas for a profile with broader MTZ the utilization of column is not efficient and they have higher LUB. It is important to operate in a region where LUB is not high since in the region of higher LUB most of the bed remains unused.
Figure 6.0 shows how column length and feed velocity affects the fraction of LUB. As the velocity increases for a given column length, the LUB also increases. The rate of increase of LUB is more prominent in short columns.
For example at a column length of 20 cm, the LUB ranges from 0.1 to 0.9, when velocity is increased from 200 cm/hr to 700 cm/hr.
In contrast, with a 40 cm column length for the same range of velocities, the LUB varies from 0.1 to 0.5. It can be inferred that if the column needs to be operated at high velocity, a larger column should be employed.
Another important consideration while operating the affinity column is the pressure drop across the bed. The pressure drop should not exceed the permissible threshold value for a given resin. The pressure drop is a function of length, velocity, bed void fraction and resin particle dimensions.
Figure 7.0 depicts the linear increase in pressure drop per unit length across the column as the velocity is increased.
The pressure drop in the column varies from 0.2 psi/cm to 0.7 psi/cm, as the feed velocity is increased from 100 cm/hr to 350 cm/hr.
It is evident from the linear trend that in equation (15), the first term dominates the second term, which further proves that laminar flow exists in the column in the range for which simulation was done.
The breakthrough time ( and the amount of mAb bound on resin till breakthrough time are functions of the length of bed and feed velocity.
Figure 8.0 depicts how varies with velocity. It can be observed that as the velocity is increased, the decrease in is not linear. Also, it increases linearly as the bed length is increased.
Figure 8.0. Effect of velocity and column length on breakthrough time. The initial feed concentration is 2 mg/ml
From Figure 6.0, it can be noticed that at very high velocity the LUB value is very high. Hence it is not economical to operate in that region. Therefore, for cost function simulations, velocity was varied from 100 cm/hr to 340 cm/hr, and the column length was varied from 20 cm to 60 cm.
The column diameter was assumed to be twice the length of the column. The amount of mAb bound to the resin bed annually is a function of resin parameters, velocity, column dimensions and the number of cycles in a year.
Figure 9.0 depicts how the annual production of ADC (productivity) is affected by column length and velocity. The annual production varies from approximately 400-1300 kg. It can be observed that for a particular column dimension, the amount of ADC produced first increases with an increase in velocity and then starts to flatten out and decrease for any given column length.
This trend can be explained by the fact that at a given column length as the velocity is increased, the amount of mAb captured decreases, which is evident from Figure 1.0
However, the increase in velocity increases the number of annual cycles of production by reducing the cycle time. Therefore, there are two competing forces that dictate the amount of ADC produced.
The initial increase in annual ADC production when velocity is increased is because of the increase in the number of cycles. When velocity is further increased, the amount of ADC produced in each cycle starts dictating the total amount of ADC produced. The productivity (amount of ADC produced per year) is maximum when the process is being operated at a velocity ranging between 120-140 cm/hr.
For estimation, it is assumed that each shift (3 shifts in a day) requires 2 operators and their average salary is US $ 60,000. To find suitable operating parameters for the production it is imperative to estimate the annual total production cost per unit amount of ADC produced.
The set of parameters that give the lowest cost per unit ADC produced will be a suitable region for operation. It is expected that the cost function will display a minimum for a particular set of parameters. For the simulation of diafiltration operation, a membrane area of 6 m2 is assumed and trans-membrane flux of 50 LMH is used. Membrane area and trans-membrane flux will affect the formulation time, which in turn will affect the number of cycles in a year. For simulation purposes, it has been assumed that 98% of the bound mAbs are converted into ADCs.
Figure 7.0 elicits how total production costs per unit amount of ADC produced varies with change in feed velocity and column dimension.
This trend of cost profile allows to find a combinatorial value of column length and feed velocity that will minimize the total production cost per unit amount of ADC produced.
Figure 10.0 shows that the cost of ADC production reaches a minimum value of approximately $85 per gm when the column is 60 cm long (120 cm diameter) and velocity is 100 cm/hr.
From the trend, it can be inferred that increasing the scale of production will help in bringing down the cost, but there is a certain limit up to which the column size can be scaled up. The maximum length up to which column can be scaled up depends on the permissible pressure drop the packed bed can withstand.
Increasing the column length will increase the pressure drop across the column and hence will put a constraint on scaling up. In figure 7, the drop in cost is more prominent when column length is increased from 20 cm to 40 cm as compared with when column length is further increased from 40 cm to 60 cm. The curve starts to flatten out when column length is increased from 40 cm to 60 cm. At any given feed velocity pressure drop across 60 cm column will be 1.5 times more than 40 cm column. Since the unit cost of production doesn’t vary much when column length ranges from 40 to 60 cm it will be judicious to go with 40 cm column.
The mAb cost was assumed to be US $ 50/gm which is consistent with the data reported by Brian Kelley in 2009.  Figure 11 shows how ADC production cost is affected by mAb cost. It can be observed that mAb cost contributes around 58% of the total annual unit production cost of ADC.
This implicates that the cost of mAb as a raw material will play an important role in predicting the cost of ADC production. The cost of mAb production varies significantly with the process scale. Hence, the source of mAb as a raw material will play a crucial role in determining the production cost of ADC. Process intensification of production will help in bringing down the CAPEX as the solid phase production method requires less number of columns and tanks than the conventional production process.
This will also lead to decreased cost of maintenance and installation. The estimated annual CAPEX for a conventional process for ADC production is US $ 528,000, whereas, for the intensified process, annual CAPEX sums up to US $ 325,500. Potentially a 62% reduction can be achieved using process intensification.
According to the data published by Market & Market research, the global market for Antibody Drug Conjugates (ADC) is expected to reach US $ 18.1 Billion by 2022. As the market for ADCs continues to grow, new and better methods for ADC production are necessary to meet the demand. ADCs have started to gain traction after the recent approval of CD30-targeting brentuximab vedotin (Adcetris®; Seattle Genetics) to treat relapsed Hodgkin lymphoma and systemic anaplastic large cell lymphoma, and HER2-targeting ado-trastuzumab emtansine (Kadcyla®; Genentech/Roche) to treat relapsed or chemotherapy-refractory HER2+ breast cancer.
Currently, there are around 60 ADCs in clinical trials and this number continues to grow.  In the span of 20 years (1987-2007) the total medical cost for treatment of cancer has nearly doubled due to the increase in the number of patients.  This number is expected to rise with further improvement in cancer diagnosis technology and an increase in cancer awareness among the general public.
Current innovations in the domain of drug discovery and immunotherapy have the potential to substantially transform the field of cancer treatment. To make sure that the approval of new drugs and therapies translates to better cancer treatment it is vital to make them affordable for patients. If the financial aspect of drugs is not addressed, many cancer patients will not be able to benefit from cutting-edge therapies.
To increase the affordability of ADCs for cancer patients it is imperative to optimize the ADC production process to reduce the cost of production and make cancer treatment financially less exorbitant. The current trend in ADC production, which employs a solution-based homogenous method has certain aspects that make it less efficient and leaves scope for development in production methodology.
To overcome the challenges presented by a solution-based homogenous method, David John et al.,  reported the experimental basis of a novel affinity resin-based heterogeneous method for ADC production using a laboratory-scale column. In our work, we have developed a rigorous model to capture the essence of this method of ADC production and have scaled it up at industrial-scale production applying the concept of process intensification. After simulating the capturing step, we estimated the amount of different raw materials required based on stoichiometric relations which depends on the desired DAR value.
Since the aim of our study was to optimize and assess the effect of operating parameters on the annual cost of ADC production per unit ADC produced, a cost function was developed. The cost function included a comprehensive list of CAPEX and OPEX items.
Our simulation was run at different operation conditions (feed velocity and column dimensions) and cost function was evaluated at each condition. For each set of simulation condition, other parameters, such as resin and diafiltration operation parameters were kept constant. Our simulation results showed that the annual unit production cost of ADC has a minimum for a given operating condition. The model presented above for mAb capturing step  can also be used at the process development stage to estimate LUB for a given operating condition and assess different resins under varying operating conditions. At the industrial scale, the simulation tool can find application in estimating the operating region which will minimize the annual unit production cost of ADC.
The kinetic aspect of reduction and conjugation step in ADC production has not been reported in the literature extensively. In our approach, we used stoichiometric relations and data available in the literature for reaction time estimation. We believe that the incorporation of kinetic parameters of reaction steps in the model will give better cycle time estimation. Further, the cost function can be expanded by adding costs involved in waste disposal and other auxiliary expenditures.
The cost of the mAb is the largest contributor in the overall production cost of ADC. Hence coupling the production processes of ADC and mAb can help in optimizing the overall production cost. Considering the advantages of the intensified solid-phase production method over the conventional liquid phase method, we believe the results of this study will be very helpful to the biopharmaceutical manufacturers in achieving the best economics involved in the production of ADC.
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