Design Guidelines of Free‐Flow Counterflow Gradient Focusing Device for Protein Fractionation

ABSTRACT

Free‐flow counterflow gradient focusing (FF‐CGF) is a promising tool for protein fractionation. This work establishes guidelines to construct an FF‐CGF system suitable for preparative applications. Numerical and analytical computations are undertaken to investigate design parameters, including device geometry, flow conditions, sample concentration, and applied voltage. This collective information serves as a design tool to guide the fabrication of the device, which, in this case, is constructed from polymethyl methacrylate (PMMA) and double‐sided tape. Furthermore, the design tool also supports device operation and provides insights into the expected resolution and throughput. Experimental results, which demonstrated the ability of the designed chip to generate a uniform counterflow gradient while separating small molecules and proteins, validated the accuracy of the design guidelines.

Abbreviations

EGM

equilibrium gradient method

EMG

exponentially modified Gaussian

EV

extreme Value

FF‐CGF

free‐flow counterflow gradient focusing

FFE

free‐flow electrophoresis

FF‐IEF

free‐flow isoelectric focusing

FFZE

free‐flow zone electrophoresis

1. Introduction

Protein fractionation is a challenging process for life science research and the pharmaceutical industry [1]. For several decades, free‐flow electrophoresis (FFE) has been used to separate and collect large quantities of proteins from complex biological mixtures. Traditionally, FFE devices consist of a separation chamber subjected to fluid flow carrying charged solutes in the longitudinal direction. An electric field is then applied in the lateral direction, and the electrophoretic mobility of the solutes within the electric field dictates their transverse velocity. This process results in the formation of distinct peaks across the separation chamber, which are then collected at separate outflow ports [2].

In traditional FFE modes such as free‐flow zone electrophoresis (FFZE), several technical challenges persist, limiting its widespread use [3, 4]. Broadening of the peaks due to molecular diffusion, as well as the parabolic velocity profile of the pressure‐driven fluid flow, presents challenges to the resolution capacity of FFE [4]. Free‐flow Isoelectric focusing (FF‐IEF) emerged to address this problem by introducing a lateral pH gradient across the separation chamber to focus proteins at their isoelectric point (pI) [5]. Peak focusing alleviates the band broadening effects of FFZE by eliminating hydrodynamic dispersion and enables larger sample injection widths [6, 7]. Unfortunately, FF‐IEF introduces new challenges at the preparative scale that limit sample throughput. The carrier ampholytes required to generate the pH gradients in FF‐IEF increase the cost of this method while also introducing the challenge of removing them from the purified sample [8] for further analysis. Further issues arise regarding the decreased solubility and increased focus times of proteins at their pI [5, 9, 10, 11], which limits the system throughput for preparative applications.

Development of free‐flow counterflow gradient focusing (FF‐CGF) has demonstrated the potential to address some of the shortcomings associated with previous FFE systems [12]. Briefly, FF‐CGF introduces a lateral counterflow across the separation chamber, orthogonal to the longitudinal fluid flow that mainly carries the separated solutes toward the collection outlets [12]. Thus, the formation of distinct peaks occurs at a location in the separation chamber where the electrophoretic velocity of the charged solute is counteracted by the fluid counterflow. This focusing mechanism is like FF‐IEF, except focus according to their electrophoretic mobility rather than their pI point. Consequently, FF‐CGF shares many similar benefits offered by FF‐IEF without the need for expensive carrier ampholytes. Additionally, maintaining a constant charge in the separation chamber alleviates long focusing times seen in FF‐IEF. Finally, the continuous addition of counterflow dilutes the focused solute streams to address solubility concerns of previous FF‐IEF systems.

An FF‐CGF system has the potential for high throughput protein fractionation, but the design of the initial prototype had several challenges. The device was made from polydimethylsiloxane (PDMS), and several steps in the fabrication process, such as plasma bonding and multilayer alignment, limit its potential to scale up for the collection of larger quantities. Furthermore, this design employed side channels with a high hydrodynamic resistance to supply the separation chamber with a uniform counterflow [12]. Although experimental results demonstrated the success of this strategy, the high‐resistance side channels limited the effective voltage drop across the separation chamber. Additional concern is raised by the material properties of PDMS that include unwanted surface absorption, inconsistent electroosmotic flow (EOF) properties, poor heat dissipation, and weak structural integrity for wide chambers, factors that can limit long‐term operation [13]. An alternative can be found in polymethyl methacrylate (PMMA), an easily machinable acrylic material. Previous preparative FFE assemblies used a thin spacer sandwiched between two PMMA plates to create the separation chamber [14].

In general, constructing an FF‐CGF device is complicated by the unique challenge of applying both a counterflow and an ionic current through the sidewalls of the separation chamber. Many factors can disrupt the counterflow gradient or introduce the unwanted effects of electrolysis and Joule heating. The goal of this study is to undertake a comprehensive investigation of these factors and then use this information to guide the construction of a device made using the preferred PMMA material. Analytical models and numerical simulations are employed to study key design parameters like the separation chamber dimensions and the applied flow rates. Porous membranes along the sidewalls are found to be well suited for supplying a uniform counterflow and electric field. The PMMA assembly easily facilitates the integration of these membranes, and fabrication protocols are provided to guide the overall construction of the device. The design is validated experimentally by the separation of small molecules and proteins, and the results demonstrate good agreement with previously developed FF‐CGF models [15, 16]. In the end, this work addresses many of the challenging aspects of FF‐CGF device design and will hopefully serve as an important guide for future experimental work.

2. Design Criteria for Stable Operation

A schematic of a typical FF‐CGF device is shown in Figure 1 where the general goal is to establish a counterflow through both sidewalls of the separation chamber that is uniform along its entire length in the longitudinal direction. This will enable a predictable and stable counterflow velocity gradient that is critical for solute focusing [12]. At the same time, these sidewalls must also allow for an ionic current to pass through to ensure an electric field across the separation region. Ion exchange membranes isolate the electrodes from the separation region to avoid the harmful effects of electrolysis such as pH variations. Meanwhile, the sample is injected at the top of the separation region before being separated, focused, and collected at the outlet channels. A process flow diagram is detailed in Figure 2, showing the relationships between crucial resistance parameters at various steps.

FIGURE 1.

(a) An overview of an FF‐CGF system (b) A layout of the three relevant layers used in the present FF‐CGF device. A PMMA cover containing the side chamber and electrode reservoir is also shown on one side of the device. PMMA, polymethyl methacrylate.

FIGURE 2.

Design flow diagram detailing relations between parameters at different design steps.

2.1. Criteria for Hydrodynamic Resistance

To ensure a uniform counterflow gradient and electric field, the side microchannels along the length of the chamber should have an approximately equal flow rate and ionic current, respectively [12]. The electrical current, $I[\mathrm{A}]$, through a rectangular microchannel can be determined from Ohm's law, and the electrical resistance, $R_e[\mathrm{\Omega }]$, can be written as follows [17]:

$$R_e=\frac{L}{{\sigma }_{b}HW}$$ (1)

where ${\sigma }_b[\mathrm{S}\mathrm{m}]$ is the bulk electrical conductivity of the solution, $L[\mathrm{m}]$, $W[\mathrm{m}]$, and $H[\mathrm{m}]$ are the channel length, width, and height, respectively. Meanwhile, the flow rate through a microfluidic channel can be determined by applying the electrical circuit analogy [17]. Thus, the hydrodynamic resistance of a microchannel, $R_{hyd}[(\mathrm{Pa}\mathrm{s})/{\mathrm{m}}^3]$, can be written as follows [17]:

$$R_{hyd}=\frac{12\eta L}{W{H}^3}{\left[1-\frac{H}{W}\left(\frac{192}{{\pi }^5}{\sum }_{n=1,3,5}^{\infty }\frac{1}{n^5}tanh\frac{n\pi W}{2H}\right)\right]}^{-1}$$ (2)

where $\eta [\mathrm{Pa}\mathrm{s}]$ is the dynamic viscosity, and tanh reflects the hyperbolic tangent function.

For both electrical and hydrodynamic resistance, when there are N side channels in parallel, the total resistance can be written as follows [17]:

$$R_{tot}=\frac{R_n}{N}$$ (3)

where $R_n$ is the resistance of each side channel. The prediction of flow rate through the side channels must also consider the resistance of the side chamber, separation chamber, and outlet channels in series, seen in the circuit approximation in Figure 3b, where the separation chamber is divided into the upper chamber (UC), middle chamber (MC), and lower chamber (LC) sections.

FIGURE 3.

(a) FF‐CGF design with side chambers connected to separation chamber via microchannels and a single outlet, (b) FF‐CGF design separated into three sections with resistances of the side chamber, side channels, and separation chamber shown.

Note that the series resistance of the separation chamber is different for each side channel [12]. Flow into a side channel in the LC section will only be subjected to the resistance by a portion of the separation chamber, whereas flow into channels in the UC section will be influenced by the entire separation chamber resistance. Consequently, the hydrodynamic resistance of the separation chamber should be negligible relative to the side channels to ensure that the flow rate through the side channels is approximately the same [18]. Figure 4a shows the numerical simulated x‐velocity in the system for different ratios of the resistance between the side channel ($R_{side}$) and separation chamber ($R_{cham}$). It is important to note that the same resistance criteria apply between the side channels and side chambers seen in Figure 1.

FIGURE 4.

(a) Simulation of x‐velocity magnitude, ⟨u⟩, for different ratios of $R_{side}/R_{cham}$. Streamlines of charged solutes are shown to illustrate the impact of the counterflow gradient uniformity. (b) Simulation of the counterflow gradient uniformity represented as $⟨u⟩$ at $z=0.9L$ relative to $⟨u⟩$ at $z=0.5L$ for a wide range of device dimensions (L × W × H).

Here, lower $R_{side}/R_{cham}$ values lead to a higher x‐velocity at the bottom of the chamber, pushing the streamlines of charged solutes towards the centre (Figure 1a). However, the x‐velocity becomes more uniform along the length of the chamber with increasing $R_{side}/R_{cham}$ values, and the focal positions of the solute streamlines remain fixed. Figure 4a shows that $R_{side}/R_{cham}$ should be at least 5 to achieve a uniform counterflow gradient indicated by the ratio of the x‐velocity at different positions along the length direction, $z=0.5L$ and $z=0.9L$, but this value can go higher for better results. Decreasing the height of the side channel is the most effective strategy for increasing the hydrodynamic resistance while minimizing the voltage drop. This is true because the electrical resistance is inversely proportional to H, whereas the hydrodynamic resistance is inversely proportional to H ³ as seen in Equations (1) and (2).

2.2. Porous Membranes

The laser engraving process on PMMA could not replicate the height requirements for the side channels established in the previous section. Thus, the porous membrane adopted to address these issues was integrated in series with the side channels to connect to the separation chamber. In general, the pressure drop across a porous membrane is calculated according to Darcy's law [19]. Therefore, applying the electric circuit analogy leads to the following hydrodynamic resistance for a porous membrane.

$$R_{hyd}=\frac{\eta L}{\mathrm{kWH}}$$ (4)

where $k[{\mathrm{m}}^2]$ is the permittivity of the material. If the porous membrane is taken to resemble a packed bed of particles, then the permeability can be approximated using the Kozeny‐Carman equation as follows [19]:

$$k=\frac{{\phi }^3{d}_p^2}{180{\left(1-\phi \right)}^2}$$ (5)

where ϕ is the porosity of the membrane, and $d_p$ is the average diameter of the particles. Note that porosity represents the fraction of empty volume in the porous membrane.

3D numerical simulations in COMSOL v5.6 were used to investigate the porous membrane assuming the Kozeny Carman approximation. In the end, assuming the separation chamber has a length of 30 mm, a width of 10 mm, and a height of 0.12 mm, the resultant resistance ratio between the simulated porous membrane and the separation chamber is about 38. This is more than enough for a uniform gradient based on the established criteria in Figure 4b (see S1 of the Supporting Information section for a more quantitative understanding and computational details of this model).

2.3. Sample Injection

Sample injection width is an important design parameter as it can influence the throughput and separation resolution [16]. To understand this process, it is helpful to reference the equation derived in a previous study that describes the x‐position during transit through the chamber [16]. Although the initial derivation assumed a mass particle entrance at $x=0$ [16], the boundary conditions can be altered to the more general form as follows (see S2 of the Supporting Information section for the full derivation):

$$x=\frac{u_{EP}}{\nabla u}\left(1-{\left(1+\frac{\nabla u}{w_0}z\right)}^{-1}\left(1-\frac{\nabla u}{u_{EP}}{x}_0\right)\right)$$ (6)

Different sample flow rates are presented in Figure 5 for different sample injection widths, and the analytical streamlines determined by Equation (6) (see Figure 5a,d) agree with the corresponding COMSOL simulations (see Figures 5b and 4e). Furthermore, Figure 5 shows how the sample injection can influence the separation resolution. In the case of Figure 5a,b, the sample flow rate appears to provide the solute stream with enough time to reach its equilibrium width. However, when the throughput is increased by a factor of 5 (see Figure 5d,e), the solute stream edges do not have sufficient time to focus, and the final distribution width is much larger. Figure 5c,f presents a practical design with a narrower injection width, but the sample flow rate is equivalent to Figure 5b,e, respectively.

FIGURE 5.

Comparing a low sample slow rate (Q_s ) in (a), (b), and (c) to a high sample flow rate (Q_s ) in (d), (e), (f), where Q_c is the flow rate on each side of the chamber. An analytical solution for particle transit is presented in (a) and (d), with the corresponding simulation of solute concentration shown in (b) and (e). An alternative simulation with a reduced injection width is also shown in (c) and (f).

Figure 5 also demonstrates how sample dilution is impacted by the sample injection. In the case of sufficient focusing (see Figure 5b), the solute stream reaches its equilibrium width relatively early, and from there it becomes increasingly diluted. In the case of insufficient focusing (see Figure 5e), the solute stream is being concentrated and diluted simultaneously, and as a result, the overall concentration remains relatively constant throughout the chamber. Therefore, Equation (6) can serve as a useful estimate of the sample dilution depending on the degree of focus.

3. Experimental Methods

3.1. Materials

All chemicals were purchased from Sigma‐Aldrich. The electrode buffer consisted of 445 mM of Tris and 445 mM of boric acid, with the pH adjusted to 8.4 using an HCl solution. This was then diluted to 89 mM of Tris and 89 mM of boric acid for the buffer counterflow. Various sample solutions were prepared in the separation buffer using xylene cyanol FF, orange G, ponceau S, rhodamine B, and fluorescein, and each dye had a concentration of 5 mg/mL. Another sample solution was prepared in the separation buffer, which consisted of bovine serum albumin (BSA), hemoglobin (Hg), and cytochrome c (Cyt C). The concentration of each protein was 50 mg/mL, and the BSA was labeled with bromophenol blue at a 1:1 molar ratio.

3.2. Device Layout

A layout of the three relevant layers is shown in Figure 1b. The separation chamber has a length of 30 mm and a width of 10 mm, and the height is defined by the thickness of the double‐sided tape (0.14 mm). The height is likely smaller due to the compression of the adhesive during bonding. To improve the uniformity of the compressed double‐sided tape thickness, a cold laminator (14Inch, INTBUYING) was used for bonding. In Figure 1b, the side channels are engraved to approximately half to depth of the bottom PMMA layer, and this allows the porous membrane to connect to the separation chamber. Meanwhile, the via holes are present to ensure that the counterflow remains evenly distributed through the side channels after exiting the porous membrane. Furthermore, the ends of the porous sheets are cut to maintain a consistent volume above each via hole, and the ends are blocked with double‐sided tape to prevent excess flow from these regions. During this process, the porous membranes formed a strong bond with the double‐sided tape, and no leakage was observed during experiments. Additionally, note the location of the sample inlet, which allows the sample to flow through the top PMMA layer and into the separation chamber (see S3 of the Supporting Information section for a detailed fabrication protocol). Finally, note the lack of outlet channels and the implementation of an outflow region that converged toward one outlet. Outlet channels were abandoned during the prototyping phase of this design as they disrupted the counterflow gradient near the bottom of the chamber.

3.3. Electrode Integration

As in the previous prototype [12], an ion exchange membrane (Nafion) is used to isolate the electrode compartment from the separation chamber. This is to ensure that the effects of electrolysis, such as pH changes and bubbles, do not disrupt the electrokinetics and the fluid flow [12]. An attempt was made to decouple the current from the counterflow input to avoid subjecting the ionic transport to the same high resistance criteria. Unfortunately, this likely created an ion concentration polarization (ICP) effect that impacted the separation significantly (see S3 of the Supporting Information section). In the end, decoupling the transport of ionic current and counterflow through the sidewalls was abandoned with the current prototype. Instead, the Nafion membrane was connected to the same side chamber as the porous membrane (see Figure 1).

3.4. Experimental Setup

Syringe pumps (Pump 11 and Pump 33, Harvard Apparatus) were used for the sample and buffer flow, whereas a high voltage supply (HVS448‐3000, LabSmith) was used to supply the electric field. A constant current mode was used to adjust for voltage changes that may arise due to ICP, Joule heating, and bubble formation. Certain access ports were plugged and then unplugged while filling the device with buffer solution, and this process was often repeated several times to mitigate the formation of bubbles.

A portion of the experimental validation of this FF‐CGF device consisted of fluorescent peak measurements. The device was mounted on an inverted epifluorescence microscope (ECLIPSE Ti, Nikon), and a high sensitivity CCD camera (Retiga 2000R, QImaging) was used to view the separation region. Illumination was supplied by a 100 W mercury halide lamp (Intensilight CHGFIE, Nikon), and filter cubes (TRITC and FITC, Nikon) were used to acquire the desired fluorescence signals. ImageJ was then used to measure the intensity of the fluorescent images, and then MATLAB was used to fit the resulting peaks with an exponentially modified Gaussian (EMG) function [20, 21] (see S4 of the Supporting Information section for further details on the peak analysis process). An image of the actual FF‐CGF mounted on the microscope is shown in Figure 6 along with all the relevant design features.

FIGURE 6.

An image of the present FF‐CGF device mounted on a microscope.

4. Results and Discussions

4.1. Device Performance

The uniformity of the counterflow gradient and electric field along the length of the chamber is demonstrated in Figure 7. The separation of the dye molecules in Figure 7a shows excellent agreement with the analytical and numerical models, and this helps validate the new design strategy that is heavily reliant on the high resistance of the porous membrane. The separation of various proteins is shown in Figure 7b, and although focusing is achieved, there appear to be some nonidealities. On the left side of the chamber, the Cyt C stream does not appear to reach its focal point as quickly as the Hg and BSA on the right. This is likely due to bubbles in the side channels or porous membrane that are disrupting the flow gradient and electric field, highlighting the importance of developing a robust protocol for removing all the bubbles from the system.

FIGURE 7.

(a) The separation of xylene cyanol FF, orange G, and ponceau S with a side flow rate of Q_c  = 40 µL/min, a top flow rate of Q_t  = 1 µL/min, and a sample flow rate of Q_s  = 0.2 µL/min. (b) The separation of Cyt C, Hg, and BSA with a side flow rate of Q_c  = 10 µL/min, a top flow rate of Q_t  = 0.5 µL/min, and a sample flow rate of Q_s  = 0.1 µL/min.

4.2. Peak Measurements

The ability of this device to measure focused peaks experimentally is shown in Figure 8. These peaks are then fitted with an EMG function [16], and the corresponding values for the average focal position ⟨x⟩ _f and the standard deviation σ are shown in Table 1.

FIGURE 8.

Peak measurements for the separation of rhodamine B (RhB) and fluorescein (FL) at different side flow rates (Q_c ) and applied currents. In addition, the top flow rate and the sample flow rate for each experiment were (a) Q_t  = 0.1 µL/min and Q_s  = 0.025 µL/min, (b) Q_t  = 0.2 µL/min and Q_s  = 0.05 µL/min, (c) Q_t  = 0.3 µL/min and Q_s  = 0.075 µL/min, and (d) Q_t  = 0.4 µL/min and Q_s  = 0.1 µL/min.

TABLE 1.

Fitted exponentially modified Gaussian (EMG) parameters and estimated separation conditions assuming 2 h = 0.012 cm, µ _EP = −3.6 × 10⁻⁴ cm²/V/s, and D = 4.3 × 10⁻⁶ cm²/s.

Gx	Qc [µL/min]	Current [µA]	Voltage [V]	〈x〉 f [cm]	σ [cm]	E [V/cm]
0.08	10	200 400	89 177	0.12 0.27	0.0265 0.0270	−2.96 −6.97
0.16	20	400 800	168 298	0.15 0.29	0.0210 0.0236	−7.72 −15.13
0.23	30	600 1200	262 550	0.15 0.30	0.0193 0.0228	−11.90 −22.80
0.31	40	800 1600	404 498	0.15 0.26	0.0182 0.0211	−15.34 −27.22

To calculate other relevant parameters, the chamber height was assumed to be around 0.012 cm. Therefore, the electric field E was approximated using the average focal position ⟨x⟩ _f , the side flow rates Q _c, and the assumption that fluorescein has an electrophoretic mobility of µ_EP  = −3.6 × 10⁻⁴ cm²/V/s [22]. In addition, nondimensional gradient number (G_x ), which is crucial for predicting the shape of the distribution [16], can be approximated by assuming a diffusion coefficient of D = 4.3 × 10⁻⁶ cm²/s [23]. In general, the peaks seen in Figure 8 appear to resemble a Gaussian shape, which is consistent with what is expected for the estimated G_x values shown in Table 1. Interestingly, as G_x increases, the peak widths are reduced, and their intensity is increased. Furthermore, a subtle peak tail emerges at higher G_x numbers, and this is particularly evident for fluorescein in Figure 8d. This peak tail is on the right side, indicating that the electroosmotic mobility for PMMA is less than the electrophoretic mobility for fluorescein (Pe_E  > 0) [24]. This result validates what is seen in previous literature, with the electroosmotic mobility of PMMA being measured to be around µ_EOF  = 2.6 × 10⁻⁴ cm²/V/s [25].

As a final note, the performance of a separation device is largely influenced by its applied voltage efficiency that is defined as the percentage of the total voltage applied to the separation chamber. Higher efficiency indicates that a greater portion of the total voltage is applied for separation rather than for other components such as the side channels connected to the separation chamber, lowering the needed total voltage, thus minimizing undesirable effects of Joule heating and electrolysis. The maximum total applied voltage in this study is 550 V (Table 1), which is significantly lower than that of the previous prototype [16], at 1284 V for a reported current of 1200 µA, while achieving comparable performance in separating a Cyt C, BSA, and Hg mixture. This demonstrates an increase in voltage efficiency when replacing the microchannels with the porous membranes.

5. Future Considerations

5.1. Design Parameters

This study focuses on establishing the guidelines above for a device that is more scalable than the original PDMS device [12]; therefore, reproducibility was not evaluated by making more devices. The important design parameters are summarized in Table S3 in Section S5 of the Supporting Information section.

Work on future FF‐CGF systems may benefit from revisiting design components with the aim of identifying steps required to approach mg/hr quantities of throughput. For example, device performance can be improved by undertaking strategies to increase hydrodynamic resistance. Modifying or sourcing porous membranes that are more suitable to generating a uniform counterflow may positively affect performance. Additionally, the integration of outlet channels for collection of separated samples, as well as the decoupling of ionic current from the high resistance membranes, are challenges that could be addressed in future studies that can explore device fabrication repeatability to achieve true preparative operation.

6. Concluding Remarks

The goal of this work was to introduce a new design for an FF‐CGF device that would make improvements on previous designs, making it more scalable for protein fractionation. First, a new fabrication method involving the lamination of PMMA and double‐sided tape was proposed. Then, the challenge of generating a uniform counterflow gradient along the length of the separation chamber was discussed in depth, and it was determined that adding porous membranes to the PMMA assembly is a practical solution. At the same time, the hydrodynamic resistance of the separation chamber, outlet channels, and side chamber also deserves consideration. During this investigation, design guidelines for maximizing the sample throughput and minimizing the effects of ICP were also provided.

As a result of these investigations, a functioning prototype was constructed, and the successful separation of small molecules and proteins highlighted the potential of this device. Moreover, the device provided some useful peak measurements that helped further the understanding of this separation method. Finally, the presence of a uniform counterflow gradient and electric field along the length of the separation chamber was confirmed, and this helps validate the design guidelines provided for this fabrication method. With that said, there are several areas of improvement that should be considered moving forward, including precise flow control through the outlet channels, increased voltage efficiency, the mitigation of ICP and Joule heating, and the removal of trapped bubbles during the experimental setup. In addition, the strategies for scaling up should be examined in more detail, as FF‐CGF can likely rival the throughput of traditional FFE devices while offering the potential of improved resolution and versatility.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Supporting Information

Courtney M., Carreno‐Molina O. M., and Ren C. L., “Design Guidelines of Free‐Flow Counterflow Gradient Focusing Device for Protein Fractionation.” ELECTROPHORESIS 46, no. 13–14 (2025): 1032–1040. 10.1002/elps.8106

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.