Direct visualization of virus removal process in hollow fiber membrane using an optical microscope

Virus removal filters developed for the decontamination of small viruses from biotherapeutic products are widely used in basic research and critical step for drug production due to their long-established quality and robust performance. A variety of imaging techniques have been employed to elucidate the mechanism(s) by which viruses are effectively captured by filter membranes, but they are limited to ‘static’ imaging. Here, we propose a novel method for detailed monitoring of ‘dynamic process’ of virus capture; specifically, direct examination of biomolecules during filtration under an ultra-stable optical microscope. Samples were fluorescently labeled and infused into a single hollow fiber membrane comprising cuprammonium regenerated-cellulose (Planova 20N). While proteins were able to pass through the membrane, virus-like particles (VLP) accumulated stably in a defined region of the membrane. After injecting the small amount of sample into the fiber membrane, the real-time process of trapping VLP in the membrane was quantified beyond the diffraction limit. The method presented here serves as a preliminary basis for determining optimum filtration conditions, and provides new insights into the structure of novel fiber membranes.

From the data presented in Figs. 3 and S1, we estimated the calibration factor, i.e., mol per unit fluorescent value (a.u.) measured in our observation condition with the 1-s exposure time.
In our measurements, 5 µL fluorescently labeled BSA, to which 23 µM DyLight488 was coupled, was infused into the hollow fiber membrane. Thus, a total of (5 µL) × (23 µM) ~ 10 -10 mol of fluorophore passed through the membrane in all directions. We detected this process by observing one representative pixel and plotted the time course of changes in signal intensity in Fig. S2. From the integrated value of the curve shown in Fig. S2, the total amount of fluorescent signal was estimated to be 1.6×10 5 a.u. We assume that all of the molecules that we injected were detected in less than 300 ms of exposure time because the curve in Fig. S2 is contiguous. The expected total fluorescent signal was corrected to be (1.6×10 5 a.u.) × (60 s / 0.3 s) ~ 3.1×10 6 a.u., as the time interval between exposures was 60 s. Based on these values, we estimated that the calibration factor was (10 -10 mol) / [(3.1×10 6 a.u.) / (0.3 s)] ~ 10 -17 mol s a.u. -1 .
The dimensions of the single hollow fiber that we used had an inner diameter of ~600 µm and a length of ~5 cm. Therefore, the area of the inner wall of the membrane was estimated to be ×(600×10 -6 m)×(5×10 -2 m) ~ 9×10 -5 m 2 .

Supplementary Discussion
In Fig. 4d in the main manuscript, we observed the process of virus-like particles (VLP) capture in a single exponential manner. Here, we discuss a possible scenario to explain our observation of VLP movement with an exponential function reaching a plateau.
We assume that there is a resistance force from the membrane (Fm) that acts against each particle, and that this force depends on the particle position (x) due to the dense structure of the membrane layers. As a simple model, fluid force (Ff), a function of the relative speed of the flow against the particle (vr), is also applied to the particle. vr is expressed as vs-v, where vs and v are the speeds of the fluid and particle, respectively. The above two forces are always balanced because particle inertia is neglected in a system with an extremely low Reynolds number, giving us the following equation as a first approximation.

Fm(x) + Ff(vr) = 0
Suppose that Ff is proportional to the speed of the particle, as in the case of a simple Newtonian fluid, then the equation can be rewritten as: where,  is the drag coefficient of the fluid against the particle.
In an actual observation, the red curve in Fig. 4d is described as: (2) where, t0 is the moment when the fluorescent signal is detected for the first time at the position close to the inner edge of the membrane; x0 is the peak position of the signal at t = t0;  is the time constant required to reach the position where the particle is captured and finally immobilized; r is a parameter indicating the depth that VLP can move in the membrane to reach the capture plateau. In Fig. 4d, we took the position of the outer edge of the membrane as x = 0, and thus the thickness of the membrane is nearly equal to x0.