key: cord-305457-t7qw1oy2
authors: Zhang, Youhong; Enden, Giora; Wei, Wei; Zhou, Feng; Chen, Jie; Merchuk, Jose C.
title: Baculovirus transit through insect cell membranes: A mechanistic approach
date: 2020-09-21
journal: Chem Eng Sci
DOI: 10.1016/j.ces.2020.115727
sha: 
doc_id: 305457
cord_uid: t7qw1oy2

Baculovirus systems are used for various purposes, but the kinetics of the infection process is not fully understood yet. We investigated the dynamics of virion movement from a medium toward the interior of insect cells and established a mechanistic model that shows an excellent fit to experimental results. It also makes possible a description of the viral dynamics on the cell surface. A novel measurement method was used to distinguish between infected cells that carry virions on their surfaces, cells that carry virions in their interior, and those carrying virions both inside and on their surface. The maximum number of virions carried by a cell: 55 viruses/cell, and the time required for viral internalization, 0.8 [Formula: see text] , are reported. This information is particularly useful for assessing the infection efficacy and the required number of virions needed to infect a given cell population. Although our model specifically concerns the infection process of Sf9 insect cells by baculovirus, it describes general features of viral infection. Some of the model features may eventually be applicable in the studies towards palliation of the COVID-19 outbreak.

The baculovirus (BV) expression vector system (BEVS) is of great interest for the production of recombinant proteins in a wide range of fields-from basic science research to the development of biomedical applications and the production of bio-insecticides [1] [2] [3] [4] . The production of recombinant proteins in BEVS is greatly affected by the characteristics and kinetics of the viral infection process-including, for instance, the multiplicity of infection (MOI), time of infection (TOI), cell cycle, cell line selection, and culture state [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] , but the early events of viral infection, such as the attachment of virions to their receptors and the kinetics of their entry into the cell, are still not entirely understood. This gap hampers the development of efficient and specific genetically engineered proteins and gene therapy vectors based on BVa goal that has lately gained much interest [1] [2] [3] [4] 8] . Since baculovirus was used for efficient gene transfer to mammalian cells in the 1990s [16] [17] , several effective baculovirus-based gene therapy vectors had been created and tested, demonstrating favorable therapeutic efficacy in laboratory and preclinical phase studies [18] [19] [20] [21] . Although the entry processes and the mechanisms involving BVs infection of insect cells or transduction of mammalian cells remain poorly understood, it has been shown that a similar mechanism may mediate GP64 binding to permissive host cells [22] [23] [24] and that BVs enter insect and mammalian cells through a clathrin-mediated endocytosis [25] [26] . Thus, comprehensively characterizing the kinetics underlying the early steps of BVs infection of insect cells is crucial both for improving the production of recombinant proteins in insect cells and for designing therapy vectors and enhancing gene transduction efficacy in therapeutic studies.

Mathematical modeling and simulations may serve as effective predictive tools in pursuing this goal [8, [14] [15] 27] , as they allow dynamical simulation of the process and estimating variables that are hard to measure directly, such as the rate of virion internalization after its attachment to the cell. Quantitative models were also employed to simulate the infection dynamics of infectious diseases. Padmanabhan and Dixit (2011) [28] constructed a kinetic model of hepatitis C virus (HCV) which accounted explicitly for the dependence of HCV entry target cells on CD81 expression. Iwami et al. (2012) [29] optimized a mathematical model to describe the kinetics of the simian/human immunodeficiency virus (SHIV) infection which improved the understanding of SHIV and human immunodeficiency virus type-1 pathogenesis.

Such models, and the virtual experiments that they facilitate, are useful for interpreting the mechanistic aspects of the viral infection process and may save time, manpower, and physical resources in predicting their outcomes. The main purpose of the current study was to construct such a model, focusing on the early stages of a high-MOI BV infection of insect cells [14, 30] , based on and tested against experimental results.

Our model embodies an interdisciplinary integration of microbiology, biology, engineering and mathematics and sets a basic mechanistic approach to the early stages of the infection process. It disregards the effect of non-infective viral mutants which might enter the cell without infecting it. It also does not address the effectiveness of infection, which may vary depending on the elapsed storage time, mainly due to viral aggregation within the viral stocks [31, 32] . As we used the same storage time in all experiments, particle aggregation did not affect the measured results. Consequently, we disregarded storage time in our model. Based on detailed and accurate measurements, our model enhances our understanding of the early BV infection process and can be potentially extended to describe the early stages of other infection processes, such as gene delivery by viruses in mammalian cells. It also provides a basis for modelling the production of foreign proteins. The present model is a first step towards the longterm goal of establishing a more elaborated model of the production process, aimed at saving time, manpower, and physical resources.

The insect cell line used in this study was Sf9 (CCTCC-GDC0008 Note that the units of MOI used here are the ratio of viral particles to cells, as counted by a flow cytometer (Becton Dickinson, San Jose, TX), while, traditionally, it is measured as plaque-forming units (PFUs) per cell or as TCID50/cell. : The ratio of FCM counts to end-point dilution assay titers ranges from 1.0 to 9.4, with an average of 3.7 and a standard deviation of 2.4 [31] . Thus, the MOIs of 100, 200 and 400 BVs/cell used in present experiments were equivalent to 25, 50 and 100 TCID50/cell.

An improved method of FCM was used to quantify baculovirus titer, as described previously [31] [32] [33] . Prior to the FCM analysis, in the final 1-mL phosphate-buffered saline (PBS, pH 8.0) solution, virion samples were fixed with 0.1% (w/v) paraformaldehyde for 30 min at 4 °C and then stained with a specific nucleic acid dye, SYBR Green I, at a commercially 6 available concentration (1× 10 −4 ) for 10 min at 80 °C. Yellow-green fluorescence microspheres (1 μm in diameter, Molecular Probes, Eugene, OR) were added (as an internal reference to the BV) to the control sample [34] . All samples were analyzed using a FACS Calibur flow cytometer (Becton Dickinson, San Jose, TX) and the threshold was set on green fluorescence (FL1-H) to eliminate the background interference, as seen in Fig. 1 .

BV particles were congregated in R1 and bead particles were congregated in R2.

Comparing the number of virion particles with yellow-green fluorescent microspheres, the BV titer was determined by FCM using CellQuest software (Becton Dickinson, San Jose, TX). To avoid the coincidence of viral particles (i.e., two or more particles simultaneously being within the sensing zone), the samples were diluted such that the total event rate was kept below 500 events/s. 

Cells were counted with a hemocytometer using trypan blue (0.5% w/v) exclusion to distinguish dead from live cells. To experimentally monitor the early stages of the infection process and detect infection in cells to which virions attach, we directly tracked GP64-the major envelope protein of the BV, which plays a crucial role in the early stages of infection.

GP64 is essential for the attachment of virions to cells in a culture and for their transport between cells in infected tissues [35] , as it is involved in the binding of the virions to host cell receptors [36] and acts to locally reduce the membrane pH, which triggers membrane fusion.

Once the virus has entered the cell by endocytosis, GP64 is necessary for stripping the nucleocapsid from its capsid proteins and for releasing the virion into the cytosol [37] [38] [39] . To label GP64 specifically and thereby detect only infected cells, we used the monoclonal antibody AcV1, which binds to GP64 but does not reduce its ability to attach to cells [25, [40] [41] [42] [43] . To differentiate between virions that are attached to the cell surface from those that have already entered it, we either permeabilized the cells or left them intact (see methods) assuming that AcV1 labeled BVs attaches to the cell surface in both permeabilized and non- To count the number of non-permeabilized infected cells, the samples were stained with 5 μL AcV1-PE without adding the permeabilization reagents. After a 30 min incubation at 4 °C in the dark, the cell samples were washed again. Finally, to obtain the optimal fluorescence signal, the cell samples were examined by FCM within 30 min. The infected and uninfected cells were detected using the scatter plot with forward scattering (FSC-H) versus side scattering (SSC-H), and then the ratio of infected to total cells was analyzed by the BD CellQuest software. Control cell samples were treated using the same steps, but without adding AcV1-PE (data not shown).

We began by establishing the capacity of Sf9 cells to carry Autographa californica multicapsid nucleopolyhedrovirus (AcMNPV)an important reference for MOI optimization.

We detected the virion titer by flow cytometry (FCM), using the fluorescent dye SYBR Green I to stain the nucleic acids of the virions [31] [32] [33] [34] . The Sf9 cells were infected with AcMNPV at MOIs of 114, 219, or 421 BVs/cell, and the obtained virion and cell profiles are shown in Table 1 Experimental data on free viruses in the medium and the infected cell concentrations for each MOI. The maximum number of virions that can attach to a cell, N, is defined here as:

where it is assumed that MOI ≥ .

Here is the final measured concentration of virions in the medium, is the final measured concentration of infected cells 9 h post-infection (ℎ ), as shown in Fig. 3 and 

In the initial stage of the study, we characterized the kinetics of non-infected Sf9 cells, which were grown under the same conditions as those used in the infection experiments (see Methods in the Attachments), but without BV infection. It was found that the simple first-order growth rate fits satisfactorily the collected data. The use of more sophisticated kinetic forms is therefore unnecessary The kinetic expression for the growth of non-infected cells is:

The solution of this expression is:

where is the cell concentration, is time, and is the growth rate factor. Regression of expression (3), based on all experimental data points in a 60ℎ experiment, yielded = 0.022[ℎ −1 ] . This kinetic rate constant was used in the mathematical model described below.

The value is lower than data reported previously for these cells, but it should be kept in mind that anyway the growth rate of the cells is sensibly lower that the infection rate. This consideration is reinforced further by the success of the assumption of constant cell concentration rate presented in 3.5.

The dynamics of the early stages of the infection process in Sf9 cells are shown in Fig. 4 for MOIs = 114, 219, and 421. The percentage of infected cells, as evaluated without permeabilization, , increased until 4 ℎ , reached a maximum of 79%, and then slowly decreased to 65% at 9 ℎ . This maximum will be explained below in terms of the balance between virus attachment and virus internalization. In contrast, the percentage of the infected cells, as evaluated when permeabilizing reagents were used in the analysis, , increased monotonically, reached a maximum of 97%, and then, either remained unchanged, or moderately increased to a plateau. This effect was observed with only minor differences between the three examined MOIs (although higher MOIs resulted in a slightly higher ),

suggesting that almost all cells were infected by or before approximately 6 ℎ . 

To model the dynamics of the early infection process, we used the following variables: x 

The infection process is viewed here as two serial steps: the first is the virion-cell encounter and its attachment to the cell surface, as defined in Eqs. (6) and (9); the second step consists of the internalization of the virion into the cell, assumed here to last a certain time,

, as reflected in Eqs. (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) . In addition, we assume that (1) The latter bears the simplifying assumption that after the first virion attachment to each untreated cell, it will appear as "infected" until all its N attachment sites are used and all its surface virions internalized.

One of the simplest ways to depict macroscopically the mechanism of virion attachment to cells is to assume that the rate of attachment is proportional to both the number of free virions and the number of unused attachment sites on the cell.

Denote the initial virion concentration in the medium as 0 and the number of virions removed from a unit volume of the medium (via attachment to cells) as ( ) . The concentration of free virions in the medium is therefore, = 0 − . Assuming that the rate of virus attachments is proportional both to free virus concentration and to the concentration of attachment sites, the differential equation describing the adsorption rate of virions can be written as:

where ( ) = ( ) + ( ) is the total cell concentration hours after TOI, and

Equation (6) 

The material balance on the infected cells in the system yields: At TOI, (0) = 0 ( 1 0 )

A balance on the pool of viable cells will include a cell growth term, already shown in Eq.

(1) to be a first-order process with a kinetic constant , and a second term for viable cell depletion by infection:

At TOI, (0) = (0) = 0

where 0 for each MOI is shown in Table 1 . 

In this case, cells containing only internalized virions cannot be distinguished from uninfected cells, since AcV1 conjugated with a fluorescent PE cannot enter into nonpermeabilized cells. Assuming that the internalization time, , is identical for all virions, we can calculate ( ), i.e., the number of virions (per unit volume of the medium) attached to cell surfaces (and, therefore, detectable) at any given time. This value is equal to ( ) for < , and is equal to the difference between the number of virions that were attached to the cells between ( − ) and for ≤ , since virions that arrived earlier than ( − ) have already been internalized and cannot be detected. Therefore,

Denoting by ( ) the number of internalized viruses at time per unit volume of the medium, we obtain:

The rate of change of ( ), ( ), at time , is:

And, following, Eq. (6):

The rate of viral internalization, ( ), at a time , is: Where ⌊ ⌋ denotes the "whole value function" (also called the "floor function"), which returns the largest integer that is smaller than or equals to x (rounded down). It follows that, for any ≥ ,

A crude approximation to ( ) is made here by assuming that the concentration of darkened cells is proportional to ( − ) for ≥ . Noting that, for < , ( ) = ( ), we obtain:

The solution of this model, represented in equations (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) , was fitted to the experimental data and the kinetic parameters k and , , and were determined. The optimization was accomplished using the MATLAB and Polymath codes. The optimized parameters are shown in Table 2 . Eqs. (6) (7) (8) (9) (10) (11) (12) (13) were solved numerically using MATLAB and the parameters were evaluated with respect to the measured data in the time interval 0 ≤ ≤ 3ℎ. Table 3 for MOI = 114. with the AcMNPV-Sf9 system shown in Table 2 . This indicates that different Baculovirus may have different internalization half-time value. Since the internalization time for each specific virus-host system is expected to be a characteristic constant, it seems that viral vectors with shorter internalization times would have some advantages in gene therapy, since they enter host cells more rapidly while the cells are robust. Therefore, the estimation of the internalization time for any potential virus-host combinations may be very important. The very low value of the constant indicates that the actual accumulation rate of dark cells ⁄ is substantially lower than the floor function shown in Eq. (19) , and yet follows a similar pattern,

given the quality of the fit.

Based on the results shown above, a crude approximation to ⁄ can be made assuming that the generation rate of darkened cells is proportional to :

As an example, Fig. 7a demonstrates the typical dynamics of the system variables ( ), 

The low growth factor, = 0.022, suggests that the cell concentration, may be treated as nearly constant at the range 0 ≤ ≤ 3ℎ. This observation is further supported by the experimental behavior of the cell concentration shown in Fig. 6 . In this section, we neglect the changes in and consider it to be a constant equal to 0 . In this case, is set to zero and Eqs. (6) (7) (8) (9) (10) (11) (12) can be integrated analytically to yield a closed-form solution for , , ,

, and . (21) where = 0 ; = ( 0 − 0 ), and is equivalent to in Eq. (5).

The closed-form solutions of , , and are shown in the Appendix.

Next, we used the closed-form solution with the parameters shown in Table 3 Note that the asymptotic value of ( ),

is independent of the kinetic constant . In fact, this is the total number of attachment sites on the cells, as might be expected. As defined above, ( ) is the number of virions per unit volume that have been captured by cells between 0 and . It reaches maximum when all cells are saturated by N virions. N is a constant, specific to each virus-host system

The approximated solution, based on a constant value of the total cell concentration, appears to be successful for our set of initial conditions. The solution of Eq. (6) can be replaced by the closed-form expression given above (Eq. (21)) without noticeable changes in the predictability capacity of the model.

In the present multi-disciplinary research, we propose a mathematical model of the early- 

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*The maximum number of virions that Sf9 cells can carry: 55 viruses/cell, is reported. *Cells that carry virions on their surface, in their interior, or both are distinguished *Analytical mathematical solution renders satisfactory results

This research was financially supported by the National Natural Science Foundation of China (20876120 and 20910102037) and the Nature Science Foundation of Hubei, China (2013CFA101). We thank Professor Qi Yipeng of Wuhan University, China, for kindly providing wt AcMNPV.

The authors declare no competing interests, financial or other.