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Methods. Author manuscript; available in PMC 2010 June 2.
Published in final edited form as:
PMCID: PMC2879882

Intensive RNAi with lentiviral vectors in mammalian cells


RNAi is a powerful technology for analyzing gene function in human cells. However, its utility can be compromised by inadequate knockdown of the target mRNA or by interpretation of effects without rigorous controls. We review lentiviral vector-based methods that enable transient or stable knockdowns to trace mRNA levels in human CD4+ T cell lines and other targets. Critical controls are reviewed, including rescue of the pre-knockdown phenotype by re-expression of the targeted gene. The time from thinking about a potential knockdown target to analysis of phenotypes can be as short as a few weeks.

1. Introduction

RNA interference (RNAi) and the green fluorescent protein (GFP) are two methodological advances that have transitioned so rapidly and effectively from discovery to widespread usefulness that they now seem indispensable to basic biomedical scientists. Their utility was recognized by Nobel Prizes awarded in 2006 and 2008, respectively. Though each of their core biological mechanisms evolved to support intricate, phenotypically striking processes – whole organism RNA silencing effects in plants and worms and the bioluminescence of ocean invertebrates – a hallmark of both technologies is relative simplicity in practice. The method reviewed here combines them with an accessible gene transfer technology that is particularly suited to facile use by HIV researchers. We describe how to establish stable, stringent RNAi using lentiviral vector transduction of short hairpin RNAs (shRNAs) followed by optional sorting for co-encoded GFP or one of its numerous spectral variants. The techniques described enable well controlled, phenotype revealing knockdowns in human T cell lines and other targets. They also allow the researcher to modulate the degree of knockdown.

Numerous in-depth reviews of RNAi and lentiviral vectors are available and other groups have used shRNA expression similarly to good effect. In keeping with the theme of this volume, we draw on our own experience to concentrate on providing practical advice to researchers studying early events in HIV-1 replication, including integration. However, the methods are easily adapted to other fields. We also discuss ways to intensify RNAi when needed, as it was for establishing the role of lens epithelium-derived growth factor (LEDGF/p75) in HIV-1 replication [1]. Similar knockdown stringency may also be useful for studying other viral dependency factors with roles in early events. Intensification can be especially significant for those factors that are spatially concentrated in a functionally critical way, e.g., by chromatin association [1]. We focus on CD4-positive T cell lines, explain proper controls to validate RNAi specificity, and also detail how to assess HIV-1 and control retrovirus phenotypes after knockdown.

shRNAs mimic natural RNAi in ways that synthetic siRNA oligonuceotides do not [2]. RNAi is initiated normally by long double-stranded RNA (dsRNA), which serves as a substrate-trigger for Dicer, a ribonuclease III that cleaves dsRNA into 21–23 nucleotide small interfering RNAs (siRNAs) [3]. siRNAs function within a multi-protein complex called the RNA-induced silencing complex (RISC) [4]. RISC contains helicase activity necessary to free the antisense guide strand to form the RNA-protein complex siRISC. The guide strand cooperates with the endonuclease Argonaute2 to guide sequence-specific degradation of mRNA 10–11 bases upstream of the 5’ end of the guide strand, ultimately leading to gene silencing [46]. While siRNAs can be administered directly and incorporate into RISC without any cellular modification, Dicer-generated siRNAs are generally more potent than their synthetic counterparts [7]. shRNAs are transcribed from sense and antisense DNA sequences, generally 19–29 nucleotides in length, which are connected by a short intervening linker [2]. Thus an advantage of shRNAs is that their stem-and-loop secondary structure generates siRNAs in a Dicer-dependent manner [8]. They also provide the obvious advantage of allowing stable expression from DNA constructs. The short length of shRNAs also minimizes potential activation of mammalian double stranded RNA-dependent protein kinase R (PKR) [9, 10], limiting broad off-target effects. shRNA expression is often carried out with RNA polymerase III (pol III) promoters (e.g. H1 and U6), which encode specific initiation and termination sequences that generate the optimal 2-nt (uracil) 3’ overhangs. However, pol II promoters can also be used. For a review of this issue, see [2].

In situations where small residua of the target protein retain significant biological activity, as exemplified by LEDGF/p75, a good approach is a gene-level knockout in mice. Human cell knockdowns and mouse cell knockouts were both instrumental for understanding the function of LEDGF/p75 in the HIV-1 life cycle [1, 11, 12]. However, murine cells have diverse, complex blocks to HIV-1 replication, which prevents testing of the full life cycle. Mouse embryonic fibroblasts are also, for a variety of experimental reasons, more challenging to adapt to controlled HIV experiments than are human primary and immortalized human CD4+ T cells. Primate cell knockouts seem logical solutions, but remain very difficult in practice. Intensified RNAi in human cells is therefore often a worthwhile alternative.

We review our approach, intensified lentiviral vector RNAi (ilvRNAi) in human T cells, in which the capacity of lentiviral vectors for effective stable transduction of both dividing and nondividing cells is combined when needed with sorting for co-transduced fluorescent proteins to achieve knockdowns of graded intensity. Properly executed, the complete method includes control shRNA transductions and re-expression with RNAiresistant cDNAs. Although lentiviral vector systems have now been derived from primate and non-primate lentiviruses (reviewed in [13] and [14]), the higher transduction efficiency of HIV-1 vectors in most human CD4+ T cell lines and primary lymphocytes (in our hands up to 10–20 fold per unit of particle reverse transcriptase activity) makes them preferred for these targets. Because the transfer vectors we use are U3-deleted, deriving cell lines with HIV-1-based vector transduction does not interfere with subsequent HIV-1 infection studies: the vectors are not rescued by replicating HIV-1 and the missing 400 nt can be used to anchor 2-long terminal repeat (LTR) circle PCR and Alu-PCR for HIV-1 challenge virus integrants.

2. Description of method

2.1 Overview

The following protocols can be adapted by any laboratory experienced in molecular biology and mammalian tissue culture. Figure 1 illustrates the basic stages of developing and using ilvRNAi, which include:

  1. Designing candidate shRNAs for the gene of interest and inserting them in the form of a synthetic cDNA adapter into a transfer vector.
  2. Screening the shRNAs to identify one or more with highest activity.
  3. Producing vector particles via high efficiency co-transfection of 293T cells with the ilvRNAi transfer vector, packaging, and envelope plasmids.
  4. Transducing target cells with active and control shRNA-expressing lentiviral vectors.
  5. Enrichment by fluorescence-activated cell sorting (FACS) for fluorescent protein expression if desired. We have used mCherry frequently, in the vector TSINcherryU6 (Fig. 2). The palette of spectral variants continues to increase [15].
    Figure 2
    ilvRNAi vector TSINcherryU6. The illustrated restriction sites are unique, allowing one step insertion of shRNAs. A unique MluI site and either SalI or XhoI is used for adaptor insertion. In addition, this vector preserves native 23 nt spacing from the ...
  6. Assaying for relevant phenotypes. These include: degree of RNAi knockdown at the mRNA and protein levels, cell viability and growth rate, CD4 and co-receptor expression, susceptibility to replication-defective HIV-1 reporter viruses and replicating HIV-1, and susceptibility to other retroviruses.
  7. Re-expressing (back-complementing) the targeted gene to show that gene function is rescued, thus controlling for specificity. When feasible, this is the most important and rigorous control experiment for RNAi projects, though many studies neglect it.

Our protocols will highlight three points: 1) achieving deep knockdown to eliminate residual protein expression; 2) assaying quantifiable, relevant endpoints to validate knockdown phenotype; and 3) attention to the right controls to verify RNAi specificity and prove gene function.

Figure 1
Outline of the ilvRNAi process.

2.2 Step-by-Step Protocol

2.2.1 Designing and cloning a shRNA-lentiviral vector

Several issues are relevant when designing an shRNA construct: the promoter, the target sequence, and the shRNA construct sequence. pol III promoters, e.g., U6 and H1, are useful because of their precise start and termination sequences. We have used both in human T cell lines.

Active siRNAs are generally 21-nt long with 3’ dinucleotide overhangs and 19-nt complementarity [16]. A number of algorithms are available for choosing optimal 19-nt targets [17, 18]. The Ambion RNAi interference web resource is helpful ( In general, it is reliably useful to choose 19-nt target sequences that begin with AA, contain less than 50% GC content, and do not contain homo-repeats greater than 3 nucleotides. Those 19-mer sequences that have been functionally validated with siRNA oligonucleotides are likely to be effective when used as shRNAs, and a review of previously published siRNAs or shRNAs is a sensible way to start. Sequences longer than 21-nt can be used, and may actually be more efficient Dicer substrates [7, 8], but there is a risk of confounding PKR induction [9, 10]. We have found both 21-mer and longer (27-mer) sequences to be effective. The chosen sense sequence is then linked to the antisense sequence with an intervening loop of variable length. We use the 9-nt sequence TTCAAGAGA [19] but most evidence suggests this is not critical. For a control shRNA target we have used actgccgttgttataggtg, which in our and others ( hands has been phenotypically neutral even at high MOIs. Figure 2 depicts transfer vector TSINcherryU6, which we have modified from the lentiviral vector of Llano et al. [1] in two ways: (1) introducing unique restriction sites that enable shRNA insert cloning in a single step; (2) making the human U6 start resemble the native promoter more closely. This is as effective as the original shRNA transfer vector when tested head to head for LEDGF/p75 knockdown and HIV-1 resistant phenotype (our unpublished data).

Sense and antisense oligonucleotides for the shRNA insert need to be synthesized so they contain the pol III termination sequence (TTTTTT) and when annealed yield adaptors at their termini that match the vector. In TSINcherryU6 (Fig. 2), MluI and SalI are positioned for this purpose.

  1. Dilute the sense and antisense shRNA oligonuceotides in TE buffer (10 mM Tris pH 8.0, 1 mM EDTA) to 1 µg/µl. When ordering, HPLC-purified oligonucleotides are preferred.
  2. Mix 2 µl of each oligonucleotide with 46 µl of 1X DNA annealing solution (10mM Tris, pH 7.5 – 8.0, 50mM NaCl, 1mM EDTA; the annealing buffer supplied by Ambion in pSilencer kits is also effective). In a thermocycler, incubate at 90°C for 3 min, then 37°C for one hour.
  3. Dilute 5 µl of annealed oligonucleotides in 45 µl of nuclease-free water. Ligate 4 µl of diluted annealed oligonucleotides with 1 µg of restriction enzyme-digested (e.g, with MluI+SalI) pTSINcherryU6 using 5U of DNA T4 ligase in a 10 µl reaction overnight at 16°C. Select the ligation against wild-type with PmeI to reduce background (heat kill the ligase first) or directly transform E. coli with 5 µl of the ligation and plate on LB ampicillin plates. A vector-only ligation control can be used to determine recircularization background. CIP treatment of the backbone requires that the oligonucleotides be phosphorylated on their 5’ ends.
  4. Screen colonies by DNA restriction digest (SacII + SalI yields a diagnostic 397 bp band, whereas the starting pTSINcherryU6 vector will yield the smaller 347 bp size).
  5. Sequence with an appropriate primer. 5’-TCATAATGATAGTAGGAGGC-3’, located 147-nt upstream of the U6 termination signal, works well.
  6. Determine RNAi efficacy by transient transfection and immunoblotting of the shRNA constructs. A useful method is to co-transfect shRNA plasmids with a plasmid expressing an epitope-tagged version of the target. Alternatively, if efficient (> 80%) transient transfection can be achieved, the endogenous protein can be measured. (In some circumstances, proceeding directly to lentiviral vector transduction may be easier for the laboratory). On average, approximately one in five screened shRNAs are usefully effective, though considerable variation is the rule. Extent of knockdown is analyzed at the mRNA level with RT-PCR or Northern blotting and protein level by immunoblotting.

2.2.2 Vector production

Lentiviral vector particle production is performed by co-transfection of the shRNA transfer vector with an envelope glycoprotein expression plasmid and a packaging plasmid. Examples of the latter include pCMVΔR8.9, which encodes gag/pol, tat and rev [20]. Alternative 4-plasmid systems supply Rev from a separate plasmid, e.g., the pLP1 + pLP2 combination (Invitrogen) or pCHGP and pCMV-Rev [21]. Rhabdoviral (VSV-G) envelope glycoprotein pseudotyping expands vector tropism and enhances vector titers and stability [22].

  • 7
    Harvest 293T cells when 60% confluent, and plate 3 × 106 cells in 12 ml in a 75 cm2 flask the day prior to transfection. Eight 75 cm2 (T75) flasks per vector are appropriate for producing enough stock for a given stable cell line. This amount of vector supernatant can be concentrated in four 36-ml Sorvall tubes, which translates to one rotor spin with 4 out of 6 buckets used. Twelve 75 cm2 flasks can also be processed in one rotor spin using all six buckets. If more vector is required, scaled-up procedures using high-area Nunc Cell Factories are helpful [23].
  • 8
    Transfect the cells the next day by the calcium-phosphate co-precipitation method, using transfection reagents equilibrated to room temperature. For each T75 flask, dilute 10 µgi of the control shRNA-expressing or the active shRNA-expressing transfer plasmid, 10 µg of an HIV vector packaging plasmid, and 3.3 µg of a VSV-G expression plasmid (e.g., pMD.G) in 1 mM Tris pH 8.0 up to a final volume of 720 µl. Add 80 µl of 2.5 M CaCl2, mix by brief vortexing and then add 800 µl of 2× HBS pH 6.95 – 7.05 while vortexing. For convenience, batch the DNA precipitate for all eight flasks in one tube. Incubate the transfection mix at room temperature for the appropriate time, generally 5–10 minutes. Empirical pre-testing of each 2× HBS batch is helpful. Test batches with pH 6.95, 7.0, and 7.05. Test transfections can be done with a GFP expression plasmid in small scale (e.g., 6-well plate). Also, timing can vary between batches of 2× HBS or even within batches when pH shifts occur with time. Optimal precipitate particle size is signaled by a faint milky turbidity when the tube is held up to the light. Vortex for one second to disperse the precipitate completely and then add it directly to the cell medium drop-wise with gentle mixing, taking care to not disrupt the 293T monolayer.
  • 9
    Remove the transfection supernatant 12 to 16 h after transfection and add 12 ml of fresh culture medium to each flask.
  • 10
    After an additional 24–48 hii harvest the tissue culture supernatant containing the vector particles.
  • 11
    Clarify by centrifugation at 800g for 10 min, and then filter through a 0.45 µm membrane (some workers simply filter the unclarified supernatant directly). Add up to 25 ml of clarified vector supernatant to a 36-ml tube (Sorvall PA thin-walled tube, catalog number 03141 or equivalent). Two T75 flasks-worth of vector supernatant can be spun in one 36-ml tube. Pipette 3 – 5 ml of 20% sucrose in 50 mM Tris pH 7.4, 100 mM NaCl under the vector supernatant. Fill each tube with phosphate-buffered saline (PBS) so that liquid is 5 mm from the top of the tube. A balance can be used to make sure opposing tubes are equal in weight. Ultracentrifuge at 100,000 to 125,000g for 2 h in a swinging bucket rotor (ex: Beckman SW32Ti part number 369694 or SW28 part number 342204) at 4°C. To re-suspend the vector pellets, add 0.5 – 1.0 ml of cold RPMI 1640 media containing 10% fetal calf serum (FCS) to each tube and incubate on ice for 15 min. Repeated up and down pipetting is generally needed to fully re-suspend pellets. Avoid making excessive bubbles. Pool the re-suspended, concentrated vector. Use immediately or store at −80°C in 100 ul aliquots.
  • 12
    To titer lentiviral vectors, transduce 5 × 104 target cells seeded in a 24-well plate with approximately half-log dilutions of the concentrated vector supernatant (e.g., 1, 0.3, 0.1, 0.03, 0.01 µl). If target cells are adherent, remove vector supernatant and wash with warmed PBS 6–16 h after transduction. Replace with fresh media. If cells are suspension, spin cells in a microfuge tube to remove vector and resuspend in fresh media. Return cells to 24 well plate. Removing the vector supernatant reduces toxicity. Toxicity is most evident in wells transduced with the highest amount of vector. Analyze transduced cells by flow cytometry for fluorescent protein expression (i.e. mCherry) 48 – 72 h post-transduction. Some fluorescent proteins (i.e. mCherry) are quenched by certain fixatives. Protocols may need adjustment to accommodate detection of such proteins. Also, if less common spectral variant fluorescent proteins are used in the HIV-1 transfer construct, check that the flow cytometer is capable of exciting and detecting the protein to avoid under-estimation of titer. Titer is calculated using the percentage of positive cells times the number of cells at the time of transduction times the vector dilution factor, and is expressed as transducing units (TU) per ml.

If vector production was successful, unconcentrated vector titers should be at least 1 × 106 TU/ml. Concentrated vectors are typically at least 1 × 108 TU/ml depending on the starting and final resuspension volumes. Generally only a fraction of a microliter of a vector with 108 TU/ml is required to fully transduce 50,000 cells. Keep this in mind when titering vector to ensure samples are in the linear range for titer calculation.

2.2.3 Generating stable cell lines

Generating stable cell lines requires transducing target cells with vector at increasing MOIs, cryopreserving and analyzing cells for a relevant knockdown phenotype. If desired, enrichment by FACS can be performed. Differential transduction efficiency and sorting allow graded RNAi intensity.

  • 13
    Plate several wells of a 24-well plate with 5 × 104 to 1 × 105 target cells. If cells grow in suspension, plate them in 200 – 300 µl. If cells are adherent, allow them to adhere to the plate before transduction. Transduce cells with the shRNA-expressing vector at a range of MOIs, e.g., from highest possible as tolerated by the cells (do not exceed a ratio of 1:1 vector volume to media volume), then at approximately four to six half-log dilutions below that. Do the same in parallel with the scramble control shRNA vector. If target cells are adherent, remove vector supernatant and wash with warmed PBS 6–16 h after transduction. Replace with fresh media. If cells are suspension, spin cells in a microfuge tube to remove vector and resuspend in fresh media. Return cells to 24 well plate. Expand the culture until approximately 107 cells are available. Suspension cells may take longer to expand. Within the first week after transduction, avoid diluting human T cell lines to below 2 × 105 cells per ml.
    Subject to FACS those cells that survive the initial transduction without appreciable toxicity. Toxicity can be due to two factors. The first is immediate effects of the vector preparations such as VSV-G exposure rather than genotoxicity, and is only seen at highest vector concentrations. The second possibility is that knockdown of the target protein is itself toxic. In this case, less intensively transduced cells can be used. Alternatively, vector designs that incorporate regulatable shRNA expression may be considered [24].
  • 14
    Optional: for intensified RNAi, use FACS for mCherry to sort both active and control shRNA cells for the 10% brightest population. Expand cells appropriately for phenotype analysis while recording growth kinetics for control and active shRNA-transduced lines.
  • 15
    Verify extent of knockdown by immunoblotting and/or RT-PCR. Once verified, analyze the relevant phenotype, pairing control and active shRNA cells in each assay. When protein level is assessed by immunoblotting, it is preferred to directly analyze physiologically relevant sub-compartments (e.g., chromatin [1]). A complete data set requires that re-expression of the target protein rescue the parental phenotype (see next section).

2.2.4 Re-expression of target protein

Potential off-target effects make proper controls necessary for correct interpretation of RNAi experiments. A consensus gold standard is target-protein re-expression and pre-knockdown phenotype rescue [25, 26]. This step also controls for possible effects of target protein over-expression, as does parallel over-expression in cells lacking the knockdown. We have used gamma-retroviral (MLV) vectors for re-expression, although stable plasmid transfection is also an option [27]. For obvious reasons, lentiviral vectors are poor choices in the presence of a knockdown of a dependency factor that acts between lentiviral entry and integration (e.g., LEDGF/p75).

  • 16
    To construct a re-expression vector, use overlap extension PCR or site-directed mutagenesis to insert approximately 5–7 synonymous mutations into the shRNA target sequence of the gene cDNA. Insert the shRNA-resistant cDNA into the MLV transfer vector. Epitope-tagging may aid in detection of the re-expressed protein though, if choosing this option, it is important to first confirm the tag does not interfere with normal protein function. A vector that permits co-expression of drug resistance genes (e.g., neomycin, puromycin, hygromycin, or phleomycin) is optimal. The protocol below utilizes a bicistronic MLV vector based on pJZ308 [28]. To produce and concentrate MLV vectors, follow steps 7–11 with the following variations. Either carry out a 3- plasmid co-transfection that includes the MLV transfer construct and VSV-G plasmid plus an MLV packaging plasmid (our preferred approach), or transfect only the transfer and VSV-G plasmids into a retroviral packaging cell line (e.g., Phoenix A cells [29]). When using an MLV packaging cell line, transfect each T75 flask of 3 × 106 cells with 10 µg of the MLV transfer vector and 3 µg of pMD.G. For vector production in regular 293T cells, transfect 3 µg of the MLV transfer vector, 3 µg MLV packaging plasmid (e.g., PHIT60, [30]) and 1 µg of pMD.G per T75 flask. Collect and concentrate the supernatant on a 20% sucrose cushion, and resuspend in RPMI 1640–10% FCS. Vector harvested from eight T75 flasks is typically concentrated down to one ml or less.
  • 17
    Generate a baseline drug kill curve by plating 105 cells/ml in a 24-well plate and adding 1 ml of either culture medium containing increasing amounts of drug, or medium without drug. Identify the minimal dose that kills all cells in one to two weeks. G418 is slow compared to puromycin, which generally kills within 3 days.
  • 18
    Transduce 105 control or knocked down cells with different amounts (e.g., 300, 200, 100 µl) of the concentrated MLV vector. Remove input vector as described above 6–16 h after transduction. Maintain the cells in fresh media for at least 48 – 72 h before adding G418 at the kill curve-determined concentration. Expand cells in selection medium to appropriate numbers for phenotypic analysis and cryopreservation.
  • 19
    Evaluate target gene re-expression by immunoblotting. Cells with protein levels roughly equivalent to the parental line are optimal. If variants of the protein of interest are re-introduced, for example to test ability of mutants to rescue function, it is important to use an epitope tag or some other immunoblotting protocol that distinguishes the mutant from the endogenous protein so that the continued absence of the latter (i.e., robust persistence of the RNAi) can be verified. Note that re-sorting for mCherry can be carried out at any point during later steps of the protocol if a drift towards endogenous protein leakage (decreased RNAi effect) occurs.
  • 20
    Assay all four cell lines (active and control shRNA knockdown and their respective back-complemented lines) for relevant phenotypes. Rescue of parental phenotype supports RNAi specificity. Challenges can be carried out with single round HIV-1 reporter viruses and with replicating HIV. In addition, stage-specific PCR for reverse transcription intermediates (linear, circular) and integrated DNA (Alu PCR) allows assignment of replication blocks to a particular stage of the life cycle [1].

3. Concluding remarks

This protocol allows researchers familiar with basic molecular biology and cell culture to rapidly and effectively perform transient or stable knockdowns with lentiviral vectors. One-step construction of ilvRNAi transfer vectors allows rapid progression from thinking about a gene target to analyzing knockdown results. RNAi intensification by sorting for stably high-expressing populations is readily performed though is not always necessary. For HIV researchers, the ability to effectively knock down individual genes in CD4+ T cells allows rapid analysis of new targets. Indeed, high throughput siRNA library-based screens [31, 32] are now identifying numerous candidate HIV-1 dependency factors that can be subjected to confirmatory studies by focused methods such as ilvRNAi. Details of these large scale transcriptome studies also illustrate how the degree of achievable intensification can matter. For example, LEDGF/p75 was originally brought to the attention of HIV researchers by an affinity-based proteomics screen for integrase interactors [33]; see [34] and [35] for reviews. It’s potency as a viral cofactor led to a prediction that it would likely be missed by broad RNAi screens [1], which turned out to be the case [31]. The second large scale screen also found minimal (3–8%) inhibition of single cycle HIV-1 infection with pooled LEDGF/p75 siRNAs [32], which prospectively might not be regarded as an actionable hit. The point is that by virtue of their breadth, such screens cannot generally approach the RNAi intensification needed to identify and confirm factors that retain viral cofactor activity at a small fraction of their endogenous levels.


We thank I. Kemler and N. Gaznick for assistance with pTSINcherryU6 construction


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iThese values can vary. Early lentiviral vector protocols emphasized quite large DNA amounts in transfections, but this is not necessarily required. We have used either 3 or 10 µg of transfer vector depending on whether we are using a 3:3:1 or 10:10:3.3 µg ratio (transfer vector to packaging to VSV-G expression plasmids). The lower amount works well for feline immunodeficiency virus (FIV)-based vectors, but we have generally used the larger amount for HIV-1 vectors. In Nunc Cell Factories, we have generally used a 3:3:1 ratio for all types of vectors to conserve DNA.

iiWe generally collect at 48 h after washing off the transfection mix. An alternative is to collect at both 24 and 48 h for both HIV and MLV vectors and pool the supernatants, but this yields twice the volume to concentrate.


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