Together is Better: mRNA Co‐Encapsulation in Lipoplexes is Required to Obtain Ratiometric Co‐Delivery and Protein Expression on the Single Cell Level

Abstract Liposomes can efficiently deliver messenger RNA (mRNA) into cells. When mRNA cocktails encoding different proteins are needed, a considerable challenge is to efficiently deliver all mRNAs into the cytosol of each individual cell. In this work, two methods are explored to co‐deliver varying ratiometric doses of mRNA encoding red (R) or green (G) fluorescent proteins and it is found that packaging mRNAs into the same lipoplexes (mingle‐lipoplexes) is crucial to efficiently deliver multiple mRNA types into the cytosol of individual cells according to the pre‐defined ratio. A mixture of lipoplexes containing only one mRNA type (single‐lipoplexes), however, seem to follow the “first come – first serve” principle, resulting in a large variation of R/G uptake and expression levels for individual cells leading to ratiometric dosing only on the population level, but rarely on the single‐cell level. These experimental observations are quantitatively explained by a theoretical framework based on the stochasticity of mRNA uptake in cells and endosomal escape of mingle‐ and single‐lipoplexes, respectively. Furthermore, the findings are confirmed in 3D retinal organoids and zebrafish embryos, where mingle‐lipoplexes outperformed single‐lipoplexes to reliably bring both mRNA types into single cells. This benefits applications that require a strict control of protein expression in individual cells.

Representative confocal images and flow cytometry scatter plots of HeLa cells receiving one, two and four successive transfections with 50/50% (w/w) of mCherry/eGFP mRNA delivered by mingle-lipoplexes or singlelipoplexes respectively. All data was averaged from three independent experiments, with three replicates per repeat (n=9). Scale bar: 100 μm. The mRNA dose was 0.2, 0.1 or 0.05 µg/well per transfection round, leading to a total mRNA amount of 0.2 µg/well after respectively the first, second or fourth transfection.

Part 2 -Statistical description of double mRNA transfections by single-and mingle-lipoplexes
The aim is to give a theoretical derivation of the correlation of the expression of two types of mRNA molecules that are delivered to cells by single-and mingle-lipoplexes. As in the main text, we define single-lipoplexes as lipoplexes that contain only one type of cargo, while mingle-lipoplexes contain a mixture of different cargo molecules. We will start with the case of a single mRNA molecule and derive the distribution (often referred to as the probability mass function or pmf in the case of discrete-valued random variables) of the number of mRNA molecules that have reached the cytosol.
We will consider the number of mRNA molecules per lipoplex, the association/uptake of lipoplexes into cells and the subsequent release of mRNA into the cytosol. Then we will expand this model to the case of two types of mRNA molecules delivered by single-lipoplexes and derive the joint distribution for uptake and cytosolic release. Next, we do the same for mingle-lipoplexes and consider expansion of the model towards protein expression, focusing in particular on deriving the correlation between the expression of both types of proteins. Finally, we consider how the model can be used to quantitatively interpret the experimental correlation values.

Distribution of the number of cytosolic cargo molecules per cell delivered by lipoplexes
We consider lipoplexes each containing cargo molecules (e.g., mRNA), where is constant. These lipoplexes associate with or internalize into cells (e.g., by endocytosis) after a certain incubation period. Let be the number of lipoplexes in a cell (which depends on the applied concentration and incubation time), which is random with distribution ( ). Of those, a certain (random) fraction will release their cargo successfully into the cell (e.g., by direct translocation over the cell membrane or by endosomal escape). Let ( ) be the number of lipoplexes that release their cargo into the cell, which is random with distribution ( For later use it is of interest to also determine the coefficient of dispersion ( ) of ( ), If we consider a cell with in total lipoplexes, then the probability of having lipoplexes of type 1 will be | ( ) Bino( ), or similarly | ( ) Bino( ) for type 2 lipoplexes. If we consider a cell with and , then the number of type 2 lipoplexes will be The probability of having lipoplexes of type 1 and lipoplexes of type 2 given is then The joint distribution ( ) is then analogously to section 1 a compound distribution, Note that completely complementary we could write that where the index refers to the first or second type of cargo molecules (or corresponding single-lipoplexes). The marginal distributions have mean and variance The covariance and (Pearson) correlation of and can be calculated from the joint distribution ( ) and the law of total covariance (Appendix 1): For or the correlation obviously tends to 0, as one would expect. Note that even though the correlation can be negative, in practice we expect a positive value. This is because cells are exposed to lipoplexes in the cell culture medium for a given amount of time. As lipoplexes will be undergoing random Brownian diffusion, arrival and uptake of lipoplexes in cells can be reasonably assumed to follow a Poisson distribution. This is under the assumption of using a relatively low lipoplex concentration so that arrival of the next lipoplex to a cell is not hindered by previously arrived lipoplexes. If ( ) ( ), with the mean number of lipoplexes per cell, then obviously ( ) . In reality, however, will not be a constant value for every cell, but will depend on cell size, cycle, and other factors that may change the uptake rate of a given cell. Therefore, for a given mean number of lipoplexes per cell [ ] we expect that in reality ( ) , so that indeed ( ) . Supplementary Fig. 8 shows orr( ) as a function of ( ) for different values of . Note that for a given value of ( ) the correlation is maximal for and decreases symmetrically for lower and higher values of .

Joint distribution of the number of cargo molecules of type 1 and 2 associated per cell
Experimentally we have not measured uptake of lipoplexes directly, but rather uptake of (labeled) cargo molecules. Given that we have cargo molecules in each lipoplex, let and denote the number of cargo molecules of type 1 and type 2 in a cell. Then, the corresponding joint distribution is The covariance and correlation become Thus we find that the correlation is the same for the number of associated lipoplexes and cargo molecules.

Joint distribution of the number of lipoplexes of type 1 and 2 per cell that successfully release their cargo into the cytosol
Now we can proceed with determining the joint distribution of the number of cargo molecules that are successfully released in the cell's cytosol. Let the total number of lipoplexes that release their cargo in a cell be as before. If we consider a cell in which lipoplexes release their cargo, then the probability that of those is of type 1 will be | ( | ) Bino( ). For and , the number of type 2 lipoplexes will then be exactly , so that | ( | ) ( ). We then have the joint distribution having mean and variance: The covariance and correlation are calculated completely analogous to Appendix 1, leading to: Note that this is exactly the same expression as derived above for Corr( ), the only difference being that ( ) is replaced by ( ) ( ) [ ] , the coefficient of dispersion of . Note that also here we expect a positive correlation, since realistically ( ) . This is because ( ) ( ( ) ), as we derived before, so that ( ) if ( ) , which is indeed the case as we have already established before. It also follows from the same relation that ( ) ( ), so that Corr( ) Corr( ) due to the fact that the correlation is a monotonically increasing function of the coefficient of dispersion. Note that Corr( ) Corr( ) for . An example for is shown in Supplementary Fig. 9 where Corr( ) is plotted as a function of ( ). Direct comparison with Supplementary Fig. 9 indeed shows that the correlation of cytosolically released cargo molecules is less than for the cell associated cargo molecules for the same values of .
The covariance and correlation are immediately obtained as showing that the correlation remains unaltered whether one considers the number of released lipoplexes or cargo molecules.
Since ( ) ( ) it follows that that Corr( ) Corr( ), i.e., the correlation between the cargo molecules released in the cytosol must be less than the correlation of the cell-associated cargo molecules. Mathematically this is due to the fact that the derived correlation functions are essentially the same monotonic increasing function of the coefficient of dispersion . Importantly and interestingly this corresponds to our experimental observation that the correlation of protein expression (which is proportional to the number of released cargo molecules) was less than the correlation of cargo uptake.

Joint distribution of the number of cell-associated cargo molecules of type 1 and 2 delivered by mingle-lipoplexes
Consider mingle-lipoplexes prepared from a mixture of type 1 and type 2 cargo molecules with relative fractions and . As before we take a constant number of cargo molecules per lipoplex.
Then the number of type 1 molecules per lipoplex follows a binomial distribution according to The covariance and correlation are (Appendix 2): where as before we defined the coefficient of dispersion ( ) ( ) [ ] and the ratio .
Contrary to the single-lipoplex case, we now find that the correlation of cargo internalization depends on the number of cargo molecules per particle. As a matter of fact, the expression for the correlation follows from the expression of single-lipoplexes with the substitution ( ) ( ), with the integer . Since the correlation for single-lipoplexes is monotonically increasing as a function of ( ), it is clear that the correlation for mingle-lipoplexes will always be larger for all values (or equal if ). For the same reason we see that the correlation of cell-associated cargo delivered by mingle-lipoplexes increases with , asymptotically approaching 1 as .
Note that, even though the correlation for mingle-lipoplexes can theoretically be negative, in practice we only expect positive correlation values. Indeed, we have already argued that ( ) , so that ( ) as well.

Joint distribution of the number of cytosolically released cargo molecules of type 1 and 2 delivered by mingle-lipoplexes
Finally we will determine the joint distribution for cytosolically released cargo molecules of type 1 and type 2, the derivation of which is entirely analogous to the cell-associated cargo case which we just considered. Assume that lipoplexes can deliver their cargo molecules in the cytosol of a given cell, so that the total number of released cargo molecules is . If we denote the number of type 1 molecules in the j th released lipoplex as , then for the released cargo molecules of type 1 and type 2 we have: ∑ Thus, for the probability of having in total molecules of type 1 and molecules of type 2 in a cell's cytosol is: The covariance and correlation follow from an identical calculation as in Appendix 2:

Corr( )
For the same reason as explained for single-lipoplexes we have that orr( ) Corr( ), which corresponds to our experimental observations when comparing the correlation of uptake and expression data. And as noted in relation to the correlation of cargo uptake by mingle complexes, also orr( ) for mingle-lipoplexes will always be positive and larger than the correlation of released cargo by single-lipoplexes, which is precisely what we have observed experimentally as well.
Due to that ( ) ( ( ) ) also here we have that orr( ) can be expressed as a function of ( ) and the probability of intracellular cargo release . A simultaneous fit of orr( ) and orr( ) to their respective experimental data could, therefore, give an experimental estimate of (and ). As a matter of fact, it would be possible to fit all uptake and expression data for both single and mingle-lipoplexes at once since we expect the distribution of , and hence ( ) to be constant for all performed experiments. This is due to the fact that identical lipoplex concentrations and incubation times were used in all experiments and the fact that lipoplex uptake can reasonably be expected to be independent of the mRNA sequence used.

Quantification of association of lipoplexes with cells
Experimentally we do not determine the number of cell-associated cargo molecules and directly, but rather quantify the fluorescence intensities and of labeled cargo molecules by flow cytometry. We assume that the fluorescence intensities are linear functions of the number of labeled cargo molecules, so that Here, ( ) is a proportionality constant that depends on the number of fluorophores per cargo molecule, fluorophore brightness and instrument settings, and is a background term that account for autofluorescence and/or a detector offset. It should be noted that the coefficient is time dependent and also depends on mRNA stability as well as protein stability. For simplicity we consider and to be constants. The joint distribution of and then readily follows from the corresponding expressions for the joint distribution of cell-associated cargo molecules: For the covariance and correlation one readily obtains Thus we find that the correlation of the fluorescence of labeled cargo molecules is identical to the correlation of the number of cell-associated cargo molecules so that the expressions for the correlation derived for single and mingle complexes remain valid.

Quantification of fluorescent protein expression
With regard to cargo release, so far we have considered the joint distribution and correlation of the number of cargo molecules of type 1 and type 2. In our experiments, however, we rather measure fluorescence protein expression (by flow cytometry). If we reasonably assume that protein expression and its fluorescence detection by flow cytometry is proportional to the number of cytosolic mRNA molecules, we can again write for the measured fluorescence intensity for each type of protein that where depends on the mRNA translation rate, fluorophore brightness and instrument settings, and is still a background term that accounts for autofluorescence and/or detector offset. As before we consider and to be constants. Entirely analogous to the previous section we have that the joint distribution for protein expression by cytosolic cargo molecules is Thus we find once more that the correlation of protein expression is identical to the correlation of the number of released cargo molecules so that the expressions for the correlation derived for single and mingle-lipoplexes remain valid.

Examples
The In addition, we reckoned it would be instructive to visualize the above derived joint distributions for lipoplex uptake and protein expression by single-and mingle-complexes as well. This requires, however, a particular choice for the distribution ( ) that describes lipoplex association to cells. As reported before 23 , nanoparticle association to cells can be pragmatically described by an overdispersed Poisson distribution in the following fashion. Assume that | is Poisson distributed with mean [ | ] , and that is gamma distributed with shape parameter and scale parameter . The resulting distribution of is a negative binomial distribution which can be written as 1 : increase of [ ] would lead to an increase of ( ) as well. Due to the monotonicity of the correlation functions, they will increase too. This is in line with our experimental observation that the correlation increased for longer particle incubation times (see main text).
The distribution that describes the total number of cytosolic cargo molecules then becomes: For clarity and convenience we here write the resulting joint distributions for all four cases: 1. Cell-associated cargo delivered by single-lipoplexes: In case of single-lipoplexes this means that the number of cargo molecules of each type always are present as a multiple of . In case of mingle-lipoplexes it is rather the sum of both types of cargo molecules that always is a multiple of . Accounting for a variable number of cargo molecules per lipoplex and a variable number of labels/expressed proteins per cargo molecule might provide for a more accurate description. Also, including experimental noise into the models would make the distributions continuous which would better match the experimental flow cytometry plots in the main manuscript. While in future work it may be of interest to introduce these factors into the model to make it more complete, it is important to note that those factors do not influence the changes in correlation between single and mingle-lipoplexes. Indeed, the current simplified model is sufficient to capture the essence of how the correlation changes between conditions, which is the primary focus of the current manuscript. For instance, the plots in Supplementary Figure 11 show how the correlation is improved when delivery happens by mingle instead of single-lipoplexes (compare B with A and D with C). Also the loss in correlation upon cargo release and protein expression, is visually clear (compare C with A and D with B) since the distributions become less elongated, or more spherical so to say.

Correlation analysis
In the present manuscript we are mostly concerned with understanding the correlation between uptake and expression from two types of mRNAs delivered by single-and mingle-lipoplexes. As already discussed above and in the main text, the theory derived here does qualitatively predict the observed trends in correlation between experiments. In addition, it is of interest to see to which 32 extent the theoretical model can describe the experimental correlation values in a quantitative way.
For convenience and clarity we here repeat the relevant expressions: 1. Cell-associated cargo delivered by single-lipoplexes: 2. Protein expression after cytosolic cargo release by single-lipoplexes: 3. Cell-associated cargo delivered by mingle-lipoplexes: 4. Protein expression after cytosolic cargo release by mingle-lipoplexes: Since (  Therefore, since is known a priori for each experiment, the different experimental correlation values that all belong to the same incubation time can be fitted all at once by the above four expressions with ( ) , and as global fitting parameters. If only three parameters can quantitatively describe the correlation values from our diverse sets of experiments, it is a clear indication that the model is a good description of reality. This turns out to be the case, as discussed in the main manuscript.

Appendix 1: Covariance and correlation of uptake of single-lipoplexes
To calculate the covariance, we use the law of total covariance, from which the correlation immediately follows as