Multiscale modeling guided potency assessment of mRNA-lipid nanoparticles

Abstract

mRNA lipid nanoparticle (mRNA-LNP) technology has emerged as a cornerstone in vaccine development due to its high delivery efficiency, molecular stability, and favorable safety profile. However, rapid and reliable potency assessment remains challenging because of limited mechanistic understanding of delivery processes and sparse experimental data. To address these gaps, we introduce a mechanism-informed, multi-scale kinetic modularized modeling framework that quantitatively captures the coupled dynamics of mRNA delivery across nanoparticle, cellular, and macroscopic scales. The model incorporates variability in LNP-cell interactions and integrates key determinants, such as dosage, LNP and cell size distributions, cell proliferation, and membrane properties—factors that critically shape delivery efficiency and response heterogeneity. Its cell-based architecture and modular design enable adaptability to diverse delivery systems and physiological contexts. By leveraging advanced multi-omics assays, including single-molecule fluorescent in situ hybridization (smFISH) for single-cell resolution of mRNA and protein expression, our framework provides mechanistically grounded modeling and robust prediction of therapeutic potency, offering a powerful platform for optimizing mRNA-based interventions.

Graphical abstract

This study develops a mechanism-informed, multi-scale single-cell kinetic model that integrates heterogeneous experimental data to capture mRNA-lipid nanoparticle (mRNA-LNP) delivery dynamics across particle, cellular, and macroscopic levels. This framework advances quantitative understanding of delivery variability and enables robust, predictive assessment of mRNA-LNP potency.

Introduction

Due to the critical role in the development of COVID-19 vaccines, the lipid nanoparticle (LNP)-mediated mRNA delivery system has attracted global attention. Designed with optimal size and specific surface properties, LNPs are beneficial for stability and delivery efficiency for nucleic acid therapies.^1,2

Potency refers to the measurable biological response elicited by a drug product and is critically dependent on its functional integrity.³ This study focuses on the cell-based potency assessment of mRNA-LNP systems by quantifying transfection efficiency and evaluating the expression levels of the target antigen protein. The dynamics of the delivery process is influenced by several factors, including dose, LNP size, mRNA-LNP concentration in the culture medium, and the densities of ligands on nanoparticles and cell surface receptors.⁴ Additionally, stochastic variables such as cell surface area and viability, as well as the surface charge of LNPs, contribute to cell-to-cell variability in mRNA-LNP uptake.^5,6,7,8 Cell-to-cell heterogeneity^9,10 can influence the overall response to mRNA-LNP delivery, which may lead to inconsistent immune activation and therapeutic outcomes in the human body.^11,12

It is particularly challenging to quantify the cumulative effect of variabilities from multiple sources on a cell-based potency measurement. Although recent studies have begun to model the variability in cell size,⁶ stochastic fluctuation of particle uptake,¹³ and gene expression,¹⁴ a comprehensive investigation into how these factors and critical quality attributes (CQAs), such as the effect of LNP size, influence delivery efficiency, and cell-based potency measurements, remains lacking. Such an analysis is crucial for guiding the quality control and optimal design of mRNA-LNP products, while reducing dependence on extensive physical experimentation.

LNP size influences uptake in two ways: LNP endocytosis rate and mRNA loading. The size of the LNP determines endocytosis rate by the balance between the adhesion energy and the deformation energy of the cell membrane.^5,15 By developing a front-tracking diffusion model, the size-dependent endocytosis rate of nanoparticle is quantified and various scaling analyses are performed in existing studies.^4,5,16,17 In addition, larger LNPs tend to carry more mRNA per particle.^18,19 Thus, for a fixed total mRNA dose, increasing the size of the LNP reduces the concentration of the particles. These coupled effects collectively determine how LNP size influences delivery process dynamics and potency variability. However, to date, the interplay between endocytosis rate and mRNA concentration at cellular and macroscopic levels have not been systematically characterized.

Another major challenge in in vitro assessments is the limited understanding of mRNA-LNP delivery kinetics in proliferating cells. Commonly used cell lines for in vitro mRNA-LNP studies, such as HEK293 and its derivatives,^20,21,22,23 as well as HeLa and HepG2 cells,^24,25,26 typically have doubling time ranging from 24 to 48 h.^20,24,27,28 Cell proliferation affects the dynamics of mRNA-LNP delivery through two primary mechanisms: it alters the LNP uptake capacity of individual cells and contributes to the dilution of intracellular molecules due to cell division. Under conditions of elevated cell density and constrained LNP supply, individual cells receive fewer nanoparticles because of resource depletion and intercellular competition. For intracellular molecule dilution, mRNA-LNP vaccines are considered safe due to the non-replicating and non-integrating nature of the exogeneous mRNA.²⁹ These properties result in progressive dilution of intracellular mRNA in proliferating cells, contributing to variability in potency. To the best of our knowledge, there is a lack of specific studies focusing on modeling mRNA-LNP delivery in proliferating cells.

The final challenge lies in performing single-cell mRNA measurements. For mRNA-LNP systems, in vitro potency assays are typically used to assess transfection efficiency, e.g., quantitative reverse transcription polymerase chain reaction (RT-qPCR).^30,31,32 And the generation of the target (antigen) protein²⁴ is also usually measured, e.g., flow cytometry.^14,23,33,34 Conventional bulk assays, such as RT-qPCR, lack the resolution to capture mRNA dynamics at the single-cell level. Although live-cell imaging has been widely used to monitor single-cell expression of fluorescent proteins,^13,35,36,37 therapeutic mRNAs encapsulated in LNPs typically do not include fluorescent reporter genes, making direct tracking of protein expression infeasible.

To address these challenges, in this study, three types of assays, including single-molecule fluorescent in situ hybridization (smFISH), flow cytometry, and RT-qPCR, are collected to provide time course measurements on the distribution changes of single-cell mRNA and protein expression, as well as mRNA concentration in the extracellular solution prior to cellular uptake. By integrating heterogeneous experimental data collected across multiple scales, we developed a multi-scale stochastic kinetic model that characterizes single-cell dynamics and the variability in interactions between LNPs and cells. This model enables mechanistic insights into intracellular delivery of mRNA and protein expression processes at molecular, cellular, and macroscopic levels. While previous studies have employed deterministic approaches to model individual subprocesses within the delivery system,^38,39,40,41 they often fail to account for cell-to-cell variability in potency. Our model overcomes this limitation by integrating intrinsic stochasticity into single-cell dynamics, enabling a more faithful representation of biological heterogeneity.

The objective of the proposed framework is to improve the prediction of cell-based potency by leveraging multi-scale kinetic modeling and modularized mechanism learning. LNP-cell membrane interactions are modeled using a Monod kinetic formulation, where binding rates are influenced by factors, such as extracellular mRNA-LNP concentration, LNP size, cell surface area, and growth rate. Upon binding, the impacts of LNP size and mRNA loading on the endocytosis rate, including both clathrin mediated and clathrin independent, are captured through a physics-informed model. Upon internalization, the released mRNA can follow one of two pathways: translation or exocytosis. Exocytosis occurs when the intracellular concentration reaches a saturation threshold. Alternatively, released mRNA is translated into the target protein at a rate proportional to its intracellular copy number. The model also incorporates dilution effects due to cell proliferation, ensuring an accurate representation of dynamic cellular processes.

The proposed multi-scale kinetic model effectively captures cell-to-cell variability in both delivery and expression processes and advances the mechanistic understanding of LNP delivery system from single-cell perspective. This modularized framework not only facilitates quality assurance but also provides mechanistic insights to guide the optimization of mRNA-LNP delivery strategies across heterogeneous target cell populations.

Results

Mechanism-informed Multi-scale kinetic model

To characterize the mechanisms of mRNA-LNP delivery and expression across molecular, cellular, and macroscopic scales, we propose a mechanism-informed multi-scale (MIMS) model with a hierarchical and modular architecture. In the following sections, we detail the core components of MIMS, including its structural design, underlying assumptions, dynamic modeling of regulatory mechanisms in subprocesses, and model inference approach.

Hierarchical and modular design of MIMS

The proposed multi-scale kinetic model aims to elucidate the underlying regulatory mechanisms governing mRNA-LNP delivery and expression across nanoparticle, cellular, and macroscopic scales; see a cartoon illustration in Figure 1. The rate at which cells metabolize mRNA-LNPs is shaped by both extracellular and intracellular factors, including nutrient availability, accumulation of metabolic waste, and cellular processes, such as growth, division, and death. Consequently, the regulatory mechanisms governing mRNA-LNP delivery and expression—captured by the parameters of the kinetic model denoted by θ—are dependent on the cell’s metabolic phase, such as the lag, exponential growth, and decline phases.

Figure 1.

Hierarchical and modular architecture of the proposed mechanism-informed multi-scale model (MIMS)

(A) A schematic illustration of the mRNA-LNP delivery and expression process, highlighting key events: (1) cellular uptake and endosomal escape, (2) mRNA exocytosis, (3) mRNA degradation, and (4) translation. (B) The cell growth module captures cell density dynamics across three phases: (1) lag phase, (2) exponential growth phase, and (3) decline phase. The cell division module models stochastic, cell area-dependent division behavior. The uptake module estimates the dynamics of intracellular mRNA copy number based on extracellular mRNA concentration, LNP content, and the sizes of both the cell and the nanoparticle. In contrast, the translation module predicts protein expression levels from intracellular mRNA abundance. (C) Schematic of the Markov chain model representing cell cycle transitions. The model divides the cell cycle into two principal phases, G1-S and G2-M, with transition probabilities P₁₂ and P₂₁ governed by the cell growth rate μ(t_h), cell area A(t_h), and the phase distribution parameter γ_G2-M. (D) Flow cytometry analysis of cell cycle distribution using Vybrant™ DyeCycle™ Violet for DNA content staining reveals two distinct peaks, corresponding to populations of cells in the G1-S and G2-M phases. (E) The cell growth curve accurately captures the dynamics of cell proliferation and delineates distinct metabolic phases with error bar. (F) Representative smFISH image used to determine cell area, with cell boundaries outlined by yellow dashed lines. (G) Probabilistic modeling on cell cycle phase transitions.

The proposed multi-scale kinetic model has a hierarchical structure across nanoparticle, cellular, and macroscopic scales. We summarize the variables of interest in Table 1. The cell-culture duration is discretized into H uniform time intervals of length Δt, with discrete time points denoted as t_h = hΔt for h = 0,1, …, H. To estimate the expected loading efficiency of LNPs, we quantified the initial extracellular mRNA concentration using RT-qPCR. The system inputs at time zero included the dose, the measured extracellular mRNA concentration s_mRNA.ex(0) (molecules), and the initial size distribution of the LNPs s_LNP.size(0) (nm).

Table 1.

Key variables in the MIMS framework

Scale	symbol	type and composition	description
Nanoparticle	sLNP(th)	vector: [sLNP.size(th),sLNP.load(th)]	nanoparticle size sLNP.size(th) and mRNA loading sLNP.load(th).
Single Cell	sMolecule(th)	vector: ${\left[s_{\text{mRNA}.in}\left(t_h\right),s_{\text{Protein}}\left(t_h\right)\right]}^{\top }$	intracellular molecular states: mRNA copy number smRNA.in(th) and protein expression intensity sProtein(th).
	sCell(th)	vector: ${\left[A\left(t_h\right),z\left(t_h\right),{\mathit{s}}_{\text{Molecule}}{\left(t_h\right)}^{\top }\right]}^{\top }$	cell state: cell area A(th), cell cycle phase z(th), and molecular contents sMolecule(th).
	v(th)	vector	single-cell reaction rates associated with delivery and expression subprocesses at time point th.
Macroscopic	X(th)	scalar	viable cell density at time th.
	smRNA.ex(th)	scalar	concentration of extracellular mRNAs encapsulated in LNPs.

At the nanoparticle scale, the state of each LNP, represented s_LNP(t_h) = [s_LNP.size(t_h), s_LNP.load(t_h)], is specified by particle size s_LNP.size(t_h) (nm) and the mRNA loading s_LNP.load(t_h). At the single-cell scale, we track the intracellular molecular state, i.e., ${\mathit{s}}_{\text{Molecule}}\left(t_h\right)={\left[s_{\text{mRNA}.in}\left(t_h\right),s_{\text{Protein}}\left(t_h\right)\right]}^{\top }$, consisting of mRNA copy number s_mRNA.in(t_h) (molecules per cell) and protein expression intensity s_Protein(t_h) in terms of relative fluorescence unit (RFU) per cell. To capture single-cell states in addition to gene and protein expression, we incorporate cell surface area A(t_h) and cell-cycle phase z(t_h) (i.e., G1, S, G2, and M), both of which influence cell division behavior. Thus, we concatenate A(t_h), z(t_h), and s_Molecule(t_h) into a single-cell state vector, i.e., ${\mathit{s}}_{\text{Cell}}\left(t_h\right)={\left[A\left(t_h\right),z\left(t_h\right),{\mathit{s}}_{\text{Molecule}}{\left(t_h\right)}^{\top }\right]}^{\top }$. At the macroscopic scale, the environmental conditions, including the viable cell density denoted as X(t_h) (cells) and the extracellular mRNA concentration denoted as s_mRNA.ex(t_h) (molecules), influence cell growth and activity to process mRNA-LNPs. Here, we focus on the extracellular mRNAs encapsulated in LNPs, as naked RNAs are unable to enter cells due to electrostatic repulsion between their negatively charged phosphate backbone and the negatively charged cell membrane. Therefore, at any time t_h, the multi-scale state variables are represented as,

$$\begin{array}{c}\mathit{u}\left(t_h\right)=\left[X\left(t_h\right),s_{\text{mRNA}.ex}\left(t_h\right),{\mathit{s}}_{\text{LNP}}\left(t_h\right),{\mathit{s}}_{\text{Cell}}\left(t_h\right)\right]\text{,}\end{array}$$ (Equation 1)

with the distributions of s_LNP(t_h) and s_Cell(t_h) characterizing the variability in the attributes of individual lipid nanoparticles and cells, respectively.

The modular design of the proposed MIMS model comprises single-cell kinetic modules that represent cell growth and single-cell delivery and expression subprocesses. The modular architecture is designed to be agnostic to cell line and LNP type, with each module can be independently adapted or replaced. Since cell lines may differ in membrane properties, proliferation dynamics, and endocytosis mechanism, this modular structure naturally accommodates such variability without specifically building mechanistic model for each LNP-cell delivery system. This architecture thereby enables broad biological generalizability among diverse cell lines and LNP types.

The cell growth module first captures single-cell area dynamics and cell-cycle state transitions, which influence the binding area of LNP endocytosis, intracellular molecule partition. Additionally, cell growth dynamics reflect the cell culture environment dynamics, enabling modeling cells’ responses to environment changes. Therefore, the cell growth module is designed to uniformly model both single-cell division dynamics and macroscopic cell density changes, while accommodating cell line-specific behaviors. Specifically, cell-cycle transitions are simulated using a Markov chain model where the transition probabilities are functions of both cell area A(t_h) and cell-cycle phase z(t_h). At the macroscopic scale, cell division events are aggregated to model the dynamics of cell population density X(t_h), i.e.,

$$\begin{array}{c}\mathbb{E}\left[\Delta X\left(t_h\right)|X\left(t_h\right)\right]=\mu \left(t_h\right)X\left(t_h\right)\Delta t\text{.}\end{array}$$ (Equation 2)

The cell density growth rate μ(t_h) serves as a proxy for cell viability and is modulated by extracellular conditions such as nutrient availability and the accumulation of metabolic waste. This time-dependent growth rate is used to infer the kinetic model parameters θ. Specifically, μ(t_h) enables identification of distinct cell metabolic phases—such as lag, exponential growth, and decline phases (see Figure 1)—allowing the model to assign phase-specific parameter values that capture dynamic changes in cellular behavior across these phases.

The single-cell delivery and expression process is modularized into c = 4 distinct subprocesses: mRNA-LNP uptake and endosomal escape, mRNA exocytosis, translation, and degradation. The reaction rates associated with these subprocesses are represented by the vector $\mathit{v}={\left[v_{\text{up}},v_{\text{exo}},v_{\text{TL}},v_{\mathrm{deg}}\right]}^{\top }$, and are functions of the multi-scale state u(t_h). Their influence on the state dynamics u(t_h) is captured using a modular framework:

$$Nv\left(u\left(t_n\right);\theta \right)={\sum }_{i=1}^c{N}_i{v}_i\left(u\left(t_n\right);\theta \right)\Delta t\text{,}$$ (Equation 3)

where N is an m×n stoichiometry matrix defining the structure of the delivery and expression reaction network, with m denoting the number of molecular species and n the number of reactions. The (p,q)-th element of N, denoted as N(p,q)specifies the number of molecules of the p-th species consumed (negative value) or produced (positive value) in each occurrence of the q-th reaction. These values serve as the stoichiometric coefficients for the p-th species in the rate equation of the q-th reaction.

• 1.Uptake and endosomal escape. The single-cell delivery process begins with mRNA-LNP uptake, during which LNPs bind to the cell membrane, are internalized, and release mRNAs through endosomal escape. The internalization rate of each nanoparticle is size dependent. Endocytosis pathways may vary across different LNP-cell membrane systems, and accordingly this module can be customized for a given delivery system. Regardless of specific endocytosis pathway, the uptake subprocess can be universally represented by the following reaction:

$$\begin{array}{c}\text{Cell}+\text{mRNA}.ex\stackrel{v_{\text{up}}\left(\mathit{u}\left(t_h\right);\mathit{\theta }\right)}{\to }\text{Cell}+\text{mRNA}.in\text{,}\end{array}$$ (Equation 4)

where mRNA.ex and mRNA.in represent extracellular and intracellular mRNAs. The combination of mRNA uptake rate and endosomal escape rate, denoted as v_up(u(t_h);θ), is modeled as a function of the multi-scale system state u(t_h) and kinetic parameter set θ.

• 2.Exocytosis. As cells internalize LNPs, they eventually reach a saturation state, at which point the released mRNAs are transported back into the extracellular environment via exocytosis. This exocytosis subprocess can be represented as follows:

$$\begin{array}{c}\text{Cell}+\text{mRNA}.in\stackrel{v_{\text{exo}}\left(\mathit{u}\left(t_h\right);\mathit{\theta }\right)}{\to }\text{Cell}+\text{mRNA}.ex\text{,}\end{array}$$ (Equation 5)

where v_exo(u(t_h);θ) represents the exocytosis rate.

• 3.Translation. While some internalized mRNAs are exported back to the extracellular environment via exocytosis, others remain in the cytoplasm and serve as templates for synthesizing amino acid chains (denoted as AA) that form the target protein within ribosomes—a process known as translation.⁴² The translation subprocess can be represented as follows:

$$\begin{array}{c}\text{mRNA}.in+AA\stackrel{v_{\text{TL}}\left(\mathit{u}\left(t_h\right);\mathit{\theta }\right)}{\to }\text{mRNA}.in+\text{Protein,}\end{array}$$ (Equation 6)

where v_TL(u(t_h);θ) represents the translation rate.

• 4.mRNA degradation. Some intracellular mRNAs eventually undergo degradation and are never utilized for translation, as represented in the following equation:

$$\begin{array}{c}\text{mRNA}.in\stackrel{v_{\mathrm{deg}}\left(\mathit{u}\left(t_h\right);\mathit{\theta }\right)}{\to }\varnothing \text{,}\end{array}$$ (Equation 7)

where v_deg(u(t_h);θ) represents the mRNA degradation rate.

To model the evolution of intracellular molecular states for each cell, denoted by s_Molecule(t_h), we employ a stochastic framework based on state transition probabilities. Specifically, the dynamics are governed by the following stochastic differential equation:

$$\begin{array}{c}\Delta {\mathrm{s}}_{Molecule}\left(t_h\right)={\mathit{N}}_{in}\mathit{v}\left(\mathit{u}\left(t_h\right);\mathit{\theta }\right)\Delta t+{\left[{\mathit{N}}_{in}\mathrm{\Sigma }\left(\mathit{v}\left(\mathit{u}\left(t_h\right);\mathit{\theta }\right)\right){\mathit{N}}_{in}^{\top }\right]}^{\frac{1}{2}}\Delta {\mathit{W}}_{t_h}\end{array}$$ (Equation 8)

where N_in is a submatrix of the stoichiometry matrix N, representing the reaction structure associated with intracellular molecules, Σ(v(u(t_h);θ)) is a diagonal covariance matrix capturing the intrinsic variability of each reaction, and $\Delta {\mathit{W}}_{t_h}$ is a Gaussian random vector with mean zero and covariance matrix diag {Δt} modeling stochastic fluctuations via Brownian motion. Equation 8 enables the modeling of stochastic single-cell dynamics by accounting for biological variability arising from multiple factors, including cell proliferation and division, changes in cell area, ligand-receptor interactions, mRNA degradation, exocytosis, and translation. These components are described in detail in the following subsections.

In the following sections, we detail the modeling of potency dynamics and variability, along with the regulatory mechanisms governing reaction rates v(u(t_h);θ). At the macroscopic scale, the rate of decrease in extracellular mRNA concentration is positively correlated with the mRNA-LNP uptake rate, up to a saturation threshold.^24,41 Additionally, cell growth rate influences both the ligand-receptor binding kinetics and the dilution of intracellular molecules. At the single-cell scale, features such as cell area and membrane tension modulate endocytosis rates. At the particle scale, LNP-specific properties—including size, shape, and surface ligand density—govern the kinetics of endocytic uptake. The interplay across these hierarchical scales collectively determines the overall efficiency of cell-based potency.

Model assumptions

The following assumptions have been made for our model.

(1) Localization of mRNA-LNP delivery. All delivery-related processes—including LNP uptake, mRNA release, and mRNA translation—are assumed to occur within the cytosol. This assumption excludes nuclear interactions associated with alternative pathways, thereby ensuring that endogenous cellular genes remain unaffected by exogenous mRNA. (2) Negligible cell area growth during the G2-M phase. Cell growth primarily occurs during the G1-S phase, while the G2-M phase is dedicated to preparing cellular components for division rather than increasing cell size.^43,44,45 Based on this biological insight, the model assumes negligible cell area growth during the G2-M phase, thereby simplifying the representation of cell division dynamics by treating cell area as static during this stage. (3) mRNA loading of LNPs is proportional to LNP volume. This assumption is supported by prior studies, which showed that mRNA loading correlates with LNP volume,^12,15 and it is reasonable to assume they are linearly correlated in computational model.¹⁷ By quantifying the initial extracellular mRNA concentration using RT-qPCR and measuring the LNP size distribution via dynamic light scattering (DLS), the expected mRNA copy number per nanoparticle can be inferred based on its volume.

Cell growth model

In the batch cell culture process, cell growth curves typically consist of multiple metabolic phases, including the lag phase, the exponential growth phase, and the decline phase.⁴⁶ A representative growth curve is shown in Figure 1E. This progression can be mathematically summarized as follows:

$$\begin{array}{c}\mu \left(t\right)=\frac{1}{X\left(t\right)}\frac{\mathbb{E}\left[dX\left(t\right)\right]}{dt}=\{\begin{array}{c}\begin{array}{cc}{\mu }_0,& \text{for}t\text{in}\text{lag}\text{phase},\end{array}\\ \begin{array}{cc}{v}_g\frac{S\left(t\right)}{K_g+S\left(t\right)}-{\mu }_d,& \text{for}t\text{in}\text{exponential}\text{phase},\end{array}\\ \begin{array}{cc}-{\mu }_d,& \text{for}t\text{in}\text{decline}\mathrm{p}\text{hase},\end{array}\end{array}\end{array}$$ (Equation 9)

where μ(t) represents the time-dependent growth rate of cell density, μ₀ represents cell growth rate in the lag phase, μ_d represents the constant cell death rate, v_g represents the max growth rate during exponential phase, K_g represents the Monod constant characterizing substrate-dependent growth, and S(t) is the concentration of a growth-related substrate in the extracellular environment at time t.

During different phases of cell growth, cells exhibit distinct metabolic behaviors,^47,48 which in turn influence the dynamics of mRNA-LNP delivery and expression. During the lag phase, cells acclimate to the new environment and do not immediately initiate division. Following adaptation, cells enter the early exponential phase, characterized by rapid proliferation and abundant nutrients,⁴⁶ during which both mRNA-LNP uptake and protein synthesis occur at elevated rates. As nutrients become depleted, cells transition into the late exponential phase, where the LNP uptake rate begins to decline. This resource limitation is captured by a time-dependent growth rate modeled using Monod kinetics, as shown in Equation 9. The substrate concentration S(t) is approximated by:

$$\begin{array}{c}S\left(t\right)=e^{-k_{\exp }\left(t-t_0^{\exp }\right)},t\ge t_0^{\exp },\end{array}$$ (Equation 10)

where k_exp is a time-scaling coefficient and $t_0^{\exp }$ marks the onset of the exponential phase. The negative exponential form of S(t) reflects nutrient consumption over time. As cell growth ceases and viable cell density begins to decline, the mRNA-LNP delivery process correspondingly slows down.

Cell area-dependent division model

While the macroscopic cell growth model in Equation 9 captures the influence of culture conditions on population-level growth dynamics, accurately modeling the dilution of intracellular molecules during cell division requires a more detailed understanding of proliferation at the single-cell level. The cell cycle is typically divided into two main phases: G1-S and G2-M as shown in Figures 1C and 1D. For simplicity, the model excludes the possibility of cells entering the quiescent G0 phase. During the G1-S phase, cells grow by replicating DNA and synthesizing essential components such as proteins and ribosomes, leading to an increase in cell area. Once a critical size threshold is reached, cells transition into the G2-M phase.⁴⁹ During this phase, the rate of cell area expansion decelerates.^43,45 Upon completion of G2-M, the parent cell undergoes division, partitioning its genetic material and intracellular contents—including mRNAs and proteins—between two daughter cells.

The proposed cell area-dependent division model integrates three key data modules: (1) cell population growth curves derived from viability assays, (2) cell size distributions obtained via smFISH, and (3) the proportion of live cells in the G2-M phase, denoted by γ_G2-M, measured through flow cytometry. The interdependence of these components is illustrated in Figures 1C–1F. To model cell-cycle dynamics and transitions between the G1-S and G2-M phases, a Markov chain framework is employed, with the transition diagram shown in Figure 1C and the associated model components detailed in Figure 1G. At any time t_h, let z(t_h) denote the cell-cycle stage of an individual cell, where z(t_h)∈G1-S if the cell is in the G1-S phase, and z(t_h)∈G2-M otherwise. The cell density growth rate, μ(t_h), reflects the frequency of cell division and governs the transition rate from G2-M to G1-S, denoted by r₂₁(t_h), which determines the corresponding transition probability P₂₁. Cell area growth primarily occurs during the G1-S phase. The transition probability from G1-S to G2-M, denoted by P₂₁(A(t_h) = a), is a function of the cell area A(t_h). For a population of cells with area distribution density q(A(t_h) = a), the expected transition probability is given by: P₁₂ = ∫ P₁₂(a)q(a)da. This formulation allows the model to account for heterogeneity in cell size across the population, linking individual cell growth dynamics to phase transition behavior in the cell cycle.

We describe the dynamics of cell area change during G1-S phase using an exponential growth model, which is commonly applied to both mammalian and plant cells.^50,51,52 Specifically, at any time t_h, if z(t_h)∈G1-S, the change in cell area A(t_h) over the interval with length Δt is given by,

$$\begin{array}{c}A\left(t_h+\Delta t\right)-A\left(t_h\right)=g\left(t_h\right)A\left(t_h\right)\Delta t\text{,}\end{array}$$ (Equation 11)

where g(t_h) is the phase-dependent cell area growth rate. Notably, the growth rate during the G2-M phase is negligible compared to that observed in the G1-S phase.

The duration of the G2-M phase is modeled as an exponentially distributed random variable with rate parameter r₂₁(t_h). Before re-entering the G1-S phase, the cell undergoes division, resulting in the partitioning of cell area and intracellular mRNA molecules between two daughter cells. As illustrated in Figure 1B, the area of one daughter cell is sampled from a binomial distribution:

$$\begin{array}{c}A\left(t_h+\Delta t\right)\mid A\left(t_h\right)\sim B\left(A\left(t_h\right),0.5\right),\end{array}$$ (Equation 12)

where A(t_h) is the parent cell area at time t_h and A(t_h+Δt) is the area of one daughter cell. According to mass balance, the area of the other daughter cell is A(t_h)-A(t_h+Δt). Molecules, including mRNA and proteins, are partitioned into daughter cells in proportion to their areas.⁵³

Given the macroscopic cell growth rate model in Equation 9, the transition rate r₂₁(t_h) from G1-S to G2-M phase can be calculated as,

$$\begin{array}{c}{r}_{21}\left(t_h\right)\approx \frac{\mu \left(t_h\right)}{{\gamma }_{\mathrm{G}2-\mathrm{M}}},\end{array}$$ (Equation 13)

where γ_G2-M is the proportion of living cells in G2-M phase. The detailed derivation of Equation 13 is presented in supplemental information. Using flow cytometry observations illustrated in Figure 1D, we can estimate the proportion of cells in G2-M phase, denoted by γ_G2-M, by sorting cells in G1-S phase and G2-M phase. The stable and coordinated relationship between cell division and cell area growth is crucial for maintaining cell area homeostasis, ensuring that a cell population maintains a stable distribution of cell sizes (or areas) over time.^51,54 This assumption is further supported by the results of the hypothesis test, as detailed in supplemental information.

Under this assumption, the transition probability from G1-S to G2-M phase for cell population can be derived as follows,

$$\begin{array}{c}P\left(\mathrm{G}1-\mathrm{S}\to \mathrm{G}2-\mathrm{M}\right)≔P\left(z\left(t_h+\Delta t\right)\in \mathrm{G}2-\mathrm{M}|z\left(t_h\right)\in \mathrm{G}1-\mathrm{S}\right)=\frac{2{\gamma }_{\mathrm{G}2-\mathrm{M}}}{1-{\gamma }_{\mathrm{G}2-\mathrm{M}}^2}\left(1-e^{-r_{21}\left(t_h\right)\Delta t}\right),\end{array}$$ (Equation 14)

and P(G1-S→G2-M) is denoted as P₁₂ for notational convenience. The derivation of Equation 14 is detailed in supplemental information.

To investigate cell-to-cell variability and single-cell dynamics, we consider the conditional transition probability for a cell with area a to progress from the G1-S phase to the G2-M phase:

$$\begin{array}{c}P\left(z\left(t_h+\Delta t\right)\in \mathrm{G}2-\mathrm{M}|z\left(t_h\right)\in \mathrm{G}1-\mathrm{S},A\left(t_h\right)=a\right)=\frac{\left(1-{\gamma }_{\mathrm{G}2-\mathrm{M}}\right)q\left(a+g\left(t_h\right)a\Delta t|z\left(t_h+\Delta t\right)\in \mathrm{G}2-\mathrm{M}\right)}{q\left(a\right)-q\left(a|z\left(t_h\right)\in \mathrm{G}2-\mathrm{M}\right){\gamma }_{\mathrm{G}2-\mathrm{M}}}{P}_{12}\text{,}\end{array}$$ (Equation 15)

where q(a) represents the distribution of cell area. The derivation of Equation 15 is detailed in supplemental information. For any cell in the G2-M phase, the conditional distribution of cell size can be derived using Bayes’ rule, i.e.,

$$\begin{array}{c}q\left(a|z\left(t_h\right)\in \mathrm{G}2-\mathrm{M}\right)=\frac{q\left(z\left(t_h\right)\in \mathrm{G}2-\mathrm{M}|A\left(t_h\right)=a\right)q\left(a\right)}{{\gamma }_{\mathrm{G}2-\mathrm{M}}}\text{.}\end{array}$$ (Equation 16)

Following Provost et al.,⁵⁵ the conditional probability that a cell is in the G2-M phase, given that its area is a, is modeled using a sigmoid function,

$$\begin{array}{c}q\left(z\left(t_h\right)\in \mathrm{G}2-\mathrm{M}|A\left(t_h\right)=a\right)=\text{Sigmoid}\left({\beta }_{1}a+{\beta }_0\right),\end{array}$$ (Equation 17)

with β₁ > 0, where β₁ and β₀ are the linear transformation coefficients of cell area. Then, by substituting Equation 17 into Equation 15, we can obtain the conditional transition probability from G1-S to G2-M phase as,

$$\begin{array}{c}P\left(z\left(t_h+\Delta t\right)\in \mathrm{G}2-\mathrm{M}|z\left(t_h\right)\in \mathrm{G}1-\mathrm{S},A\left(t_h\right)=a\right)=\frac{\left(1-{\gamma }_{\mathrm{G}2-\mathrm{M}}\right)\text{Sigmoid}\left({\beta }_1\left(a+g\left(t_h\right)\Delta t\right)+{\beta }_0\right)}{\left(1-\text{Sigmoid}\left({\beta }_{1}a+{\beta }_0\right)\right){\gamma }_{\mathrm{G}2-\mathrm{M}}}{P}_{12}\text{.}\end{array}$$ (Equation 18)

The detailed derivation is provided in supplemental information.

Stochastic mRNA-LNP uptake

The mRNA-LNP uptake process involves two key steps: binding and endocytosis. The uptake rate of the mRNA-LNP, denoted by v_up(t_h), is governed by the size of the nanoparticle. LNP could be uptaken via multiple endocytosis pathways for the same cell line and LNP formulation.^56,57 For example, in HEK293 cell system, both clathrin-mediated and clathrin-independent endocytosis may occur simultaneously.⁵⁷ In the clathrin-mediated endocytosis, HEK293 cells overexpress apolipoprotein E (ApoE),^58,59 which binds to LNPs and serves as the ligand of clathrin-mediated endocytosis.^60,61 In contrast, during clathrin-independent endocytosis (i.e., micropinocytosis), LNPs are internalized via non-specific interactions with membrane. Therefore, assuming a spherical nanoparticle and a locally flat cell membrane, we formulate endocytosis models for both (1) clathrin-mediated endocytosis and (2) clathrin-independent endocytosis, with a particular focus on macropinocytosis.

• (1)Clathrin-mediated endocytosis. For clathrin-mediated endocytosis, free receptors on the membrane diffuse toward the LNP and bind to ligands on its surface. Once all ligands are engaged, the complex is fully wrapped and internalized by the cell (see Figure 1A). The size of the LNP and its ligand density determine the number of available binding sites, which in turn dictates the number of binding events required for successful uptake.

Given the nanoparticle size s_LNP.size(t_h), the membrane wrapping time is calculated according to the model proposed by Gao et al.⁴ as follows,

$$\begin{array}{c}{t}_w\left({\mathrm{s}}_{\text{LNP}.\text{size}}\left(t_h\right)\right)={\left(\frac{s_{\text{LNP}.\text{size}}\left(t_h\right)}{{\alpha }_{en}\sqrt{D}}\right)}^2,\end{array}$$ (Equation 19)

where D is diffusivity of membrane receptors, and α_en is a constant referred to as the “speed factor”, derived from the energy balance equation:

$$\begin{array}{c}{e}_{RL}-\frac{1}{2}\frac{B{\kappa }_p^2}{{\xi }_L}=f\left({\alpha }_{en}\right)-\ln f\left({\alpha }_{en}\right)-1,\end{array}$$ (Equation 20)

with $f\left({\alpha }_{up}\right)=\tilde{\xi }+\frac{{\alpha }_{en}^2\left(1-\tilde{\xi }\right)E_1\left({\alpha }_{en}^2\right)}{{\alpha }_{en}^2{E}_1\left({\alpha }_{en}^2\right)-e^{-{\alpha }_{en}^2}}$. Here, e_RL is the receptor-ligand adhesion energy, estimated to be approximately 15k_BT at 300 K⁶², a representative temperature for nanoparticle delivery studies.⁴ The bending modulus B is typically taken as 20k_BT,^62,63 and the nanoparticle curvature is given by ${\kappa }_p=\frac{1}{s_{\text{LNP}.\text{size}}\left(t_h\right)}\text{.}$ Ligand density on the LNP surface is denoted by ξ_L, and $\tilde{\xi }$ represents the ratio of receptor to ligand density; both are model-fitted parameters. For computational simplicity, α_en is treated as a constant, determined using the average LNP size.

• (2)Macropinocytosis. For macropinocytosis, the membrane bending energy is balanced by non-specific interactions, including van der Waals, steric, electrostatic, acid-base forces,⁶⁴ and the free energy of actin polymerization.⁶⁵ While the bending energy is the same as aforementioned ligand-receptor interaction model, the non-specific energy can be modeled by a phenomenological equation⁶⁶ as,

$$\begin{array}{c}{F}_{ns}={\int }_0^{a\left(t\right)}\frac{\sigma }{S}\exp \left[-\frac{S}{\delta }\right]dx\text{,}\end{array}$$ (Equation 21)

where S is the fixed separation distance between cell membrane and LNP surface during macropinocytosis, σ is a stiffness parameter, and δ is a characteristic decay length. By balancing the bending energy, the wrapping time is mathematically equivalent to Equation 19 with ${\alpha }_{en}\sqrt{D}\propto \sqrt{\frac{\sigma }{S}\exp \left[-\frac{S}{\delta }\right]}$.

Since mRNA loading is proportional to the LNP volume,^19,20 the internalization rate of mRNA molecules is given by:

$$\begin{array}{c}{v}_{\text{en}}={\left(\frac{{\alpha }_{\text{en}}\sqrt{D}}{s_{\text{LNP}.\text{size}}\left(t_h\right)}\right)}^2{k}_{pa}{s}_{LNP}^3\left(t_h\right)\propto {\alpha }_{\text{en}}^2{s}_{\text{LNP}.\text{size}}\left(t_h\right),\end{array}$$ (Equation 22)

where k_pa is the proportionality parameter relating mRNA loading to LNP volume. Thus, the rate of mRNA endocytosis is governed by both energy dynamics α_en and volume-based LNP loading.

The extracellular mRNA concentration directly influences intracellular mRNA levels.^4,25,67 To account for cell-LNP interactions, we define a normalized extracellular LNP concentration as,

$$\begin{array}{c}{\tilde{s}}_{\text{LNP}.ex}\left(t_h\right)=\frac{s_{\text{mRNA}.ex}\left(t_h\right)}{X\left(t_h\right){\overline{s}}_{\text{LNP}.\text{size}}^3\left(t_h\right)}\text{,}\end{array}$$ (Equation 23)

where ${\overline{s}}_{\text{LNP}.\text{size}}^3\left(t_h\right)$ is the average LNP radius and X(t_h) is the total cell count at time t_h. The term $\frac{s_{\text{mRNA}.ex}\left(t_h\right)}{X\left(t_h\right)}$ represents the mRNA concentration per cell, which is further scaled by the LNP volume ${\overline{s}}_{\text{LNP}.\text{size}}^3\left(t_h\right)$ to reflect the effective concentration of LNPs available for uptake.

The mRNA uptake rate v_up(t_h) is modeled using an empirical Monod-type formulation that combines LNP binding and internalization dynamics:

$$\begin{array}{c}{v}_{\text{up}}\left(t_h\right)=v_{en}\frac{{\tilde{s}}_{\text{LNP}.ex}\left(t_h\right)}{K_{\text{bind}}+{\tilde{s}}_{\text{LNP}.ex}\left(t_h\right)}\frac{A\left(t_h\right)}{K_A+A\left(t_h\right)},\end{array}$$ (Equation 24)

where v_en is the LNP size-dependent internalization factor, as defined in Equation 22. The first saturation term in Equation 24 captures the dependence of uptake rate on the normalized extracellular mRNA-LNP concentration ${\tilde{s}}_{\text{LNP}.ex}\left(t_h\right)$, with K_bind representing the half-saturation constant for LNP-cell membrane binding. This constant may be influenced by factors such as LNP surface charge, cell membrane properties,⁵ and membrane ruffle formation in macropinocytosis.⁶⁸ The second saturation term accounts for the effect of cell surface area A(t_h) on uptake rate. Experimental studies^6,69 and observations (see Figure 2D) indicate that larger cell size enhances uptake. The parameter K_A denotes the half-saturation constant for area-dependent effects, with saturation reflecting biological constraints such as limited energetic capacity for endocytosis or receptor-mediated regulation.^70,71

Figure 2.

Measurements and predictions on cell area dynamics and LNP size distribution

(A) Histogram of experimentally measured LNP size distribution. (B) Representative smFISH imagings with scale bar showing intracellular distribution of eGFP mRNA at 1 h and 2 days post-transfection in HEK293FT cells, the purple areas represent cell nucleus and white dots represent mRNA molecule, respectively. (C) Violin plots comparing observed and simulated cell area distributions over time for two administered doses: 0.01 mg and 0.05 mg. (D) Scatterplot analysis reveals a weak positive correlation between cell area and intracellular mRNA copy number, supported by statistically significant two-sided p values. (E) Q-Q plots comparing simulated and observed cell area distributions over time.

Upon cellular entry, mRNA will be released into the cell through endosomal escape. We modeled the intracellular mRNA molecule change due to mRNA uptake as a normally distributed random variable:

$$\begin{array}{c}\Delta s_{\text{mRNA}.in}^{\text{up}}\left(t_h\right)\sim \mathcal{N}\left(k_{\text{escape}}{v}_{\text{up}}\left(t_h\right),{\sigma }_{\text{up}}^2{k_{\text{escape}}v}_{\text{up}}\left(t_h\right)\right),\end{array}$$ (Equation 25)

where v_up(t_h) is obtained from Equation 24, ${\sigma }_{\text{up}}^2$ represents the uptake variability accounting for multiple sources, i.e., empty LNPs and stochastic LNP binding events, and k_escape represents the endosomal escape rate.

mRNA degradation and exocytosis

To account for mRNA degradation and exocytosis, the intracellular mRNA concentration dynamics are modeled as follows:

$$\begin{array}{c}{s}_{\text{mRNA}.in}\left(t_h+\Delta t\right)=s_{\text{mRNA}.in}\left(t_h\right)+\Delta s_{\text{mRNA}.in}\left(t_h\right)-v_{\mathrm{deg}}{s}_{\text{mRNA}.in}\left(t_h\right)\text{,}\end{array}$$ (Equation 26)

where v_deg denotes the intracellular mRNA degradation rate. The change in intracellular mRNA concentration due to uptake and exocytosis is given by

$$\begin{array}{c}\Delta s_{\text{mRNA}.in}\left(t_h\right)=\Delta s_{\text{mRNA}.in}^{\text{up}}\left(t_h\right)-\Delta s_{\text{mRNA}.in}^{\text{exo}}\left(t_h\right)\text{,}\end{array}$$ (Equation 27)

where mRNA exocytosis amount $\Delta s_{\text{mRNA}.in}^{\text{exo}}\left(t_h\right)$ is modeled using empirical Monod kinetics, incorporating stochastic variability through a normally distributed random process: $\Delta s_{\text{mRNA}.in}^{\text{exo}}\left(t_h\right)\sim \mathcal{N}\left(v_{\text{exo}}\left(s_{\text{mRNA}.in}\left(t_h\right)\right),{\sigma }_{\text{exo}}^2{v}_{\text{exo}}\left(s_{\text{mRNA}.in}\left(t_h\right)\right)\right)$. Here, the mean exocytosis rate is defined by a Monod-type saturation function:

$$\begin{array}{c}{v}_{\text{exo}}\left(s_{\text{mRNA}.in}\left(t_h\right)\right)=v_{\text{exo}}\frac{s_{\text{mRNA}.in}\left(t_h\right)}{K_{\text{exo}}+s_{\text{mRNA}.in}\left(t_h\right)},\end{array}$$ (Equation 28)

where v_exo is the maximum mRNA efflux rate, K_exo is the empirical half-saturation constant characterizing mRNA efflux, and ${\sigma }_{\text{exo}}^2$ represents the coefficient of variation, capturing stochastic fluctuations in the exocytosis process. This formulation captures both the nonlinear saturation behavior of mRNA efflux and its inherent variability, enabling more realistic simulation of intracellular transport dynamics.

Since naked RNAs released via exocytosis cannot re-enter cells due to electrostatic repulsion, the extracellular mRNA concentration—encapsulated within LNPs—is updated by accounting for uptake dynamics across all viable cells with density X(t_h), as follows:

$$\begin{array}{c}\Delta s_{\text{mRNA}.ex}\left(t_h\right)=-\sum _{i=1}^{X\left(t_h\right)}\Delta s_{\text{mRNA}.in}^{\text{up},i}\left(t_h\right)\text{,}\end{array}$$ (Equation 29)

where $\Delta s_{\text{mRNA}.in}^{\text{up},i}\left(t_h\right)$ denotes the mRNA uptake rate by the i-th cell at time t_h. This formulation captures the net depletion of extracellular mRNA due to cellular uptake, excluding contributions from exocytosed naked mRNA.

mRNA translation

The aforementioned model describes the process from mRNA-LNP uptake to intracellular mRNA release. Once cells adapt to their environment, they exhibit distinct translation rates across different metabolic phases. The protein accumulation in a single cell, denoted by

$$\begin{array}{c}\Delta s_{\text{Protein}}\left(t_h\right)\sim \mathcal{N}\left(v_{\text{TL}}\left(t_h\right)s_{\text{mRNA}.in}\left(t_h\right)\Delta t,{\sigma }_{\text{TL}}^2{v}_{\text{TL}}\left(t_h\right)s_{\text{mRNA}.in}\left(t_h\right)\Delta t\right)\text{,}\end{array}$$ (Equation 30)

where v_TL(t_h) is the phase-specific translation rate, and ${\sigma }_{\text{TL}}^2$ is the translation variability coefficient. This variability is influenced by stochastic factors such as mRNA stability and innate immune activation.⁷²

Model inference method

The proposed MIMS model, built upon a single-cell kinetic framework, enables simulation of gene and protein expression trajectories at the single-cell level. The metabolic phase-specific cell growth model is initially calibrated using macroscopic measurements of viable cell density. In parallel, the cell division model is calibrated based on the estimated growth rate and the observed distribution of cell areas. Given the inputs—including the initial extracellular mRNA concentration s_mRNA.ex(0), the calibrated single-cell division model, and the initial LNP size distribution s_LNP.size(0)—MIMS simulates the distribution of multivariate state trajectories τ = {u(t₀),u(t₁), …,u(t_H)} according to the following probabilistic formulation:

$$\begin{array}{c}{P}_{\mathit{\theta }}\left(\mathit{\tau }\right)=P\left(\mathit{u}\left(0\right)\right)\prod _{h=1}^H{P}_{\mathit{\theta }}\left(\mathit{u}\left(t_h\right)|\mathit{u}\left(t_{h-1}\right)\right)\text{,}\end{array}$$ (Equation 31)

where the state transition model P_θ(u(t_h)|u(t_h-1)) is governed by mechanistic parameters θ. These parameters define modular processes including cell growth, area-dependent division, mRNA-LNP uptake, mRNA degradation, exocytosis, and translation.

The multi-scale measurements used in this study provide heterogeneous and partial observations of the underlying state variables. These measurements include: (1) initial measurements of extracellular mRNA concentration and LNP size distribution, obtained using RT-qPCR and DLS, respectively; (2) time-resolved single-cell joint distributions of intracellular mRNA count and cell size obtained via smFISH; and (3) time-resolved single-cell distributions of protein expression levels obtained via flow cytometry.

For the k-th potency measurement, denoted by s_k (i.e., intracellular mRNA count or protein expression), collected at time t_k,i with time index i = 1,2, …,H_k, the empirical distribution of single-cell expression is represented by P(s_k(t_k,i)). The model-predicted distribution is denoted by ${\hat{P}}_{\mathit{\theta }}\left(s_k\left(t_{k,i}\right)\right)$. To optimize θ, we minimize the Wasserstein loss,⁷³ which quantifies the distance between the empirical and predicted distributions:

$$\begin{array}{c}{\hat{\mathit{\theta }}}^{\ast }=\arg \underset{\mathit{\theta }}{\min }\sum _{k=1}^K\sum _{i=1}^{H_k}{W}_p\left(P\left(s_k\left(t_{k,i}\right)\right),{\hat{P}}_{\mathit{\theta }}\left(s_k\left(t_{k,i}\right)\right)\right)=\arg \underset{\mathit{\theta }}{\min }\sum _{k=1}^K\sum _{i=1}^{H_k}{\left({\underset{0}{\overset{1}{\int }}\left|F_{k,i}^{-1}\left(q\right)-{\hat{F}}_{k,i,\mathit{\theta }}^{-1}\left(q\right)\right|}^{p}dq\right)}^{\frac{1}{p}}\text{,}\end{array}$$ (Equation 32)

where K denotes the number of potency measurements, $F_{k,i}^{-1}$ and ${\hat{F}}_{k,i,\mathit{\theta }}^{-1}$ are the quantile functions of the empirical and predicted distributions, respectively. In our analysis, we let p = 1, simplifying the Wasserstein distance to the average absolute difference between empirical quantiles: $\frac{1}{n}\left(\sum _{j=1}^n\left|p_{k,i}^{\left(j\right)}-{\hat{p}}_{k,i}^{\left(j\right)}\right|\right)$, where $p_{k,i}^{\left(j\right)}$ and ${\hat{p}}_{k,i}^{\left(j\right)}$ are the j-th empirical quantile of P(s_k(t_k,i)) and ${\hat{P}}_{\mathit{\theta }}\left(s_k\left(t_{k,i}\right)\right)$, respectively, and n is the number of quantiles used.

To ensure the Wasserstein distance is comparable across datasets with varying scales, we define the loss function using a scaled version of the Wasserstein distance:

$$\begin{array}{c}{\hat{\mathit{\theta }}}^{\ast }=\arg \underset{\mathit{\theta }}{\min }\sum _{k=1}^K\sum _{i=1}^{H_k}\tilde{W}\left(P\left(s_k\left(t_{k,i}\right)\right),{\hat{P}}_{\mathit{\theta }}\left(s_k\left(t_{k,i}\right)\right)\right),\end{array}$$ (Equation 33)

where the scaled Wasserstein distance is given by

$$\begin{array}{c}\tilde{W}\left(P\left(s_k\left(t_{k,i}\right)\right),{\hat{P}}_{\mathit{\theta }}\left(s_k\left(t_{k,i}\right)\right)\right)=\frac{1}{n}\sum _{j=1}^n\frac{\left|p_{k,i}^{\left(j\right)}-{\hat{p}}_{k,i}^{\left(j\right)}\right|}{p_{k,i}^{\left(j\right)}}\text{.}\end{array}$$ (Equation 34)

The scaling ensures that the loss remains consistent regardless of the magnitude of the underlying data distributions. To optimize the model parameters, we employ the Adam optimizer.⁷⁴

Therefore, the developed cell-based potency assessment framework integrates mechanistic insights with heterogeneous experimental datasets collected across multiple scales, using model parameter optimization. By incorporating iterative updates informed by advanced and cost-effective assays, this approach enhances our understanding of the dynamics and variability of mRNA-LNP delivery and expression at the cellular level.

In-vitro assay data analysis

This section presents experimental observations from the in vitro studies on eGFP mRNA-LNP delivery and expression, conducted using HEK293FT cells over a 7-days period. The eGFP system enables direct measurements, including smFISH and flow cytometry, and thus provides precise quantification of mRNA copy number and protein expression.

At the macroscopic scale, RT-qPCR was employed to measure the initial extracellular mRNA concentration. Concurrently, cell viability data were collected to characterize the metabolic phases of cell growth. At the single-cell scale, flow cytometry was used to quantify the proportion of viable cells across different stages of the cell cycle. smFISH assays provided time course measurements of intracellular eGFP mRNA copy numbers, while brightfield imaging of fixed cells was used to determine cell area. Additionally, eGFP protein expression levels were assessed via flow cytometry. To investigate the impact of nanoparticle size on cellular uptake and potency variability, the size distribution of mRNA-LNPs was measured using DLS.²¹

Viable cell number

The 7-days cell viability measurements from three biological replicates are presented in Figure 1E. During the initial 24 h, cell viability increases gradually, reflecting a slow proliferation rate. After this period, a sharp rise in both the expected cell counts and inter-replicate variability is observed. Between 120 and 144 h, the cell count begins to decline, indicating a reduction in viable cells following the peak growth phase. Based on the observed growth kinetics, three distinct metabolic phases of cell growth are identified: (1) lag phase (0–3 h): characterized by minimal cell division as cells adapt to the culture conditions. (2) Exponential phase (4–95 h): marked by rapid cell proliferation. This phase can be further subdivided into early exponential phase (4–23 h) and late exponential phase (24–95 h). (3) Decline phase (96–168 h): cell proliferation decelerates and subsequently diminishes, likely due to nutrient exhaustion, accumulation of cytotoxic metabolites, or other stress-induced inhibitory factors within the culture environment.

Cell cycle

Cells in the G1-S and G2-M phases were sorted as shown in Figure 1D. Among the 31, 407 cells analyzed, 21, 932 cells (69.8%) were classified as being in the G1-S phase, while 9, 475 cells (30.2%) were in the G2-M phase. Accordingly, the proportion of viable cells in the G2-M phase is assumed to be constant and set as γ_G2-M = 30.2% in Equation 13.

Initial extracellular mRNA copy number

RT-qPCR was employed to quantify the initial mRNA copy numbers of mRNA-LNPs in the extracellular medium. Measurements from three biological replicates are summarized in Table 2.

Table 2.

Initial extracellular eGFP mRNA molecule copy numbers measured by RT-qPCR

	dose = 0.01 mg	dose = 0.05 mg
Replicate 1	109, 500, 488	598, 183, 138
Replicate 2	41, 794, 286	445, 503, 342
Replicate 3	48, 603, 399	201, 679, 148
Average	66, 632, 724	415, 121, 876
Standard deviation	37,280,355	199, 990, 321

Intracellular mRNA copy number and cell area

The smFISH assay was employed to obtain time course measurements of single-cell mRNA copy number and corresponding cell area within 2 days. smFISH enables visualization of individual RNA molecules as discrete fluorescent spots within cells. Experiments were conducted in three biological replicates using 0.01 mg and 0.05 mg doses, with 100 cells sampled at each time point for each dose and replicate. Figure 2D presents a scatterplot of cell area versus intracellular mRNA count, revealing a weak positive correlation under both dosing conditions with significant two-sided p value. This relationship is substantially weaker than the linear proportionality reported by Rees et al.,⁶ suggesting that mRNA-LNP binding and uptake could be modulated by saturation and inhibition mechanisms intrinsic to living cells—such as energy availability and receptor expression.

To characterize the single-cell distribution of intracellular mRNA levels, smFISH data from all biological replicates were pooled and visualized as green violin plots in Figure 3A. Summary statistics corresponding to these distributions are provided in supplemental information Table S3.

Figure 3.

Intracellular mRNA copy number prediction results

The predictive results demonstrate the model’s performance when trained on data from one dose condition and validated on another. (A) Violin plots illustrate both measured and predicted intracellular mRNA copy numbers over time for two dose conditions: 0.01 mg (top) and 0.05 mg (bottom). Experimental measurements are shown in green, while model predictions are shown in orange. (B) Quantile-Quantile (Q-Q) plots compare predicted and measured intracellular mRNA copy numbers at selected time points (4–48 h) for the same two dose conditions: 0.01 mg (top) and 0.05 mg (bottom).

Outliers were removed using the filtration procedure described by Tukey⁷⁵ to enhance model robustness. The experimental results align with previous studies,^13,67 showing that intracellular mRNA levels rise sharply within the first 24 h and subsequently plateau, maintaining a relatively stable concentration over the remainder of the observation period.

To evaluate the distribution of cell area over time, we constructed Q-Q plots to assess the temporal consistency of cell area distributions, as described in supplemental information. The results indicate that the distribution stabilizes after 4 h, as illustrated in Figure 2C.

eGFP intensity

Flow cytometry was used to quantify eGFP protein expression intensity across three biological replicates within 7 days, using 0.01 mg and 0.05 mg doses (see Figure 4). When comparing eGFP-expressing cells to the negative control, we found that cellular autofluorescence significantly interferes with the detection of fluorescence signals in cells exhibiting low eGFP expression.⁷⁶ This interference introduces considerable uncertainty in the quantification of low-intensity eGFP signals. To ensure both interpretability and robustness, our analysis is restricted to high-expression cells, defined as those exhibiting eGFP intensity values ≥360 RFU. This threshold corresponds to the initial protein intensity cutoff, as indicated by the vertical line in Figure 4.

Figure 4.

Scatterplots illustrate the time course measurements of eGFP expression

Each row corresponds to a different dose (0.01 mg and 0.05 mg), while columns correspond to time points post-treatment. The horizontal axis denotes the fluorescence intensity measured in the KO525 channel. The vertical axis indicates side-scattered light area (SSC-A). Blue and orange points denote experimental samples treated with 0.01 mg and 0.05 mg doses, respectively. Gray points represent negative controls, which is measured at 0 h post-treatment.

Then, high-intensity data from all three replicates were pooled and visualized as green violin plots in Figure 5A whose statistics are presented in supplemental information Table S3. Outliers were removed using Tukey’s filtration method.⁷⁵ For both 0.01 mg and 0.05 mg doses of eGFP mRNA-LNPs, the mean and variance of eGFP expression increased gradually over time, reaching a plateau at approximately 120 h. Beyond this point, the protein expression level remains stable, suggesting convergence to a translation saturation threshold.

Figure 5.

Protein expression prediction results

The predictive results demonstrate the model’s performance when trained on data from one dose condition and validated on another. (A) Violin plots illustrate the distribution of both measured and predicted positive eGFP intensity (RFU ≥360) over time under two dosing conditions: 0.01 mg (top) and 0.05 mg (bottom). Green curves represent experimental measurements, while orange curves indicate model predictions. (B) Quantile-Quantile (Q-Q) plots compare predicted versus observed eGFP expression levels at selected time points (24–168 h). Data points include both fitting results (yellow crosses) and validation results (purple circles) for the two dosing conditions: 0.01 mg (top) and 0.05 mg (bottom).

LNP size

DLS was used to characterize the particle size distribution of mRNA-loaded LNPs in phosphate-buffered saline (PBS). The size distribution of LNPs is presented in Figure 2A. The overall particle diameters distribution closely approximates a normal distribution, with mean value of 116.42 nm and standard deviation of 38.12 nm.

MIMS model implementation and validation

To characterize cellular mechanisms, we first calibrated the cell density model described in Equation 9 using cell viability measurements. This was followed by fitting the cell division model to time course data of cell area. We then assessed the predictive accuracy of the multi-scale kinetic MIMS model by comparing its outputs against intracellular mRNA copy numbers and eGFP protein expression levels. Upon successful validation, we performed in silico experiments to explore how dosage, LNP size, and cell area influence the dynamics and variability of gene and protein expression. The simulation results show strong agreement with previously reported findings, further demonstrating the reliability and robustness of the proposed MIMS framework.

Simulation of cell growth and cell division

HEK293FT cells are widely employed in mRNA-LNP delivery studies due to their high transfection efficiency,^77,78 robust protein expression capabilities,^61,79 and rapid proliferation rate.²⁷ Our fitted cell growth model accurately reproduces the experimentally measured HEK293FT cell density over time, as shown in Figure 1E. Importantly, the model captures all three phases of cell growth, aligning well with observations from batch-cultured HEK293FT systems.^27,80,81

Building on this validated macroscopic model of cell population dynamics, we developed a complementary cell division model that accurately predicts the distribution of cell areas, as shown in Figure 2C. Together, these models offer distinct yet synergistic perspectives on cell proliferation. The cell growth model describes population-level dynamics driven by external resource availability, while the cell area-dependent division model provides a finer-grained view at the single-cell level, incorporating internal regulatory factors such as cell size and cell-cycle progression. During proliferation, cells tend to maintain a stable distribution of cell areas, indicating that cell size plays a regulatory role in division.^51,54,82,83 Assuming a constant proportion of cells across different cell-cycle phases, both the division rate and the transition rate from the G1-S phase to the G2-M phase are modulated by the resource-dependent cell growth rate, as described in Equation 13 and Equation 14. Notably, larger cells in the G1-S phase exhibit a higher probability of progressing to the G2-M phase, as modeled by Equation 15.

Model prediction of mRNA-LNP potency

To evaluate the predictive performance of the MIMS model in capturing single-cell gene and protein expression dynamics and variability, we employed cross-validation. Specifically, the model was trained on one dose dataset and independently validated against a separate dose dataset to ensure robustness.

For protein expression intensity prediction, we focused on values exceeding the negative control threshold (360 RFU), as illustrated in Figure 4. This threshold was established based on observations from the negative control to mitigate the confounding effects of cell autofluorescence.^7,14 Since too few cells positively express eGFP before 24 h when dose is 0.01 mg, we only predict the protein expression after 24 h.

Figures 3A and 3B visualize the predicted distribution of intracellular mRNA copy numbers at the single-cell level. Quantitative evaluation of the model’s performance—including relative errors in the mean, standard deviation, and the overall distributions of gene and protein expression—is summarized in supplemental information Table S4. Violin plots illustrate the empirical distributions from both model predictions and experimental assay measurements, while Quantile-Quantile (QQ) plots reveal the linear correspondence between predicted and observed distributions. The proposed multi-scale kinetic model demonstrates strong and consistent predictive performance in capturing gene and protein expression dynamics, as well as cell-to-cell variability. While the limited detection sensitivity of eGFP constrains protein expression predictions to 24 h post-transfection, the proposed model reliably characterizes the delivery process within this window, as demonstrated by accurate predictions of intracellular mRNA copy numbers. Furthermore, the model generalizes well to dose-response conditions not included in the training data, providing accurate and reliable predictions beyond the scope of the original experiments.

As shown in Figure 3A, smFISH assay results reveal that intracellular mRNA concentrations increase rapidly within the first 24 h post-treatment and subsequently stabilize at a steady-state level. While Ashraf et al.⁶⁷ proposed a fixed saturation threshold for single-cell mRNA expression, our experimental data suggest that the saturation level is dose dependent. Specifically, at a dose of 0.01 mg, the mRNA copy number plateaus around 260 spots per cell, whereas at a dose of 0.05 mg, the saturation level increases to approximately 300 spots per cell.

The developed multi-scale kinetic model accounts for the observed differences in saturation levels and links them to the dose-dependent uptake rate of mRNA-LNPs. Specifically, the LNP uptake rate increases with dose, as described by Equation 24, until it reaches a saturation state. As exocytosis transports some mRNA back into the extracellular environment, the exocytosis rate is constrained by a maximum rate v_exo, as defined in Equation 28. At a fixed dose level, individual cells regulate intracellular mRNA concentration through a dynamic balance of three processes: influx of mRNA via LNP uptake, loss of mRNA through exocytosis (the cellular mechanism for releasing molecules), and dilution of mRNA during cell division. This regulatory mechanism enables cells to maintain mRNA homeostasis despite external perturbations and growth. Cell size further influences this balance. Larger cells tend to exhibit faster mRNA-LNP uptake and are more prone to division, while smaller cells show slower uptake and exocytosis rates and are less likely to divide. These size-dependent dynamics add another layer of complexity to intracellular mRNA regulation.

Simulation-based prediction of potency across varying doses

The validated multi-scale kinetic model was used to perform in silico experiments to investigate the effect of dose on mRNA-LNP potency. To characterize the dose-response relationship, simulations were conducted at five dose levels: 0.005, 0.01, 0.025, 0.05, and 0.1 mg, with results shown in Figure 6. In each case, the initial mRNA concentration was scaled proportionally to the dose, assuming encapsulation within mRNA-LNPs of uniform size, as illustrated in Figure 2A. The resulting dose-response curve exhibits a sigmoid-like profile, consistent with observations by Yasar et al.¹⁴ As the dose increases, the variability in intracellular mRNA concentration also rises, aligning with findings from Rees et al.⁶ Notably, the MIMS model, unlike the live-cell imaging approach used by Leonhardt et al.,¹³ captures single-cell dynamics using cost-efficient fixed-cell imaging, enabling reliable dose-response predictions without the need for live-cell imaging techniques.

Figure 6.

In silico experiment results characterizing the impact of dose, LNP size, and cell area on mRNA-LNP delivery outcomes

Violin plots of predicted intracellular mRNA copy number (top row) and eGFP protein expression (bottom row) across three sources of variability: dose (left), LNP size (middle), and cell area (right). For each condition, distributions are shown at selected time points (mRNA: 12, 24, and 48 h; protein: 24, 48, and 72 h). In the top row of cell area, green and yellow denote experimental observations and model simulations, respectively. For LNP size and cell area in silico experiments, the mRNA-LNP doses are 0.01 mg.

The simulation results (Figure 6) indicate a sharp increase in mRNA uptake efficiency with increasing dose, reaching a plateau at approximately 0.5 μL. This trend is consistent with experimental findings reported by Leonhardt et al.,¹³ Rees et al.,⁶ and Jiang et al.⁸⁴ Given comparable eGFP nanoparticle sizes, the model-generated dose-response curve closely matches that of Leonhardt et al.,¹³ despite relying solely on fixed-cell assay data. Additionally, the simulations reveal that cell-to-cell variability in intracellular mRNA levels increases with dose, further corroborating the findings of Rees et al.⁶ The predicted protein expression response also aligns well with trends and variability reported in the literature, such as studies by Yasar et al.,¹⁴ Shen et al.,⁸⁵ and Munson et al.²⁶

Notably, compared to previous studies, the developed multi-scale kinetic model offers a more interpretable framework for predicting dose-response behavior. Since the uptake rate in Equation 24 follows the Monod equation, the mRNA-LNP internalization rate is constrained by the parameter v_en, which is influenced by factors such as LNP size, ligand density, and receptor density. When cell area and LNP size are held constant, increasing the dose enhances the LNP-cell membrane binding rate. This binding rate is modulated by the half-saturation constant K_bind, which reflects underlying cellular regulatory mechanisms, including energy availability and cell culture conditions. Consequently, within the proposed framework, the selection of the mRNA-LNP uptake rate is inherently linked to the cell growth rate, providing mechanistic insight into dose-dependent variability.

LNP size-dependent potency in mRNA-LNP delivery

The validated multi-scale kinetic model was employed to perform in silico experiments investigating the influence of LNP size on delivery potency. Specifically, we simulated the potency of mRNA-LNP formulations across a range of LNP sizes to assess their impact on the delivery system’s effectiveness. Five representative LNP sizes were selected based on quantiles of the experimental size distribution: 58.8 nm (4 quantile), 78.8 nm (22 quantile), 106 nm (53 quantile), 142 nm (83 quantile) and 190 nm (98 quantile). To simplify the analysis, size variation within each case was neglected. The initial dose for all simulations was set to 0.01 mg.

As illustrated in Figure 6, the simulated average potency reaches its peak when the LNP size is approximately 106–142 nm. Deviations from this optimal size—either smaller or larger—result in reduced potency. This finding is consistent with observations reported in the literature from both in vitro even in vivo studies.⁸⁶ Within the optimal size range, cell-to-cell variation in potency is maximized, suggesting a highly heterogeneous response across the cell population. In contrast, smaller LNPs exhibit limited mRNA encapsulation capacity. Although they demonstrate higher binding rates at a fixed dose, their overall mRNA uptake is inefficient due to the reduced loading per particle. Additionally, the increased membrane curvature induced by smaller LNPs elevates the elastic energy cost during internalization.⁴ Conversely, excessively large LNPs suffer from lower binding rates and prolonged internalization times. In both suboptimal size regimes, mRNA uptake becomes uniformly low across the cell population, leading to diminished variability in cellular response.

We conducted a systematic simulation study to construct a response surface that characterizes the influence of LNP size on the expected intracellular mRNA copy number. This surface serves as a guide for selecting the optimal LNP size to maximize mRNA delivery efficiency. The simulated response surface, which exhibits a quadratic-like trend (supplemental information Figure S2), enables identification of an optimal size range based on average mRNA uptake. Using intracellular mRNA copy numbers measured at 24 and 48 h as evaluation criteria, we performed an exhaustive search and identified an optimal LNP size range of 106–142 nm, with a peak around 110 nm. This finding is consistent with experimental observations reported in the literature. For instance, Walther et al.²³ reported an optimal LNP size of 150 nm for HEK293FT cells, outperforming larger particles (245 nm) in terms of transfection efficiency. Similarly, McMillan et al.²² investigated LNP-mediated mRNA expression in HEK293 cells and found an optimal size range of 105–138 nm for maximizing potency, which closely aligns with our simulation results.

Influence of cell area on LNP uptake efficiency

The validated multi-scale kinetic model was used to conduct in silico experiments examining how cell area influences mRNA-LNP uptake. As illustrated in Figure 2D, both the magnitude of LNP uptake and its cell-to-cell variability show a positive correlation with cell area. This trend is consistent with prior observations in lipid-based and other nanoparticle delivery systems.^6,7,87 To investigate the mechanistic underpinnings of this correlation, we performed simulations and analyzed mRNA potency predictions across four quartiles of cell area (Q1–Q4), corresponding to the 0–25^th, 25–50^th, 50–75^th, and 75–100^th percentiles of the measured cell area distribution. The results are presented in Figure 6.

Simulation predictions of intracellular mRNA copy numbers closely match experimental observations from the smFISH assay for the first three cell area quartiles (Q1–Q3), with a slight overestimation observed in the largest quartile (Q4). These results suggest a positive correlation between cell area and mRNA uptake, though the relationship is sublinear. Notably, the developed multi-scale kinetic model captures this quantitative trend effectively. While larger cells may possess more surface receptors, enabling higher LNP uptake rates,^6,7 this advantage may be transient due to cell cycle dynamics. According to the cell area-dependent division model described in (Equation 12), (Equation 13), (Equation 14), (Equation 15), (Equation 16), (Equation 17), larger cells are more likely to enter mitosis, during which intracellular mRNA levels are diluted through partitioning between daughter cells.

The proposed framework enhances our understanding of how the internalization rate responds to changes in cell area, ultimately approaching a saturation point. Monod kinetics is applied to model ligand diffusion and receptor-mediated internalization in Equation 24, particularly in scenarios where LNP ligands bind to a finite number of cell surface receptors—a quantity that scales with cell area. Under this model, the empirical constant K_A modulates the sensitivity of the uptake rate to cell area. In addition, K_bind reflects the LNP-receptor binding affinity, thereby linking molecular interaction strength to macroscopic uptake behavior.⁸⁸

Discussion

While mRNA vaccines—particularly those developed for COVID-19—have demonstrated high efficacy, challenges remain in optimizing their delivery and expression efficiency, especially in proliferating cells. Enhancing CQAs, such as LNP size, is essential for maximizing the potency and therapeutic effectiveness of LNP-based mRNA delivery systems.^34,61,89 However, this optimization is often constrained by the high cost and time requirements associated with conventional experimental approaches. Furthermore, the influence of additional variables—such as cell density, proliferation rate, and dynamic changes in cell morphology—on mRNA-LNP potency remains insufficiently characterized and poorly understood.

The proposed MIMS addresses these challenges by capturing the underlying mechanisms of the mRNA-LNP delivery and expression process. This model accounts for the interactive effects of multiple factors on potency across molecular, cellular, and macroscopic scales. By integrating with advanced assays (such as smFISH and flow cytometry) capable of quantifying gene and protein expression at the single-cell level, MIMS enhances mechanistic understanding and enables robust potency prediction. Importantly, it provides a predictive distribution that captures cell-to-cell variability, supporting the development of rapid and reliable quality control strategies for mRNA-LNP formulations.

This single-cell multi-scale framework provides mechanistic insights into how CQAs influence mRNA-LNP potency and drive to cell-to-cell variability. As demonstrated in prior studies,^6,7 variability in LNP uptake is a universal, biologically fundamental phenomenon rather than experimental noise, arising from factors such as cell size, cell-cycle state, and stochastic endocytic events. In contrast, earlier studies were usually bulk-based,^39,40 which systematically obscured cellular heterogeneity. Capturing the full distribution of single-cell responses to mRNA-LNP delivery is therefore essential for accurately predicting therapeutic outcomes. While a few studies have investigated variability in delivery efficiency, they have not fully elucidated the underlying sources of heterogeneity observed in in vitro potency assays. For instance, Leonhardt et al.¹³ proposed a statistical framework for modeling mRNA-lipoplex delivery, attributing cell-to-cell variability in uptake primarily to stochastic fluctuations in endosomal loading and lysis. Similarly, Rees et al.⁶ developed a probabilistic model to examine the effects of cell membrane properties and dosage on delivery variability. However, their approaches lack mechanistic interpretability of the LNP binding process, leaving key stochastic drivers of this variability uncharacterized.

The validated MIMS model identified LNP size as a key contributor to cell-to-cell variability in uptake, particularly through its effects on internalization kinetics and binding efficiency. Both theoretical^4,5,17 and experimental studies^90,91 have shown that internalization time exhibits a V-shaped relationship with LNP size: as size increases beyond a lower threshold, internalization time decreases until reaching an optimal size, after which it increases again. While this size-dependent internalization behavior is well established at the single-particle level, in vitro LNP uptake is also modulated by dose and cell density dynamics. Additionally, intracellular mRNA copy number is influenced by the mRNA loading per LNP.⁹² The MIMS model captures the combined effects of these factors on mRNA-LNP uptake. Larger LNPs can encapsulate more mRNA^19,20; however, at a fixed mRNA dose, this results in fewer total particles, reducing the number of LNP-receptor binding events. This mechanistic insight explains the reduced transfection efficiency observed by Liao et al.²⁰ for high-loading LNPs at constant mRNA dose, as well as the lower long-term antibody titers reported in mice administered larger LNPs.⁸⁶

The developed MIMS model advances quantitative understanding of how various sources of uncertainty contribute to cell-to-cell variability in potency during in vitro mRNA-LNP delivery. Intracellular mRNA copy number increases progressively with LNP uptake but is simultaneously reduced by three key processes: (1) dilution due to cell division, (2) exocytosis of mRNA, and (3) mRNA degradation. The stochastic nature of each of these processes further amplifies variability in potency. While uptake and degradation have been quantitatively modeled in prior studies,^13,39,40 the contributions of cell division and exocytosis remain largely unquantified. Commonly used cell lines in mRNA-LNP studies—such as HEK293 and its derivatives,^20,21,22,23 as well as HeLa cells^24,25,26—exhibit doubling times ranging from 24 to 45 h.^27,28 Therefore, for in vitro potency assessments extending beyond 24 h, dilution of exogenous mRNA and its translated proteins become a significant contributor to variability. MIMS incorporates this effect through a cell division module, where cell area dynamics influence both receptor abundance and division rate, thereby modulating intracellular mRNA levels over time. This mechanistic insight also helps elucidate the role of the cell cycle in mRNA-LNP potency.^6,93,94 Moreover, as described in Equation 29, proliferating cells continuously deplete extracellular mRNA-LNPs through uptake, introducing a time-dependent reduction in available LNPs—a factor rarely considered in previous models.

Prior studies have shown that identical mRNA-LNP formulations can elicit different responses across cell lines.^22,25 The proposed framework utilized a modular architecture to capture this variability. In the proposed framework, five critical modules require modeling: (1) cell growth dynamics, (2) mRNA-LNP uptake and endosomal escape, (3) mRNA exocytosis, (4) translation, and (5) mRNA degradation. In this study, HEK293FT serves as the validated baseline of proposed framework. Other cell lines, depending on the similarity of their delivery pathways to HEK293, i.e., HeLa^61,95 or induced pluripotent stem cells (iPSCs), may require either parameter re-fitting alone or additional customization of the growth and uptake modules. Therefore, experimental validation of the proposed framework across diverse cell lines represents an important direction for future work.

This study also opens more promising avenues for future research. One key direction is the quantitative characterization of LNP-cell membrane binding affinity, which governs the empirical coefficient K_bind in the Monod model describing mRNA-LNP uptake kinetics. Binding affinity is influenced by multiple interacting factors, including ligand and receptor densities, LNP surface charge, and lipid composition. A systematic investigation into how these physicochemical parameters and CQAs affect the dynamics and variability of the uptake process could deepen mechanistic understanding and inform the optimal design and quality control of mRNA-LNP products.

Another important area for future investigation is the empty LNP subpopulation effects. Empty LNPs are inevitable byproducts of LNP preparation and influence transfection efficiency,⁹² and current modeling framework captures their random effects by tuning the mRNA loading parameter k_pa of Equation 22 and the uptake variability factor σ_up of Equation 25. However, this framework does not incorporate all mechanistic effects of empty LNPs, i.e., competing ApoE,⁹² which possibly leads to dynamic LNP ligand density heterogeneity, and results in LNP-to-LNP endocytosis variability. Future work in mechanistically modeling the LNP-ApoE binding will be critical in understanding LNP-level delivery heterogeneity.

The finally important area is the regulation of protein expression—a central determinant of potency—through improved characterization of translation rates and mRNA degradation kinetics across different mRNA sequences. Understanding how mRNA structural features influence RNA stability and protein synthesis would significantly enhance the mechanistic modeling of post-delivery gene expression.

Materials and methods

LNP formulation

We used PM-LNP-0021 eGFP mRNA-LNP product provided by ProMab Biotechnologies, Inc. These LNPs are formulated with, ionizable lipid, DSPC, cholesterol, and DMG-PEG2000 at optimal molar concentration for a high rate of encapsulation and efficient mRNA delivery. LNPs are suspended in PBS (-Ca, -Mg) (pH: 7.0–7.4).

In vitro assays

Cell culture

HEK293FT cells (Thermo Fisher Scientific cat# R700-07) were cultured following the manufacturer’s protocol and maintained in high glucose Dulbecco’s modified Eagle’s medium (DMEM) with GlutaMax (Fisher Scientific cat# 10566016), 10% fetal bovine serum (FBS), 1% MEM non-essential amino acids (Thermo Fisher Scientific cat# R700-07), 1% supplementary GlutaMax (Fisher Scientific cat# 35-050-061), 1% MEM sodium pyruvate (Thermo Fisher Scientific cat# 11360070), 1% Pen-Strep (Fisher Scientific cat# BW17-602E), and 500 μg/mL geneticin (Thermo Fisher Scientific cat# 10131035). Cell lines were tested PCR-negative for mycoplasma contamination (ATCC cat# 30 1012K).

Viable cell number

To test the viable cell number, a total of 12,500 HEK293FT cells were seeded into each well of a 96-well ELISA assay microplate (Fisher Scientific cat# 07- 000–627) in 150 μL of growth medium and incubated for 24 h to allow cell attachment. Cell number and viability were assessed at 1, 4, 12, 24, 48, 72, 96, 120, 144, and 168 h (h) using a TC20™ Automated Cell Counter (Bio-Rad), following the manufacturer’s protocol. Trypan blue exclusion (Bio-Rad, #145–0022) was used to distinguish viable cells from non-viable ones.

RT-qPCR

LNP-encapsulated RNA was extracted using Trizol reagent (Thermo Scientific cat# 15-596-026) and resuspended in nuclease-free water. Residual genomic DNA was removed by treatment with DNase I (Thermo Scientific cat# PI89836). Reverse transcription of RNA was performed using SuperScript III Reverse Transcriptase (Thermo Scientific cat# 18-080-093). Quantification of the resulting cDNA was carried out using Luna Universal qPCR Master Mix (New England Biolabs cat# M3004S). The sequences are provided in supplemental information.

smFISH

By acquiring image stacks, the spatial distribution of each RNA species can be accurately reconstructed at the single-cell level. A total of 12, 500 HEK293FT cells were seeded into each well of an 8-well chambered coverglass (Thermo Scientific cat# 12-565-470) in 300 μL of growth medium and incubated for 24 h to allow cell attachment. Cells were treated with two volumes (0.01 mg and 0.05 mg) of eGFP mRNA-loaded LNPs at various time points: 48, 36, 24, 12, 4, and 1 h prior to fixation. Cells were fixed with 4% formaldehyde solution and permeabilized overnight in 70% ethanol. For smFISH, 0.05 mg of eGFP-specific probe mixture was added to 50 μL hybridization buffer (containing 10% dextran sulfate, 10% formamide, and 2× SSC) and the samples were incubated overnight at 37°C. Following hybridization, samples were washed twice with wash buffer (10% formamide and 2× SSC), and cell nuclei were stained with DAPI (Thermo Scientific cat# EN62248). Imaging was performed using a Nikon inverted research microscope equipped with a Plan Apo λ 100 × 1.45 oil immersion objective. Four wavelengths were recorded: Alexa 488, Alexa 594, DAPI, and Brightfield. The smFISH images were processed using a custom analysis pipeline to segment individual cells, apply spot detection thresholds, and count RNA spots. Single-cell segmentation was conducted using the MATLAB-based RajLab Image Tools suite: https://bitbucket.org/arjunrajlaboratory/rajlabimagetools/wiki/Home. The probe sequences are provided in supplemental information.

Flow cytometry for cell cycle

A 1 mL suspension of HEK293FT cells was prepared at a concentration of 1× 10⁶ cells/mL in growth medium. Vybrant™ DyeCycle™ Violet (Thermo Fisher Scientific, Cat# V35003) was added to a final concentration of 5 μM (1 μL per 1 mL of cell suspension), mixed gently, and incubated at 37 for 30 min, protected from light. Cells were maintained at 37°C until flow cytometry acquisition and analyzed live—without washing or fixation—using 405 nm excitation laser and emission detection centered at ∼450/50 nm.

Flow cytometry for protein expression

A total of 12, 500 HEK293FT cells were seeded in each 96-well ELISA Assay Microplates (Fisher Scientific cat# 07-000-627) with 150 μL of growth medium and incubated for 24 h to allow cell attachment. Cells were treated with two volumes (0.01 mg and 0.05 mg) of eGFP mRNA-loaded lipid nanoparticles (ProMab cat# PM-LNP-0021) across three rows of wells at the following time points: 168, 144, 120, 96, 72, 48, 24, 12, 4, and 1 h prior to analysis. Following treatment, the medium was aspirated, and cells were washed once with phosphate-buffered saline (PBS) containing 5% bovine serum albumin (BSA). Cells were then resuspended in 200 μL PBS with 5% BSA for flow cytometry analysis. Flow cytometry was performed using a Beckman Coulter Cytoflex Cell Analyzer, with fluorescence detection on the KO525 channel. Data were preprocessed and analyzed for event counts using FlowJo software.

DLS

For measurements in PBS, LNPs were diluted at a ratio of 1:500. DLS detects fluctuations in scattered light intensity caused by Brownian motion of particles, allowing for the determination of their size distribution. This technique provides insight into the physical properties of the nanoparticles under different environmental conditions. For further details, refer to Long et al.²¹

Data and code availability

The code is available at: https://github.com/sibylla00/mRNA-LNP_delivery. All experimental data are available at: https://drive.google.com/drive/folders/1qCQhijxH2t431aENzbT2GLBgc9DZy7q4?usp=share_link.

Acknowledgments

This work is supported in part by funds from National Institute of Standards and Technology Grant 70NANB21H086, 70NANB24H293, and National Science Foundation Grant CAREER CMMI-2442970. Work at the Center for Theoretical Biological Physics was supported by the National Science Foundation (grant PHY-2019745). We also acknowledge generous support from the Northeastern University Explorer cluster and the Northeastern University Research Computing staff.

Author contributions

Y.Y., conceptualization [lead], formal analysis [lead], investigation [equal], methodology [lead], software [equal], visualization [lead], and writing – original draft [lead]; Y.Q., data curation [lead], investigation [equal], software [equal], validation [lead], visualization [lead], and writing – original draft [equal]; K.W., formal analysis [equal], methodology [lead], and writing – review and editing [equal]; Y.L., data curation [equal], investigation [equal], software [equal], and validation [equal]; G.S., conceptualization [equal] and writing – review and editing [equal]; P.C.W., writing – review and editing [equal]; S.H.R., conceptualization [lead], data curation [equal], project administration [equal], resources [lead], supervision [lead], and writing – review and editing [equal]; W.X., conceptualization [lead], methodology [equal], project administration [lead], resources [lead], supervision [lead], and writing – review and editing [lead]).

Declaration of interests

No competing interest is declared.