This protocol provides an approach to formulation optimization over mixture, continuous, and categorical study factors that minimizes subjective choices in the experimental design construction. For the analysis phase, an effective and easy-to-use modeling fitting procedure is employed.
We present a Quality by Design (QbD) styled approach for optimizing lipid nanoparticle (LNP) formulations, aiming to offer scientists an accessible workflow. The inherent restriction in these studies, where the molar ratios of ionizable, helper, and PEG lipids must add up to 100%, requires specialized design and analysis methods to accommodate this mixture constraint. Focusing on lipid and process factors that are commonly used in LNP design optimization, we provide steps that avoid many of the difficulties that traditionally arise in the design and analysis of mixture-process experiments by employing space-filling designs and utilizing the recently developed statistical framework of self-validated ensemble models (SVEM). In addition to producing candidate optimal formulations, the workflow also builds graphical summaries of the fitted statistical models that simplify the interpretation of the results. The newly identified candidate formulations are assessed with confirmation runs and optionally can be conducted in the context of a more comprehensive second-phase study.
Lipid nanoparticle (LNP) formulations for in vivo gene delivery systems generally involve four constituent lipids from the categories of ionizable, helper, and PEG lipids1,2,3. Whether these lipids are being studied alone or simultaneously with other non-mixture factors, experiments for these formulations require "mixture" designs because – given a candidate formulation – increasing or decreasing the ratio of any one of the lipids necessarily leads to a corresponding decrease or increase in the sum of the ratios of the other three lipids.
For illustration, it is supposed that we are optimizing an LNP formulation that currently uses a set recipe that will be treated as the benchmark. The goal is to maximize the potency of the LNP while secondarily aiming to minimize the average particle size. The study factors that are varied in the experiment are the molar ratios of the four constituent lipids (ionizable, cholesterol, DOPE, PEG), the N:P ratio, the flow rate, and the ionizable lipid type. The ionizable and helper lipids (including cholesterol) are allowed to vary over a wider range of molar ratio, 10-60%, than PEG, which will be varied from 1-5% in this illustration. The benchmark formulation recipe and the ranges of the other factors and their rounding granularity are specified in Supplementary File 1. For this example, the scientists are able to perform 23 runs (unique batches of particles) in a single day and would like to use that as their sample size if it meets the minimum requirements. Simulated results for this experiment are provided in Supplementary File 2 and Supplementary File 3.
Rampado and Peer4 have published a recent review paper on the topic of designed experiments for the optimization of nanoparticle-based drug delivery systems. Kauffman et al.5 considered LNP optimization studies using fractional factorial and definitive screening designs6; however, these types of designs cannot accommodate a mixture constraint without resorting to the use of inefficient "slack variables"7 and are not typically used when mixture factors are present7,8. Instead, "optimal designs" capable of incorporating a mixture constraint are traditionally used for mixture-process experiments9. These designs target a user-specified function of the study factors and are only optimal (in one of a number of possible senses) if this function captures the true relationship between the study factors and responses. Note that there is a distinction in the text between "optimal designs" and "optimal formulation candidates", with the latter referring to the best formulations identified by a statistical model. Optimal designs come with three main disadvantages for mixture-process experiments. First, if the scientist fails to anticipate an interaction of the study factors when specifying the target model, then the resulting model will be biased and can produce inferior candidate formulations. Second, optimal designs place most of the runs on the exterior boundary of the factor space. In LNP studies, this can lead to a large number of lost runs if the particles do not form correctly at any extremes of the lipid or process settings. Third, scientists often prefer to have experimental runs on the interior of the factor space to gain a model-independent sense of the response surface and to observe the process directly in previously unexplored regions of the factor space.
An alternative design principle is to target an approximate uniform coverage of the (mixture-constrained) factor space with a space-filling design10. These designs sacrifice some experimental efficiency relative to optimal designs9 (assuming the entire factor space leads to valid formulations) but present several benefits in a trade-off that are useful in this application. The space-filling design does not make any a priori assumptions about the structure of the response surface; this gives it the flexibility to capture unanticipated relationships between the study factors. This also streamlines the design generation because it does not require making decisions about which regression terms to add or remove as the desired run size is adjusted. When some design points (recipes) lead to failed formulations, space-filling designs make it possible to model the failure boundary over the study factors while also supporting statistical models for the study responses over the successful factor combinations. Finally, the interior coverage of the factor space allows for model-independent graphical exploration of the response surface.
To visualize the mixture factor subspace of a mixture-process experiment, specialized triangular "ternary plots" are used. Figure 1 motivates this usage: in the cube of points where three ingredients are each allowed to range from 0 to 1, the points that satisfy a constraint that the sum of the ingredients equals 1 are highlighted in red. The mixture constraint on the three ingredients reduces the feasible factor space to a triangle. In LNP applications with four mixture ingredients, we produce six different ternary plots to represent the factor space by plotting two lipids at a time against an "Others" axis that represents the sum of the other lipids.
Figure 1: Triangular factor regions. In the space-filling plot within the cube, the small grey dots represent formulations that are inconsistent with the mixture constraint. The larger red points lie on a triangle inscribed within the cube and represent formulations for which the mixture constraint is satisfied. Please click here to view a larger version of this figure.
In addition to the lipid mixture factors, there are often one or more continuous process factors such as N:P ratio, buffer concentration, or flow rate. Categorical factors may be present, such as ionizable lipid type, helper lipid type, or buffer type. The goal is to find a formulation (a mixture of lipids and settings for process factors) that maximizes some measure of potency and/or improves physiochemical characteristics such as minimizing particle size and PDI (polydispersity index), maximizing percent encapsulation, and minimizing side effects – such as body weight loss – in in vivo studies. Even when starting from a reasonable benchmark recipe, there may be interest in re-optimizing given a change in the genetic payload or when considering changes in the process factors or lipid types.
Cornell7 provides a definitive text on the statistical aspects of mixture and mixture-process experiments, with Myers et al.9 providing an excellent summary of the most relevant mixture design and analysis topics for optimization. However, these works can overload scientists with statistical details and with specialized terminology. Modern software for the design and analysis of experiments provides a robust solution that will sufficiently support most LNP optimization problems without having to appeal to the relevant theory. While more complicated or high-priority studies will still benefit from collaboration with a statistician and may employ optimal rather than space-filling designs, our goal is to improve the comfort level of scientists and to encourage optimization of LNP formulations without appealing to inefficient one-factor-at-a-time (OFAT) testing11 or simply settling for the first formulation that satisfies specifications.
In this article, a workflow is presented that utilizes statistical software to optimize a generic LNP formulation problem, addressing design and analysis issues in the order that they will be encountered. In fact, the method will work for general optimization problems and is not restricted to LNPs. Along the way, several common questions that arise are addressed and recommendations are provided that are grounded in experience and in simulation results12. The recently developed framework of self-validated ensemble models (SVEM)13 has greatly improved the otherwise fragile approach to analyzing results from mixture-process experiments, and we use this approach to provide a simplified strategy for formulation optimization. While the workflow is constructed in a general manner that could be followed using other software packages, JMP 17 Pro is unique in offering SVEM along with the graphical summary tools that we have found to be necessary to simplify the otherwise arcane analysis of mixture-process experiments. As a result, JMP-specific instructions are also provided in the protocol.
SVEM employs the same linear regression model foundation as the traditional approach, but it allows us to avoid tedious modifications that are required to fit a "full model" of candidate effects by using either a forward selection or a penalized selection (Lasso) base approach. Additionally, SVEM provides an improved "reduced model" fit that minimizes the potential for incorporating noise (process plus analytical variance) that appears in the data. It works by averaging the predicted models resulting from repeatedly reweighting the relative importance of each run in the model13,14,15,16,17,18. SVEM provides a framework for modeling mixture-process experiments that is both easier to implement than traditional single-shot regression and yields better quality optimal formulation candidates12,13. The mathematical details of SVEM are beyond the scope of this paper and even a cursory summary beyond the relevant literature review would distract from its main advantage in this application: it allows a simple, robust, and accurate click-to-run procedure for practitioners.
The presented workflow is consistent with the Quality by Design (QbD)19 approach to pharmaceutical development20. The result of the study will be an understanding of the functional relationship that links the material attributes and process parameters to critical quality attributes (CQAs)21. Daniel et al.22 discuss using a QbD framework specifically for RNA platform production: our workflow could be used as a tool within this framework.
The experiment described in the Representative Results section was carried out in accordance with the Guide for the Care and Use of Laboratory Animals and the procedures were performed following guidelines established by our Institutional Animal Care and Use Committee (IACUC). 6-8 week old female Balb/C mice were commercially obtained. Animals received ad libitum standard chow and water and were housed under standard conditions with 12 hour light/dark cycles, at a temperature of 65-75 °F (~18-23 °C) with 40-60% humidity.
1. Recording the study purpose, responses, and factors
NOTE: Throughout this protocol, JMP 17 Pro is used for designing and analyzing the experiment. Equivalent software can be used following similar steps. For examples and further instructions for all the steps performed in Section 1, please refer to Supplementary File 1.
Figure 2: Cause and effect diagram. The diagram shows common factors in an LNP formulation optimization problem. Please click here to view a larger version of this figure.
2. Creation of the design table with a space-filling design
Figure 3: Study factors and ranges. Screenshots of settings within experimental software are useful for reproducing the study setup. Please click here to view a larger version of this figure.
Figure 4: Initial output for a space-filling design. Showing the first two rows of the table, settings need to be rounded to the desired precision while also making sure that the lipid amounts sum to 1. The benchmark was added to the table manually. Please click here to view a larger version of this figure.
Figure 5: Formatted study table. The factor levels have been rounded and formatted and a Run ID column has been added. Please click here to view a larger version of this figure.
Figure 6: Design points on a ternary plot. The 23 formulations are shown as a function of the corresponding Ionizable, Helper and "Others" (Cholesterol+PEG) ratios. The green point in the center represents the benchmark 33:33:33:1 molar ratio of Ionizable (H101):Cholesterol:Helper (DOPE):PEG. Please click here to view a larger version of this figure.
Figure 7: Distribution of non-mixture process factors in the experiment. The histograms show how the experimental runs are spaced across Ionizable Lipid Type, N:P ratio, and Flow Rate. Please click here to view a larger version of this figure.
3. Running the experiment
4. Analyzing the experimental results
Figure 8: Observed potency readings from the experiment. The points show the potency values that were observed from the 23 runs; the replicated benchmark runs are shown in green. Please click here to view a larger version of this figure.
Figure 9: Software dialog for initiating the analysis. The candidate effects have been entered along with the target potency response, and the No Intercept option has been unchecked. Please click here to view a larger version of this figure.
Figure 10. Additional dialog for specifying SVEM options. By default, the lipid main effects are forced into the model. Because an intercept is included, we recommend unchecking these boxes in order not to force the effects. Please click here to view a larger version of this figure.
Figure 11: Actual by predicted plot. This figure plots the observed Potency against the value predicted for each formulation by the SVEM model. The correlation need not be as strong as it is in this example, but the expectation is to see at least a moderate correlation and to check for outliers. Please click here to view a larger version of this figure.
Figure 12: Prediction profiler. The top two rows of graphs show the slices of the predicted response function at the optimum formulation (as identified by the SVEM approach). The bottom row of graphs shows the weighted "desirability" of the formulation, which is a function of the last column of graphs which shows that Potency should be maximized, and Size should be minimized. Please click here to view a larger version of this figure.
Figure 13: Three optimal formulation candidates from SVEM-Forward Selection. Changing the relative importance weighting of the responses can lead to different optimal formulations. Please click here to view a larger version of this figure.
Figure 14: Ternary plots for the percentile of desirability. The plot shows the 50,000 formulations color coded by percentile of desirability, where the desirability is set with importance weight of 1.0 for maximizing Potency and 0.2 for minimizing size, these plots show that the optimal region of formulations consists of lower percentages of ionizable lipid and higher percentages of PEG. Please click here to view a larger version of this figure.
Figure 15: Ternary plot for the predicted Size. The plot shows the size predictions from the SVEM model for each of the 50,000 formulations. Size is minimized with higher percentages of helper lipid and maximized with lower percentages of helper. Since the other factors vary freely across the 50,000 plotted formulations, this implies that this relationship holds across the ranges of the other factors (PEG, flow rate, etc.). Please click here to view a larger version of this figure.
Figure 16: Violin plots for the desirability of formulations involving the three different ionizable lipid types. Each of the 50,000 points represents a unique formulation from throughout the allowed factor space. The peaks of these distributions are the maximal values of desirability that are calculated analytically with the prediction profiler. H102 has the largest peak and thus produces the optimal formulation. The SVEM approach to building the model that generates this output automatically filters out statistically insignificant factors: the purpose of this graph is to consider practical significance across the factor levels. Please click here to view a larger version of this figure.
5. Confirmation runs
Figure 17: Table of ten optimal candidates to be run as confirmation runs. The True Potency and True Size have been filled in from the simulation generating functions (without any added process or analytical variation). Please click here to view a larger version of this figure.
6. Optional: Designing a follow-up study to be run concurrently with the confirmation runs
7. Documenting the study's final scientific conclusions
This approach has been validated across both broadly classified lipid types: MC3-like classical lipids and lipidoids (e.g., C12-200), generally derived from combinatorial chemistry. Compared to a benchmark LNP formulation developed using a One Factor at a Time (OFAT) method, the candidate formulations generated through our workflow frequently demonstrate potency improvements of 4- to 5-fold on a logarithmic scale, such as shown in the mouse liver luciferase readings in Figure 18. Table 1 depicts the corresponding enhancements in mouse liver luciferase expression observed over the benchmark control performance throughout two optimization phases (an initial study and a subsequent follow-up study). In the first phase, focus was on optimizing the lipid ratios while keeping other factors constant. In the follow-up study, an additional helper lipid type was introduced and optimization was performed considering both the lipid ratio composition and the helper lipid type. Consequently, the newly introduced helper lipid type was selected to be used with the associated optimized lipid composition. The significant enhancement in potency suggests that these optimized compositions may exhibit superior endosomal escape capabilities25.
Simulations can be used to show the expected quality of the optimal candidate produced by this procedure. Within the framework of the example experiment used in the protocol, we can repeat the simulation many times for different run sizes and evaluate the results according to the simulated process-generating function. A JMP script for this purpose is provided in Supplementary File 4. Specifically, a space-filling design was generated and the response columns were populated with values from our generator functions, plus noise representing analytical and process variation. We fit these simulated responses with different analysis techniques (including SVEM Forward Selection) to produce a corresponding candidate optimal recipe. The candidates from each analysis method are then compared to the value of the true optimum from the generating functions. Figure 19 illustrates the average percent of the maximal theoretical response achieved by each of the three analysis methods using space-filling designs of size given on the horizontal axis. The full model, which includes all candidate effects and does not reduce the model based on the statistical significance of those effects, performs the worst. Much of the additional work that traditionally goes into fitting regression models for mixture-process experiments involves modifications (removing the intercept, forcing the mixture main effects, precluding the use of pure quadratic mixture effects, etc.) that are required to fit this full model9, and from this perspective, those procedures are unnecessary12. Furthermore, this model cannot be fit until the design size reaches the number of effects in the model. At smaller experimental sizes, we can fit the traditional forward selection method, which outperforms the full model with respect to the average performance of the optimal candidate formulation for each fixed experimental size. Likewise, the SVEM modification to this forward selection approach further improves the performance of the optimal candidates. This plot reveals that using SVEM-Forward Selection12,13 to analyze a 24-run space-filling experiment achieves the same average quality typically requiring 50 runs when analyzed with a traditional forward selection (targeting minimum AICc) model. Although actual performance will vary from process to process, this simulation – along with published results on SVEM12,13,16,17,26– demonstrates the potential of this modeling procedure for formulation optimization.
Figure 18: Improvement in liver luciferase expression following two rounds of experimentation. Round 0 shows the liver luciferase reading for the benchmark formulation; Round 1 shows the liver luciferase reading after the first experiment which optimizes the LNP constituent lipid molar ratios; Round 2 shows the liver luciferase reading after the second experiment which further optimizes the constituent molar ratios while also considering an additional helper lipid type. Please click here to view a larger version of this figure.
Figure 19: Quality of optimal formulation as a function of experimental size and statistical model. The vertical axis represents the percentage of theoretical maximum desirability, and the horizontal axis represents the size of the space-filling design. Each point shows the mean over 150 simulations. The blue line (triangles) represents the full model (without any elimination of statistically insignificant effects), the amber (circles) line represents the traditional AICc-based forward selection model (with an intercept and without forcing mixture main effects), and the green line (upside down triangles) represents the SVEM-based forward selection model (with an intercept and without forcing mixture main effects). Please click here to view a larger version of this figure.
Round | Particle ID | Luciferase expression in the Liver (photon/sec) |
0 | Control Benchmark | 8.E+06 |
1 | Optimized over Lipid Ratios | 2.E+09 |
2 | Optimized over Lipid Ratios and Helper Lipid Type | 8.E+10 |
Table 1: Systematic improvement in luciferase expression through Design of Experiment (DOE) optimization. This table illustrates the significant enhancement in the expression of luciferase, with an up to 10,000-fold improvement on the photon/second scale, from the initial benchmark to the final "optimal candidate".
Supplementary File 1: 04APR2023 Summary.docx – This document provides a record of the study including its purpose, the responses assessed, the factors considered, and the total number of runs executed. Please click here to download this File.
Supplementary File 2: 23_run_simulated_experiment.jmp – A JMP file with the simulated experiment and its results. This file also includes attached analysis scripts compatible with JMP 17 Pro. Please click here to download this File.
Supplementary File 3: 23_run_simulated_experiment.xlsx – An Excel file that includes the simulated experiment and its results, suitable for readers who may not have access to JMP. Please click here to download this File.
Supplementary File 4: mixture simulation 20DEC22.jsl – This is a JMP 17 Pro script used to simulate LNP formulation experiments and evaluate the performance of different analysis methods. The script uses the SVEM-Forward Selection (no intercept) approach, which is the key analysis method used in this workflow. Please click here to download this File.
Modern software for the design and analysis of mixture-process experiments makes it possible for scientists to improve their lipid nanoparticle formulations in a structured workflow that avoids inefficient OFAT experimentation. The recently developed SVEM modeling approach eliminates many of the arcane regression modifications and model reduction strategies that may have previously distracted scientists with extraneous statistical considerations. Once the results are collected, the SVEM analysis framework offers an approach that is both easier to implement and tends to produce better models than traditional modeling approaches13. Furthermore, the graphical analyses that are based on the prediction formulas for each response are easily interpretable by scientists, giving a clear summary of the marginal behavior of the response over individual factors as well as small groups of factors without requiring the interpretation of highly correlated parameter estimates from a regression model. This allows scientists to focus on assessing practical significance across study factors after SVEM has automatically removed statistically insignificant effects.
The workflow has been used in practice to systematically vary lipid composition and formulation parameters such as N/P ratio, flow rate, and mixing ratio for optimization and to select the best helper lipid types, ionizable lipid types, and buffer types. The goals across these examples usually include maximizing in vivo or in vitro potency and encapsulating varying payloads like mRNA or DNA for relevant in vivo targets such as liver cells, or sometimes across multiple cell-types in the case of in vitro applications. For specific applications, we may need to balance biophysical properties such as size, PDI, zeta potential, and percent encapsulation while examining in vivo potency. Additionally, the goal is to find a potent, yet well-tolerated formulation and so we may include responses such as change in body weight, cytokine response, or elicitation of liver enzymes such as AST/ALT in the analysis. Patterns have emerged from numerous LNP experiments. Notably, alterations in the molar ratio of the ionizable lipid and the N/P ratio seem to significantly impact RNA encapsulation. Moreover, changes in the PEG molar ratio appear to affect particle stability, as indicated by influences on size and PDI. In general, an excess of PEG in the LNP core tends to have a detrimental effect on potency in mice.
Performance improvements are especially noticeable when more than one response is targeted: even if the benchmark already performs well with respect to the primary response (e.g., potency), joint optimization typically maintains or improves the behavior with respect to the primary response while simultaneously improving behavior with respect to other responses (minimizing PDI, size, or bodyweight loss). We validate the authenticity of these improvements with confirmation runs, wherein we prepare and directly compare the benchmark formulation (possibly with a replicate) and new candidate formulations.
The design phase of this workflow has several critical steps. First, ensure that the factors and their ranges are correctly entered into the space-filling design platform. Second, use graphics and subject matter knowledge to confirm the feasibility of each resulting formulation before initiating the experiment. Finally, execute the experiment following the randomized order specified by the design table. Adhering to this sequence helps prevent unmeasured covariates – such as the order of formulation production or ambient temperature – from confounding the factors under study. The space-filling designs are easier to construct – with less potential for user error than optimal mixture-process designs, which require extra decisions during setup that may frustrate inexperienced users and discourage them from using designed experiments. Nevertheless, after working through this protocol, scientists may benefit from additional reading on how optimal designs could potentially replace space-filling designs in the protocol, such as described in Chapter 6 of Goos and Jones (2011)27. Especially for follow-up studies that "zoom in" on an optimal region – where there is less concern about failures along the mixture boundaries – D-optimal designs can be more efficient than space-filling designs.
Likewise, the analysis phase of this workflow has several critical steps. First, ensure that the model specifies an appropriate set of candidate effects, including interactions, rather than only the main (first-order) effects of the factors. Second, employ SVEM Forward Selection as the modeling framework. Third, disable the default No Intercept option and avoid forcing mixture main effects. Finally, correctly set the desirability functions for the responses before initiating optimization. For users without access to SVEM, the best approach is to use traditional forward selection (targeting minimum AICc) for the regression problem12. The protocol mentions that it is also possible to use SVEM Lasso: on average, this approach gives similar results to SVEM Forward Selection, though for particular datasets the two approaches may produce slightly different optimal formulations that could be compared with confirmation runs12. However, SVEM Lasso will give inferior modeling results if the user makes the easy mistake of forgetting to disable the default No Intercept option12: for this reason, we have used SVEM Forward Selection as the default method, since it is more robust to this option.
The primary limitation of this method is that there will be occasional studies with greater complexity that will benefit from the help of a statistician for design and analysis. Situations where the run budget is more limited than usual (below the minimum heuristic), the responses are binary, there are a large number of categorical factors or levels of a single categorical factor, where a research goal is to consider eliminating one or more mixture factors from the recipe, or where there are additional constraints on the factor space may be approached differently by a statistician, such as by using optimal or hybrid12,28 designs or by adding additional structure to the design. Specifically, a hybrid design could be formed by creating a space-filling design with most of the budgeted runs and then "augmenting" the design with the remaining runs (usually 2-4) using a D-optimal criterion. Another hybrid approach is to generate a space-filling design over the mixture (lipid) and continuous (process) factors, and then afterward to add any categorical factors using an "optimal" allocation of factor levels. Nevertheless, the simplified space-filling design approach taken in the protocol has been developed over the past few years in the process of running dozens of LNP formulation optimization experiments, and we believe it offers a robust approach that will work successfully in most cases while also giving scientists confidence in their ability to utilize designed experiments.
The authors have nothing to disclose.
We are grateful to the editor and to the anonymous referees for suggestions that improved the article.