Name: a workflow for lipid nanoparticle (lnp) formulation optimization using designed mixture-process experiments and self-validated ensemble models (svem)
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We are grateful to the editor and to the anonymous referees for suggestions that&#160;improved&#160;the article.

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 &#176;F (~18-23 &#176;C) wi...

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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 appro...

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 &#34;mixture&#34; 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 &#34;slack variables&#34;7 and are not typically used when mixture factors are present7,8. Instead, &#34;optimal designs&#34; 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 &#34;optimal designs&#34; and &#34;optimal formulation candidates&#34;, 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 &#34;ternary plots&#34; 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 &#34;Others&#34; axis that represents the sum of the other lipids.
<img alt="Figure 1" class="xfigimg" src="/files/ftp_upload/65200/65200fig01.jpg" /> 
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. <a href="https://www.jove.com/files/ftp_upload/65200/65200fig01large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
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 &#34;full model&#34; of candidate effects by using either a forward selection or a penalized selection (Lasso) base approach. Additionally, SVEM provides an improved &#34;reduced model&#34; 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.

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			<td>JMP Pro 17.1</td>
			<td>JMP Statistical Discovery LLC</td>
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a workflow for lipid nanoparticle (lnp) formulation optimization using designed mixture-process experiments and self-validated ensemble models (svem)

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.

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. Tab...

Watch this Scientific Journal Video about A Workflow for Lipid Nanoparticle LNP Formulation Optimization using Designed Mixture-Process Experiments and Self-Validated Ensemble Models SVEM at JoVE.com

A Workflow for Lipid Nanoparticle LNP Formulation Optimization using Designed Mixture-Process Experiments and Self-Validated Ensemble Models SVEM

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.

A Workflow for Lipid Nanoparticle (LNP) Formulation Optimization using Designed Mixture-Process Experiments and Self-Validated Ensemble Models (SVEM)

We present a Quality by Design (QbD) styled approach for optimizing lipid nanoparticle (LNP) formulations, aiming to offer scientists an accessible ...

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