Chemotherapy-induced diarrhea presents a constant challenge for the development of safe and tolerable drugs. It is among the primary reasons for treatment interruption during drug development and clinical trials: the incidence of chemotherapy-induced diarrhea has been estimated to be as high as 80% [21]. For a given chemotherapeutic compound, this toxicity can be mitigated by carefully selecting a dose and a dosing regimen before a first-in-human study, and these should be decided through non-clinical experiments and fit-for-purpose mathematical modeling & simulations. Traditionally, non-clinical toxicity studies involve animal experiments, but gastrointestinal toxicity does not always translate between species: some dosages can be tolerated in animals but are devastating to humans, and vice versa [22].
Purpose
We can surmount the interspecies difference by working with human cells, usually in the form of enteroids/organoids/organ-on-a-chip systems, but this approach is not without its own caveats. In vivo crypts and organoids show marked differences, and though great progress has been made to make these systems replicate in vivo crypts as closely as possible, the results are not immediately translatable [22]. These differences include, but are not limited to, a lack of a supporting mesenchyme layer (with signaling cells of its own, which are involved in extensively studied injury-recovery feedback mechanisms), zonation/compartmentalization differences due to the different geometries, and mechanical/physical differences that are relevant to cellular proliferation and mobility (caused by the different geometries and surrounding environments). Therefore, a dictionary is required to translate the in vitro data into clinical adverse effect prediction observed in real patients, for which a QSP model is a suitable choice.
Computational Modeling Approach
In pursuit of this dictionary, we developed an agent-based model that simulated the interactions of individual cells (the agents) interacting in the geometry of the crypt. The model incorporates all the major cell types and multiple clinically relevant signaling mechanisms. It replicates the geometry, physical and mechanical forces and cell zonation of in vivo crypts and demonstrates many experimentally observed phenotypes. With the assumption that the mechanistic action of a drug is the same in organoids and real crypts, we used this agent-based model to transfer the experimentally observed effects in organoids into predictions of chemotherapy-induced diarrhea in real patients.
The intestinal crypt is particularly amenable to an agent-based modelling approach. The compartmentalization of the cells in the crypt, and the inner workings of signaling mechanisms that cause this, are well studied, with bountiful single-cell data (including signaling knockouts [23], ablations of single types of cells [24], and more [25]) with spatial and temporal resolution. Indeed, building an agent-based model of the gastrointestinal crypt is not a new concept, but our new model contains an unprecedented number of sub-systems (internal protein networks and intercellular signaling mechanisms), allowing it to recreate many clinically relevant phenotypes, recovering from a variety of injuries in experimentally verified fashion.
For the development of the model, we focused on three key tenets (in roughly ascending order of importance): computational speed/efficiency, modularity, and a focus on emergent behavior. Computational speed has long plagued agent-based modelling and is a topic of great interest. The simulation of all the agents can be computationally intensive and hence time consuming [26], but in our current model, a full virtual drug exposure with all analytics obtained from the model can be calculated within minutes on a standard consumer laptop. In a pharmacological setting, this is a vital feature: a quick, efficient model allows many more trial simulations for greater accuracy in results, increasing flexibility in testing hypotheses and vastly improving ease of use.
The ABM is comprised of multiple sub-systems, such as those describing intercellular signaling, the cell’s DNA integrity, the cell cycle proteins, etc., which are mathematical models in their own right. Each individual piece of the model was chosen according to current knowledge, but this can, and will, change over time: because of this, the sub-systems of the model are modular such that each sub-system is easily replaceable without a full-scale reparameterization of the model. This also allows us to expand the model to introduce new pathways and modalities that may be required for better understanding of a drug’s action.
We focused on five signaling mechanisms that have been experimentally demonstrated to be vital for the correct functioning of the intestinal epithelium (to-be-published workby Louis Gall et al, “An agent-based model of the mouse small intestinal epithelium enables the prediction of the spatiotemporal dynamics of drug-induced events at multiple scales”). Briefly, these include the following signaling mechanisms: Wnt, Notch, BMP, ZNRF3/RNF43 and Hippo-YAP mediated contact inhibition. Based on these signals, the cells follow rules which determine whether the cell should proliferate or differentiate, and if so what type of cell to become. In total, we considered seven types of cells (stem cells, absorptive progenitors, secretory progenitors, Paneth cells, enterocytes, enteroendocrine and goblet cells) that form over 99% of the intestinal epithelium [27].
Cellular proliferation in the model is governed by internal cell cycles in each cell, represented by a previously published mathematical model [28] with an additional set of equations describing the cell’s DNA and RNA content. The cell cycle proteins, along with the DNA and RNA levels, are used to govern cellular proliferation: rising and falling cyclin levels thereby determining a cell’s progression through the division cycle, and the integrity of DNA is checked at cell cycle checkpoints. The model can be viewed as a collection of individually simple rules that combine to produce the complex emergent behaviors and phenotypes exhibited by the crypt-villus complex. The net result of the myriad internal and inter-cellular protein networks is a model that is driven constantly towards the homeostatic state, capable of responding to and recovering from injury and insult in a realistic manner. Here, it should be stressed that we can still verify the model outputs with comparison to experimental data, making the model quantitative.
All these sub-systems can be individually perturbed to simulate the effects of drugs. The workflow of the model is shown in Fig 3. We first coupled a PK model for the concentration of a drug to the sub-cellular systems of the ABM, fitting the effects of the drug on single cells according to the data obtained from organoid experiments. We then simulate this drug-cell interaction in every cell of the ABM, allowing us to replicate the propagation of this perturbation from the single-cell level to the entire epithelial tissue. This is the main translational step, wherein we used the model to translate non-clinical experiments on organoids to robust clinical predictions of gastrointestinal toxicity in real patients.
We built an agent-based model with multiple clinically relevant signaling pathways and internal protein interaction networks. The core ABM can be viewed as a platform, which is designed to be readily expandable, eliminating the need for the redevelopment and parameterization of entirely new, bespoke models for each drug. Rather than a collection of equations calibrated to explain known data, we have constructed an in-silico crypt structure which can be used for hypothesis generation and testing of the safety of a drug. Our agent-based modelling was possible for the gastrointestinal crypt because of the abundance of suitable data in the intestinal epithelium, which can be difficult to obtain (in terms of time and money, and experimental techniques needed to isolate and analyze the relevant biological systems). The necessary information includes temporal and spatial data (with a resolution of the scale of individual cells), knowledge of the types, location and lineages of a single cell and a clear understanding of the multiple signaling networks that influence cell differentiation and zonation.
In summary, this modeling approach facilitates the translation from experiments on human cells to real-world predictions of gastrointestinal toxicity such as therapy-induced diarrhea. This model may be further used for understanding of pathology to develop a new drug related to intestinal cell structure (e.g., inflammatory bowel disease). We expect that this approach will save time and money by reducing/removing the need for animal experiments, and thereby expediting the development of safer and/or more efficacious drugs for patients.