Organoids are engineered three-dimensional tissue cultures derived from stem cells and capable of self-renewal and self-organization into a variety of progenitors and differentiated cell types. An organoid resembles the cellular structure of an organ and retains some of its functionality, while still being amenable to in vitro experimental study. Compared with two-dimensional cultures, the three-dimensional structure of organoids provides a more realistic environment and structural organization of in vivo organs. Similarly, organoids are better suited to reproduce signaling pathway dynamics in vitro, due to a more realistic physiological environment. As such, organoids are a valuable tool to explore the dynamics of organogenesis and offer routes to personalized preclinical trials of cancer progression, invasion, and drug response. Complementary to experiments, mathematical and computational models are valuable instruments in the description of spatiotemporal dynamics of organoids. Simulations of mathematical models allow the study of multiscale dynamics of organoids, at both the intracellular and intercellular levels. Mathematical models also enable us to understand the underlying mechanisms responsible for phenotypic variation and the response to external stimulation in a cost- and time-effective manner. Many recent studies have developed laboratory protocols to grow organoids resembling different organs such as the intestine, brain, liver, pancreas, and mammary glands. However, the development of mathematical models specific to organoids remains comparatively underdeveloped. Here, we review the mathematical and computational approaches proposed so far to describe and predict organoid dynamics, reporting the simulation frameworks used and the models’ strengths and limitations.

Cellular systems have evolved numerous mechanisms to adapt to environmental stimuli, underpinned by dynamic patterns of gene expression. In addition to gene transcription regulation, modulation of protein levels, dynamics and localization are essential checkpoints governing cell functions. The introduction of inducible promoters has allowed gene expression control using orthogonal molecules, facilitating its rapid and reversible manipulation to study gene function. However, differing protein stabilities hinder the generation of protein temporal profiles seen in vivo. Here, we improve the Tet-On system integrating conditional destabilising elements at the post-translational level and permitting simultaneous control of gene expression and protein stability. We show, in mammalian cells, that adding protein stability control allows faster response times, fully tunable and enhanced dynamic range, and improved in silico feedback control of gene expression. Finally, we highlight the effectiveness of our dual-input system to modulate levels of signalling pathway components in mouse Embryonic Stem Cells.

Cellular systems have evolved numerous mechanisms to finely control signalling pathway activation and properly respond to changing environmental stimuli. This is underpinned by dynamic spatiotemporal patterns of gene expression. Indeed, in addition to gene transcription and translation regulation, modulation of protein levels, dynamics and localization are also essential checkpoints that govern cell functions.The introduction of tetracycline-inducible promoters has allowed gene expression control using orthogonal small molecules, facilitating rapid and reversible manipulation to study gene function in biological systems. However, differing protein stabilities means this solely transcriptional regulation is insufficient to allow precise ON-OFF dynamics, thus hindering generation of temporal profiles of protein levels seen in vivo.We developed an improved Tet-On based system augmented with conditional destabilising elements at the post-translational level that permits simultaneous control of gene expression and protein stability. Integrating these properties to control expression of a fluorescent protein in mouse Embryonic Stem Cells (mESCs), we found that adding protein stability control allows faster response times to changes in small molecules, fully tunable and enhanced dynamic range, and vastly improved microfluidic-based in-silico feedback control of gene expression. Finally, we highlight the effectiveness of our dual-input system to finely modulate levels of signalling pathway components in stem cells.fusion protein of the herpes simplex virus VP16 activation domain and of the Escherichia coli Tet repressor protein (TetR) 9 . The presence of tetracycline or its derivative doxycycline prevents the interaction of the tTA to the tetO, blocking gene expression (Tet-Off system). The reverse-tTA (rtTA) is a tTA variant allowing gene expression activation in presence of an inducer; the resulting Tet-On system is generally preferred when rapid and dynamic gene induction is required 4,13 . A major limitation of inducible promoters is the significant time delay in switching proteins OFF and ON when using Tet-On and Tet-off systems, respectively 14 , diminishing the possibility of using these approaches to generate dynamic patterns of gene expression that faithfully recapitulate those observed natively 1 . Slow kinetic responses are also common to other techniques targeting precursor DNA or mRNA molecules (e.g. RNA interference 15 ), likely due to significantly different rates of innate protein degradation 15 .Recently, an alternative approach, relying on conditional protein destabilization to modulate turnover by the cellular degradation machinery, has been harnessed to probe complex biological functions. Engineered mutants of FKBP12 that are rapidly and constitutively degraded in mammalian cells can directly confer protein destabilization to the protein they are fused with. Addition of synthetic ligands, that bind the Destabilising Domain (DD) of FKBP12, prevent degradation and so can be used to alter levels of the f...

Organoids offer a powerful model to study cellular self-organisation, the growth of specific tissue morphologies in-vitro, and to assess potential medical therapies. However, the intrinsic mechanisms of these systems are not entirely understood yet, which can result in variability of organoids due to differences in culture conditions and basement membrane extracts used. Improving the standardisation of organoid cultures is essential for their implementation in clinical protocols. Developing tools to assess and predict the behaviour of these systems may produce a more robust and standardised biological model to perform accurate clinical studies. Here we developed an algorithm to automate crypt-like structure counting on intestinal organoids in both in-vitro and in-silico images. In addition, we modified an existing two-dimensional agent-based mathematical model of intestinal organoids to better describe the system physiology, and evaluated its ability to replicate budding structures compared to new experimental data we generated. The crypt-counting algorithm proved useful in approximating the average budding structures found in our in-vitro intestinal organoid culture images on days 3 and 7 after seeding. Our changes to the in-silico model maintain the potential to produce simulations that replicate the number of budding structures found on days 5 and 7 of in-vitro data. The present study aims to aid in quantifying key morphological structures and provide a method to compare both in-vitro and in-silico experiments. Our results could be extended later to 3D in-silico models.

ObjectivesTo illustrate the epidemiologic and cost-effectiveness impact of shifting the focus from population-based screening toward a targeted management approach for genital chlamydia infection.DesignModeling study, implementing an individual-based, stochastic, dynamic network model.SettingHong Kong.PopulationA hypothetical sample network of 10,000 people with a partnership distribution based on Hong Kong's sexually active population of reproductive age (age 18–49 years).InterventionsIn this study, we present several scenarios with different implementations of universal vs. targeted screening (based on partner numbers). We also explored the impact of (1) screening only, (2) screening plus expedited partner therapy, and (3) screening plus partner testing.Primary outcome measuresChange of chlamydia prevalence before and after implementing the different strategies. The cost-effectiveness analysis reports total direct cost from a health provider perspective, the QALYs gained, and incremental cost-effectiveness ratios (ICER).ResultsIn comparing the effects of universal screening only and targeted screening of the high-risk population, the mean prevalence during the 10th year of intervention was 2.75 ± 0.30% and 2.35 ± 0.21%, respectively (compared with 3.24 ± 0.30% and 3.35 ± 0.21% before the interventions, respectively). The addition of contact tracing to the latter targeted screening scenario reduces the mean prevalence during the 10th year of intervention to 1.48 ± 0.13% (compared with 3.31 ± 0.33% at baseline) in the best-case of testing before treatment and maximal contact-tracing effectiveness (40%). Overall, the most effective scenarios were those for which interventions focused on the high-risk population defined by the number of partners, with contact tracing included. The ICER for targeted screening with contact tracing at 20% and 40% efficiency was $4,634 and $7,219 per QALY gained, respectively (10-year time horizon). Expedited partner therapy did not significantly impact overall chlamydia prevalence and caused overtreatment.ConclusionsOur study suggests that targeted screening with strengthened contact tracing efforts is the most cost-effective strategy to reduce the prevalence of chlamydia in Hong Kong.