In silico methods integrate physical and biochemical models with computational tools, and are a powerful support for tissue engineering. They are particularly relevant for studying organoids and assembloids: the multiplicity of parameters which condition organoid growth and morphology can be explored in virtual models, facilitating experimental design, and enabling prediction and extrapolation of behaviour and function. Here we use statistical physics and evolutionary algorithms to predict how cells in cerebral constructs cooperate to share resources (oxygen) and generate functional forms.
Kleiber’s Law (KL) is a universal law of biology, stating that the metabolic rate of an organism scales with its body size according to a quarter-power law 1. Its pertinence for designing human-relevant in vitro models 2–4 has been highlighted. However, KL is formulated as a deterministic framework, although fluctuations and heterogeneity are inevitable, and known to shape the response of biological systems to external perturbations (nanoparticles, viruses). We generated joint distributions of construct masses and metabolic rates, developing new statistical tools to test whether and in which organoid size range a generalized stochastic formulation for KL 5 applies. KL is combined with physical, metabolic and mechanical constraints to generate in silico models of organoids with different shapes and sizes to identify optimal design criteria for functional models.
We found that stochasticity significantly restricted the range of construct sizes complying with KL, implying that to date many cellular models may lack translatability 6. Evolutionary algorithms based on the optimization of a cost function which incorporates resource uptake, surface energy and cooperative metabolic effort have enabled the generation of model datasets. These studies are used to assess to what extent morphometry or metabolic phenomena affect organoid formation and growth and to identify experimental design specifications to obtain constructs with translational value.
In silico models enable the definition of criteria for designing brain organoids and assembloids with translational value and hence useful for robust in vitro to in vivo extrapolation, paving the way towards predictive and precision medicine and reducing animal tests. Ongoing experimental validation suggests that three dimensional constructs manifest cooperative behaviour and that rather than being discarded, variability and fluctuations in organoids confer robustness.
1. Savage, V. M. et al. The predominance of quarter-power scaling in biology. Funct. Ecol. 18, 257–282 (2004).
2. Ucciferri, N., Sbrana, T. & Ahluwalia, A. Allometric Scaling and Cell Ratios in Multi-Organ in vitro Models of Human Metabolism. Front. Bioeng. Biotechnol. 2, 74 (2014).
3. Ahluwalia, A. Allometric scaling in-vitro. Sci. Rep. 7, 42113 (2017).
4. Magliaro, C., Rinaldo, A. & Ahluwalia, A. Allometric Scaling of physiologically-relevant organoids. Sci. Rep. 9, (2019).
5. Zaoli, S. et al. Generalized size scaling of metabolic rates based on single-cell measurements with freshwater phytoplankton. Proc. Natl. Acad. Sci. U. S. A. 116, 17323–17329 (2019).
6. Botte, E. et al. Scaling of joint mass and metabolism fluctuations in in silico cell-laden spheroids. Proc. Natl. Acad. Sci. 118, e2025211118 (2021)."