• in silico modelling
• cell-laden microspheres
• oxygen metabolism
• size-related scaling
• biomimetic models
• biological heterogeneities

Metabolic scaling is an inherent feature of living systems holding across species. As organismal metabolism governs resource management in biological communities and underpins any physiological process, the power-law formulation (i.e., the Kleiber's law - KL) of this phenomenon sets a universal constraint for life. Hence, KL has started to be considered relevant also in the biomedical field, being reasonably assumed as a necessary condition to design biomimetic models. However, current scaling frameworks are yet to provide an exhaustive description of metabolic patterns, since a number of biophysical traits and mechanisms potentially affecting size-related scaling are still underrated or even neglected. Several aspects of paramount importance thus need to be addressed before properly exploiting metabolic scaling as a testbench for predictivity and translatability of cellular models.
In this light, the overall aim of my Ph.D. has been to tackle some of these challenges for broadening the view on metabolic scaling and refining its actual formulation, moving towards the development of a novel paradigm for biomimetic design based on the coherence with such ubiquitous characteristic of life as a fundamental criterion. A suite of quantitative engineering methods underlying the systematic integration of computational and experimental tools have been used for all studies performed to this purpose and reported in the thesis. Specifically, my effort has mainly focused on three scaling-related aspects: the kinetics of cellular oxygen (O2) consumption as a function of the aggregation state and experimental conditions of the system (Chapters 2 and 3), the estimation of whole-construct metabolic rates and eventually associated allometries in real in vitro contexts (Chapters 4 and 5) and the impact of biological heterogeneities on such scaling behaviours (Chapter 6). Each point has been investigated in in silico or in vitro aggregates of hepatic (i.e., HepG2) cells throughout different levels of complexity, spanning from single cells up to ensembles of 3D constructs, under the hypothesis that O2 metabolism represents a reliable proxy of the overall metabolism of a living system.
Since the way cells consume O2 and modulate its uptake crucially influences metabolic scaling, the first analysis has regarded the characterization of O2 consumption kinetics. In particular, empirical parameters defining the Micahealis-Menten (MM) kinetic model (i.e., sOCR and kM) have been identified in single cells as well as monolayer cultures and cell-laden microspheres at different cell densities by means of cutting-edge sensing technologies combined with a purposely developed multiparameter identification algorithm. The generality of the implemented procedure for identifying kinetic parameters has allowed the extraction of sOCR and kM from O2 concentration profiles irrespective of the specific aggregation level tested. Remarkably, HepG2 cells have displayed lower values of sOCR and higher of kM when in isolation rather than in 2D and 3D aggregates, suggesting that aggregation enhances O2 consumption probably due to endogenous interactions and the more in vivo-like microenvironment that cells are exposed to. This characterization step has highlighted that such MM parameters also depend on cell density, leading to a decrease in the average O2 uptake of cells when more densely packed in both monolayers and microspheres. This may indicate a cooperative behaviour in terms of O2 metabolism in conditions of resource sharing, which is not explicitly expressed in the current formulation of the MM model. No systematic differences have been instead noticed between the two spatial arrangements of cell aggregates. The cooperative dynamics revealed in this thesis might be integrated in the MM formulation of the consumption kinetics as an explicit dependency of sOCR and kM on a purposely defined index, describing the aggregate dimensionality rather than just the cell density.
An experimental procedure for measuring metabolic rates of cell aggregates has been then developed and applied to cell-laden microspheres, isolated or coexisting in a common environment. In the former case, microspheres crafted at a standard in vitro cell density have been tested to evaluate their metabolic scaling behaviour. To date, this has represented the first attempt of empirically assessing the physiological relevance of cellular models leveraging on KL. Whole-construct metabolic rates estimated from O2 concentration profiles are in line with computational predictions; specifically, they have displayed isometric scaling, thus suggesting that currently fabricated hepatic microspheres may lack predictive and translational power. In vitro constructs based on the encapsulation of cells in hydrogel matrices shaped through extrusion-based techniques are indeed characterized by cell densities far from values observed in vivo (~ two orders of magnitude lower), because of limitations imposed by physical constraints related to the fabrication process. In addition, the investigated size range cannot be extended to higher masses due to the diffusion-limited O2 supply and potential onset of significant necrotic cores. Given that, further increasing the complexity of 3D cell aggregates to achieve the quarter-power scaling of their O2 consumption needs the introduction of multiple cell phenotypes – be they artificially embedded in multi-cellular microspheres or self-organized in organoids – properly chosen to promote the onset of specific crosstalk and signalling pathways characteristic of the biological tissue of interest, which could drive the modulation of O2 metabolism and thus the emergence of non-isometric scaling.
On the other hand, the estimation of individual metabolic rates in multi-construct systems has been oriented to develop an in silico-in vitro framework for investigating whether and how coexistence affects O2 consumption and subsequent scaling behaviours. Suitable configurations have been implemented in silico and then adapted to be reproduced in vitro. Computationally, spheroidal constructs have been shown to reduce their metabolic rate when closely coexisting in high number. In accordance, such conditions also lead to the narrowing of the size range corresponding to non-isometric scaling as well as to lower values of the associated exponent. Such results have been corroborated by experimental tests. These preliminary results suggest the use of in silico and in vitro models of simple cellular systems as promising tools to study metabolic dynamics typical of biological communities at larger scales, such as natural ecosystems, with fundamental implications which might go beyond the biomedical field. Further investigations are needed to achieve this goal, extending the analysis to multi-construct systems involving individuals characterized, for instance, by different phenotypical traits, sizes and random spatial distribution within the shared environment, as well as exposed to fluctuating exercise conditions.
The majority of scaling studies still consider living systems as exhaustively defined by average physiological parameters, as KL does. However, heterogeneities constitute an essential and unavoidable feature in biology, also underlying whole-system consequences of resource utilization as well as community adaptations to external stimuli or disturbances. In this light, the last part of this thesis has focused on the introduction of stochasticity in the current scaling framework. In particular, an in silico pipeline for the assessment of metabolic scaling in the presence of variability has been developed and, as a proof of concept, applied to scale joint distributions of mass and metabolic rate of computer-generated populations of spheroidal cell aggregates. The methodology is gathered around an optimization algorithm for the normalization and collapse of simulated datasets, allowing the identification of scaling exponents according to the generalized formulation of KL. Using the pipeline, a size window of physiological relevance has been determined for such digital spheroids laden with two different cell phenotypes, defined as the intersection of mass ranges in which a negligible non-viable volume forms and a non-isometric scaling of metabolic rates holds. The results show a physiologically relevant window narrower than those previously estimated by means of a deterministic approach and associated to non-isometric exponents significantly deviating from 3/4. Moreover, the amplitude of introduced heterogeneities has been demonstrated to modulate scaling parameters. This represents quantitative evidence that fluctuations must be incorporated for consistently studying metabolic scaling in biological systems and claims for the role of diversity – and its extent – in shaping the demand and intake of resources in living communities. Beyond the proof-of-concept application, the designed pipeline is aimed at a broad use for scaling experimental joint distributions of size and metabolism from samples of different origin, such as cellular models in vitro or organismal populations in natural ecosystems. However, as estimated in this thesis exploiting the potential of in silico methods, at least 104 joint measurements are necessary to get statistically significant collapses, calling for the establishment of novel, high-throughput methodologies to experimentally probe size-related metabolism. Alternatively, model fitting and data augmentation strategies (e.g., Markov Chain-based Monte Carlo methods) could be included as a support to create useful joint datasets. More specifically, such Bayesian approaches might be evaluated to merge actual data and a priori knowledge, in order to construct posterior probability density functions representative of the joint distributions of interest. Furthermore, the stochastic scaling framework proposed here might be used for quantitatively evaluating the impact of specific stressors or perturbations on metabolic patterns in communities.
To conclude, this Ph.D. thesis has moved a crucial step to establish metabolic scaling as a necessary constraint for biomimetic design, providing a quantitative paradigm to fully tap the potential of in silico and in vitro cell-based modelling. Ground-breaking implications may regard the development of human-relevant models for applications in tissue engineering and precision medicine, as well as the improvement of alternative approaches to animal testing. Given the centrality of metabolism to life, results and further developments of this work might have broader significance, concerning metabolic processes of ecological interest with possible impact on species conservation, developmental biology or climate dynamics.