Antifragility is a recently coined word used to describe the opposite of fragility. Systems or organisms can be described as antifragile if they derive a benefit from systemic variability, volatility, randomness, or disorder. Herein, we introduce a mathematical framework to quantify the fragility or antifragility of cancer cell lines in response to treatment variability. This framework enables straightforward prediction of the optimal dose treatment schedule for a range of treatment schedules with identical cumulative doses. We apply this framework to non-small-cell lung cancer cell lines with evolved resistance to ten anti-cancer drugs. We show the utility of this antifragile framework when applied to 1) treatment resistance, and 2) collateral sensitivity of sequential monotherapies. 

References

Strobl, Maximilian AR, Alexandra L. Martin, Jeffrey West, Jill Gallaher, Mark Robertson-Tessi, Robert Gatenby, Robert Wenham, Philip K. Maini, Mehdi Damaghi, and Alexander RA Anderson. "To modulate or to skip: De-escalating PARP inhibitor maintenance therapy in ovarian cancer using adaptive therapy." Cell Systems 15, no. 6 (2024): 510-525. https://www.cell.com/cell-systems/fulltext/S2405-4712(24)00118-2 

Pierik, L., McDonald, P., Anderson, A.R.A., West, Jeffrey. Second-Order Effects of Chemotherapy Pharmacodynamics and Pharmacokinetics on Tumor Regression and Cachexia. Bull Math Biol 86, 47 (2024). https://doi.org/10.1007/s11538-024-01278-0  

West, Jeffrey, et al. "Antifragile therapy." bioRxiv (2020): 2020-10. https://doi.org/10.1101/2020.10.08.331678  

Antifragility in targeted therapy https://www.biorxiv.org/content/10.1101/2020.10.08.331678v2.abstract 

Antifragility in dose-response 

https://www.mdpi.com/1099-4300/25/2/343 

Antifragility in cell-cell interactions https://www.biorxiv.org/content/10.1101/2023.02.27.530257v1.abstract 

Antifragility in pharmacokinetics https://www.biorxiv.org/content/10.1101/2023.06.14.544974v1 

We extend techniques and learnings about the stochastic properties of nonlinear responses from finance to medicine, particularly oncology, where it can inform dosing and intervention. We define antifragility. We propose uses of risk analysis for medical problems, through the properties of nonlinear responses (convex or concave). We (1) link the convexity/concavity of the dose-response function to the statistical properties of the results; (2) define “antifragility” as a mathematical property for local beneficial convex responses and the generalization of “fragility” as its opposite, locally concave in the tails of the statistical distribution; (3) propose mathematically tractable relations between dosage, severity of conditions, and iatrogenics. In short, we propose a framework to integrate the necessary consequences of nonlinearities in evidence-based oncology and more general clinical risk management. 

References

Taleb, Nassim Nicholas, and Jeffrey West. "Working with convex responses: Antifragility from finance to oncology." Entropy 25.2 (2023): 343. https://doi.org/10.3390/e25020343 

We review the concept of ecosystem resilience in its relation to ecosystem integrity from an information theory approach. We summarize the literature on the subject identifying three main narratives: ecosystem properties that enable them to be more resilient; ecosystem response to perturbations; and complexity. We also include original ideas with theoretical and quantitative developments with application examples. The main contribution is a new way to rethink resilience, that is mathematically formal and easy to evaluate heuristically in real-world applications: ecosystem antifragility. An ecosystem is antifragile if it benefits from environmental variability. Antifragility therefore goes beyond robustness or resilience because while resilient/robust systems are merely perturbation-resistant, antifragile structures not only withstand stress but also benefit from it. 

References

Equihua M, Espinosa Aldama M, Gershenson C, López-Corona O, Munguía M, Pérez-Maqueo O, Ramírez-Carrillo E. 2020. Ecosystem antifragility: beyond integrity and resilience. PeerJ 8:e8533 https://doi.org/10.7717/peerj.8533

Combining well-established non-equilibrium thermodynamic principles and a system dynamics approach, we define, for the first time, the concept of planetary antifragility as changes in Fisher information of Earth’s entropy production. Loss of antifragility implies a compounding problem because human perturbations such as climate or land-use changes are increasing, but at the same time, the planet is losing its capacity to respond to them.

References

López-Corona, Oliver, et al. "ESD Ideas: planetary antifragility: a new dimension in the definition of the safe operating space for humanity." Earth System Dynamics 13.3 (2022): 1145-1155. https://doi.org/10.5194/esd-13-1145-2022 

Human health is strongly mediated by the gut microbiota ecosystem, which, in turn, depends not only on its state but also on its dynamics and how it responds to perturbations. Healthy microbiota ecosystems tend to have criticality and antifragile dynamics corresponding to a maximum complexity configuration, which may be assessed with information and network theory analysis.

References

Isaac, G-Santoyo., et al. "Potential long consequences from internal and external ecology: loss of gut microbiota antifragility in children from an industrialized population compared with an indigenous rural lifestyle." Journal of Developmental Origins of Health and Disease (2023): 1-12. https://doi.org/10.1017/S2040174423000144 

One of the most characteristic properties of many vertebrate neural systems is the layered organization of different cell types. This cytoarchitecture exists in the cortex, the retina, the hippocampus, and many other parts of the central nervous system. The developmental mechanisms of neural layer formation have been subject to substantial experimental efforts. Here, we provide a general computational model for cortical layer formation in 3D physical space. We show that this multiscale, agent-based model, comprising two distinct stages of apoptosis, can account for the wide range of neuronal numbers encountered in different cortical areas and species. Our results demonstrate the phenotypic richness of a basic state diagram structure. Importantly, apoptosis allows for changing the thickness of one layer without automatically affecting other layers. Therefore, apoptosis increases the flexibility for evolutionary change in layer architecture. Notably, slightly changed gene regulatory dynamics recapitulate the characteristic properties observed in neurodevelopmental diseases.

References

Bauer, R., Clowry, G.J. and Kaiser, M., 2021. Creative destruction: a basic computational model of cortical layer formation. Cerebral Cortex, 31(7), pp.3237-3253. https://academic.oup.com/cercor/article/31/7/3237/6148913 

Modeling and handling uncertainty in closed-loop robot control tasks is still an openly debated and fruitful area of research. In an arena where control theory provides its most powerful tools and robotics provides its more pragmatic deployments, emerging approaches need to overcome well-established ”recipes”. Antifragile control is a new approach to control, which approaches control synthesis from the perspective of capturing the peculiarities of the response of the system to control. First and second-order effects provide useful hints on where and how to issue control signals that can drive the systems in regions of the solutions space where the system is not only robust to uncertainty and volatility but can also gain from it and anticipate future uncertain events.

References

C. Axenie and M. Saveriano, "Antifragile Control Systems: The Case of Mobile Robot Trajectory Tracking Under Uncertainty and Volatility," in IEEE Access, vol. 11, pp. 138188-138200, 2023, doi: 10.1109/ACCESS.2023.3339988. https://ieeexplore.ieee.org/document/10345540 

Aside the traditional pulsed therapy schemes, multiple control-theoretic approaches, such as robust and optimal control, were developed with the aim to capture the complex tumor–immune–drug dynamics and compute an optimal and robust drug dosing that minimizes the tumor and preserves as much as possible normal cells. However, there is always a trade-off between tumor reduction and normal cells kill. Antifragile control emerges as a control-theoretic framework capable of gaining from: 1) the uncertainty describing tumor–immune–drug interactions, 2) the volatility of drug response curves in patient populations, and 3) the variability in tumor response, immune capabilities, and drug resistance patterns of a patient-tumor pair. This is achieved through the formal implementation in a control-theoretic framework of the three main pillars: 1) redundant overcompensation, 2) structure-variability, and 3) high-frequency control activity.

References

Axenie, Cristian, Daria Kurz, and Matteo Saveriano. "Antifragile Control Systems: The Case of an Anti-Symmetric Network Model of the Tumor-Immune-Drug Interactions." Symmetry 14.10 (2022): 2034. https://doi.org/10.3390/sym14102034 

 In this work, we consider a novel system for road traffic control based on a network of interacting oscillators. Such a model has the advantage to capture temporal and spatial interactions of traffic light phasing as well as the network-level evolution of the traffic macroscopic features (i.e. flow, density). In this study, we propose a new realization of the antifragile control framework to control a network of interacting oscillator-based traffic light models to achieve region-level flow optimization. We demonstrate that antifragile control can capture the volatility of the urban road environment and the uncertainty about the distribution of the disruptions that can occur. We complement our control-theoretic design and analysis with experiments on a real-world setup comparatively discussing the benefits of an antifragile design for traffic control.

References

Axenie, Cristian. "Antifragile Control Systems: The case of an oscillator-based network model of urban road traffic dynamics." arXiv preprint arXiv:2210.10460 (2022). https://doi.org/10.48550/arXiv.2210.10460 

The ”steep derivatives” of traffic flows do not allow the optimal and robust control to converge to the best phase duration value. In order to achieve high-performance (i.e. minimizing metrics such as time loss or maximizing average speed), we synthesized an antifragile controller based on Reinforcement Learning (RL). Based on the first and second derivatives, we add new terms in the state and reward term in RL, thus the RL algorithm is able to anticipate disturbances and exhibit antifragility.

References

Sun, Linghang; Genser, Alexander; Axenie, Cristian, Grossi, Margherita, Kouvelas, Anastasios; Makridis, Michail (2024), The fragile nature of road transportation systems, https://doi.org/10.48550/ARXIV.2402.00924 

Sun, Linghang; Makridis, Michail; Genser, Alexander; Axenie, Cristian, Grossi, Margherita, Kouvelas, Anastasios(2024), Exploring antifragility in traffic networks: Anticipating and gaining from disruptions with reinforcement learning, 2024 TRB Annual Meeting Online Program Archive, https://doi.org/10.48550/ARXIV.2402.12665 

Sun Linghang, Makridis Michail, Genser Alexander, Axenie Cristian, Grossi Margherita, and Kouvelas Anastasios, "Exploring antifragility in traffic networks: Anticipating disturbances with reinforcement learning", 23rd Swiss Transport Research Conference (STRC 2023), http://hdl.handle.net/20.500.11850/616083 

Axenie, Cristian. "Antifragile Control Systems: The case of an oscillator-based network model of urban road traffic dynamics." arXiv preprint arXiv:2210.10460 (2022). https://doi.org/10.48550/arXiv.2210.10460