From reductionism to realism: Holistic mathematical modelling for complex biological systems

Abstract

At its core, the physics paradigm adopts a reductionist approach, aiming to understand fundamental phenomena by decomposing them into simpler, elementary processes. While this strategy has been tremendously successful in physics, it has often fallen short in addressing fundamental questions in the biological sciences. This arises from the inherent complexity of biological systems, characterised by heterogeneity, polyfunctionality and interactions across spatiotemporal scales. Nevertheless, the traditional framework of complex systems modelling falls short, as its emphasis on broad theoretical principles has often failed to produce predictive, empirically-grounded insights. To advance towards actionable mathematical models in biology, we argue, using neuroscience as a case study, that it is necessary to move beyond reductionist approaches and instead embrace the complexity of biological systems - leveraging the growing availability of high-resolution data and advances in high-performance computing. We advocate for a holistic mathematical modelling paradigm that harnesses rich representational structures such as annotated and multilayer networks, employs agent-based models and simulation-based approaches, and focuses on the inverse problem of inferring system dynamics from observations. We emphasise that this approach is fully compatible with the search for fundamental biophysical principles, and highlight the potential it holds to drive progress in mathematical biology over the next two decades.

14 pages, 5 figures

References in corpus (38)

• Emergence of scaling in random networks
• Community structure in social and biological networks
• Novel type of phase transition in a system of self-driven particles
• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Multilayer Networks
• A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
• Deep learning for universal linear embeddings of nonlinear dynamics
• The physics of higher-order interactions in complex systems
• Are biological systems poised at criticality?
• Next Generation Reservoir Computing
• Colloquium: Criticality and dynamical scaling in living systems
• VAMPnets: Deep learning of molecular kinetics
• The ground truth about metadata and community detection in networks
• Structure and inference in annotated networks
• Griffiths phases and the stretching of criticality in brain networks
• Mathematical frameworks for oscillatory network dynamics in neuroscience
• Quantifying dissipation using fluctuating currents
• The Algorithmic Origins of Life
• Dynamical Variational Autoencoders: A Comprehensive Review
• Stochastic thermodynamics of computation
• A Bayesian machine scientist to aid in the solution of challenging scientific problems
• Inferring collective dynamical states from widely unobserved systems
• The low-rank hypothesis of complex systems
• Inferring the dynamics of underdamped stochastic systems
• Autonomous inference of complex network dynamics from incomplete and noisy data
• Nonlinear stochastic modeling with Langevin regression
• Identifying nonlinear dynamical systems via generative recurrent neural networks with applications to fMRI
• Variance Sum Rule for Entropy Production
• High-Performance Reconstruction of Microscopic Force Fields from Brownian Trajectories
• Collective behavior from surprise minimization
• Neuronal Oscillations on Evolving Networks: Dynamics, Damage, Degradation, Decline, Dementia, and Death
• Neural parameter calibration for large-scale multi-agent models
• Learning the Non-Equilibrium Dynamics of Brownian Movies
• Tackling the subsampling problem to infer collective properties from limited data
• Interpretable statistical representations of neural population dynamics and geometry
• Inverse Occam's razor
• Evolving Scientific Discovery by Unifying Data and Background Knowledge with AI Hilbert