Strategies for calibrating models of biology

Abstract

Computational and mathematical modelling has become a valuable tool for investigating biological systems. Modelling enables prediction of how biological components interact to deliver system-level properties and extrapolation of biological system performance to contexts and experimental conditions where this is unknown. A model's value hinges on knowing that it faithfully represents the biology under the contexts of use, or clearly ascertaining otherwise and thus motivating further model refinement. These qualities are evaluated through calibration, typically formulated as identifying model parameter values that align model and biological behaviours as measured through a metric applied to both. Calibration is critical to modelling but is often underappreciated. A failure to appropriately calibrate risks unrepresentative models that generate erroneous insights. Here, we review a suite of strategies to more rigorously challenge a model's representation of a biological system. All are motivated by features of biological systems, and illustrative examples are drawn from the modelling literature. We examine the calibration of a model against distributions of biological behaviours or outcomes, not only average values. We argue for calibration even where model parameter values are experimentally ascertained. We explore how single metrics can be non-distinguishing for complex systems, with multiple-component dynamic and interaction configurations giving rise to the same metric output. Under these conditions, calibration is insufficiently constraining and the model non-identifiable: multiple solutions to the calibration problem exist. We draw an analogy to curve fitting and argue that calibrating a biological model against a single experiment or context is akin to curve fitting against a single data point. Though useful for communicating model results, we explore how metrics that quantify heavily emergent properties may not be suitable for use in calibration. Lastly, we consider the role of sensitivity and uncertainty analysis in calibration and the interpretation of model results. Our goal in this manuscript is to encourage a deeper consideration of calibration, and how to increase its capacity to either deliver faithful models or demonstrate them otherwise.

Statistical Techniques Complement UML When Developing Domain Models of Complex Dynamical Biosystems

“…Following the approach of Andrews et al [5] and the example of Read et al [13], we have chosen to commence the domain modelling process with a cartoon-like diagram, termed an expected behaviours diagram (Fig 3). This diagram depicts the observable phenomena of the IL-1 stimulated NF- κ B signalling pathway, along with the known interactions between system components that generate system-wide behaviours.…”

“…The diagram also provides us with an opportunity to define a number of hypotheses on how these known component interactions may yield the observable phenomena. The expected behaviours diagram therefore provides a diagrammatic view of the relationship between the real-world domain and the domain model [13]. …”

“…We have chosen to follow the approach of Read et al [13] in using UML as the basis to semi-formally define the domain model of our complex dynamical biosystem. Along with a number of UML diagrammatic notations (UML v2.4, [10]), a number of less formal cartoon diagrams were also used to ensure the biological meaning could be conveyed efficiently.…”

“…With specific reference to domain modelling, UML has also been used by Read et al [13], to define the domain model of the intercellular interactions within an autoimmune disease (Experimental Autoimmune Encephalomyelitis, an animal form of multiple sclerosis), and Alden et al [4], to define the domain model of cell interactions within tissue formation in the immune system (specifically the lymphoid organ). In addition to UML, the Systems Biology Graphical Notation (SBGN) [14] has also been used as a diagrammatic notation to model biological systems, such as the Toll-like receptor network [15] and the mTOR signalling network [16].…”

Models of the Gut for Analyzing the Impact of Food and Drugs

“…Where possible, such parameter values can be experimentally ascertained or extracted from literature. Where this is not possible, owing to either the model's abstract nature or its articulation of dynamics not amenable to experimentation, calibration or “fitting” against in vivo and in vitro data is warranted …”