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Systems biology (un)certainties
P. D. W. Kirk^1 ∗†, A. C. Babtie^2 ∗†, M. P. H. Stumpf^2 ∗†
(^1) MRC Biostatistics Unit, Cambridge Institute of Public Health, CB2 0SR, UK (^2) Centre for Integrative Systems Biology and Bioinformatics, Imperial College London, SW7 2AZ, UK ∗To whom correspondence should be addressed; E-mail: a.babtie@imperial.ac.uk, paul.kirk@mrc-bsu.cam.ac.uk, m.stumpf@imperial.ac.uk.
Modelers must restore confidence in Systems and Computational Biology by avoiding over-interpretation of mathematical models and providing adequate assessments of uncertainty.
Systems Biology, some have claimed ( 1 ), is attempting the impossible and is doomed to fail. Possible definitions abound, but Systems Biology is widely understood (including here) to be an approach for studying the behavior of systems of interacting biological components, that relies on combining experiments with computational and mathematical reasoning. Mod- eling complex systems occurs throughout the sciences, so it is perhaps not immediately clear why it should attract greater controversy in molecular and cell biology than elsewhere. We contend that the way in which models are often presented and (over) interpreted in the litera- ture is at least partly to blame. As with experimental results, the key to successfully reporting a mathematical model is an honest appraisal and representation of uncertainty: in the models predictions, parameters, and (where appropriate) in the structure of the model itself. Deriving
biological models is rarely straightforward. Although biology is, of course, subject to the same fundamental physical laws e.g. conservation of mass, energy and momentum as the other sciences, these often do not provide a good starting point for understanding how biological or- ganisms and systems work. Biological modeling instead emphasizes context-specific levels of abstraction and relies upon experimental observations to decide if a particular model is useful. Typically, not all terms in a biological model are known or observable directly, and except for some highly specific systems it is impossible to measure the abundances of all the key players (molecules, cells or individuals) simultaneously and continuously. Thus, despite being often overlooked, the challenge is not only to identify descriptions and mathematical representations that provide insight, but also to communicate the inevitable uncertainty in the models (possibly many) unknowns. Although some authors have strongly advocated substituting these unknowns for estimates obtained from exogenous experimental assays ( 2 ), this is (a) often impossible, (b) rarely enough (since these estimates are themselves subject to considerable uncertainty), and (c) missing an opportunity to extract this information from the endogenous experimental data. In this context, Bayesian inference procedures ( 3 ), which naturally permit the integration of external prior knowledge or beliefs with newly observed data, may provide the most natural framework for expressing and reporting uncertainty. The number of unknowns in a model is partly determined by the scale of the system being studied. A biological system may range in scale from a few interacting molecules to whole populations of organisms, and this can have a huge impact on both the modeling approach and the associated assessment of uncertainty. For small systems, it might be possible to rely solely on strong prior knowledge and specify a model structure that reflects known interactions. For larger systems, automated network inference al- gorithms have been employed (4, 5). Such data-driven, hypothesis-generating approaches are often opposed, on the basis that the complexity of the biological system will render impossi- ble the inverse problem of learning the true and complete underlying network ( 1 ). However,
that will break as many models as possible (12, 13). For example, we have found that dose- response curves typically provide too little discriminatory power, whereas carefully designed time-resolved analyses allow us to study even complicated models, e.g. in the context of pro- teasomal dynamics ( 14 ). Many of the criticisms of model development in Systems Biology stem from a lack of appreciation of the variety of roles that can be played by mathematical modeling ( 1 ). Such antipathy is partly driven by overstating implications and consequences of models, perhaps due to poor understanding of statistical learning and the value of report- ing uncertainties. Frequent fallacies and bad practices continue to thrive, including the use of correlation to capture causal relationships, failure to address multiple testing problems, lack of confidence sets for parameters and models, and many more. The fact that models are sim- plified (but not simplistic) representations of real systems is precisely the property that makes them attractive to explore the consequences of our assumptions, and identify where we lack understanding of the principles governing a biological system. We should start to think of mod- els as tools to uncover mechanisms that cannot be directly observed, akin to microscopes or NMR machines ( 15 ). Used and interpreted appropriately, with due attention paid to inherent uncertainties, the mathematical and computational modeling of biological systems allows us to explore hypotheses and learn about nature. But the relevance of these models depends on our ability to assess, understand, communicate and, ultimately cherish their uncertainties.
References and Notes
- S. Brenner, Philosophical transactions of the Royal Society of London. Series B, Biological sciences 365 , 207 (2010).
- E. U. Azeloglu, R. Iyengar, Science signaling 8 , fs8 (2015).
- I. G. Johnston, et al., eLife 4 , e07464 (2015).
Scales of biologicalsystems
Populations oforganisms
Multicellularorganisms
Groups of cells Single cells Sub-cellularpathways
Biomolecules cell response
B A C
Figure 1: Mathematical models usually represent elements of a biological system at one scale. Systems biologists frequently focus on cellular and subcellular scale systems. Choosing the appropriate degree of abstraction and simplification can be influenced by current knowledge about the system, the quality and quantity of experimental data, the computational demands of a particular modeling approach, and the modeling aims. For example, when studying a signaling pathway, one must decide which biomolecules and interactions to include in a model. The scope of the model may be restricted to a single pathway or it might include the influence of parts of a wider interconnected network of signaling pathways.
