Quantitative computational models play an increasingly important role in modern biology. Such models typically involve many free parameters, and assigning their values is often a substantial obstacle to model development. Directly measuring in vivo biochemical parameters is difficult, and collectively fitting them to other experimental data often yields large parameter uncertainties. Nevertheless, in earlier work we showed in a growth-factor-signaling model that collective fitting could yield well-constrained predictions, even when it left individual parameters very poorly constrained. We also showed that the model had a “sloppy” spectrum of parameter sensitivities, with eigenvalues roughly evenly distributed over many decades. Here we use a collection of models from the literature to test whether such sloppy spectra are common in systems biology. Strikingly, we find that every model we examine has a sloppy spectrum of sensitivities. We also test several consequences of this sloppiness for building predictive models. In particular, sloppiness suggests that collective fits to even large amounts of ideal time-series data will often leave many parameters poorly constrained. Tests over our model collection are consistent with this suggestion. This difficulty with collective fits may seem to argue for direct parameter measurements, but sloppiness also implies that such measurements must be formidably precise and complete to usefully constrain many model predictions. We confirm this implication in our growth-factor-signaling model. Our results suggest that sloppy sensitivity spectra are universal in systems biology models. The prevalence of sloppiness highlights the power of collective fits and suggests that modelers should focus on predictions rather than on parameters.

Models of biochemical regulation in prokaryotes and eukaryotes, typically consisting of a set of first-order nonlinear ordinary differential equations, have become increasingly popular of late. These systems have large numbers of poorly known parameters, simplified dynamics, and uncertain connectivity: three key features of a class of problems we call sloppy models, which are shared by many other high-dimensional multiparameter nonlinear models. We use a statistical ensemble method to study the behavior of these models, in order to extract as much useful predictive information as possible from a sloppy model, given the available data used to constrain it. We discuss numerical challenges that emerge in using the ensemble method for a large system. We characterize features of sloppy model parameter fluctuations by various spectral decompositions and find indeed that five parameters can be used to fit an elephant. We also find that model entropy is as important to the problem of model choice as model energy is to parameter choice.

Magnetic resonance imaging enables the noninvasive mapping of both anatomical white matter connectivity and dynamic patterns of neural activity in the human brain. We examine the relationship between the structural properties of white matter streamlines (structural connectivity) and the functional properties of correlations in neural activity (functional connectivity) within 84 healthy human subjects both at rest and during the performance of attention-and memory-demanding tasks. We show that structural properties, including the length, number, and spatial location of white matter streamlines, are indicative of and can be inferred from the strength of resting-state and task-based functional correlations between brain regions. These results, which are both representative of the entire set of subjects and consistently observed within individual subjects, uncover robust links between structural and functional connectivity in the human brain.uman cognitive function is supported by large-scale interactions between different regions of the brain. The anatomical scaffolding that mediates these interactions can be described by a structural connectome that maps the spatial layout of white matter (1). Structural connectivity (SC), defined by the physical properties of these direct anatomical connections, supports the relay of electrical signals between brain regions. Neurophysiological events can similarly be described by a functional connectome that maps coordinated changes in neuronal activity, field potentials, blood flow, or energy consumption (2). Functional connectivity (FC), defined by temporal correlations in such neurophysiological events, reflects the resting-state and task-dependent strengths of correlated activity in different brain regions (3-5). The estimation of structural and functional connectivity from different experimental techniques raises two complementary questions about the quantitative relationships between structural and functional connectomes: (i) to what extent can the resting-state and task-dependent strengths of functional correlations between brain regions be inferred from structural connectomes, and (ii) to what extent can the physical properties of anatomical connections be inferred from functional connectomes?Connectomes, whether examined at the neural or systems level, are networks whose structural properties, such as the length and number of connections, can differentially impact functional properties, such as local or global correlations in temporal dynamics. Whereas the length and density of anatomical connections are thought to impact functional processes such as information segregation and integration (6, 7), the extent to which such relationships are robustly observed in the human brain is not well understood. Previous studies have been limited in scope to specific anatomical connections and brain regions, small sample sizes, and resting-state neural activity (8-13) and have consequently left several fundamental questions unanswered. How do variations in structural features, such a...

Accumulating evidence suggests that the brain can efficiently process both external and internal information. The processing of internal information is a distinct “offline” cognitive mode that requires not only spontaneously generated mental activity; it has also been hypothesized to require a decoupling of attention from perception in order to separate competing streams of internal and external information. This process of decoupling is potentially adaptive because it could prevent unimportant external events from disrupting an internal train of thought. Here, we use measurements of pupil diameter (PD) to provide concrete evidence for the role of decoupling during spontaneous cognitive activity. First, during periods conducive to offline thought but not during periods of task focus, PD exhibited spontaneous activity decoupled from task events. Second, periods requiring external task focus were characterized by large task evoked changes in PD; in contrast, encoding failures were preceded by episodes of high spontaneous baseline PD activity. Finally, high spontaneous PD activity also occurred prior to only the slowest 20% of correct responses, suggesting high baseline PD indexes a distinct mode of cognitive functioning. Together, these data are consistent with the decoupling hypothesis, which suggests that the capacity for spontaneous cognitive activity depends upon minimizing disruptions from the external world.