Consistent robustness analysis (CRA) identifies biologically relevant properties of regulatory network models

Causal drift, robust signaling, and complex disease

The phenotype of many regulatory circuits in which mutations can cause complex, polygenic diseases is to some extent robust to DNA mutations that affect circuit components. Here I demonstrate how such mutational robustness can prevent the discovery of genetic disease determinants. To make my case, I use a mathematical model of the insulin signaling pathway implicated in type 2 diabetes, whose signaling output is governed by 15 genetically determined parameters. Using multiple complementary measures of a parameter's importance for this phenotype, I show that any one disease determinant that is crucial in one genetic background will be virtually irrelevant in other backgrounds. In an evolving population that drifts through the parameter space of this or other robust circuits through DNA mutations, the genetic changes that can cause disease will vary randomly over time. I call this phenomenon causal drift. It means that mutations causing disease in one (human or non-human) population may have no effect in another population, and vice versa. Causal drift casts doubt on our ability to infer the molecular mechanisms of complex diseases from non-human model organisms.

Velocity response curves demonstrate the complexity of modeling entrainable clocks

Circadian clocks are biological oscillators that regulate daily behaviors in organisms across the kingdoms of life. Their rhythms are generated by complex systems, generally involving interlocked regulatory feedback loops. These rhythms are entrained by the daily light/dark cycle, ensuring that the internal clock time is coordinated with the environment. Mathematical models play an important role in understanding how the components work together to function as a clock which can be entrained by light. For a clock to entrain, it must be possible for it to be sped up or slowed down at appropriate times. To understand how biophysical processes affect the speed of the clock, one can compute velocity response curves (VRCs). Here, in a case study involving the fruit fly clock, we demonstrate that VRC analysis provides insight into a clock׳s response to light. We also show that biochemical mechanisms and parameters together determine a model׳s ability to respond realistically to light. The implication is that, if one is developing a model and its current form has an unrealistic response to light, then one must reexamine one׳s model structure, because searching for better parameter values is unlikely to lead to a realistic response to light.

Model Misinterpretation within Biology: Phenotypes, Statistics, Networks, and Inference

Models of myriad forms are rapidly becoming central to biology. These range from statistical models that are fundamental to the interpretation of experimental results to ordinary differential equation models that attempt to describe the results in a mechanistic format. Models will be more and more essential to biologists but this growing importance requires all model users to become more sophisticated about what is in a model and how that limits the usability of the model. This review attempts to relay the potential pitfalls that can lie within a model.

Efficient characterization of high-dimensional parameter spaces for systems biology

Background

A biological system's robustness to mutations and its evolution are influenced by the structure of its viable space, the region of its space of biochemical parameters where it can exert its function. In systems with a large number of biochemical parameters, viable regions with potentially complex geometries fill a tiny fraction of the whole parameter space. This hampers explorations of the viable space based on "brute force" or Gaussian sampling.

Results

We here propose a novel algorithm to characterize viable spaces efficiently. The algorithm combines global and local explorations of a parameter space. The global exploration involves an out-of-equilibrium adaptive Metropolis Monte Carlo method aimed at identifying poorly connected viable regions. The local exploration then samples these regions in detail by a method we call multiple ellipsoid-based sampling. Our algorithm explores efficiently nonconvex and poorly connected viable regions of different test-problems. Most importantly, its computational effort scales linearly with the number of dimensions, in contrast to "brute force" sampling that shows an exponential dependence on the number of dimensions. We also apply this algorithm to a simplified model of a biochemical oscillator with positive and negative feedback loops. A detailed characterization of the model's viable space captures well known structural properties of circadian oscillators. Concretely, we find that model topologies with an essential negative feedback loop and a nonessential positive feedback loop provide the most robust fixed period oscillations. Moreover, the connectedness of the model's viable space suggests that biochemical oscillators with varying topologies can evolve from one another.

Conclusions

Our algorithm permits an efficient analysis of high-dimensional, nonconvex, and poorly connected viable spaces characteristic of complex biological circuitry. It allows a systematic use of robustness as a tool for model discrimination.

The contributions of interlocking loops and extensive nonlinearity to the properties of circadian clock models

BACKGROUND

Sensitivity and robustness are essential properties of circadian clock systems, enabling them to respond to the environment but resist noisy variations. These properties should be recapitulated in computational models of the circadian clock. Highly nonlinear kinetics and multiple loops are often incorporated into models to match experimental time-series data, but these also impact on model properties for clock models.

METHODOLOGY/PRINCIPAL FINDINGS

Here, we study the consequences of complicated structure and nonlinearity using simple Goodwin-type oscillators and the complex Arabidopsis circadian clock models. Sensitivity analysis of the simple oscillators implies that an interlocked multi-loop structure reinforces sensitivity/robustness properties, enhancing the response to external and internal variations. Furthermore, we found that reducing the degree of nonlinearity could sometimes enhance the robustness of models, implying that ad hoc incorporation of nonlinearity could be detrimental to a model's perceived credibility.

CONCLUSION

The correct multi-loop structure and degree of nonlinearity are therefore critical in contributing to the desired properties of a model as well as its capacity to match experimental data.