Inverse problems from biomedicine: inference of putative disease mechanisms and robust therapeutic strategies

Efficient parameterization of large-scale dynamic models based on relative measurements

MOTIVATION

Mechanistic models of biochemical reaction networks facilitate the quantitative understanding of biological processes and the integration of heterogeneous datasets. However, some biological processes require the consideration of comprehensive reaction networks and therefore large-scale models. Parameter estimation for such models poses great challenges, in particular when the data are on a relative scale.

RESULTS

Here, we propose a novel hierarchical approach combining (i) the efficient analytic evaluation of optimal scaling, offset and error model parameters with (ii) the scalable evaluation of objective function gradients using adjoint sensitivity analysis. We evaluate the properties of the methods by parameterizing a pan-cancer ordinary differential equation model (>1000 state variables, >4000 parameters) using relative protein, phosphoprotein and viability measurements. The hierarchical formulation improves optimizer performance considerably. Furthermore, we show that this approach allows estimating error model parameters with negligible computational overhead when no experimental estimates are available, providing an unbiased way to weight heterogeneous data. Overall, our hierarchical formulation is applicable to a wide range of models, and allows for the efficient parameterization of large-scale models based on heterogeneous relative measurements.

AVAILABILITY AND IMPLEMENTATION

Supplementary code and data are available online at http://doi.org/10.5281/zenodo.3254429 and http://doi.org/10.5281/zenodo.3254441.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Assessing the Dynamics and Complexity of Disease Pathogenicity Using 4-Dimensional Immunological Data

Investigating disease pathogenesis and personalized prognostics are major biomedical needs. Because patients sharing the same diagnosis can experience different outcomes, such as survival or death, physicians need new personalized tools, including those that rapidly differentiate several inflammatory phases. To address these topics, a pattern recognition-based method (PRM) that follows an inverse problem approach was designed to assess, in <10 min, eight concepts: synergy, pleiotropy, complexity, dynamics, ambiguity, circularity, personalized outcomes, and explanatory prognostics (pathogenesis). By creating thousands of secondary combinations derived from blood leukocyte data, the PRM measures synergic, pleiotropic, complex and dynamic data interactions, which provide personalized prognostics while some undesirable features-such as false results and the ambiguity associated with data circularity-are prevented. Here, this method is compared to Principal Component Analysis (PCA) and evaluated with data collected from hantavirus-infected humans and birds that appeared to be healthy. When human data were examined, the PRM predicted 96.9 % of all surviving patients while PCA did not distinguish outcomes. Demonstrating applications in personalized prognosis, eight PRM data structures sufficed to identify all but one of the survivors. Dynamic data patterns also distinguished survivors from non-survivors, as well as one subset of non-survivors, which exhibited chronic inflammation. When the PRM explored avian data, it differentiated immune profiles consistent with no, early, or late inflammation. Yet, PCA did not recognize patterns in avian data. Findings support the notion that immune responses, while variable, are rather deterministic: a low number of complex and dynamic data combinations may be enough to, rapidly, unmask conditions that are neither directly observable nor reliably forecasted.

Scalable Inference of Ordinary Differential Equation Models of Biochemical Processes

Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about the behavior of latent variables or the process under new experimental conditions. Complementarily, inference of model structure can be used to identify the most plausible model structure from a set of candidates, and, thus, gain novel biological insight. Several toolboxes can infer model parameters and structure for small- to medium-scale mechanistic models out of the box. However, models for highly multiplexed datasets can require hundreds to thousands of state variables and parameters. For the analysis of such large-scale models, most algorithms require intractably high computation times. This chapter provides an overview of the state-of-the-art methods for parameter and model inference, with an emphasis on scalability.

Scalable Parameter Estimation for Genome-Scale Biochemical Reaction Networks

Mechanistic mathematical modeling of biochemical reaction networks using ordinary differential equation (ODE) models has improved our understanding of small- and medium-scale biological processes. While the same should in principle hold for large- and genome-scale processes, the computational methods for the analysis of ODE models which describe hundreds or thousands of biochemical species and reactions are missing so far. While individual simulations are feasible, the inference of the model parameters from experimental data is computationally too intensive. In this manuscript, we evaluate adjoint sensitivity analysis for parameter estimation in large scale biochemical reaction networks. We present the approach for time-discrete measurement and compare it to state-of-the-art methods used in systems and computational biology. Our comparison reveals a significantly improved computational efficiency and a superior scalability of adjoint sensitivity analysis. The computational complexity is effectively independent of the number of parameters, enabling the analysis of large- and genome-scale models. Our study of a comprehensive kinetic model of ErbB signaling shows that parameter estimation using adjoint sensitivity analysis requires a fraction of the computation time of established methods. The proposed method will facilitate mechanistic modeling of genome-scale cellular processes, as required in the age of omics.

In this manuscript, we introduce a scalable method for parameter estimation for genome-scale biochemical reaction networks. Mechanistic models for genome-scale biochemical reaction networks describe the behavior of thousands of chemical species using thousands of parameters. Standard methods for parameter estimation are usually computationally intractable at these scales. Adjoint sensitivity based approaches have been suggested to have superior scalability but any rigorous evaluation is lacking. We implement a toolbox for adjoint sensitivity analysis for biochemical reaction network which also supports the import of SBML models. We show by means of a set of benchmark models that adjoint sensitivity based approaches unequivocally outperform standard approaches for large-scale models and that the achieved speedup increases with respect to both the number of parameters and the number of chemical species in the model. This demonstrates the applicability of adjoint sensitivity based approaches to parameter estimation for genome-scale mechanistic model. The MATLAB toolbox implementing the developed methods is available from http://ICB-DCM.github.io/AMICI/.

A method for inverse bifurcation of biochemical switches: inferring parameters from dose response curves

Background

Within cells, stimuli are transduced into cell responses by complex networks of biochemical reactions. In many cell decision processes the underlying networks behave as bistable switches, converting graded stimuli or inputs into all or none cell responses. Observing how systems respond to different perturbations, insight can be gained into the underlying molecular mechanisms by developing mathematical models. Emergent properties of systems, like bistability, can be exploited to this purpose. One of the main challenges in modeling intracellular processes, from signaling pathways to gene regulatory networks, is to deal with high structural and parametric uncertainty, due to the complexity of the systems and the difficulty to obtain experimental measurements. Formal methods that exploit structural properties of networks for parameter estimation can help to overcome these problems.

Results

We here propose a novel method to infer the kinetic parameters of bistable biochemical network models. Bistable systems typically show hysteretic dose response curves, in which the so called bifurcation points can be located experimentally. We exploit the fact that, at the bifurcation points, a condition for multistationarity derived in the context of the Chemical Reaction Network Theory must be fulfilled. Chemical Reaction Network Theory has attracted attention from the (systems) biology community since it connects the structure of biochemical reaction networks to qualitative properties of the corresponding model of ordinary differential equations. The inverse bifurcation method developed here allows determining the parameters that produce the expected behavior of the dose response curves and, in particular, the observed location of the bifurcation points given by experimental data.

Conclusions

Our inverse bifurcation method exploits inherent structural properties of bistable switches in order to estimate kinetic parameters of bistable biochemical networks, opening a promising route for developments in Chemical Reaction Network Theory towards kinetic model identification.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-014-0114-2) contains supplementary material, which is available to authorized users.

Differentiation between genomic and non-genomic feedback controls yields an HPA axis model featuring hypercortisolism as an irreversible bistable switch

Background

The hypothalamic-pituitary-adrenal axis (HPA axis) is a major part of the neuroendocrine system responsible for the regulation of the response to physical or mental stress and for the control of the synthesis of the stress hormone cortisol. Dysfunctions of the HPA axis characterized by either low (hypocortisolism) or increased (hypercortisolism) cortisol levels are implicated in various pathological conditions. Their understanding and therapeutic correction may be supported by mathematical modeling and simulation of the HPA axis.

Methods

Mass action and Michaelis Menten enzyme kinetics were used to provide a mechanistic description of the feedback mechanisms within the pituitary gland cells by which cortisol inhibits its own production. A separation of the nucleus from the cytoplasm by compartments enabled a differentiation between slow genomic and fast non-genomic processes. The model in parts was trained against time resolved ACTH stress response data from an in vitro cell culture of murine AtT-20 pituitary tumor cells and analyzed by bifurcation discovery tools.

Results

A recently found pituitary gland cell membrane receptor that mediates rapid non-genomic actions of glucocorticoids has been incorporated into our model of the HPA axis. As a consequence of the distinction between genomic and non-genomic feedback processes our model possesses an extended dynamic repertoire in comparison to existing HPA models. In particular, our model exhibits limit cycle oscillations and bistable behavior associated to hypocortisolism but also features a (second) bistable switch which captures irreversible transitions in hypercortisolism to elevated cortisol levels.

Conclusions

Model predictive control and inverse bifurcation analysis have been previously applied in the simulation-based design of therapeutic strategies for the correction of hypocortisolism. Given the HPA model extension presented in this paper, these techniques may also be used in the study of hypercortisolism. As an example, we show how sparsity enforcing penalization may suggest network interventions that allow the return from elevated cortisol levels back to nominal ones.