Inverse problems from biomedicine

Lu, James; August, Elias; Koeppl, Heinz

doi:10.1007/s00285-012-0523-z

Cited by 6 publications

(6 citation statements)

References 44 publications

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“…Inverse problems were examined with several (although not too many) data structures, which assessed well-conserved properties of biological systems (28, 63, 64). While direct or forward problems have historically predominated in Biomedicine, when the goal is to “discover” what, usually, is not observable, inverse problem-oriented methods may yield more information even when the size of the data analyzed is small–as demonstrated here.…”

Section: Future Stepsmentioning

confidence: 99%

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

et al. 2019

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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.

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Section: Future Stepsmentioning

confidence: 99%

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

et al. 2019

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“…Adjoint sensitivity analysis is known to be superior to the forward sensitivity analysis when the number of parameters is large [30]. Adjoint sensitivity analysis has been used for inference of biochemical reaction networks [31–33]. However, the methods were never picked up by the systems and computational biology community, supposedly due to the theoretical complexity of adjoint methods, a missing evaluation on a set of benchmark models, and an absence of an easy-to-use toolbox.…”

Section: Introductionmentioning

confidence: 99%

Scalable Parameter Estimation for Genome-Scale Biochemical Reaction Networks

et al. 2017

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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.

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“…In particular, the method uses the location of the bifurcation points given by experimental data a to infer the kinetic parameters, exploiting the condition derived in [ 12 ]. In contrast to other methods developed for inverse bifurcation analysis which use generic bifurcation conditions [ 13 , 14 ] and can therefore be used for any system of ordinary differential equations, our method is specific for chemical reaction networks since it exploits their particular structural properties, bringing additional insight into the inverse bifurcation problem for chemical reaction systems.…”

Section: Introductionmentioning

confidence: 99%

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

2014

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

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Inverse problems from biomedicine

Cited by 6 publications

References 44 publications

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

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

Scalable Parameter Estimation for Genome-Scale Biochemical Reaction Networks

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

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