Observability of complex systems

A quantitative description of a complex system is inherently limited by our ability to estimate the system's internal state from experimentally accessible outputs. Although the simultaneous measurement of all internal variables, like all metabolite concentrations in a cell, offers a complete de...

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Published inProceedings of the National Academy of Sciences - PNAS Vol. 110; no. 7; pp. 2460 - 2465
Main Authors Liu, Yang-Yu, Slotine, Jean-Jacques, Barabási, Albert-László
Format Journal Article
LanguageEnglish
Published United States National Academy of Sciences 12.02.2013
National Acad Sciences
SeriesFrom the Cover
Subjects
Algebra
Biochemical Phenomena - physiology
Biochemistry
Biological Sciences
Biomarkers
Chemical reactions
Complex systems
Dynamical systems
Inference
Linear systems
Metabolism
Metabolites
Models, Biological
Physical Sciences
Sensors
System observability
Systems Analysis
Systems Biology - methods
Systems Theory
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Summary:A quantitative description of a complex system is inherently limited by our ability to estimate the system's internal state from experimentally accessible outputs. Although the simultaneous measurement of all internal variables, like all metabolite concentrations in a cell, offers a complete description of a system's state, in practice experimental access is limited to only a subset of variables, or sensors. A system is called observable if we can reconstruct the system's complete internal state from its outputs. Here, we adopt a graphical approach derived from the dynamical laws that govern a system to determine the sensors that are necessary to reconstruct the full internal state of a complex system. We apply this approach to biochemical reaction systems, finding that the identified sensors are not only necessary but also sufficient for observability. The developed approach can also identify the optimal sensors for target or partial observability, helping us reconstruct selected state variables from appropriately chosen outputs, a prerequisite for optimal biomarker design. Given the fundamental role observability plays in complex systems, these results offer avenues to systematically explore the dynamics of a wide range of natural, technological and socioeconomic systems.
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Edited by Giorgio Parisi, University of Rome, Rome, Italy, and approved December 26, 2012 (received for review September 6, 2012)
Author contributions: Y.-Y.L., J.-J.S., and A.-L.B. designed research; Y.-Y.L., J.-J.S., and A.-L.B. performed research; Y.-Y.L. contributed analytic tools; Y.-Y.L. analyzed data; and Y.-Y.L. and A.-L.B. wrote the paper.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.1215508110