Publications about 'identification'
Articles in journal or book chapters
  1. E.D. Sontag. Dynamic compensation, parameter identifiability, and equivariances. PLoS Computational Biology, 13:e1005447, 2017. Note: Preprint was in bioRxiv, 2016.[WWW] [PDF] Keyword(s): fcd, fold-change detection, scale invariance, dynamic compensation, identifiability, observability.
    A recent paper by Karin et al. introduced a mathematical notion called dynamical compensation (DC) of biological circuits. DC was shown to play an important role in glucose homeostasis as well as other key physiological regulatory mechanisms. Karin et al.\ went on to provide a sufficient condition to test whether a given system has the DC property. Here, we show how DC is a reformulation of a well-known concept in systems biology, statistics, and control theory -- that of parameter structural non-identifiability. Viewing DC as a parameter identification problem enables one to take advantage of powerful theoretical and computational tools to test a system for DC. We obtain as a special case the sufficient criterion discussed by Karin et al. We also draw connections to system equivalence and to the fold-change detection property.

  2. P. Bastiaens, M. R. Birtwistle, N. Bluthgen, F. J. Bruggeman, K.-H. Cho, C. Cosentino, A. de la Fuente, J. B. Hoek, A. Kiyatkin, S. Klamt, W. Kolch, S. Legewie, P. Mendes, T. Naka, T. Santra, E.D. Sontag, H. V. Westerhoff, and B. N. Kholodenko. Silence on the relevant literature and errors in implementation. Nature Biotech, 33:336-339, 2015. [PDF] Keyword(s): reverse engineering, systems biology, systems identification.
    This letter discusses a paper in the same journal which reported a method for reconstructing network topologies. Here we show that the method is a variant of a previously published method, modular response analysis. We also demonstrate that the implementation of the algorithm in that paper using statistical similarity measures as a proxy for global network responses to perturbations is erroneous and its performance is overestimated.

  3. E.D. Sontag. Modularity, retroactivity, and structural identification. In H. Koeppl, G. Setti, M. di Bernardo, and D. Densmore, editors, Design and Analysis of Biomolecular Circuits, pages 183-202. Springer-Verlag, 2011. [PDF] Keyword(s): modularity, retroactivity, identification.
    Many reverse-engineering techniques in systems biology rely upon data on steady-state (or dynamic) perturbations --obtained from siRNA, gene knock-down or overexpression, kinase and phosphatase inhibitors, or other interventions-- in order to understand the interactions between different ``modules'' in a network. This paper first reviews one such popular such technique, introduced by the author and collaborators, and focuses on why conclusions drawn from its use may be misleading due to ``retroactivity'' (impedance or load) effects. A theoretical result characterizing stoichiometric-induced steady-state retroactivity effects is given for a class of biochemical networks.

  4. E.D. Sontag, Y. Wang, and A. Megretski. Input classes for identification of bilinear systems. IEEE Transactions Autom. Control, 54:195-207, 2009. Note: Also arXiv math.OC/0610633, 20 Oct 2006, and short version in ACC'07.[PDF] Keyword(s): realization theory, observability, identifiability, bilinear systems.
    This paper asks what classes of input signals are sufficient in order to completely identify the input/output behavior of generic bilinear systems. The main results are that step inputs are not sufficient, nor are single pulses, but the family of all pulses (of a fixed amplitude but varying widths) do suffice for identification.

  5. E.D. Sontag. Network reconstruction based on steady-state data. Essays in Biochemistry, 45:161-176, 2008. [PDF] Keyword(s): systems biology, biochemical networks, gene and protein networks, reverse engineering, systems identification.
    The ``reverse engineering problem'' in systems biology is that of unraveling of the web of interactions among the components of protein and gene regulatory networks, so as to map out the direct or local interactions among components. These direct interactions capture the topology of the functional network. An intrinsic difficulty in capturing these direct interactions, at least in intact cells, is that any perturbation to a particular gene or signaling component may rapidly propagate throughout the network, thus causing global changes which cannot be easily distinguished from direct effects. Thus, a major goal in reverse engineering is to use these observed global responses - such as steady-state changes in concentrations of active proteins, mRNA levels, or transcription rates - in order to infer the local interactions between individual nodes. One approach to solving this global-to-local problem is the ``Modular Response Analysis'' (MRA) method proposed in work of the author with Kholodenko et. al. (PNAS, 2002) and further elaborated in other papers. The basic method deals only with steady-state data. However, recently, quasi-steady state MRA has been used by Santos et. al. (Nature Cell Biology, 2007) for quantifying positive and negative feedback effects in the Raf/Mek/Erk MAPK network in rat adrenal pheochromocytoma (PC-12) cells. This paper presents an overview of the MRA technique, as well as a generalization of the algorithm to that quasi-steady state case.

  6. E.D. Sontag and Y. Wang. Uniformly Universal Inputs. In Alessandro Astolfi, editor, Analysis and Design of Nonlinear Control Systems, volume 224, pages 9-24. Springer-Verlag, London, 2007. [PDF] Keyword(s): observability, identification.
    A result is presented showing the existence of inputs universal for observability, uniformly with respect to the class of all continuous-time analytic systems. This represents an ultimate generalization of a 1977 theorem, for bilinear systems, due to Alberto Isidori and Osvaldo Grasselli.

  7. P. Berman, B. Dasgupta, and E.D. Sontag. Algorithmic issues in reverse engineering of protein and gene networks via the modular response analysis method. Annals of the NY Academy of Sciences, 1115:132-141, 2007. [PDF] Keyword(s): systems biology, biochemical networks, gene and protein networks, reverse engineering, systems identification, graph algorithms.
    This paper studies a computational problem motivated by the modular response analysis method for reverse engineering of protein and gene networks. This set-cover problem is hard to solve exactly for large networks, but efficient approximation algorithms are given and their complexity is analyzed.

  8. P. Berman, B. Dasgupta, and E.D. Sontag. Randomized approximation algorithms for set multicover problems with applications to reverse engineering of protein and gene networks. Discrete Applied Mathematics Special Series on Computational Molecular Biology, 155:733-749, 2007. [PDF] Keyword(s): systems biology, biochemical networks, gene and protein networks, systems identification, reverse engineering.
    This paper investigates computational complexity aspects of a combinatorial problem that arises in the reverse engineering of protein and gene networks, showing relations to an appropriate set multicover problem with large "coverage" factor, and providing a non-trivial analysis of a simple randomized polynomial-time approximation algorithm for the problem.

  9. B. Dasgupta, P. Berman, and E.D. Sontag. Computational complexities of combinatorial problems with applications to reverse engineering of biological networks. In D. Liu and F-Y. Wan, editors, Advances in Computational Intelligence: Theory & Applications, pages 303-316. World Scientific, Hackensack, 2006. Keyword(s): systems biology, biochemical networks, gene and protein networks, reverse engineering, systems identification, theory of computing and complexity.

  10. N.A.W. van Riel and E.D. Sontag. Parameter estimation in models combining signal transduction and metabolic pathways: The dependent input approach. IET Systems Biology, 153:263-274, 2006. [PDF] Keyword(s): systems biology, biochemical networks, parameter identification.
    Biological complexity and limited quantitative measurements impose severe challenges to standard engineering methodologies for systems identification. This paper presents an approach, justified by the theory of universal inputs for distinguishability, based on replacing unmodeled dynamics by fictitious `dependent inputs'. The approach is particularly useful in validation experiments, because it allows one to fit model parameters to experimental data generated by a reference (wild-type) organism and then testing this model on data generated by a variation (mutant), so long as the mutations only affect the unmodeled dynamics that produce the dependent inputs. As a case study, this paper addresses the pathways that control the nitrogen uptake fluxes in baker's yeast Saccharomyces cerevisiae enabling it to optimally respond to changes in nitrogen availability. Well-defined perturbation experiments were performed on cells growing in steady-state. Time-series data of extracellular and intracellular metabolites were obtained, as well as mRNA levels. A nonlinear model was proposed, and shown to be structurally identifiable given input/output data. The identified model correctly predicted the responses of different yeast strains and different perturbations.

  11. M. Andrec, B.N. Kholodenko, R.M. Levy, and E.D. Sontag. Inference of signaling and gene regulatory networks by steady-state perturbation experiments: structure and accuracy. J. Theoret. Biol., 232(3):427-441, 2005. Note: Supplementary materials are here: [PDF] Keyword(s): systems biology, biochemical networks, gene and protein networks, systems identification, reverse engineering.
    One of the fundamental problems of cell biology is the understanding of complex regulatory networks. Such networks are ubiquitous in cells, and knowledge of their properties is essential for the understanding of cellular behavior. This paper studies the effect of experimental uncertainty on the accuracy of the inferred structure of the networks determined using the method in "Untangling the wires: a novel strategy to trace functional interactions in signaling and gene networks".

  12. P. Kuusela, D. Ocone, and E.D. Sontag. Learning Complexity Dimensions for a Continuous-Time Control System. SIAM J. Control Optim., 43(3):872-898, 2004. [PDF] [doi:] Keyword(s): theory of computing and complexity, VC dimension.
    This paper takes a computational learning theory approach to a problem of linear systems identification. It is assumed that input signals have only a finite number k of frequency components, and systems to be identified have dimension no greater than n. The main result establishes that the sample complexity needed for identification scales polynomially with n and logarithmically with k.

  13. E.D. Sontag, A. Kiyatkin, and B.N. Kholodenko. Inferring dynamic architecture of cellular networks using time series of gene expression, protein and metabolite data. Bioinformatics, 20(12):1877-1886, 2004. Note: Supplementary materials are here: [PDF] [doi:] Keyword(s): systems biology, biochemical networks, systems identification, gene and protein networks, reverse engineering.
    High-throughput technologies have facilitated the acquisition of large genomics and proteomics data sets. However, these data provide snapshots of cellular behavior, rather than help us reveal causal relations. Here, we propose how these technologies can be utilized to infer the topology and strengths of connections among genes, proteins, and metabolites by monitoring time-dependent responses of cellular networks to experimental interventions. We show that all connections leading to a given network node, e.g., to a particular gene, can be deduced from responses to perturbations none of which directly influences that node, e.g., using strains with knock-outs to other genes. To infer all interactions from stationary data, each node should be perturbed separately or in combination with other nodes. Monitoring time series provides richer information and does not require perturbations to all nodes.

  14. B.N. Kholodenko, A. Kiyatkin, F.J. Bruggeman, E.D. Sontag, H.V. Westerhoff, and J. Hoek. Untangling the wires: a novel strategy to trace functional interactions in signaling and gene networks. Proceedings of the National Academy of Sciences USA, 99:12841-12846, 2002. [PDF] Keyword(s): systems biology, biochemical networks, reverse engineering, gene and protein networks, protein networks, gene networks, systems identification.
    Emerging technologies have enabled the acquisition of large genomics and proteomics data sets. This paper proposes a novel quantitative method for determining functional interactions in cellular signaling and gene networks. It can be used to explore cell systems at a mechanistic level, or applied within a modular framework, which dramatically decreases the number of variables to be assayed. The topology and strength of network connections are retrieved from experimentally measured network responses to successive perturbations of all modules. In addition, the method can reveal functional interactions even when the components of the system are not all known, in which case some connections retrieved by the analysis will not be direct but correspond to the interaction routes through unidentified elements. The method is tested and illustrated using computer-generated responses of a modeled MAPK cascade and gene network.

  15. E.D. Sontag. For differential equations with r parameters, 2r+1 experiments are enough for identification. J. Nonlinear Sci., 12(6):553-583, 2002. [PDF] Keyword(s): identifiability, observability, systems biology, biochemical networks, parameter identification.
    Given a set of differential equations whose description involves unknown parameters, such as reaction constants in chemical kinetics, and supposing that one may at any time measure the values of some of the variables and possibly apply external inputs to help excite the system, how many experiments are sufficient in order to obtain all the information that is potentially available about the parameters? This paper shows that the best possible answer (assuming exact measurements) is 2r+1 experiments, where r is the number of parameters.

  16. B. DasGupta and E.D. Sontag. A polynomial-time algorithm for checking equivalence under certain semiring congruences motivated by the state-space isomorphism problem for hybrid systems. Theor. Comput. Sci., 262(1-2):161-189, 2001. [PDF] [doi:] Keyword(s): hybrid systems, computational complexity.
    The area of hybrid systems concerns issues of modeling, computation, and control for systems which combine discrete and continuous components. The subclass of piecewise linear (PL) systems provides one systematic approach to discrete-time hybrid systems, naturally blending switching mechanisms with classical linear components. PL systems model arbitrary interconnections of finite automata and linear systems. Tools from automata theory, logic, and related areas of computer science and finite mathematics are used in the study of PL systems, in conjunction with linear algebra techniques, all in the context of a "PL algebra" formalism. PL systems are of interest as controllers as well as identification models. Basic questions for any class of systems are those of equivalence, and, in particular, if state spaces are equivalent under a change of variables. This paper studies this state-space equivalence problem for PL systems. The problem was known to be decidable, but its computational complexity was potentially exponential; here it is shown to be solvable in polynomial-time.

  17. M. A. Dahleh, E.D. Sontag, D. N. C. Tse, and J. N. Tsitsiklis. Worst-case identification of nonlinear fading memory systems. Automatica, 31(3):503-508, 1995. [PDF] [doi:]
    We consider the problem of characterizing possible supply functions for a given dissipative nonlinear system, and provide a result that allows some freedom in the modification of such functions.

  18. E.D. Sontag. Bilinear realizability is equivalent to existence of a singular affine differential I/O equation. Systems Control Lett., 11(3):181-187, 1988. [PDF] [doi:] Keyword(s): identification, identifiability, observability, observation space.
    For continuous time analytic input/output maps, the existence of a singular differential equation relating derivatives of controls and outputs is shown to be equivalent to bilinear realizability. A similar result holds for the problem of immersion into bilinear systems. The proof is very analogous to that of the corresponding, and previously known, result for discrete time.

  19. E.D. Sontag. On the length of inputs necessary in order to identify a deterministic linear system. IEEE Trans. Automat. Control, 25(1):120-121, 1980. [PDF]
    The family of m-input, n-dimensional linear systems can be globally Identified with a generic input sequence of length 2mn. This bound is the best possible. A best bound is proved also for a corresponding local identification problem.

Conference articles
  1. F. Menolascina, R. Stocker, and E.D. Sontag. In-vivo identification and control of aerotaxis in Bacillus subtilis. In Proc. IEEE Conf. Decision and Control, Dec. 2016, pages 764-769, 2016. [PDF] Keyword(s): identification, systems biology, aerotaxis, B. subtilis.
    Combining in-vivo experiments with system identification methods, we determine a simple model of aerotaxis in B. subtilis, and we subsequently employ this model in order to compute the sequence of oxygen gradients needed in order to achieve set-point regulation with respect to a signal tracking the center of mass of the bacterial population. We then successfully validate both the model and the control scheme, by showing that in-vivo positioning control can be achieved via the application of the precomputed inputs in-vivo in an open-loop configuration.

  2. M. Skataric and E.D. Sontag. Remarks on model-based estimation of nonhomogeneous Poisson processes and applications to biological systems. In Proc. European Control Conference, Strasbourg, France, June 2014, pages 2052-2057, 2014. [PDF] Keyword(s): systems biology, random dynamical systems.
    This paper studies model-based estimation methods of a rate of a nonhomogeneous Poisson processes that describes events arising from modeling biological phenomena in which discrete events are measured. We describe an approach based on observers and Kalman filters as well as preliminary simulation results, and compare these to other methods (not model-based) in the literature. The problem is motivated by the question of identification of internal states from neural spikes and bacterial tumbling behavior.

  3. E.D. Sontag. Remarks on structural identification, modularity, and retroactivity. In Proc. IEEE Conf. Decision and Control, Atlanta, Dec. 2010, pages ThA23.1, 2010. [PDF] Keyword(s): modularity, retroactivity, identification.
    Summarized conference version of ``Modularity, retroactivity, and structural identification''.

  4. E.D. Sontag, Y. Wang, and A. Megretski. Remarks on Input Classes for Identification of Bilinear Systems. In Proceedings American Control Conf., New York, July 2007, pages 4345-4350, 2007. Keyword(s): realization theory, observability, identifiability, bilinear systems.

  5. P. Kuusela, D. Ocone, and E.D. Sontag. Remarks on the sample complexity for linear control systems identification. In IFAC Workshop on Adaptation and Learning in Control and Signal Processing, ALCOSP2001, Cernobbio-Como, Italy, 29-31 August, 2001, pages 431-436, 2001.

  6. M.A. Dahleh, E.D. Sontag, D.N.C. Tse, and J.N. Tsitsiklis. Worst-case identification of nonlinear fading memory systems. In Proc. Amer. Automatic Control Conf., Chicago, June 1992, pages 241-245, 1992.



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