Dynamical structure function identifiability conditions enabling signal structure reconstruction

in The proceedings of the 51st IEEE Conference on Decision and Control (CDC) (2012, December)

Networks of controlled dynamical systems exhibit a variety of interconnection patterns that could be interpreted as the structure of the system. One such interpretation of system structure is a system's ... [more ▼]

Networks of controlled dynamical systems exhibit a variety of interconnection patterns that could be interpreted as the structure of the system. One such interpretation of system structure is a system's signal structure, characterized as the open-loop causal dependencies among manifest variables and represented by its dynamical structure function. Although this notion of structure is among the weakest available, previous work has shown that if no a priori structural information is known about the system, not even the Boolean structure of the dynamical structure function is identifiable. Consequently, one method previously suggested for obtaining the necessary a priori structural information is to leverage knowledge about target specificity of the controlled inputs. This work extends these results to demonstrate precisely the a priori structural information that is both necessary and sufficient to reconstruct the network from input-output data. This extension is important because it significantly broadens the applicability of the identifiability conditions, enabling the design of network reconstruction experiments that were previously impossible due to practical constraints on the types of actuation mechanisms available to the engineer or scientist. The work is motivated by the proteomics problem of reconstructing the Per-Arnt-Sim Kinase pathway used in the metabolism of sugars. [less ▲]

Mathematical relationships between representations of structure in linear interconnected dynamical systems

in The proceedings of the 2011 American Control Conference (ACC) (2011)

A dynamical system can exhibit structure on multiple levels. Different system representations can capture different elements of a dynamical system's structure. We consider LTI input-output dynamical ... [more ▼]

A dynamical system can exhibit structure on multiple levels. Different system representations can capture different elements of a dynamical system's structure. We consider LTI input-output dynamical systems and present four representations of structure: complete computational structure, subsystem structure, signal structure, and input output sparsity structure. We then explore some of the mathematical relation ships that relate these different representations of structure. In particular, we show that signal and subsystem structure are fundamentally different ways of representing system structure. A signal structure does not always specify a unique subsystem structure nor does subsystem structure always specify a unique signal structure. We illustrate these concepts with a numerical example. [less ▲]

Robust dynamical network structure reconstruction

Scientific Conference (2010)

Motivated by biological applications, this paper addresses the problem of network reconstruction from data. Previous work has shown necessary and sufficient conditions for network reconstruction of noise ... [more ▼]

Motivated by biological applications, this paper addresses the problem of network reconstruction from data. Previous work has shown necessary and sufficient conditions for network reconstruction of noise-free LTI systems. This paper assumes that the conditions for network reconstruction have been met but here we additionally take into account noise and unmodelled dynamics (including nonlinearities). Algorithms are therefore proposed to reconstruct dynamical (Boolean) network structure from time-series (steady-state) data respectively in presence of noise and nonlinearities. In order to identify the network structure that generated the data, we compute the smallest distances between the measured data and the data that would have been generated by particular Boolean structures. Information criteria and optimisation technique balancing such distance and model complexity are introduced to search for the true structure. We conclude with biologically-inspired network reconstruction examples which include noise and nonlinearities. [less ▲]

Network structure preserving model reduction with weak a priori structural information

in The proceedings of the Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (2009)

This paper extends a state projection method for structure preserving model reduction to situations where only a weaker notion of system structure is available. This weaker notion of structure ... [more ▼]

This paper extends a state projection method for structure preserving model reduction to situations where only a weaker notion of system structure is available. This weaker notion of structure, identifying the causal relationship between manifest variables of the system, is especially relevant is settings such as systems biology, where a clear partition of state variables into distinct subsystems may be unknown, or not even exist. The resulting technique, like similar approaches, does not provide theoretical performance guarantees, so an extensive computational study is conducted, and it is observed to work fairly well in practice. Moreover, conditions characterizing structurally minimal realizations and sufficient conditions characterizing edge loss resulting from the reduction process, are presented. [less ▲]

Network Structure Preserving Model Reduction: Results of a Simulation Study

in The proceedings of the Third International Conference on Foundations of Systems Biology in Engineering (FOSBE 2009) (2009)

Reconstructed models of biochemical networks often reflect the high level of complexity inherent in the biological system being modeled. The difficulties of predicting gene expression and analyzing the ... [more ▼]

Reconstructed models of biochemical networks often reflect the high level of complexity inherent in the biological system being modeled. The difficulties of predicting gene expression and analyzing the effects of individual perturbations at a system-wide resolution are exacerbated by model complexity. This paper extends a state projection method for structure preserving model reduction to a particular model class of reconstructed networks known as dynamical structure functions. In contrast to traditional approaches where a priori knowledge of partitions on unmeasured species is required, dynamical structure functions require a weaker notion of system structure, specifying only the causal relationship between measured chemical species of the system. The resulting technique, like similar approaches, does not provide theoretical performance guarantees, so an extensive computational study is conducted, and it is observed to work fairly well in practice. Moreover, sufficient conditions, characterizing edge loss resulting from the reduction process, are presented. [less ▲]

Control Theory and Systems Biology

in Iglesias, P. A.; Ingalls, B. P. (Eds.) Dynamical structure Functions in Network Reconstruction (2009)

Presenting a control-theoretic treatment of stoichiometric systems, ... local parametric sensitivity analysis, the two approaches yield identical results. ...

Dynamical structure analysis of sparsity and minimality heuristics for reconstruction of biochemical networks

in The proceedings of the 47th IEEE Conference on Decision and Control (2008)

Network reconstruction, i.e. obtaining network structure from input-output information, is a central theme in systems biology. A variety of approaches aim to obtaining structural information from ... [more ▼]

Network reconstruction, i.e. obtaining network structure from input-output information, is a central theme in systems biology. A variety of approaches aim to obtaining structural information from available data. Previous work has introduced dynamical structure functions as a tool for posing and solving the network reconstruction problem. Even for linear time invariant systems, reconstruction requires specific additional information not generated in the typical system identification process. This paper demonstrates that such extra information can be obtained through a limited sequence of system identification experiments on structurally modified systems, analogous to gene silencing and overexpression experiments. In the absence of such extra information, we discuss whether combined assumptions of network sparsity and minimality contribute to the recovery of the network dynamical structure. We provide sufficient conditions for a transfer function to have a completely decoupled minimal realization, and demonstrate that every transfer function is arbitrarily close to one that admits a perfectly decoupled minimal realization. This indicates that the assumptions of sparsity and minimality alone do not lend insight into the network structure. [less ▲]