Robustness Analysis of Large-Scale Stochastic Systems
Lead Research Organisation:
University of Glasgow
Department Name: School of Engineering
Abstract
Stochasticity in biomolecular networks is an important factor in understanding the fundamental mechanisms behind various physiological responses. It has been shown that stochastic effects in molecular interactions cannot be ignored in many cases, since they have major impacts on the dynamics of the networks. On the other hand, the modelling and analysis of whole biological systems will usually result in extremely large size problems. Hence, as the requirement for the mathematical modelling of biological systems becomes more realistic, we have to deal with large-scale stochastic systems, and the corresponding robustness analysis problem is more complicated and difficult. In this research, we aim to extend current robustness analysis methodologies using a novel geometrical interpretation of robustness analysis combined with a probabilistic framework so that it can be applicable for large-scale stochastic systems. While robustness analysis problems have usually been formulated using linear algebra approaches, we suggest a geometrical approach, such that the robustness analysis problem can be posed as two manifold intersections. With this geometrical condition, the robustness analysis can be performed for the cases including stochastic noises and it can be applicable for large-scale systems because the algorithm could be parallelised so that the calculations are performed on a distributed computing system. This research will facilitate our understanding of the fundamental structures and sources of robustness of biological systems, which is a key factor in improving drug development for various diseases, since it will allow us to find the weakest (fragile) structure of the system and hence to develop efficient medical therapies.
People |
ORCID iD |
Jongrae Kim (Principal Investigator) |
Publications
Cheng D
(2012)
Approximation of boolean networks
Jong-Rae Kim (Author)
(2012)
Approximation of boolean networks
Jong-Rae Kim (Author)
(2011)
Model-based compensation for multi-packet transmission in networked control systems
Jong-Rae Kim (Author)
(2011)
Low-degree nodes having strong local effects but weak global effects could be drug targets
Jong-Rae Kim (Author)
(2011)
PDV-based packet length allocation for networked control systems
Kim J
(2016)
Robustness Analysis of Network Modularity
in IEEE Transactions on Control of Network Systems
Yun-Bo Zhao
(2011)
Simplified algorithm and framework for networked predictive control systems
in Proceeding Chinese Control Conference
Zhao Y
(2012)
Offline model predictive control-based gain scheduling for networked control systems
in IET Control Theory & Applications
Zhao Y
(2012)
Compensation and stochastic modeling of discrete-time networked control systems with data packet disorder
in International Journal of Control, Automation and Systems
Zhao Y
(2013)
Aggregation Algorithm Towards Large-Scale Boolean Network Analysis
in IEEE Transactions on Automatic Control
Zhao Y
(2011)
Error Bounded Sensing for Packet-Based Networked Control Systems
in IEEE Transactions on Industrial Electronics
Zhao Y
(2011)
LFT-free µ-analysis of LTI/LPTV systems
Zhao Y
(2013)
On the delay effects of different channels in Internet-based networked control systems
in International Journal of Systems Science
Description | Life is a system of self-organised many molecular-level components. Understanding how these components interact each other and unravelling important underlying mechanisms are the cornerstone towards full comprehension of life. One of the profound characteristics of life is robustness, which is observed even in very primitive cellular life. Resistant to environmental changes and sustaining functionality to noisy interactions among the components are inherent characteristics of all life. Systems Biology interprets life as an organised system of many components. The ultimate questions that we have pursued are how the robustness of life is emerged from many components and how to quantify the robustness. Towards the answers to the ultimate questions, efficient algorithms for robustness analysis of life in different mathematical descriptions are developed as follows: Firstly, we developed an efficient method to simulate noisy molecular interactions, which combines an approximate method with an error correction method. The approximation error is increased as the simulation time increases. The error is estimated by a few exact noise simulations and reduced by updating the simulation. The efficiency was demonstrated by the oscillation network of molecular concentration in amoebae. In addition, a systematic way of quantifying the noise effect with uncertain parameters are developed. Secondly, biological systems have finite life-span and it is not necessary that they are robust longer than the restricted time length. Mathematically, this is challenging as finite time characteristics cannot be easily checked through existing mathematical terms. Although some may unstable, they may perfectly acceptable for a shorter period of time if the states only diverge slowly. We developed an efficient finite-time system quantification method, which estimates the bounds of the states. The algorithm is applied to estimate the finite time behaviour of ErbB network, which is the biological network related to human breast cancer. Thirdly, in order to study much large-scale systems, we need to use some different mathematical descriptions. Boolean network is a promising approach for modelling large-scale systems, where the states are binary, on or off, which resembles to activation or inactivation of some genes. As the Boolean has only two states, the properties whether multiple Boolean states are converge to some states or show any periodical behaviour are the main interest in analysing the Boolean system. Existing algorithms to reveal these can deal with only small size systems. We develop an algorithm that reduces this limitation significantly by separating original networks into smaller subnetworks and combining each subnetwork analysis. This algorithm only takes a few seconds to reveal all stationary and periodic solutions of T-cell receptor kinetics. Finally, static network analysis provides different levels of robustness of biological systems. Static network is composed of nodes and edges. Nodes represent various molecular species and edges represent direct interaction between two nodes connected. Among many properties in the network, especially, modular or community structure are believed to be the origin of robustness. We studied brain network modular structure to find any differences between socio-economical performance among people. In addition, robustness of modular structure of large-scale networks shows correlation between critical perturbations and drug targets in human protein-protein interactions. The algorithms developed will be further used to expand for our understanding about essential properties of life in future. |
Exploitation Route | Robustness is a fundamental property of nature and human-made systems. Systems that we are interested in most have become large and the large-scale systems are hard to design and analyse. We developed computational methods to efficiently perform these tasks. The results would be the stepping stone towards full understanding of complex large-scale systems. |
Sectors | Aerospace, Defence and Marine,Environment,Healthcare,Manufacturing, including Industrial Biotechology,Pharmaceuticals and Medical Biotechnology,Security and Diplomacy,Transport |
Description | EOARD Research Grant |
Amount | $30,000 (USD) |
Organisation | European Office of Aerospace Research & Development (EOARD) |
Sector | Public |
Country | United Kingdom |
Start | 05/2013 |
End | 04/2014 |
Description | Industrial Secondment |
Amount | £20,000 (GBP) |
Organisation | Royal Academy of Engineering |
Sector | Charity/Non Profit |
Country | United Kingdom |
Start | 07/2012 |
End | 12/2012 |
Description | Research Visiting |
Organisation | Korea Advanced Institute of Science and Technology (KAIST) |
Department | Department of Bio & Brain Engineering |
Country | Korea, Republic of |
Sector | Academic/University |
PI Contribution | I and my RA (Dr Yun-Bo Zhao) provided an expertise in control engineering and dynamic modelling/computation analysis technologies including parallel processing implementation using graphical processing unit. |
Collaborator Contribution | I was invited to KAIST twice between 2009 and 2014 for one month period each. I had established close research collaboration with the members of their teams, whose expertise are in systems biology. I obtained the fundamental knowledge and skills in interpreting biological data. |
Impact | - Low-degree nodes having strong local effects but weak global effects could be drug targets (Poster). The 12th International Conference on Systems Biology, Heidelberg/Mannheim, Germany, 28 Aug.-1 Sept. 2011. - We developed a new research topic in network biology about robustness of community structure initiated 2011 and I was invited as one of the speakers in Gordon Research Conferences, Neuroethology: Behaviour, Evolution & Neurobiology, Networks, Circuits and Module, Mount Snow Resort, West Dover, VT, USA, 18-23rd August, 2013. |
Start Year | 2009 |
Description | Research Visiting to China |
Organisation | Chinese Academy of Mathemetics and Systems Science |
Department | Institute of Systems Science |
Country | China |
Sector | Academic/University |
PI Contribution | Provide systems biology problems for boolean network analysis |
Collaborator Contribution | Provide mathematical techniques for analysing boolean network analysis |
Impact | - First visiting was funded by Royal Academy of Engineering - Inviting a student of Professor Cheng, Yin Zhao, to UK in 2012, which was funded by University of Glasgow - Zhao, Y., Kim, J. and Filippone, M. "Aggregation algorithm towards large-scale Boolean network analysis, IEEE Trans. on Automatic Control, Vol. 58, No. 8, pp. 1976-1985, August, 2013 - Second visiting in 2013 was funded by the Institute in Beijing, China |
Start Year | 2011 |