Recent advances in high-throughput technologies for biological data acquisition have spurred a br... more Recent advances in high-throughput technologies for biological data acquisition have spurred a broad interest in the development of mathematical models for biological phenomena. S-systems, which offer a good compromise between accuracy and mathematical flexibility, are a promising framework for modeling the dynamical behavior of genetic regulatory networks (GRNs), as well as that of biochemical pathways. In the S-system modeling framework,
Recent years have witnessed extensive research activity in modeling genetic regulatory networks (... more Recent years have witnessed extensive research activity in modeling genetic regulatory networks (GRNs) as well as in developing therapeutic intervention strategies for such networks. S-systems, which offer a good compromise between accuracy and mathematical flexibility, are a promising framework for modeling the dynamical behavior of GRNs, as well as that of biochemical pathways. In this paper, an intervention strategy is
Proceedings of 1995 34th IEEE Conference on Decision and Control, 1995
The Hermite Biehler theorem gives necessary and sufficient conditions for Hurwitz stability of a ... more The Hermite Biehler theorem gives necessary and sufficient conditions for Hurwitz stability of a polynomial in terms of certain interlacing conditions. In the present paper, the authors generalize the Hermite Biehler theorem to situations where the test polynomial is not necessarily stable, by studying the phase properties of the “frequency response” of a polynomial. Examples are used throughout the paper
The Hermite±Biehler theorem gives necessary and sucient conditions for the Hurwitz stability of a... more The Hermite±Biehler theorem gives necessary and sucient conditions for the Hurwitz stability of a polynomial in terms of certain interlacing conditions. In this paper, we generalize the Hermite±Biehler theorem to situations where the test polynomial is not necessarily Hurwitz. The generalization is given in terms of an analytical expression for the dierence between the numbers of roots of the polynomial in the open left-half and open right-half planes. The result can be used to solve important stabilization problems in control theory and is, therefore, of both academic as well as practical interest. Ó 0024-3795/99/$ -see front matter Ó 1999 Elsevier Science Inc. All rights reserved. PII: S 0 0 2 4 -3 7 9 5 ( 9 9 ) 0 0 0 6 9 -5 Linear Algebra and its Applications 302±303 (1999) 135±153
IEEE Journal of Biomedical and Health Informatics, 2014
The uncontrolled cell proliferation that is characteristically associated with cancer is usually ... more The uncontrolled cell proliferation that is characteristically associated with cancer is usually accompanied by alterations in the genome and cell metabolism. Indeed, the phenomenon of cancer cells metabolizing glucose using a less efficient anaerobic process even in the presence of normal oxygen levels, termed the Warburg effect, is currently considered to be one of the hallmarks of cancer. Diabetes, much like cancer, is defined by significant metabolic changes. Recent epidemiological studies have shown that diabetes patients treated with the antidiabetic drug Metformin, have significantly lowered risk of cancer as compared to patients treated with other anti-diabetic drugs. We utilize a Boolean logic model of the pathways commonly mutated in cancer to not only investigate the efficacy of Metformin for cancer therapeutic purposes but also demonstrate how Metformin in concert with other cancer drugs could provide better and less toxic clinical outcomes as compared to using cancer drugs alone.
ABSTRACT Oxidative stress is a consequence of normal cellular metabolism. The effective functioni... more ABSTRACT Oxidative stress is a consequence of normal cellular metabolism. The effective functioning of the pathway responding to oxidative stress protects the cellular DNA against oxidative damage and its failure can induce aberrant cellular behaviour leading to diseases such as neurodegenerative disorders and cancer. Thus, understanding the normal signalling present in oxidative stress response pathways and determining possible signalling alterations leading to disease could provide us with useful pointers for therapeutic purposes. Using knowledge of oxidative stress response pathways from the literature, a Boolean network model is developed whose simulated behaviour is consistent with earlier experimental observations from the literature.
The Hermite±Biehler theorem gives necessary and sucient conditions for the Hurwitz stability of a... more The Hermite±Biehler theorem gives necessary and sucient conditions for the Hurwitz stability of a polynomial in terms of certain interlacing conditions. In this paper, we generalize the Hermite±Biehler theorem to situations where the test polynomial is not necessarily Hurwitz. The generalization is given in terms of an analytical expression for the dierence between the numbers of roots of the polynomial in the open left-half and open right-half planes. The result can be used to solve important stabilization problems in control theory and is, therefore, of both academic as well as practical interest. Ó 0024-3795/99/$ -see front matter Ó 1999 Elsevier Science Inc. All rights reserved. PII: S 0 0 2 4 -3 7 9 5 ( 9 9 ) 0 0 0 6 9 -5 Linear Algebra and its Applications 302±303 (1999) 135±153
Intervention in a gene regulatory network is used to help it avoid undesirable states, such as th... more Intervention in a gene regulatory network is used to help it avoid undesirable states, such as those associated with a disease. Several types of intervention have been studied in the framework of a probabilistic Boolean network (PBN), which is essentially a finite collection of Boolean networks in which at any discrete time point the gene state vector transitions according to the rules of one of the constituent networks. For an instantaneously random PBN, the governing Boolean network is randomly chosen at each time point. For a context-sensitive PBN, the governing Boolean network remains fixed for an interval of time until a binary random variable determines a switch. The theory of automatic control has been previously applied to find optimal strategies for manipulating external (control) variables that affect the transition probabilities of an instantaneously random PBN to desirably affect its dynamic evolution over a finite time horizon. This paper discusses the extension of external control to context-sensitive PBNs.
Recent advances in high-throughput technologies for biological data acquisition have spurred a br... more Recent advances in high-throughput technologies for biological data acquisition have spurred a broad interest in the development of mathematical models for biological phenomena. S-systems, which offer a good compromise between accuracy and mathematical flexibility, are a promising framework for modeling the dynamical behavior of genetic regulatory networks (GRNs), as well as that of biochemical pathways. In the S-system modeling framework,
Recent years have witnessed extensive research activity in modeling genetic regulatory networks (... more Recent years have witnessed extensive research activity in modeling genetic regulatory networks (GRNs) as well as in developing therapeutic intervention strategies for such networks. S-systems, which offer a good compromise between accuracy and mathematical flexibility, are a promising framework for modeling the dynamical behavior of GRNs, as well as that of biochemical pathways. In this paper, an intervention strategy is
Proceedings of 1995 34th IEEE Conference on Decision and Control, 1995
The Hermite Biehler theorem gives necessary and sufficient conditions for Hurwitz stability of a ... more The Hermite Biehler theorem gives necessary and sufficient conditions for Hurwitz stability of a polynomial in terms of certain interlacing conditions. In the present paper, the authors generalize the Hermite Biehler theorem to situations where the test polynomial is not necessarily stable, by studying the phase properties of the “frequency response” of a polynomial. Examples are used throughout the paper
The Hermite±Biehler theorem gives necessary and sucient conditions for the Hurwitz stability of a... more The Hermite±Biehler theorem gives necessary and sucient conditions for the Hurwitz stability of a polynomial in terms of certain interlacing conditions. In this paper, we generalize the Hermite±Biehler theorem to situations where the test polynomial is not necessarily Hurwitz. The generalization is given in terms of an analytical expression for the dierence between the numbers of roots of the polynomial in the open left-half and open right-half planes. The result can be used to solve important stabilization problems in control theory and is, therefore, of both academic as well as practical interest. Ó 0024-3795/99/$ -see front matter Ó 1999 Elsevier Science Inc. All rights reserved. PII: S 0 0 2 4 -3 7 9 5 ( 9 9 ) 0 0 0 6 9 -5 Linear Algebra and its Applications 302±303 (1999) 135±153
IEEE Journal of Biomedical and Health Informatics, 2014
The uncontrolled cell proliferation that is characteristically associated with cancer is usually ... more The uncontrolled cell proliferation that is characteristically associated with cancer is usually accompanied by alterations in the genome and cell metabolism. Indeed, the phenomenon of cancer cells metabolizing glucose using a less efficient anaerobic process even in the presence of normal oxygen levels, termed the Warburg effect, is currently considered to be one of the hallmarks of cancer. Diabetes, much like cancer, is defined by significant metabolic changes. Recent epidemiological studies have shown that diabetes patients treated with the antidiabetic drug Metformin, have significantly lowered risk of cancer as compared to patients treated with other anti-diabetic drugs. We utilize a Boolean logic model of the pathways commonly mutated in cancer to not only investigate the efficacy of Metformin for cancer therapeutic purposes but also demonstrate how Metformin in concert with other cancer drugs could provide better and less toxic clinical outcomes as compared to using cancer drugs alone.
ABSTRACT Oxidative stress is a consequence of normal cellular metabolism. The effective functioni... more ABSTRACT Oxidative stress is a consequence of normal cellular metabolism. The effective functioning of the pathway responding to oxidative stress protects the cellular DNA against oxidative damage and its failure can induce aberrant cellular behaviour leading to diseases such as neurodegenerative disorders and cancer. Thus, understanding the normal signalling present in oxidative stress response pathways and determining possible signalling alterations leading to disease could provide us with useful pointers for therapeutic purposes. Using knowledge of oxidative stress response pathways from the literature, a Boolean network model is developed whose simulated behaviour is consistent with earlier experimental observations from the literature.
The Hermite±Biehler theorem gives necessary and sucient conditions for the Hurwitz stability of a... more The Hermite±Biehler theorem gives necessary and sucient conditions for the Hurwitz stability of a polynomial in terms of certain interlacing conditions. In this paper, we generalize the Hermite±Biehler theorem to situations where the test polynomial is not necessarily Hurwitz. The generalization is given in terms of an analytical expression for the dierence between the numbers of roots of the polynomial in the open left-half and open right-half planes. The result can be used to solve important stabilization problems in control theory and is, therefore, of both academic as well as practical interest. Ó 0024-3795/99/$ -see front matter Ó 1999 Elsevier Science Inc. All rights reserved. PII: S 0 0 2 4 -3 7 9 5 ( 9 9 ) 0 0 0 6 9 -5 Linear Algebra and its Applications 302±303 (1999) 135±153
Intervention in a gene regulatory network is used to help it avoid undesirable states, such as th... more Intervention in a gene regulatory network is used to help it avoid undesirable states, such as those associated with a disease. Several types of intervention have been studied in the framework of a probabilistic Boolean network (PBN), which is essentially a finite collection of Boolean networks in which at any discrete time point the gene state vector transitions according to the rules of one of the constituent networks. For an instantaneously random PBN, the governing Boolean network is randomly chosen at each time point. For a context-sensitive PBN, the governing Boolean network remains fixed for an interval of time until a binary random variable determines a switch. The theory of automatic control has been previously applied to find optimal strategies for manipulating external (control) variables that affect the transition probabilities of an instantaneously random PBN to desirably affect its dynamic evolution over a finite time horizon. This paper discusses the extension of external control to context-sensitive PBNs.
Uploads
Papers by Aniruddha Datta