In this paper, we combine kinetic modelling and patient gene expression data analysis to elucidat... more In this paper, we combine kinetic modelling and patient gene expression data analysis to elucidate biological mechanisms by which melanoma becomes resistant to the immune system and to immunotherapy. To this end, we systematically perturbed the parameters in a kinetic model and performed a mathematical analysis of their impact, thereby obtaining signatures associated with the emergence of phenotypes of melanoma immune sensitivity and resistance. Our phenotypic signatures were compared with published clinical data on pretreatment tumor gene expression in patients subjected to immunotherapy against metastatic melanoma. To this end, the differentially expressed genes were annotated with standard gene ontology terms and aggregated into metagenes. Our method sheds light on putative mechanisms by which melanoma may develop immunoresistance. Precisely, our results and the clinical data point to the existence of a signature of intermediate expression levels for genes related to antigen presentation that constitutes an intriguing resistance mechanism, whereby micrometastases are able to minimize the combined anti-tumor activity of complementary responses mediated by cytotoxic T cells and natural killer cells, respectively. Finally, we computationally explored the efficacy of cytokines used as low-dose co-adjuvants for the therapeutic anticancer vaccine to overcome tumor immunoresistance. In many solid cancer types, the interaction between the tumor and the immune system is a key element governing critical steps in the tumor progression path 1 ; its deep understanding is necessary to design efficient anticancer immunotherapies. In recent times, a number of published works suggest the use of a systemic approach combining quantitative experimental data and mathematical modeling to dissect the tumor-immune system interaction 2,3. However, most of these modelling efforts focus on representing and simulating cell-to-cell processes and do not consider the intracellular networks controlling immune and tumor cells, thereby losing the chance to integrate and analyze omics data on the molecular events underlying the tumor-immunity interaction and the immune-based therapies. The immune system is by definition multi-scale because it involves complex biochemical networks that regulate cell fate across cell boundaries 4 , and also because immune cells communicate with each other by direct contact or through secretion of local or systemic signals 3,6–8. Moreover, immune cells and cancer cells interact, and these interactions are affected by the tumor microenvironment. The complex nature of this tumor-immunity-microenvironment interaction favors and sometimes requires a systemic approach in its analysis 2 .
The authors discuss the role of the Raf kinase inhibitory protein (RKIP) as a modulator of oscill... more The authors discuss the role of the Raf kinase inhibitory protein (RKIP) as a modulator of oscillations in NFB signalling. A mathematical model of the NFB signalling pathway was derived and the Lyapunov-Andronov theory was used to analyse dynamical properties of the system. The analytical results were complemented by predictive numerical simulations. Our results suggest that the nature of oscillations, emerging under sustained stimulation of the system, depends on the interplay between the IB kinase (IKK) stimulation and the inhibitory action of RKIP. The authors found a mathematical relation that defines isoclines in IKK and RKIP levels for which the properties of oscillations are conserved and changes in the stimulation can be compensated by modulating RKIP inhibition. On the other hand, the shifting from the current isocline provokes modulation in either the amplitude (for stronger stimulation) or the frequency (for weaker stimulation).
In this article we present and test a strategy to integrate, in a sequential manner, sensitivity ... more In this article we present and test a strategy to integrate, in a sequential manner, sensitivity analysis, bifurcation analysis and predictive simulations. Our strategy uses some of these methods in a coordinated way such that information, generated in one step, feeds into the definition of further analyses and helps refining the structure of the mathematical model. The aim of the
We develop a multi-level model, using ordinary differential equations, based on quantitative expe... more We develop a multi-level model, using ordinary differential equations, based on quantitative experimental data, accounting for murine erythropoiesis. At the sub-cellular level, the model includes a description of the regulation of red blood cell differentiation through Epo-stimulated JAK2-STAT5 signalling activation, while at the cell population level the model describes the dynamics of (STAT5-mediated) red blood cell differentiation from their progenitors. Furthermore, the model includes equations depicting the hypoxiamediated regulation of hormone erythropoietin blood levels. Take all together, the model constitutes a multi-level, feedback loop-regulated biological system, involving processes in different organs and at different organisational levels.
We consider in this paper a family of modified hyperchaotic Rössler systems and investigate both ... more We consider in this paper a family of modified hyperchaotic Rössler systems and investigate both problems of understanding hyperchaos–chaos–hyperchaos transition and computing the prediction time. These systems were obtained and numerically investigated by Nikolov and Clodong [Nikolov S, Clodong S. Occurrence of regular, chaotic and hyperchaotic behavior in a family of modified Rossler hyperchaotic systems. Chaos, Solitons & Fractals 2004;22:407–31].
Biochimica et Biophysica Acta (BBA) - Proteins and Proteomics, 2014
A decade of successful results indicates that systems biology is the appropriate approach to inve... more A decade of successful results indicates that systems biology is the appropriate approach to investigate the regulation of complex biochemical networks involving transcriptional and post-transcriptional regulations. It becomes mandatory when dealing with highly interconnected biochemical networks, composed of hundreds of compounds, or when networks are enriched in non-linear motifs like feedback and feedforward loops. An emerging dilemma is to conciliate models of massive networks and the adequate description of non-linear dynamics in a suitable modeling framework. Boolean networks are an ideal representation of massive networks that are humble in terms of computational complexity and data demand. However, they are inappropriate when dealing with nested feedback/feedforward loops, structural motifs common in biochemical networks. On the other hand, models of ordinary differential equations (ODEs) cope well with these loops, but they require enormous amounts of quantitative data for a full characterization of the model. Here we propose hybrid models, composed of ODE and logical sub-modules, as a strategy to handle large scale, non-linear biochemical networks that include transcriptional and post-transcriptional regulations. We illustrate the construction of this kind of models using as example a regulatory network centered on E2F1, a transcription factor involved in cancer. The hybrid modeling approach proposed is a good compromise between quantitative/qualitative accuracy and scalability when considering large biochemical networks with a small highly interconnected core, and module of transcriptionally regulated genes that are not part of critical regulatory loops. This article is part of a Special Issue entitled: Computational Proteomics, Systems Biology & Clinical Implications. Guest Editor: Yudong Cai.
Q1 A number of experiments have shown that p53 expression levels can display oscillatory behaviou... more Q1 A number of experiments have shown that p53 expression levels can display oscillatory behaviour in response to certain stress signals. Mathematical modelling has been used to investigate these dynamics, but these studies mostly focused on the analysis of p53 alone and very little has been discussed about the effects of p53 oscillations on downstream molecules and pathways. In this work, mathematical modelling and bifurcation analysis are combined to investigate under which conditions the oscillation of p53 could propagate to its direct downstream transcription targets. The authors' model analysis suggests that oscillations of p53 will propagate only to proteins with medium-fast mRNA and protein turnover rates. The authors, furthermore, retrieved data concerning the half-life of messenger RNA and protein for a number of p53-promoted genes and found that, according to their model, most of them are not able to inherit the oscillation of p53 because of their slow turnover rates for both mRNA and protein levels. However, their analysis indicates that p53 oscillation may actually fine-tune the expression pattern of a protein when it is integrated with a second oscillatory signal. The authors also consider the case of additional regulatory loops affecting p53 oscillations and which involve proteins transcriptionally induced by p53. This is the case for 14-3-3s, a protein that targets MDM2, the key negative regulator p53, for enhanced degradation. Their analytical and numerical results suggest that the addition of feedback-loop regulation, like the one exerted by 14-3-3s, may modulate basic properties of p53 oscillation and induce quick cessation of them under certain physiological conditions. Moreover, their analysis suggests that the interplay between DNA damage level and 14-3-3s regulation may induce bistability in the oscillation of p53.
In this paper, we combine kinetic modelling and patient gene expression data analysis to elucidat... more In this paper, we combine kinetic modelling and patient gene expression data analysis to elucidate biological mechanisms by which melanoma becomes resistant to the immune system and to immunotherapy. To this end, we systematically perturbed the parameters in a kinetic model and performed a mathematical analysis of their impact, thereby obtaining signatures associated with the emergence of phenotypes of melanoma immune sensitivity and resistance. Our phenotypic signatures were compared with published clinical data on pretreatment tumor gene expression in patients subjected to immunotherapy against metastatic melanoma. To this end, the differentially expressed genes were annotated with standard gene ontology terms and aggregated into metagenes. Our method sheds light on putative mechanisms by which melanoma may develop immunoresistance. Precisely, our results and the clinical data point to the existence of a signature of intermediate expression levels for genes related to antigen presentation that constitutes an intriguing resistance mechanism, whereby micrometastases are able to minimize the combined anti-tumor activity of complementary responses mediated by cytotoxic T cells and natural killer cells, respectively. Finally, we computationally explored the efficacy of cytokines used as low-dose co-adjuvants for the therapeutic anticancer vaccine to overcome tumor immunoresistance. In many solid cancer types, the interaction between the tumor and the immune system is a key element governing critical steps in the tumor progression path 1 ; its deep understanding is necessary to design efficient anticancer immunotherapies. In recent times, a number of published works suggest the use of a systemic approach combining quantitative experimental data and mathematical modeling to dissect the tumor-immune system interaction 2,3. However, most of these modelling efforts focus on representing and simulating cell-to-cell processes and do not consider the intracellular networks controlling immune and tumor cells, thereby losing the chance to integrate and analyze omics data on the molecular events underlying the tumor-immunity interaction and the immune-based therapies. The immune system is by definition multi-scale because it involves complex biochemical networks that regulate cell fate across cell boundaries 4 , and also because immune cells communicate with each other by direct contact or through secretion of local or systemic signals 3,6–8. Moreover, immune cells and cancer cells interact, and these interactions are affected by the tumor microenvironment. The complex nature of this tumor-immunity-microenvironment interaction favors and sometimes requires a systemic approach in its analysis 2 .
The authors discuss the role of the Raf kinase inhibitory protein (RKIP) as a modulator of oscill... more The authors discuss the role of the Raf kinase inhibitory protein (RKIP) as a modulator of oscillations in NFB signalling. A mathematical model of the NFB signalling pathway was derived and the Lyapunov-Andronov theory was used to analyse dynamical properties of the system. The analytical results were complemented by predictive numerical simulations. Our results suggest that the nature of oscillations, emerging under sustained stimulation of the system, depends on the interplay between the IB kinase (IKK) stimulation and the inhibitory action of RKIP. The authors found a mathematical relation that defines isoclines in IKK and RKIP levels for which the properties of oscillations are conserved and changes in the stimulation can be compensated by modulating RKIP inhibition. On the other hand, the shifting from the current isocline provokes modulation in either the amplitude (for stronger stimulation) or the frequency (for weaker stimulation).
In this article we present and test a strategy to integrate, in a sequential manner, sensitivity ... more In this article we present and test a strategy to integrate, in a sequential manner, sensitivity analysis, bifurcation analysis and predictive simulations. Our strategy uses some of these methods in a coordinated way such that information, generated in one step, feeds into the definition of further analyses and helps refining the structure of the mathematical model. The aim of the
We develop a multi-level model, using ordinary differential equations, based on quantitative expe... more We develop a multi-level model, using ordinary differential equations, based on quantitative experimental data, accounting for murine erythropoiesis. At the sub-cellular level, the model includes a description of the regulation of red blood cell differentiation through Epo-stimulated JAK2-STAT5 signalling activation, while at the cell population level the model describes the dynamics of (STAT5-mediated) red blood cell differentiation from their progenitors. Furthermore, the model includes equations depicting the hypoxiamediated regulation of hormone erythropoietin blood levels. Take all together, the model constitutes a multi-level, feedback loop-regulated biological system, involving processes in different organs and at different organisational levels.
We consider in this paper a family of modified hyperchaotic Rössler systems and investigate both ... more We consider in this paper a family of modified hyperchaotic Rössler systems and investigate both problems of understanding hyperchaos–chaos–hyperchaos transition and computing the prediction time. These systems were obtained and numerically investigated by Nikolov and Clodong [Nikolov S, Clodong S. Occurrence of regular, chaotic and hyperchaotic behavior in a family of modified Rossler hyperchaotic systems. Chaos, Solitons & Fractals 2004;22:407–31].
Biochimica et Biophysica Acta (BBA) - Proteins and Proteomics, 2014
A decade of successful results indicates that systems biology is the appropriate approach to inve... more A decade of successful results indicates that systems biology is the appropriate approach to investigate the regulation of complex biochemical networks involving transcriptional and post-transcriptional regulations. It becomes mandatory when dealing with highly interconnected biochemical networks, composed of hundreds of compounds, or when networks are enriched in non-linear motifs like feedback and feedforward loops. An emerging dilemma is to conciliate models of massive networks and the adequate description of non-linear dynamics in a suitable modeling framework. Boolean networks are an ideal representation of massive networks that are humble in terms of computational complexity and data demand. However, they are inappropriate when dealing with nested feedback/feedforward loops, structural motifs common in biochemical networks. On the other hand, models of ordinary differential equations (ODEs) cope well with these loops, but they require enormous amounts of quantitative data for a full characterization of the model. Here we propose hybrid models, composed of ODE and logical sub-modules, as a strategy to handle large scale, non-linear biochemical networks that include transcriptional and post-transcriptional regulations. We illustrate the construction of this kind of models using as example a regulatory network centered on E2F1, a transcription factor involved in cancer. The hybrid modeling approach proposed is a good compromise between quantitative/qualitative accuracy and scalability when considering large biochemical networks with a small highly interconnected core, and module of transcriptionally regulated genes that are not part of critical regulatory loops. This article is part of a Special Issue entitled: Computational Proteomics, Systems Biology & Clinical Implications. Guest Editor: Yudong Cai.
Q1 A number of experiments have shown that p53 expression levels can display oscillatory behaviou... more Q1 A number of experiments have shown that p53 expression levels can display oscillatory behaviour in response to certain stress signals. Mathematical modelling has been used to investigate these dynamics, but these studies mostly focused on the analysis of p53 alone and very little has been discussed about the effects of p53 oscillations on downstream molecules and pathways. In this work, mathematical modelling and bifurcation analysis are combined to investigate under which conditions the oscillation of p53 could propagate to its direct downstream transcription targets. The authors' model analysis suggests that oscillations of p53 will propagate only to proteins with medium-fast mRNA and protein turnover rates. The authors, furthermore, retrieved data concerning the half-life of messenger RNA and protein for a number of p53-promoted genes and found that, according to their model, most of them are not able to inherit the oscillation of p53 because of their slow turnover rates for both mRNA and protein levels. However, their analysis indicates that p53 oscillation may actually fine-tune the expression pattern of a protein when it is integrated with a second oscillatory signal. The authors also consider the case of additional regulatory loops affecting p53 oscillations and which involve proteins transcriptionally induced by p53. This is the case for 14-3-3s, a protein that targets MDM2, the key negative regulator p53, for enhanced degradation. Their analytical and numerical results suggest that the addition of feedback-loop regulation, like the one exerted by 14-3-3s, may modulate basic properties of p53 oscillation and induce quick cessation of them under certain physiological conditions. Moreover, their analysis suggests that the interplay between DNA damage level and 14-3-3s regulation may induce bistability in the oscillation of p53.
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Papers by S. Nikolov