Low-dimensional negative feedback systems (NFSs) were developed within a signal flow model to describe the oscillatory activities of NF-kB caused by interactions with its inhibitor IkBa. The NFSs were established as 3rd- and 4th-order... more
Low-dimensional negative feedback systems (NFSs) were developed within a signal flow model to describe the oscillatory activities of NF-kB caused by interactions with its inhibitor IkBa. The NFSs were established as 3rd- and 4th-order linear systems containing unperturbed and perturbed negative feedback (NF) loops with constant or time-varying NF strengths and a feed-forward loop. NF-related analytical solutions to the NFSs representing the time courses of NF-kB and IkBa were determined and their exact mathematical relationship was found.
The NFS’s parameters were determined to fit the experimental time courses of NF-kB in TNF-a-stimulated embryonic fibroblasts, rela-/- embryonic fibroblasts reconstituted with RelA, C9L cells, GFP-p65 knock-in embryonic fibroblasts and embryogenic fibroblasts lacking IkBb and IkBe, LPS-stimulated IC-21 macrophages treated or not with DCPA, and anti-IgM-stimulated DT40 B-lymphocytes. The unperturbed and perturbed NFSs describing the above biosystems generated isochronous and non-isochronous solutions, depending on a constant or time-varying NF strength, respectively.
The oscillation period of the NF-coupled solutions, the phase difference between them and the time delays in the appearance of cytoplasmic IkBa after stimulation of NF-kB were determined. A significant divergence between the IkBa solutions to the NFSs and the IkBa experimental courses led to a rejection of the NF coupling between NF-kB and IkBa in the above biosystems. It was shown that neither the linearity nor the low dimensionality of the NFSs altered the NF relationship and the divergence between the IkBa solutions to the NFS and IkBa experimental time courses. Although the NF relationship between IkBa and NF-kB was not confirmed in all the experimental data analysed, delayed negative feedback was found in some cases.
The NFS’s parameters were determined to fit the experimental time courses of NF-kB in TNF-a-stimulated embryonic fibroblasts, rela-/- embryonic fibroblasts reconstituted with RelA, C9L cells, GFP-p65 knock-in embryonic fibroblasts and embryogenic fibroblasts lacking IkBb and IkBe, LPS-stimulated IC-21 macrophages treated or not with DCPA, and anti-IgM-stimulated DT40 B-lymphocytes. The unperturbed and perturbed NFSs describing the above biosystems generated isochronous and non-isochronous solutions, depending on a constant or time-varying NF strength, respectively.
The oscillation period of the NF-coupled solutions, the phase difference between them and the time delays in the appearance of cytoplasmic IkBa after stimulation of NF-kB were determined. A significant divergence between the IkBa solutions to the NFSs and the IkBa experimental courses led to a rejection of the NF coupling between NF-kB and IkBa in the above biosystems. It was shown that neither the linearity nor the low dimensionality of the NFSs altered the NF relationship and the divergence between the IkBa solutions to the NFS and IkBa experimental time courses. Although the NF relationship between IkBa and NF-kB was not confirmed in all the experimental data analysed, delayed negative feedback was found in some cases.
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<jats:p>The coupled uniform sequential reaction systems (CUSERS) model, which allows for determining the structure of signaling pathways with incomplete information from the temporal patterns of their components, was applied to the... more
<jats:p>The coupled uniform sequential reaction systems (CUSERS) model, which allows for determining the structure of signaling pathways with incomplete information from the temporal patterns of their components, was applied to the experimental records of activities of TLR4 downstream species IKK and NF-<jats:italic>κ</jats:italic>B in LPS-stimulated wild-type (WT), MyD88-deficient and TRIF-deficient macrophages. New signaling pathways targeting IKK were revealed in MyD88-deficient and TRIF-deficient macrophages, and shown to be described by the coupled systems formed by 3- and 5-component or 5- and 10-component pathways, respectively. By comparing the temporal pattern of IKK in WT macrophages with those in MyD88-deficient and TRIF-deficient macrophages, two new signaling pathways, which were absent in the above defective macrophages, were found and described by a system formed by coupling 9- and 10-component pathways. As a direct consequence of the above findings, a coupled system composed of six different 3-, 5-, 5-, 9-, 10- and 10-component pathways targeting IKK and describing its temporal pattern, IKK(<jats:italic>f</jats:italic>), in WT macrophages was constructed. This system significantly modifies the canonical NF-<jats:italic>κ</jats:italic>B signaling by introducing novel pathways of IKK activation. The expression of nuclear NF-<jats:italic>κ</jats:italic>B in WT macrophages was found to depend on two different signaling pathways and to be modelled by a coupled system composed of 1- and 4-component or 2- and 8-component pathways, in dependence on sampling frequencies used in different experiments. From the three-modal NF-<jats:italic>κ</jats:italic>B(<jats:italic>t</jats:italic>) temporal pattern in LPS-stimulated WT fibroblasts, three 1-, 12- and 17-component signaling pathways targeting nuclear NF-<jats:italic>κ</jats:italic>B were determined.</jats:p>
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ABSTRACT
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A control of the first‐line human defence system, using mechanisms analogous to specific and non‐specific (parametric) triggering of phagocytosis, is proposed on the basis of an autocatalytic model of biphasic modulation of phagocyte... more
A control of the first‐line human defence system, using mechanisms analogous to specific and non‐specific (parametric) triggering of phagocytosis, is proposed on the basis of an autocatalytic model of biphasic modulation of phagocyte luminescence by experimental peptide medicines. Properties of the autocatalytic model are described and its catastrophe and bifurcation sets determined. The mechanism analogous to parametric triggering is shown to result from a fold catastrophe produced by the changes in the autocatalytic interaction parameter characterising a given peptide preparation. Usefulness of the model was shown by its application to two distinct peptide preparations having different immunomodulatory properties.
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A novel mathematical model for determining the forms of signaling pathways, ranging from linear structures to networks, on the basis of single-mode and multimodal time courses of immune responses under the condition of incomplete... more
A novel mathematical model for determining the forms of signaling pathways, ranging from linear structures to networks, on the basis of single-mode and multimodal time courses of immune responses under the condition of incomplete information, was elaborated. The subcellular immune processes and systems lacking the kinetic parameters still remain, in general, undetermined by deterministic quantitative models, which has resulted in the resignation from these models in favor of the so-called kinetically agnostic models. The model proposed in this paper intends to give a deterministic description of signaling pathways implicated in immune responses with unknown kinetic parameters. To do that, uniform sequential reaction systems and coupled sequential reaction systems were constructed using systems of differential equations and the novel notions of uniform functions, transition, coupling and branch operations founded on the assumptions of a uniform distribution of unknown rate constants, mass action kinetics, and first-order kinetics. Reaction step-dependent analytical solutions to the uniform sequential systems were expressed by the means of the incomplete gamma function and unambiguously characterized using, amongst others, the Lambert W function, which were necessary to obtain strict analytical solutions to those systems. These systems were validated by comparing their solutions with those obtained for ordinary sequential systems, regarded as the systems with complete information. The numerical solutions to the uniform sequential systems obtained by the Lederberg-Marquardt method were compared with those obtained by the Lambert W function. The signaling pathways were determined by analyzing the uniform sequential and coupled sequential reaction systems that describe the time courses of multimodal immune responses. Bi- and tri-modal immune processes representing temporal expressions of the transcription factor T-bet, the IL-12Rβ2 receptor, the IL-4, Tbx21 and Twist1 genes—all in helper T cells, calcium ion in 2G12.1 T cell hybridoma, c-Fos sumoylation in serum-stimulated HeLa cells, and IFN-γ-secreting cytotoxic T cells were modeled. Application of the coupled uniform sequential systems to the above immune processes allowed accurate approximations of their time behavior and to determine the structures of the signaling pathways and to predict some. A notion of the fractional reaction step, and its meaning in revealing the coupled sequential systems behind the seeming sequential ones, was introduced and analyzed. A consistent approach to the different forms of signaling pathways, beginning from the linear sequential systems through coupled (nonlinear) sequential ones to networks, was presented together with an algebraic insight into those systems.
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A chemiluminescence (CL) study of diphenyleneiodonium-inhibited NADPH oxidase was performed on a cellular system containing neutrophils stimulated by phorbol myristate acetate, indicating a complex bimodal structure of CL processes... more
A chemiluminescence (CL) study of diphenyleneiodonium-inhibited NADPH oxidase was performed on a cellular system containing neutrophils stimulated by phorbol myristate acetate, indicating a complex bimodal structure of CL processes corresponding to different stages of the inhibition. The complex structure of these processes was described by a superposition of two logistic-exponential (LE) models, characterizing these processes as bimodal ones. To determine the mechanistic foundation of the LE model-described processes, a generalized form of the second-order dynamic system of CL reactions, the solution to which corresponds to the LE model, was constructed. The diphenyleneiodonium effects on neutrophil NADPH oxidase were separated from the total bimodal CL of the whole measurement system by the use of difference CL processes. These difference processes were also found to be bimodal; thus, inhibitor-induced reduction of CL could be described by a second-order dynamic system. The rate constants and initial concentrations in this dynamic system were determined by the least squares method applied to numerical solutions approximating the difference processes. Using interrelations between the parameters of the dynamic system, cooperative effects in the inhibitor reactions with NADPH oxidase were found and described quantitatively. Other evidences of cooperativity were obtained from integral characteristics of the CL reduction process, i.e. dose-response and progress curves, determined by numerical integration of the LE models constituting the superposition. On this basis, it was also possible to detect a specific binding of the inhibitor to the enzyme. Finally, putative reaction mechanisms suggested by the model obtained were considered and compared with those known at present.
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Research Interests: Medicine and Luminescence
Shows how the essential ecotoxicological question of constructing a quantitative model of the interactions between environmental stress factors, and their synergistic effects resulting in a biosystem's perturbation, even in its... more
Shows how the essential ecotoxicological question of constructing a quantitative model of the interactions between environmental stress factors, and their synergistic effects resulting in a biosystem's perturbation, even in its pathology, has been formulated from a systemic viewpoint. The proposed model has been developed on the basis of the multicorrelational structure of heavy‐metal concentrations in the blood of pregnant women with a high environmental exposure to those metals. The proposed model uses an original notion of the interaction which allows one to find and explain the observed connection between the phenomenon of spontaneous abortion as an environmentally induced foetal pathology and some heavy metals, particularly cadmium and lead.
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Research Interests: Medicine and Luminescence
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<jats:p>The coupled uniform sequential reaction systems (CUSERS) model, which allows for determining the structure of signaling pathways with incomplete information from the temporal patterns of their components, was applied to the... more
<jats:p>The coupled uniform sequential reaction systems (CUSERS) model, which allows for determining the structure of signaling pathways with incomplete information from the temporal patterns of their components, was applied to the experimental records of activities of TLR4 downstream species IKK and NF-<jats:italic>κ</jats:italic>B in LPS-stimulated wild-type (WT), MyD88-deficient and TRIF-deficient macrophages. New signaling pathways targeting IKK were revealed in MyD88-deficient and TRIF-deficient macrophages, and shown to be described by the coupled systems formed by 3- and 5-component or 5- and 10-component pathways, respectively. By comparing the temporal pattern of IKK in WT macrophages with those in MyD88-deficient and TRIF-deficient macrophages, two new signaling pathways, which were absent in the above defective macrophages, were found and described by a system formed by coupling 9- and 10-component pathways. As a direct consequence of the above findings, a coupled system composed of six different 3-, 5-, 5-, 9-, 10- and 10-component pathways targeting IKK and describing its temporal pattern, IKK(<jats:italic>f</jats:italic>), in WT macrophages was constructed. This system significantly modifies the canonical NF-<jats:italic>κ</jats:italic>B signaling by introducing novel pathways of IKK activation. The expression of nuclear NF-<jats:italic>κ</jats:italic>B in WT macrophages was found to depend on two different signaling pathways and to be modelled by a coupled system composed of 1- and 4-component or 2- and 8-component pathways, in dependence on sampling frequencies used in different experiments. From the three-modal NF-<jats:italic>κ</jats:italic>B(<jats:italic>t</jats:italic>) temporal pattern in LPS-stimulated WT fibroblasts, three 1-, 12- and 17-component signaling pathways targeting nuclear NF-<jats:italic>κ</jats:italic>B were determined.</jats:p>
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A novel mathematical model for determining the forms of signaling pathways, ranging from linear structures to networks, on the basis of single-mode and multimodal time courses of immune responses under the condition of incomplete... more
A novel mathematical model for determining the forms of signaling pathways, ranging from linear structures to networks, on the basis of single-mode and multimodal time courses of immune responses under the condition of incomplete information, was elaborated. The subcellular immune processes and systems lacking the kinetic parameters still remain, in general, undetermined by deterministic quantitative models, which has resulted in the resignation from these models in favor of the so-called kinetically agnostic models. The model proposed in this paper intends to give a deterministic description of signaling pathways implicated in immune responses with unknown kinetic parameters. To do that, uniform sequential reaction systems and coupled sequential reaction systems were constructed using systems of differential equations and the novel notions of uniform functions, transition, coupling and branch operations founded on the assumptions of a uniform distribution of unknown rate constants,...
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A control of the first-line human defence system, using mechanisms analogous to specific and non-specific (parametric) triggering of phagocytosis, is proposed on the basis of an autocatalytic model of biphasic modulation of phagocyte... more
A control of the first-line human defence system, using mechanisms analogous to specific and non-specific (parametric) triggering of phagocytosis, is proposed on the basis of an autocatalytic model of biphasic modulation of phagocyte luminescence by experimental peptide medicines. Properties of the autocatalytic model are described and its catastrophe and bifurcation sets determined. The mechanism analogous to parametric triggering is shown to result from a fold catastrophe produced by the changes in the autocatalytic interaction parameter characterising a given peptide preparation. Usefulness of the model was shown by its application to two distinct peptide preparations having different immunomodulatory properties.
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A method for approximation of the Shannon entropy of Gaussian photon-counting processes with infinite history was constructed on the memory function of these processes, described by autoregressive-integrated moving average (ARIMA) models.... more
A method for approximation of the Shannon entropy of Gaussian photon-counting processes with infinite history was constructed on the memory function of these processes, described by autoregressive-integrated moving average (ARIMA) models. Most frequently, photon-counting processes are stationary or nonstationary multidimensional Gaussian discrete-time stochastic ones which justify the use of the ARIMA models. Starting from the memory function, a memory time-equivalent
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A chemiluminescence (CL) study of diphenyleneiodonium-inhibited NADPH oxidase was performed on a cellular system containing neutrophils stimulated by phorbol myristate acetate, indicating a complex bimodal structure of CL processes... more
A chemiluminescence (CL) study of diphenyleneiodonium-inhibited NADPH oxidase was performed on a cellular system containing neutrophils stimulated by phorbol myristate acetate, indicating a complex bimodal structure of CL processes corresponding to different stages of the inhibition. The complex structure of these processes was described by a superposition of two logistic-exponential (LE) models, characterizing these processes as bimodal ones. To determine the mechanistic foundation of the LE model-described processes, a generalized form of the second-order dynamic system of CL reactions, the solution to which corresponds to the LE model, was constructed. The diphenyleneiodonium effects on neutrophil NADPH oxidase were separated from the total bimodal CL of the whole measurement system by the use of difference CL processes. These difference processes were also found to be bimodal; thus, inhibitor-induced reduction of CL could be described by a second-order dynamic system. The rate constants and initial concentrations in this dynamic system were determined by the least squares method applied to numerical solutions approximating the difference processes. Using interrelations between the parameters of the dynamic system, cooperative effects in the inhibitor reactions with NADPH oxidase were found and described quantitatively. Other evidences of cooperativity were obtained from integral characteristics of the CL reduction process, i.e. dose-response and progress curves, determined by numerical integration of the LE models constituting the superposition. On this basis, it was also possible to detect a specific binding of the inhibitor to the enzyme. Finally, putative reaction mechanisms suggested by the model obtained were considered and compared with those known at present.