THERMODYNAMIC TRANSITIONS ON METABOLISM AND …€¦ · THERMODYNAMIC TRANSITIONS ON METABOLISM AND...
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THERMODYNAMIC TRANSITIONS ON METABOLISM AND PROLIFERATION OF GLUCOCORTICOID-TREATED ACUTE LEUKEMIA CELLS George I. Lambrou 1 , Aristotelis Chatziioannou 2 , Apostolos Zaravinos 3 , Theodoros Karakonstantakis 4 , Maria Adamaki 1 , Maria Braoudaki 1 and Spiros A. Vlahopoulos 1 1 1 st Department of Pediatrics, University of Athens, Thivon & Levadeias, 11527 Goudi, Athens; 2 Institute of Biological Research & Biotechnology, National Hellenic Research Foundation, 48 Vassileos Constantinou Av., Athens, Greece; 3 Molecular Medicine Research Center and Laboratory of Molecular and Medical Genetics; Department of Biological Sciences; University of Cyprus; 1678, Nicosia, Cyprus; 4 Aghia Sofia Children’s Hospital, Biochemical Department, Thivon Str. 11527, Athens-Goudi, Greece. INTRODUCTION AIM OF STUDY Glucocorticoids play an essential part in anti-leukemic therapies. Resistance is considered crucial for disease prognosis. Glucocorticoids influence the metabolic properties of the leukemic cells. We have previously shown that glucocorticoid treatment in low concentrations manifests a mitogenic effect. A critical established action of glucocorticoid treatment is its apoptotic effect on leukemic cells. However, little is known about the molecular response of malignant cells following exposure to glucocorticoids. Even less is known about the cell proliferation dynamics governing leukemic cells under glucocorticoid influence. Growth and metabolic features are assumed to be of nonlinear nature. A model based prediction of glucocorticoid effects is derived by applying a non-linear fitting approximation to the measured parameters. The aim of the present study was to study the proliferation dynamics of CCRF-CEM leukemia cells under glucocorticoid treatment. Proliferation dynamics was measured with respect to thermodynamic point of view. MATERIALS AND METHODS The CCRF-CEM leukemic cell line was treated with different concentrations of prednisolone. Cells were studied with hemocytometry, flow cytometry, biochemical measurements for basic metabolic factors and finally data have been analyzed with the Matlab ® computing environment. RESULTS CONCLUSIONS We attempted to create a modeling framework, along with its mathematical formulation, in order to describe the dynamics of leukemic cells under the influence of glucocorticoids. Our analysis included two factors: a) cell population, including changes in viability and cell death, and b) metabolic factors. We suggest that the transition of the cell system that we have studied from the one state to the next, follows complicated dynamics, where it manifests almost in all cases an oscillatory behavior. We suggest that thermodynamic transitions also could follow non- linear dynamics of oscillatory behavior. The use of mathematical and modeling tools for the discovery of such mechanisms is a unique method for the understanding of complicated biological systems. Many research efforts are dedicated to the improvement of the existing or to the development of new pharmaceuticals. Modeling approaches could assist in such efforts as they would provide with a more in-depth understanding of biological systems. The general idea is to be able to predict the future states of a system based on the present ones. This has proved to be a difficult task since biological systems follow non-linear behavior and, unlike physical systems, there are only a few generalizations that can be formulated. 1) Mathematical Formulation of Hypothesis: To model glucocorticoid effects, a mathematical model was set that enabled numerical solutions for the study of their effects. The model presumed that the fraction of cells linked to a certain phenotypic effect can be derived from the previous total cell population so, let N e,t+1 be the cell population under a certain effect. In the present analysis, this effect can be either cell viability or cell death. Therefore, the total population estimate under the impact of a given effect will be given by: Where k e,t is a generalized nonlinear coefficient of the effect e in the population N e,t at time t. ,( 1) , , et et et N k N 2) Glucose uptake decreased from low to high prednisolone concentrations. Prednisolone concentration of 10uM appeared to be the limit of this change. This was observed via measuring the consumption of glucose (Figure 1A) and the concentration of the metabolite lactic acid (Figure 1B). Figure 1. Measurements of metabolic factors in the prednisolone treated CCRF-CEM cells. Following factors were determined: Glucose as a function of time and concentration (A, C); Lactic Acid similarly (B, D); Alkaline Phosphatase (ALP) (E); Lactate Dehydrogenase (F); Ca ++ (G); K + (H) and Na + (I). 3) Glucose was measured on the cell culture supernatants (CG). We assumed that glucose entering the cell was transformed as a total into ATPs and pyruvate. Since cells presumably follow a lactic acid fermentation cycle, pyruvate should be transformed into lactate through Lactate Dehydrogenase (LDH). Additionally, LDH was measured as a function of the total population of necrotic cells (CLDH). At the same time the measured lactate (CLA) was considered to be diffused from both living and apoptotic cells and also released from necrotic cells due to cell membrane lysis. Finally, we accounted for three possible cell fates: progression of proliferation (Nv), necrosis (Nn) and apoptosis (Nta) (Figure 2). 4) The determination of the factor k was implemented with numerical approximations. We assumed that k is a non-linear factor. The first aim was to determine how k changes as a function of concentration. In order to do this we used the simplified model that is presented in Figure 3. 5) LDH correlation with the respective number of necrotic cells: The population of untreated cells and of cells treated with a large dose of prednisolone (700uM) was positively correlated with LDH concentration (Figure 4). We assume that all other glucocorticoid concentrations beside necrotic cell death, also lead to the rupture of the cell membrane and cell lysis. Interestingly, the largest concentration expected to show a lytic effect due to the overdose per se, exhibited a negative correlation, exactly matching that of cells with no glucocorticoid treatment. We further attempted to model the total cell population over time as a function of the various drug concentrations. 6) Cells followed complicated dynamics under glucocorticoid treatment (Figure 5): The manifested oscillatory behavior indicated that cells proliferate with nonlinear dynamics and despite the very few data points, their behavior could still be revealed. In addition, the plotting of the phase-space of metabolic factors showed that the transition from one state to the other also follows oscillations (Figure 6). This finding indicates a complex machinery both in glucose metabolism as well as in thermodynamic transitions of our system. Finally, to gain a more detailed picture of the dynamics of the studied populations, we created 3D plots of the total population vs. the prednisolone concentrations and the three populations we studied using flow cytometry. In the 3D space, the data were fitted with two polynomial equations of 5th order for both the x and y variables (Figure 7). Figure 5. Phase-space analysis of the different populations manifested complex dynamics with respect to time. In particular total population (A), viable cells (B), apoptotic cells (C) and necrotic cells (D) manifested oscillatory behavior as far as the k factor is concerned as modeled with Fourier series. Figure 7. Three dimensional polynomial (A) and quadratic Lowess fitting (B) of the total population N at t vs. t+1 and vs. the prednisolone concentrations (C p ) (A). Also, in this figure the polynomial (C) and quadratic Lowess (D) of the three cell populations i.e. viable cells (N v ), apoptotic cells (N ta ) and necrotic cells (N n ) are presented. Figure 2. Distributions of the CEM cells in total population measurements (A); necrotic population (B); viable cell population (C); apoptotic population (D) and total cell death population (E). Figure 3. A schematic representation of the model approach for cell population in transitions between cell cycle phases and cell death. Figure 4. Correlation of necrotic cell population with LDH. Figure 6. Fitting of glucose concentration C G,t vs. C G,t+1 (A), lactate C LA,t vs. C LA,t+1 (B) and C LDH,t vs. C LDH, t+1 (C). The factor k manifested again complicated dynamics resembling oscillatory behavior.
Transcript of THERMODYNAMIC TRANSITIONS ON METABOLISM AND …€¦ · THERMODYNAMIC TRANSITIONS ON METABOLISM AND...
THERMODYNAMIC TRANSITIONS ON METABOLISM AND PROLIFERATION OF GLUCOCORTICOID-TREATED ACUTE LEUKEMIA CELLS
George I. Lambrou1, Aristotelis Chatziioannou2, Apostolos Zaravinos3, Theodoros Karakonstantakis4, Maria Adamaki1, Maria Braoudaki1 and Spiros A. Vlahopoulos1
1 1st Department of Pediatrics, University of Athens, Thivon & Levadeias, 11527 Goudi, Athens; 2 Institute of Biological Research & Biotechnology, National Hellenic Research Foundation, 48 Vassileos Constantinou Av., Athens, Greece; 3 Molecular MedicineResearch Center and Laboratory of Molecular and Medical Genetics; Department of Biological Sciences; University of Cyprus; 1678, Nicosia, Cyprus; 4 Aghia Sofia Children’s Hospital, Biochemical Department, Thivon Str. 11527, Athens-Goudi, Greece.
INTRODUCTION
AIM OF STUDY
Glucocorticoids play an essential part in anti-leukemic therapies. Resistance is considered crucial for disease prognosis. Glucocorticoids influence the metabolic properties of the leukemic cells. We have previously shown that glucocorticoid treatment in low concentrations manifests a mitogenic effect. A critical established actionof glucocorticoid treatment is its apoptotic effect on leukemic cells. However, little is known about the molecular response of malignant cells following exposure to glucocorticoids. Even less is known about the cell proliferation dynamics governing leukemic cells under glucocorticoid influence. Growth and metabolic features areassumed to be of nonlinear nature. A model based prediction of glucocorticoid effects is derived by applying a non-linear fitting approximation to the measured parameters.
The aim of the present study was to study the proliferation dynamics of CCRF-CEM leukemia cells under glucocorticoid treatment. Proliferation dynamics was measuredwith respect to thermodynamic point of view.
MATERIALS AND METHODSThe CCRF-CEM leukemic cell line was treated with different concentrations of prednisolone. Cells were studied with hemocytometry, flow cytometry, biochemical measurements for basicmetabolic factors and finally data have been analyzed with the Matlab® computing environment.
RESULTS
CONCLUSIONSWe attempted to create a modeling framework, along with its mathematical formulation, in order to describe the dynamics of leukemic cells under the influence of glucocorticoids. Ouranalysis included two factors: a) cell population, including changes in viability and cell death, and b) metabolic factors. We suggest that the transition of the cell system that we have studiedfrom the one state to the next, follows complicated dynamics, where it manifests almost in all cases an oscillatory behavior. We suggest that thermodynamic transitions also could follow non-linear dynamics of oscillatory behavior. The use of mathematical and modeling tools for the discovery of such mechanisms is a unique method for the understanding of complicated biologicalsystems. Many research efforts are dedicated to the improvement of the existing or to the development of new pharmaceuticals. Modeling approaches could assist in such efforts as theywould provide with a more in-depth understanding of biological systems. The general idea is to be able to predict the future states of a system based on the present ones. This has proved to bea difficult task since biological systems follow non-linear behavior and, unlike physical systems, there are only a few generalizations that can be formulated.
1) Mathematical Formulation of Hypothesis: To model glucocorticoid effects, a mathematical model was set that enabled numerical solutions for the study of their effects. Themodel presumed that the fraction of cells linked to a certain phenotypic effect can be derived from the previous total cell population so, let Ne,t+1 be the cell population under a certaineffect. In the present analysis, this effect can be either cell viability or cell death. Therefore, the total population estimate under the impact of a given effect will be given by:Where ke,t is a generalized nonlinear coefficient of the effect e in the population Ne,t at time t.
,( 1) , ,e t e t e tN k N
2) Glucose uptake decreased from low to high prednisolone concentrations. Prednisolone concentration of 10uM appeared to be the limit of this change. This wasobserved via measuring the consumption of glucose (Figure 1A) and the concentration of the metabolite lactic acid (Figure 1B).
Figure 1. Measurements of metabolic factors in theprednisolone treated CCRF-CEM cells. Following factors weredetermined: Glucose as a function of time and concentration (A,C); Lactic Acid similarly (B, D); Alkaline Phosphatase (ALP)(E); Lactate Dehydrogenase (F); Ca++ (G); K+ (H) and Na+ (I).
3) Glucose was measured on the cell culture supernatants (CG). We assumed that glucose entering the cell was transformed as a total into ATPs and pyruvate. Since cellspresumably follow a lactic acid fermentation cycle, pyruvate should be transformed into lactate through Lactate Dehydrogenase (LDH). Additionally, LDH was measured as a function of thetotal population of necrotic cells (CLDH). At the same time the measured lactate (CLA) was considered to be diffused from both living and apoptotic cells and also released from necroticcells due to cell membrane lysis. Finally, we accounted for three possible cell fates: progression of proliferation (Nv), necrosis (Nn) and apoptosis (Nta) (Figure 2).
4) The determination of the factor k was implemented with numerical approximations. We assumed that k is a non-linear factor. The first aim was to determine how kchanges as a function of concentration. In order to do this we used the simplified model that is presented in Figure 3.
5) LDH correlation with the respective number of necrotic cells: The population of untreated cells and of cells treated with a large dose of prednisolone (700uM) waspositively correlated with LDH concentration (Figure 4). We assume that all other glucocorticoid concentrations beside necrotic cell death, also lead to the rupture of the cell membrane andcell lysis. Interestingly, the largest concentration expected to show a lytic effect due to the overdose per se, exhibited a negative correlation, exactly matching that of cells with noglucocorticoid treatment. We further attempted to model the total cell population over time as a function of the various drug concentrations.
6) Cells followed complicated dynamics under glucocorticoid treatment (Figure 5): The manifested oscillatory behavior indicated that cells proliferate with nonlineardynamics and despite the very few data points, their behavior could still be revealed. In addition, the plotting of the phase-space of metabolic factors showed that the transition from one stateto the other also follows oscillations (Figure 6). This finding indicates a complex machinery both in glucose metabolism as well as in thermodynamic transitions of our system. Finally, togain a more detailed picture of the dynamics of the studied populations, we created 3D plots of the total population vs. the prednisolone concentrations and the three populations we studiedusing flow cytometry. In the 3D space, the data were fitted with two polynomial equations of 5th order for both the x and y variables (Figure 7).
Figure 5. Phase-space analysis of the differentpopulations manifested complex dynamics with respectto time. In particular total population (A), viable cells(B), apoptotic cells (C) and necrotic cells (D) manifestedoscillatory behavior as far as the k factor is concerned asmodeled with Fourier series.
Figure 7. Three dimensional polynomial (A) andquadratic Lowess fitting (B) of the totalpopulation N at t vs. t+1 and vs. theprednisolone concentrations (Cp) (A). Also, inthis figure the polynomial (C) and quadraticLowess (D) of the three cell populations i.e.viable cells (Nv), apoptotic cells (Nta) andnecrotic cells (Nn) are presented.
Figure 2. Distributions of the CEM cells in total populationmeasurements (A); necrotic population (B); viable cellpopulation (C); apoptotic population (D) and total cell deathpopulation (E).
Figure 3. A schematic representationof the model approach for cellpopulation in transitions between cellcycle phases and cell death.
Figure 4. Correlation of necrotic cell population with LDH.
Figure 6. Fitting of glucoseconcentration CG,t vs. CG,t+1 (A),lactate CLA,t vs. CLA,t+1 (B) andCLDH,t vs. CLDH, t+1 (C). The factork manifested again complicateddynamics resembling oscillatorybehavior.
