Ildefonso M. De la Fuente

Global self-regulation of the cellular metabolic structure.

Background Different studies have shown that cellular enzymatic activities are able to self-organize spontaneously, forming a metabolic core of reactive processes that remain active under different growth conditions while the rest of the molecular catalytic reactions exhibit structural plasticity. This global cellular metabolic structure appears to be an intrinsic characteristic common to all cellular organisms. Recent work performed with dissipative metabolic networks has shown that the fundamental element for the spontaneous emergence of this global self-organized enzymatic structure could be the number of catalytic elements in the metabolic networks. Methodology/Principal Findings In order to investigate the factors that may affect the catalytic dynamics under a global metabolic structure characterized by the presence of metabolic cores we have studied different transitions in catalytic patterns belonging to a dissipative metabolic network. The data were analyzed using non-linear dynamics tools: power spectra, reconstructed attractors, long-term correlations, maximum Lyapunov exponent and Approximate Entropy; and we have found the emergence of self-regulation phenomena during the transitions in the metabolic activities. Conclusions/Significance The analysis has also shown that the chaotic numerical series analyzed correspond to the fractional Brownian motion and they exhibit long-term correlations and low Approximate Entropy indicating a high level of predictability and information during the self-regulation of the metabolic transitions. The results illustrate some aspects of the mechanisms behind the emergence of the metabolic self-regulation processes, which may constitute an important property of the global structure of the cellular metabolism.

Dynamic behavior in glycolytic oscillations with phase shifts

Practically all of the studies of glycolytic oscillations in homogeneous spatial mediums have been performed through the construction of systems of ordinary differential equations and the search for their solutions. In this kind of modelling, the system dynamic behavior is considered to depend only on the values adopted by the parameters related to the dependent variables. In the present work, the modeling of a biochemical system through a system of functional differential equations with delay allows us to analyse the consequences that the variations in the parametric values linked to the independent variable (time) have upon the integral solutions of the system. In our model, the delays correspond with phase shifts in the initial functions for two dependent variables. The results of our researches show that when a instability-generating multienzymatic mechanism suffers variations of the delay time in any of its variables, a wide range of different dynamic responses can be produced. Our work is presented as an enlargement on the dynamic study of biochemical oscillations in general and, particularly, the glycolytic oscillations, under the consideration of the existence of variations in the phase shifts during the oscillations of metabolites involved in the studied reactive processes.

Attractor Metabolic Networks

Background The experimental observations and numerical studies with dissipative metabolic networks have shown that cellular enzymatic activity self-organizes spontaneously leading to the emergence of a Systemic Metabolic Structure in the cell, characterized by a set of different enzymatic reactions always locked into active states (metabolic core) while the rest of the catalytic processes are only intermittently active. This global metabolic structure was verified for Escherichia coli, Helicobacter pylori and Saccharomyces cerevisiae, and it seems to be a common key feature to all cellular organisms. In concordance with these observations, the cell can be considered a complex metabolic network which mainly integrates a large ensemble of self-organized multienzymatic complexes interconnected by substrate fluxes and regulatory signals, where multiple autonomous oscillatory and quasi-stationary catalytic patterns simultaneously emerge. The network adjusts the internal metabolic activities to the external change by means of flux plasticity and structural plasticity. Methodology/Principal Findings In order to research the systemic mechanisms involved in the regulation of the cellular enzymatic activity we have studied different catalytic activities of a dissipative metabolic network under different external stimuli. The emergent biochemical data have been analysed using statistical mechanic tools, studying some macroscopic properties such as the global information and the energy of the system. We have also obtained an equivalent Hopfield network using a Boltzmann machine. Our main result shows that the dissipative metabolic network can behave as an attractor metabolic network. Conclusions/Significance We have found that the systemic enzymatic activities are governed by attractors with capacity to store functional metabolic patterns which can be correctly recovered from specific input stimuli. The network attractors regulate the catalytic patterns, modify the efficiency in the connection between the multienzymatic complexes, and stably retain these modifications. Here for the first time, we have introduced the general concept of attractor metabolic network, in which this dynamic behavior is observed.

The Number of Catalytic Elements Is Crucial for the Emergence of Metabolic Cores

Background Different studies show evidence that several unicellular organisms display a cellular metabolic structure characterized by a set of enzymes which are always in an active state (metabolic core), while the rest of the molecular catalytic reactions exhibit on-off changing states. This self-organized enzymatic configuration seems to be an intrinsic characteristic of metabolism, common to all living cellular organisms. In a recent analysis performed with dissipative metabolic networks (DMNs) we have shown that this global functional structure emerges in metabolic networks with a relatively high number of catalytic elements, under particular conditions of enzymatic covalent regulatory activity. Methodology/Principal Findings Here, to investigate the mechanism behind the emergence of this supramolecular organization of enzymes, we have performed extensive DMNs simulations (around 15,210,000 networks) taking into account the proportion of the allosterically regulated enzymes and covalent enzymes present in the networks, the variation in the number of substrate fluxes and regulatory signals per catalytic element, as well as the random selection of the catalytic elements that receive substrate fluxes from the exterior. The numerical approximations obtained show that the percentages of DMNs with metabolic cores grow with the number of catalytic elements, converging to 100% for all cases. Conclusions/Significance The results show evidence that the fundamental factor for the spontaneous emergence of this global self-organized enzymatic structure is the number of catalytic elements in the metabolic networks. Our analysis corroborates and expands on our previous studies illustrating a crucial property of the global structure of the cellular metabolism. These results also offer important insights into the mechanisms which ensure the robustness and stability of living cells.

On the Dynamics of the Adenylate Energy System: Homeorhesis vs Homeostasis

Biochemical energy is the fundamental element that maintains both the adequate turnover of the biomolecular structures and the functional metabolic viability of unicellular organisms. The levels of ATP, ADP and AMP reflect roughly the energetic status of the cell, and a precise ratio relating them was proposed by Atkinson as the adenylate energy charge (AEC). Under growth-phase conditions, cells maintain the AEC within narrow physiological values, despite extremely large fluctuations in the adenine nucleotides concentration. Intensive experimental studies have shown that these AEC values are preserved in a wide variety of organisms, both eukaryotes and prokaryotes. Here, to understand some of the functional elements involved in the cellular energy status, we present a computational model conformed by some key essential parts of the adenylate energy system. Specifically, we have considered (I) the main synthesis process of ATP from ADP, (II) the main catalyzed phosphotransfer reaction for interconversion of ATP, ADP and AMP, (III) the enzymatic hydrolysis of ATP yielding ADP, and (IV) the enzymatic hydrolysis of ATP providing AMP. This leads to a dynamic metabolic model (with the form of a delayed differential system) in which the enzymatic rate equations and all the physiological kinetic parameters have been explicitly considered and experimentally tested in vitro. Our central hypothesis is that cells are characterized by changing energy dynamics (homeorhesis). The results show that the AEC presents stable transitions between steady states and periodic oscillations and, in agreement with experimental data these oscillations range within the narrow AEC window. Furthermore, the model shows sustained oscillations in the Gibbs free energy and in the total nucleotide pool. The present study provides a step forward towards the understanding of the fundamental principles and quantitative laws governing the adenylate energy system, which is a fundamental element for unveiling the dynamics of cellular life.

Elements of the cellular metabolic structure.

A large number of studies have shown the existence of metabolic covalent modifications in different molecular structures, able to store biochemical information that is not encoded by the DNA. Some of these covalent mark patterns can be transmitted across generations (epigenetic changes). Recently, the emergence of Hopfield-like attractor dynamics has been observed in the self-organized enzymatic networks, which have the capacity to store functional catalytic patterns that can be correctly recovered by the specific input stimuli. The Hopfield-like metabolic dynamics are stable and can be maintained as a long-term biochemical memory. In addition, specific molecular information can be transferred from the functional dynamics of the metabolic networks to the enzymatic activity involved in the covalent post-translational modulation so that determined functional memory can be embedded in multiple stable molecular marks. Both the metabolic dynamics governed by Hopfield-type attractors (functional processes) and the enzymatic covalent modifications of determined molecules (structural dynamic processes) seem to represent the two stages of the dynamical memory of cellular metabolism (metabolic memory). Epigenetic processes appear to be the structural manifestation of this cellular metabolic memory. Here, a new framework for molecular information storage in the cell is presented, which is characterized by two functionally and molecularly interrelated systems: a dynamic, flexible and adaptive system (metabolic memory) and an essentially conservative system (genetic memory). The molecular information of both systems seems to coordinate the physiological development of the whole cell.

Modeling the ascorbate-glutathione cycle in chloroplasts under light/dark conditions.

BackgroundLight/dark cycles are probably the most important environmental signals that regulate plant development. Light is essential for photosynthesis, but an excess, in combination with the unavoidable presence of atmospheric oxygen inside the chloroplast, leads to excessive reactive oxygen species production. Among the defense mechanisms that activate plants to cope with environmental stress situations, it is worth noting the ascorbate-glutathione cycle, a complex metabolic pathway in which a variety of photochemical, chemical and enzymatic steps are involved.ResultsWe herein studied the dynamic behavior of this pathway under light/dark conditions and for several consecutive days. For this purpose, a mathematical model was developed including a variable electron source with a rate law proportional to the intensity of solar irradiance during the photoperiod, and which is continuously turned off at night and on again the next day. The model is defined by a nonlinear system of ordinary differential equations with an on/off time-dependent input, including a parameter to simulate the fact that the photoperiod length is not constant throughout the year, and which takes into account the particular experimental kinetics of each enzyme involved in the pathway. Unlike previous models, which have only provided steady-state solutions, the present model is able to simulate diurnal fluctuations in the metabolite concentrations, fluxes and enzymatic rates involved in the network.ConclusionsThe obtained results are broadly consistent with experimental observations and highlight the key role played by ascorbate recycling for plants to adapt to their surrounding environment. This approach provides a new strategy to in vivo studies to analyze plant defense mechanisms against oxidative stress induced by external changes, which can also be extrapolated to other complex metabolic pathways to constitute a useful tool to the scientific community in general.

Vitronectin and dermcidin serum levels predict the metastatic progression of AJCC I-II early-stage melanoma.

Like many cancers, an early diagnosis of melanoma is fundamental to ensure a good prognosis, although an important proportion of stage I–II patients may still develop metastasis during follow‐up. The aim of this work was to discover serum biomarkers in patients diagnosed with primary melanoma that identify those at a high risk of developing metastasis during the follow‐up period. Proteomic and mass spectrophotometry analysis was performed on serum obtained from patients who developed metastasis during the first years after surgery for primary tumors and compared with that from patients who remained disease‐free for more than 10 years after surgery. Five proteins were selected for validation as prognostic factors in 348 melanoma patients and 100 controls by ELISA: serum amyloid A and clusterin; immune system proteins; the cell adhesion molecules plakoglobin and vitronectin and the antimicrobial protein dermcidin. Compared to healthy controls, melanoma patients have high serum levels of these proteins at the moment of melanoma diagnosis, although the specific values were not related to the histopathological stage of the tumors. However, an analysis based on classification together with multivariate statistics showed that tumor stage, vitronectin and dermcidin levels were associated with the metastatic progression of patients with early‐stage melanoma. Although melanoma patients have increased serum dermcidin levels, the REPTree classifier showed that levels of dermcidin <2.98 μg/ml predict metastasis in AJCC stage II patients. These data suggest that vitronectin and dermcidin are potent biomarkers of prognosis, which may help to improve the personalized medical care of melanoma patients and their survival.

Estimation of preterm labor immediacy by nonlinear methods

Preterm delivery affects about one tenth of human births and is associated with an increased perinatal morbimortality as well as with remarkable costs. Even if there are a number of predictors and markers of preterm delivery, none of them has a high accuracy. In order to find quantitative indicators of the immediacy of labor, 142 cardiotocographies (CTG) recorded from women consulting because of suspected threatened premature delivery with gestational ages comprehended between 24 and 35 weeks were collected and analyzed. These 142 samples were divided into two groups: the delayed labor group (n = 75), formed by the women who delivered more than seven days after the tocography was performed, and the anticipated labor group (n = 67), which corresponded to the women whose labor took place during the seven days following the recording. As a means of finding significant differences between the two groups, some key informational properties were analyzed by applying nonlinear techniques on the tocography recordings. Both the regularity and the persistence levels of the delayed labor group, which were measured by Approximate Entropy (ApEn) and Generalized Hurst Exponent (GHE) respectively, were found to be significantly different from the anticipated labor group. As delivery approached, the values of ApEn tended to increase while the values of GHE tended to decrease, suggesting that these two methods are sensitive to labor immediacy. On this paper, for the first time, we have been able to estimate childbirth immediacy by applying nonlinear methods on tocographies. We propose the use of the techniques herein described as new quantitative diagnosis tools for premature birth that significantly improve the current protocols for preterm labor prediction worldwide.

Metastasis of Cutaneous Melanoma: Risk Factors, Detection and Forecasting

In this work, we present a quantitative analysis of cutaneous melanoma based on 615 patients attended in Cruces University Hospital between 1988 and 2012. First, we studied which characteristics are more associated with the metastasis of this kind of cancer. We observed that people with light eyes, light hair, an ulcerated nevus, or exposed to the sun during working hours, had more risk to suffer from metastasis. Besides, a big diameter or a thick nevus (measured by Breslow’s depth) were also associated with this condition. Next, we evaluated the metastasis detection capability of the tests performed in this hospital, which indicated that X-rays and CT scan were the best techniques for metastasis detection, since they identified this condition successfully in 80% and 93.5% of the cases, respectively. Moreover, we concluded that the blood test was very inaccurate, since it recognized the presence of metastasis in only 40% of the cases and failed in the rest. Consequently, we suggest the replacement of this test in order to save money, time, and avoid the misdiagnosis of cutaneous melanoma metastasis. Finally, we built a predictive model to forecast the time that takes for metastasis to happen, based on Breslow’s depth. This tool could be used not only for improving the programming appointment management of the dermatology section, but also for detecting metastasis sooner.