Teaching systems biology.

Advances in systems biology are increasingly dependent upon the integration of various types of data and different methodologies to reconstruct how cells work at the systemic level. Thus, teams with a varied array of expertise and people with interdisciplinary training are needed. So far this training was thought to be more productive if aimed at the Masters or PhD level. At this level, multiple specialised and in-depth courses on the different subject matters of systems biology are taught to already well-prepared students. This approach is mostly based on the recognition that systems biology requires a wide background that is hard to find in undergraduate students. Nevertheless, and given the importance of the field, the authors argue that exposition of undergraduate students to the methods and paradigms of systems biology would be advantageous. Here they present and discuss a successful experiment in teaching systems biology to third year undergraduate biotechnology students at the University of Lleida in Spain. The authors' experience, together with that from others, argues for the adequateness of teaching systems biology at the undergraduate level. [Includes supplementary material].

New methods to explore marine resources for Alzheimer's therapeutics.

Despite the long history of drug discovery from natural sources, the marine environment, which covers 70% of the Earth's surface, is still relatively unexplored. Intense competition for limited resources drives the evolution of specific and potent chemical defenses distinct from their terrestrial counterparts. Based on this rationale, we recently began screening extracts derived from marine invertebrate and cyanobacterial samples for BACE-1 inhibitors in a chemiluminescent enzyme-fragment complementation (EFC) assay. The results of this broad screening are presented here, along with our progress towards the development of a secondary LC-MS homogeneous affinity assay. Incubation of the extracts active in the EFC assay with BACE1, subsequent isolation of the enzyme-inhibitor complex and then analysis of the small molecule inhibitor by LC-MS rapidly links a chemical structure to biological activity. This approach enables the rapid target-orientated discovery of BACE-1 inhibitors from marine sources.

[Application of artificial neural networks for risk stratification of hospital mortality]. / Aplicación de las redes neuronales artificiales para la estratificación de riesgo de mortalidad hospitalaria.

OBJECTIVE: To compare the ability of an artificial neural network (ANN) to predict hospital mortality with that of the Acute Physiology and Chronic Health Evaluation II (APACHE II) system and multiple logistic regression (LR). A secondary objective was to compare the allocation of individual probability among the models. METHOD: The variables required for calculating the APACHE II were prospectively collected. A total of 1146 patients were divided (randomly 70% and 30%) into the Development (800) and the Validation (346) sets. With the same variables an LR model and an ANN were carried out (a 3-layer perceptron trained by algorithm backpropagation with bootstrap resampling and with 9 nodes in the hidden layer) in the Development set. The models developed were contrasted with the Validation set and their discrimination properties were evaluated using the area under the ROC curve (AUC [95% CI]) and calibration with the Hosmer-Lemeshow C (HLC) test. Differences between the probabilities were evaluated using the Bland-Altman test. RESULTS: The Validation set showed an APACHE II with an AUC = 0.79 (0.75-0.84) and HLC = 11 (p = 0.329); LR model AUC = 0.81 (0.76-0.85) and HLC = 29 (p = 0.0001) and an ANN AUC = 0.82 (0.77-0.86) and HLC = 10 (p = 0.404). The patients with the most important differences in the allocation of probability between LR and ANN (8% of the total) were neurological. The worst results were found in trauma patients with an AUC of not greater than 0.75 in all the models. In respiratory patients, the ANN achieved the best AUC = 0.87 (0.78-0.91). CONCLUSIONS: The ANN was able to stratify hospital mortality risk by using the APACHE II system variables. The ANN tended to achieve better results than LR, since, in order to work, it does not require lineal restrictions or independent variables. Allocation of individual probability differed in each model.

Aplicación de las redes neuronales artificiales para la estratificación de riesgo de mortalidad hospitalaria / Application of artificial neural networks for risk stratification of hospital mortality

Objetivo: Comparar la capacidad de predicción de mortalidad hospitalaria de una red neuronal artificial (RNA) con el Acute Physiology and Chronic Health Evaluation II (APACHE II) y la regresión logística (RL), y comparar la asignación de probabilidades entre los distintos modelos. Método: Se recogen de forma prospectiva las variables necesarias para el cálculo del APACHE II. Disponemos de 1.146 pacientes asignándose aleatoriamente (70 y 30 por ciento) al grupo de Desarrollo (800) y al de Validación (346). Con las mismas variables se genera un modelo de RL y de RNA (perceptrón de 3 capas entrenado por algoritmo de backpropagation con remuestreo bootstrap y con 9 nodos en la capa oculta) en el grupo de desarrollo. Se comparan los tres modelos en función de los criterios de discriminación con el área bajo la curva ROC (ABC [IC del 95 por ciento]) y de calibración con el test de HosmerLemeshow C (HLC). Las diferencias entre las probabilidades se valoran con el test de Bland-Altman. Resultados: En el grupo de validación, el APACHE II con ABC de 0,79 (0,75-0,84) y HLC de 11 (p = 0,329); modelo RL, ABC de 0,81 (0,76-0,85) y HLC de 29 (p = 0,0001), y en RNA, ABC de 0,82 (0,77-0,86) y HLC de 10 (p = 0,404). Los pacientes con mayores diferencias en la asignación de probabilidad entre RL y RN (8 por ciento del total) son pacientes con problemas neurológicos. Los peores resultados se obtienen en los pacientes traumáticos (ABC inferior a 0,75 en todos los modelos). En los pacientes respiratorios, la RNA alcanza los mejores resultados (ABC = 0,87 [0,78-0,91]).Conclusiones: Una RNA es capaz de estratificar el riesgo de mortalidad hospitalaria utilizando las variables del sistema APACHE II. La RNA consigue mejores resultados frente a RL, sin alcanzar significación, ya que no trabaja con restricciones lineales ni de independencia de variables, con una diferente asignación de probabilidad individual entre los modelos (AU)

Power-law modeling based on least-squares criteria: consequences for system analysis and simulation.

The power-law formalism was initially derived as a Taylor series approximation in logarithmic space for kinetic rate-laws. The resulting models, either as generalized mass action (GMA) or as S-systems models, allow to characterize the target system and to simulate its dynamical behavior in response to external perturbations and parameter changes. This approach has been succesfully used as a modeling tool in many applications from cell metabolism to population dynamics. Without leaving the general formalism, we recently proposed to derive the power-law representation in an alternative way that uses least-squares (LS) minimization instead of the traditional derivation based on Taylor series [B. Hernández-Bermejo, V. Fairén, A. Sorribas, Math. Biosci. 161 (1999) 83-94]. It was shown that the resulting LS power-law mimics the target rate-law in a wider range of concentration values than the classical power-law, and that the prediction of the steady-state using the LS power-law is closer to the actual steady-state of the target system. However, many implications of this alternative approach remained to be established. We explore some of them in the present work. Firstly, we extend the definition of the LS power-law within a given operating interval in such a way that no preferred operating point is selected. Besides providing an alternative to the classical Taylor power-law, that can be considered a particular case when the operating interval is reduced to a single point, the LS power-law so defined is consistent with the results that can be obtained by fitting experimental data points. Secondly, we show that the LS approach leads to a system description, either as an S-system or a GMA model, in which the systemic properties (such as the steady-state prediction or the log-gains) appear averaged over the corresponding interval when compared with the properties that can be computed from Taylor-derived models in different operating points within the considered operating range. Finally, we also show that the LS description leads to a global, accurate description of the system when it is submitted to external forcing.

Analysis and prediction of the effect of uncertain boundary values in modeling a metabolic pathway.

The integration of large quantities of biological information into mathematical models of cell metabolism provides a way for quantitatively evaluating the effect of parameter changes on simultaneous, coupled, and, often, counteracting processes. From a practical point of view, the validity of the model's predictions would critically depend on its quality. Among others, one of the critical steps that may compromise this quality is to decide which are the boundaries of the model. That is, we must decide which metabolites are assumed to be constants, and which fluxes are considered to be the inputs and outputs of the system. In this article, we analyze the effect of the experimental uncertainty on these variables on the system's characterization. Using a previously defined model of glucose fermentation in Saccharomyces cerevisiae, we characterize the effect of the uncertainty on some key variables commonly considered to be constants in many models of glucose metabolism, i.e., the intracellular pH and the pool of nucleotides. Without considering if this variability corresponds to a possible true physiological phenomenon, the goal of this article is to illustrate how this uncertainty may result in an important variability in the systemic responses predicted by the model. To characterize this variability, we analyze the utility and limitations of computing the sensitivities of logarithmic-gains (control coefficients) to the boundary parameters. With the exception of some special cases, our analysis shows that these sensitivities are good indicators of the dependence of the model systemic behavior on the parameters of interest.

Estimating age-related trends in cross-sectional studies using S-distributions.

Growth trends in children are often based on cross-sectional studies, in which a sample of the population is investigated at one given point in time. Estimating age-related percentiles in such studies involves fitting data distributions, each of which is specific for one age group, and a subsequent smoothing of the percentile curves. The first requirement for this process is the selection of a distributional form that is expected to be consistent with the observed data. If a goodness-of-fit test reveals significant discrepancies between the data and the best-fitting member of this distributional form, an alternative distribution must be found. In practice, there is seldom an objective argument for selecting any particular distribution. Also, different distributions can yield very similar fits, so that any selection is somewhat arbitrary. Finally, the shapes of the observed distributions may change throughout the age range so drastically that no single traditional distribution can fit them all in a satisfactory manner. To overcome these difficulties in population studies, non-parametric smoothing techniques and normalizing transformations have been used to derive percentile curves. In this paper we present an alternative strategy in the form of a flexible parametric family of statistical distributions: the S-distribution. We suggest a method that guides the search for well-fitting S-distributions for groups of observed distributions. The method is first tested with simulated data sets and subsequently applied to actual weight distributions of girls of different ages. As far as the results can be tested, they are consistent with observations and with results from other methods.

Grx5 glutaredoxin plays a central role in protection against protein oxidative damage in Saccharomyces cerevisiae.

Glutaredoxins are members of a superfamily of thiol disulfide oxidoreductases involved in maintaining the redox state of target proteins. In Saccharomyces cerevisiae, two glutaredoxins (Grx1 and Grx2) containing a cysteine pair at the active site had been characterized as protecting yeast cells against oxidative damage. In this work, another subfamily of yeast glutaredoxins (Grx3, Grx4, and Grx5) that differs from the first in containing a single cysteine residue at the putative active site is described. This trait is also characteristic for a number of glutaredoxins from bacteria to humans, with which the Grx3/4/5 group has extensive homology over two regions. Mutants lacking Grx5 are partially deficient in growth in rich and minimal media and also highly sensitive to oxidative damage caused by menadione and hydrogen peroxide. A significant increase in total protein carbonyl content is constitutively observed in grx5 cells, and a number of specific proteins, including transketolase, appear to be highly oxidized in this mutant. The synthetic lethality of the grx5 and grx2 mutations on one hand and of grx5 with the grx3 grx4 combination on the other points to a complex functional relationship among yeast glutaredoxins, with Grx5 playing a specially important role in protection against oxidative stress both during ordinary growth conditions and after externally induced damage. Grx5-deficient mutants are also sensitive to osmotic stress, which indicates a relationship between the two types of stress in yeast cells.

Power-law modeling based on least-squares minimization criteria.

The power-law formalism has been successfully used as a modeling tool in many applications. The resulting models, either as Generalized Mass Action or as S-systems models, allow one to characterize the target system and to simulate its dynamical behavior in response to external perturbations and parameter changes. The power-law formalism was first derived as a Taylor series approximation in logarithmic space for kinetic rate-laws. The especial characteristics of this approximation produce an extremely useful systemic representation that allows a complete system characterization. Furthermore, their parameters have a precise interpretation as local sensitivities of each of the individual processes and as rate-constants. This facilitates a qualitative discussion and a quantitative estimation of their possible values in relation to the kinetic properties. Following this interpretation, parameter estimation is also possible by relating the systemic behavior to the underlying processes. Without leaving the general formalism, in this paper we suggest deriving the power-law representation in an alternative way that uses least-squares minimization. The resulting power-law mimics the target rate-law in a wider range of concentration values than the classical power-law. Although the implications of this alternative approach remain to be established, our results show that the predicted steady-state using the least-squares power-law is closest to the actual steady-state of the target system.

Mathematical models of purine metabolism in man.

Experimental and clinical data on purine metabolism are collated and analyzed with three mathematical models. The first model is the result of an attempt to construct a traditional kinetic model based on Michaelis-Menten rate laws. This attempt is only partially successful, since kinetic information, while extensive, is not complete, and since qualitative information is difficult to incorporate into this type of model. The data gaps necessitate the complementation of the Michaelis-Menten model with other functional forms that can incorporate different types of data. The most convenient and established representations for this purpose are rate laws formulated as power-law functions, and these are used to construct a Complemented Michaelis-Menten (CMM) model. The other two models are pure power-law-representations, one in the form of a Generalized Mass Action (GMA) system, and the other one in the form of an S-system. The first part of the paper contains a compendium of experimental data necessary for any model of purine metabolism. This is followed by the formulation of the three models and a comparative analysis. For physiological and moderately pathological perturbations in metabolites or enzymes, the results of the three models are very similar and consistent with clinical findings. This is an encouraging result since the three models have different structures and data requirements and are based on different mathematical assumptions. Significant enzyme deficiencies are not so well modeled by the S-system model. The CMM model captures the dynamics better, but judging by comparisons with clinical observations, the best model in this case is the GMA model. The model results are discussed in some detail, along with advantages and disadvantages of each modeling strategy.

Validation and steady-state analysis of a power-law model of purine metabolism in man.

The paper introduces a model of human purine metabolism in situ. Chosen from among several alternative system descriptions, the model is formulated as a Generalized Mass Action system within Biochemical Systems Theory and validated with analyses of steady-state and dynamic characteristics. Eigenvalue and sensitivity analyses indicate that the model has a stable and robust steady-state. The model quite accurately reproduces numerous biochemical and clinical observations in healthy subjects as well as in patients with disorders of purine metabolism. These results suggest that the model can be used to assess biochemical and clinical aspects of human purine metabolism. It provides a means of exploring effects of enzyme deficiencies and is a potential tool for identifying steps of the pathway that could be the target of therapeutical intervention. Numerous quantitative comparisons with data are given. The model can be used for biomathematical exploration of relationships between enzymic deficiencies and clinically manifested diseases.

Regulation of motoneuronal calcitonin gene-related peptide (CGRP) during axonal growth and neuromuscular synaptic plasticity induced by botulinum toxin in rats.

The aim of this study was to examine whether changes in rat motoneuronal calcitonin gene-related peptide (CGRP) can be correlated with axonal growth and plasticity of neuromuscular synapses. Nerve terminal outgrowth was induced by local paralysis with botulinum toxin. Normal adult soleus and tibialis anterior did not show detectable CGRP content at the motor endplates. Following botulinum toxin injection there was a progressive, transient and bimodal increase in CGRP in both motoneuron cell bodies which innervated poisoned muscles and their motor endplates. CGRP content was moderately increased 1 day after paralysis and, after an initial decline, reached a peak 20 days after injection. This was followed by a gradual decrease and a return to normal levels at the 200th day. CGRP changes in intoxicated endplates were less evident in the tibialis anterior than in the soleus muscle. The CGRP content in motoneurons was positively correlated with the degree of intramuscular nerve sprouting found by silver staining. In situ hybridization revealed an increase in CGRP mRNA in spinal cord motoneurons 20 days after toxin administration. We conclude that motoneurons regulate their CGRP in situations in which peripheral synapse remodelling and plasticity occur.

Comparative characterization of the fermentation pathway of Saccharomyces cerevisiae using biochemical systems theory and metabolic control analysis: model definition and nomenclature.

Mathematical tools that involve the determination of systemic responses to small changes in metabolites or enzymes have demonstrated their utility for analyzing metabolic pathways. The different methodologies based on these ideas allow for modeling and analyzing biochemical pathways focusing on the coordinate behavior of the whole system. However, one must become familiar with the difference in nomenclature and methodology to relate the models and results obtained by applying these techniques and to appreciate their potential for answering fundamental questions about biochemical systems. In the following three papers we show how this can be facilitated by comparing the nomenclature, methodology, and results of the two leading techniques in this area, metabolic control analysis and biochemical systems theory, using a model of the fermentation pathway in Saccharomyces cerevisiae as a reference system. In the present paper we review the nomenclature, technical concepts, and related experimental measurements while creating a practical dictionary for the reference system that makes the relatedness of the two approaches more apparent. In the second paper, subtitled Steady-State Analysis, we show that both approaches give the same picture for many systemic responses of the reference system. In the third paper of this series, subtitled Model Validation and Dynamic Behavior, we show that the quality of the model can be assessed by studying the sensitivity to changes in the system parameters. We hope to illustrate the usefulness of these tools in providing an interpretation of the experimental measurements in a specific metabolic pathway.

Comparative characterization of the fermentation pathway of Saccharomyces cerevisiae using biochemical systems theory and metabolic control analysis: steady-state analysis.

In the preceding paper in this issue, we have shown that metabolic control analysis and biochemical systems theory use the same experimental information to describe a metabolic system. In this paper, we analyze the steady-state properties of this pathway by applying both methods. Our results show the correspondence of the steady-state characterizations and illustrate the relationships between the different nomenclatures used. With both approaches, we identify metabolite pools that are strongly influenced by changes in enzyme concentration when cells are immobilized at pH 5.5. In the final paper of this series, which follows, we discuss the need to assess the quality of a model and the potential difficulties that may arise if the steady-state characterization is accepted without testing its quality. We then validate the different models using parameter sensitivity concepts.

Comparative characterization of the fermentation pathway of Saccharomyces cerevisiae using biochemical systems theory and metabolic control analysis: model validation and dynamic behavior.

In the first two papers of this series (immediately preceding, this issue), we characterized the steady-state properties of a model of a fermentation pathway in Saccharomyces cerevisiae in four experimental conditions. In each of these conditions, the pictures obtained by metabolic control analysis and biochemical systems theory were coincident, which illustrates the relatedness of the two approaches. In this paper we analyze the quality of this description by means of the tools available within biochemical systems theory, and we show that in some of the experimental conditions studied the system is poorly characterized. The most critical condition corresponds to the immobilization of the cells at pH 5.5, in which the kinetic characterization appears to be inaccurate. Furthermore, sensitivity analysis and the study of the local steady-state stability identify the most critical parameters. The results of these analyses are confirmed by the predictions of the dynamic response of the model using its S-system representation. This illustrates the utility of these tools and warns against using the steady-state characterization without testing its validity.

Structure identifiability in metabolic pathways: parameter estimation in models based on the power-law formalism.

An important step in understanding a metabolic pathway is to identify its structure, in terms of the flow of material and information. In pursuing this goal, the available information for a given system is usually obtained from experiments in vitro and comes from different sources. Frequently, the final set of regulatory signals acting in the system in vivo is unclear, and some kind of test is needed on the intact system. Besides defining an appropriate experimental approach, identification of the regulatory pattern needs a theoretical framework in which the different experimental measurements can be evaluated and a final picture can be agreed on. Mathematical approaches based on sensitivity coefficients provide a useful tool for addressing this problem. Within this framework, the appropriate parameters are related to both the structure of the reaction network and the signals that regulate the target system. Thus the identification of the regulatory structure can be related to the estimation of the appropriate set of parameters. In pursuing this goal, we will show the limitations of using steady-state measurements and the usefulness of using dynamic data. We suggest a way to test the regulatory pattern in a given metabolic pathway by combining both kinds of data, and we show, by using a reference system, the potential of the method suggested.

Enzyme-enzyme interactions and metabolite channelling: alternative mechanisms and their evolutionary significance.

Metabolite channelling may result from different kinetic mechanisms in which enzyme-enzyme interactions occur, so that intermediates are not released into the bulk solution and cannot be used by enzymes outside the channel. From an evolutionary point of view, the emergence of such mechanisms may provide new functional possibilities for the system, which would result in a selective advantage. Hence, it would be useful to evaluate the objective advantages provided by the various options by considering different criteria for functional effectiveness. Following this strategy, the goal of this paper is to compare a model for a free-diffusion two-enzyme system with two different models with inclusion of enzyme-enzyme interactions. In addition, models with simultaneous free and interacting branches are also analysed, and their advantages or disadvantages are presented. Basic guidelines are suggested that help in predicting the occurrence of specific mechanisms in different circumstances, and provide theoretical evidence in support of the hypothesis that no single solution simultaneously optimizes all the possible desired properties of the system.

Metabolic pathway characterization from transient response data obtained in situ: parameter estimation in S-system models.

The actual values of internal metabolites and fluxes can be measured by a number of experimental techniques and they provide important information for evaluating the properties of a metabolic pathway in situ. In this paper we propose a strategy to properly exploit this information. The suggested approach permits estimation of a set of parameters on the whole system so that a useful model can be constructed and used to describe its components and systemic properties and to predict its behavior under new conditions. A simulated reference pathway is provided to validate this method and to show its utility in metabolic studies.

Calcitonin gene-related peptide in rat spinal cord motoneurons: subcellular distribution and changes induced by axotomy.

Using light and electron microscopy, a study has been made of the changes of calcitonin gene-related peptide-like immunoreactivity in rat lumbar spinal cord motoneurons during cell body response to sciatic nerve injury. At light microscopy level, calcitonin gene-related peptide-like immunoreactivity was evaluated using an indirect immunofluorescence technique combined with Fast Blue retrograde tracing and a peroxidase-antiperoxidase procedure. The calcitonin gene-related peptide changes to sciatic nerve transection and crushing were compared. Calcitonin gene-related peptide-like immunoreactivity was transiently increased after the peripheral nerve lesion, but the response was sustained for a longer period when the peripheral nerve was transected and nerve regeneration prevented. The first changes in calcitonin gene-related peptide-like immunoreactivity were detected four days after nerve crush or transection. In animal spinal cords to which nerve crush had been applied, the maximal enhancement of immunoreactivity was found 11 days after lesion. This was followed by a gradual decline, normal levels being attained 45 days after nerve crushing. When the nerve was transected, the response was similar, but the maximal calcitonin gene-related peptide-like immunoreactivity was maintained over a period of between 11 and 30 days. As with crushing, an important decrease was observed after 45 days. The ultrastructural compartmentation of calcitonin gene-related peptide-like immunoreactivity was studied using either peroxidase-antiperoxidase method or immunogold labelling. Calcitonin gene-related peptide-like immuno-reactivity was located in restricted sacs of the Golgi complex, multivesicular bodies, small vesicles and tubulo-vesicular structures. Large, strongly labelled vesicles resembling secretory granules were also observed in neuronal bodies. Our results reveal that the increase of calcitonin gene-related peptide in motoneurons is a relevant change the cell body undergoes in response to peripheral injury. The ultrastructural location of the peptide distribution suggests specific compartmentation on tubulo-vesicular structures connected with the Golgi complex which form a network in the neuronal cytoplasm. The distribution pattern observed may be related to the sorting and delivery of calcitonin gene-related peptide to secretory vesicles.

Biochemical systems theory: increasing predictive power by using second-order derivatives measurements.

Models based on the power-law formalism provide a useful tool for analyzing metabolic systems. Within this methodology, the S-system variant furnishes the best strategy. In this paper we explore an extension of this formalism by considering second-order derivative terms of the Taylor series which the power-law is based upon. Results show that the S-system equations which include second-order Taylor coefficients give better accuracy in predicting the response of the system to a perturbation. Hence, models based on this new approach could provide a useful tool for quantitative purposes if one is able to measure the required derivatives experimentally. In particular we show the utility of this approach when it comes to discriminating between two mechanisms that are equivalent in the S-system a representation based on first-order coefficients. However, the loss of analytical tractability is a serious disadvantage for using this approach as a general tool for studying metabolic systems.