Improving network inference: The impact of false positive and false negative conclusions about the presence or absence of links.

BACKGROUND: A reliable inference of networks from data is of key interest in the Neurosciences. Several methods have been suggested in the literature to reliably determine links in a network. To decide about the presence of links, these techniques rely on statistical inference, typically controlling the number of false positives, paying little attention to false negatives. NEW METHOD: In this paper, by means of a comprehensive simulation study, we analyse the influence of false positive and false negative conclusions about the presence or absence of links in a network on the network topology. We show that different values to balance false positive and false negative conclusions about links should be used in order to reliably estimate network characteristics. We propose to run careful simulation studies prior to making potentially erroneous conclusion about the network topology. RESULTS: Our analysis shows that optimal values to balance false positive and false negative conclusions about links depend on the network topology and characteristic of interest. COMPARISON WITH EXISTING METHODS: Existing methods rely on a choice of the rate for false positive conclusions. They aim to be sure about individual links rather than the entire network. The rate of false negative conclusions is typically not investigated. CONCLUSIONS: Our investigation shows that the balance of false positive and false negative conclusions about links in a network has to be tuned for any network topology that is to be estimated. Moreover, within the same network topology, the results are qualitatively the same for each network characteristic, but the actual values leading to reliable estimates of the characteristics are different.

Disentangling regular and chaotic motion in the standard map using complex network analysis of recurrences in phase space.

Recurrence in the phase space of complex systems is a well-studied phenomenon, which has provided deep insights into the nonlinear dynamics of such systems. For dissipative systems, characteristics based on recurrence plots have recently attracted much interest for discriminating qualitatively different types of dynamics in terms of measures of complexity, dynamical invariants, or even structural characteristics of the underlying attractor's geometry in phase space. Here, we demonstrate that the latter approach also provides a corresponding distinction between different co-existing dynamical regimes of the standard map, a paradigmatic example of a low-dimensional conservative system. Specifically, we show that the recently developed approach of recurrence network analysis provides potentially useful geometric characteristics distinguishing between regular and chaotic orbits. We find that chaotic orbits in an intermittent laminar phase (commonly referred to as sticky orbits) have a distinct geometric structure possibly differing in a subtle way from those of regular orbits, which is highlighted by different recurrence network properties obtained from relatively short time series. Thus, this approach can help discriminating regular orbits from laminar phases of chaotic ones, which presents a persistent challenge to many existing chaos detection techniques.

Community control in cellular protein production: consequences for amino acid starvation.

Deprivation of essential nutrients can have stark consequences for many processes in a cell. We consider amino acid starvation, which can result in bottlenecks in mRNA translation when ribosomes stall due to lack of resources, i.e. tRNAs charged with the missing amino acid. Recent experiments also show less obvious effects such as increased charging of other (non-starved) tRNA species and selective charging of isoaccepting tRNAs. We present a mechanism which accounts for these observations and shows that production of some proteins can actually increase under starvation. One might assume that such responses could only be a result of sophisticated control pathways, but here we show that these effects can occur naturally due to changes in the supply and demand for different resources, and that control can be accomplished through selective use of rare codons. We develop a model for translation which includes the dynamics of the charging and use of aminoacylated tRNAs, explicitly taking into account the effect of specific codon sequences. This constitutes a new control mechanism in gene regulation which emerges at the community level, i.e. via resources used by all ribosomes.

Integrative Model of Oxidative Stress Adaptation in the Fungal Pathogen Candida albicans.

The major fungal pathogen of humans, Candida albicans, mounts robust responses to oxidative stress that are critical for its virulence. These responses counteract the reactive oxygen species (ROS) that are generated by host immune cells in an attempt to kill the invading fungus. Knowledge of the dynamical processes that instigate C. albicans oxidative stress responses is required for a proper understanding of fungus-host interactions. Therefore, we have adopted an interdisciplinary approach to explore the dynamical responses of C. albicans to hydrogen peroxide (H2O2). Our deterministic mathematical model integrates two major oxidative stress signalling pathways (Cap1 and Hog1 pathways) with the three major antioxidant systems (catalase, glutathione and thioredoxin systems) and the pentose phosphate pathway, which provides reducing equivalents required for oxidative stress adaptation. The model encapsulates existing knowledge of these systems with new genomic, proteomic, transcriptomic, molecular and cellular datasets. Our integrative approach predicts the existence of alternative states for the key regulators Cap1 and Hog1, thereby suggesting novel regulatory behaviours during oxidative stress. The model reproduces both existing and new experimental observations under a variety of scenarios. Time- and dose-dependent predictions of the oxidative stress responses for both wild type and mutant cells have highlighted the different temporal contributions of the various antioxidant systems during oxidative stress adaptation, indicating that catalase plays a critical role immediately following stress imposition. This is the first model to encapsulate the dynamics of the transcriptional response alongside the redox kinetics of the major antioxidant systems during H2O2 stress in C. albicans.

Contribution of Fdh3 and Glr1 to Glutathione Redox State, Stress Adaptation and Virulence in Candida albicans.

The major fungal pathogen of humans, Candida albicans, is exposed to reactive nitrogen and oxygen species following phagocytosis by host immune cells. In response to these toxins, this fungus activates potent anti-stress responses that include scavenging of reactive nitrosative and oxidative species via the glutathione system. Here we examine the differential roles of two glutathione recycling enzymes in redox homeostasis, stress adaptation and virulence in C. albicans: glutathione reductase (Glr1) and the S-nitrosoglutathione reductase (GSNOR), Fdh3. We show that the NADPH-dependent Glr1 recycles GSSG to GSH, is induced in response to oxidative stress and is required for resistance to macrophage killing. GLR1 deletion increases the sensitivity of C. albicans cells to H2O2, but not to formaldehyde or NO. In contrast, Fdh3 detoxifies GSNO to GSSG and NH3, and FDH3 inactivation delays NO adaptation and increases NO sensitivity. C. albicans fdh3⎔ cells are also sensitive to formaldehyde, suggesting that Fdh3 also contributes to formaldehyde detoxification. FDH3 is induced in response to nitrosative, oxidative and formaldehyde stress, and fdh3Δ cells are more sensitive to killing by macrophages. Both Glr1 and Fdh3 contribute to virulence in the Galleria mellonella and mouse models of systemic infection. We conclude that Glr1 and Fdh3 play differential roles during the adaptation of C. albicans cells to oxidative, nitrosative and formaldehyde stress, and hence during the colonisation of the host. Our findings emphasise the importance of the glutathione system and the maintenance of intracellular redox homeostasis in this major pathogen.

Networks: On the relation of bi- and multivariate measures.

A reliable inference of networks from observations of the nodes' dynamics is a major challenge in physics. Interdependence measures such as a the correlation coefficient or more advanced methods based on, e.g., analytic phases of signals are employed. For several of these interdependence measures, multivariate counterparts exist that promise to enable distinguishing direct and indirect connections. Here, we demonstrate analytically how bivariate measures relate to the respective multivariate ones; this knowledge will in turn be used to demonstrate the implications of thresholded bivariate measures for network inference. Particularly, we show, that random networks are falsely identified as small-world networks if observations thereof are treated by bivariate methods. We will employ the correlation coefficient as an example for such an interdependence measure. The results can be readily transferred to all interdependence measures partializing for information of thirds in their multivariate counterparts.

Network inference in the presence of latent confounders: the role of instantaneous causalities.

BACKGROUND: Detecting causal interactions in multivariate systems, in terms of Granger-causality, is of major interest in the Neurosciences. Typically, it is almost impossible to observe all components of the system. Missing certain components can lead to the appearance of spurious interactions. The aim of this study is to demonstrate the effect of this and to demonstrate that distinction between latent confounders and volume conduction is possible in some cases. NEW METHOD: Our new method uses a combination of renormalised partial directed coherence and analysis of the (partial) covariance matrix of residual noise process to detect instantaneous, spurious interactions. Sub-network analyses are performed to infer the true network structure of the underlying system. RESULTS: We provide evidence that it is possible to distinguish between instantaneous interactions that occur as a result of a latent confounder and those that occur as a result of volume conduction. COMPARISON WITH EXISTING METHODS: Our novel approach demonstrates to what extent inference of unobserved important processes as well as the distinction between latent confounders and volume conduction is possible. We suggest a combination of measures of Granger-causality and covariance selection models to achieve this numerically. CONCLUSIONS: Sub-network analyses enable a much more precise and correct inference of the true underlying network structure in some cases. From this it is possible to distinguish between unobserved processes and volume conduction. Our approach is straightforwardly adaptable to various measures of Granger-causality emphasising its ubiquitous successful applicability.

Assessing the strength of directed influences among neural signals: an approach to noisy data.

BACKGROUND: Measurements in the neurosciences are afflicted with observational noise. Granger-causality inference typically does not take this effect into account. We demonstrate that this leads to false positives conclusions and spurious causalities. NEW METHOD: State space modelling provides a convenient framework to obtain reliable estimates for Granger-causality. Despite its previous application in several studies, the analytical derivation of the statistics for parameter estimation in the state space model was missing. This prevented a rigorous evaluation of the results. RESULTS: In this manuscript we derive the statistics for parameter estimation in the state space model. We demonstrate in an extensive simulation study that our novel approach outperforms standard approaches and avoids false positive conclusions about Granger-causality. COMPARISON WITH EXISTING METHODS: In comparison with the naive application of Granger-causality inference, we demonstrate the superiority of our novel approach. The wide-spread applicability of our procedure provides a statistical framework for future studies. The application to mice electroencephalogram data demonstrates the immediate applicability of our approach. CONCLUSIONS: The analytical derivation of the statistics presented in this manuscript enables a rigorous evaluation of the results of Granger causal network inference. It is noteworthy that the statistics can be readily applied to various measures for Granger causality and other approaches that are based on vector autoregressive models.

Optimized spectral estimation for nonlinear synchronizing systems.

In many fields of research nonlinear dynamical systems are investigated. When more than one process is measured, besides the distinct properties of the individual processes, their interactions are of interest. Often linear methods such as coherence are used for the analysis. The estimation of coherence can lead to false conclusions when applied without fulfilling several key assumptions. We introduce a data driven method to optimize the choice of the parameters for spectral estimation. Its applicability is demonstrated based on analytical calculations and exemplified in a simulation study. We complete our investigation with an application to nonlinear tremor signals in Parkinson's disease. In particular, we analyze electroencephalogram and electromyogram data.

The impact of latent confounders in directed network analysis in neuroscience.

In the analysis of neuroscience data, the identification of task-related causal relationships between various areas of the brain gives insights about the network of physiological pathways that are active during the task. One increasingly used approach to identify causal connectivity uses the concept of Granger causality that exploits predictability of activity in one region by past activity in other regions of the brain. Owing to the complexity of the data, selecting components for the analysis of causality as a preprocessing step has to be performed. This includes predetermined-and often arbitrary-exclusion of information. Therefore, the system is confounded by latent sources. In this paper, the effect of latent confounders is demonstrated, and paths of influence among three components are studied. While methods for analysing Granger causality are commonly based on linear vector autoregressive models, the effects of latent confounders are expected to be present also in nonlinear systems. Therefore, all analyses are also performed for a simulated nonlinear system and discussed with regard to applications in neuroscience.

From START to FINISH: the influence of osmotic stress on the cell cycle.

The cell cycle is a sequence of biochemical events that are controlled by complex but robust molecular machinery. This enables cells to achieve accurate self-reproduction under a broad range of different conditions. Environmental changes are transmitted by molecular signalling networks, which coordinate their action with the cell cycle. The cell cycle process and its responses to environmental stresses arise from intertwined nonlinear interactions among large numbers of simpler components. Yet, understanding of how these pieces fit together into a coherent whole requires a systems biology approach. Here, we present a novel mathematical model that describes the influence of osmotic stress on the entire cell cycle of S. cerevisiae for the first time. Our model incorporates all recently known and several proposed interactions between the osmotic stress response pathway and the cell cycle. This model unveils the mechanisms that emerge as a consequence of the interaction between the cell cycle and stress response networks. Furthermore, it characterises the role of individual components. Moreover, it predicts different phenotypical responses for cells depending on the phase of cells at the onset of the stress. The key predictions of the model are: (i) exposure of cells to osmotic stress during the late S and the early G2/M phase can induce DNA re-replication before cell division occurs, (ii) cells stressed at the late G2/M phase display accelerated exit from mitosis and arrest in the next cell cycle, (iii) osmotic stress delays the G1-to-S and G2-to-M transitions in a dose dependent manner, whereas it accelerates the M-to-G1 transition independently of the stress dose and (iv) the Hog MAPK network compensates the role of the MEN network during cell division of MEN mutant cells. These model predictions are supported by independent experiments in S. cerevisiae and, moreover, have recently been observed in other eukaryotes.

A systems biology analysis of long and short-term memories of osmotic stress adaptation in fungi.

BACKGROUND: Saccharomyces cerevisiae senses hyperosmotic conditions via the HOG signaling network that activates the stress-activated protein kinase, Hog1, and modulates metabolic fluxes and gene expression to generate appropriate adaptive responses. The integral control mechanism by which Hog1 modulates glycerol production remains uncharacterized. An additional Hog1-independent mechanism retains intracellular glycerol for adaptation. Candida albicans also adapts to hyperosmolarity via a HOG signaling network. However, it remains unknown whether Hog1 exerts integral or proportional control over glycerol production in C. albicans. RESULTS: We combined modeling and experimental approaches to study osmotic stress responses in S. cerevisiae and C. albicans. We propose a simple ordinary differential equation (ODE) model that highlights the integral control that Hog1 exerts over glycerol biosynthesis in these species. If integral control arises from a separation of time scales (i.e. rapid HOG activation of glycerol production capacity which decays slowly under hyperosmotic conditions), then the model predicts that glycerol production rates elevate upon adaptation to a first stress and this makes the cell adapts faster to a second hyperosmotic stress. It appears as if the cell is able to remember the stress history that is longer than the timescale of signal transduction. This is termed the long-term stress memory. Our experimental data verify this. Like S. cerevisiae, C. albicans mimimizes glycerol efflux during adaptation to hyperosmolarity. Also, transient activation of intermediate kinases in the HOG pathway results in a short-term memory in the signaling pathway. This determines the amplitude of Hog1 phosphorylation under a periodic sequence of stress and non-stressed intervals. Our model suggests that the long-term memory also affects the way a cell responds to periodic stress conditions. Hence, during osmohomeostasis, short-term memory is dependent upon long-term memory. This is relevant in the context of fungal responses to dynamic and changing environments. CONCLUSIONS: Our experiments and modeling have provided an example of identifying integral control that arises from time-scale separation in different processes, which is an important functional module in various contexts.

Combinatorial stresses kill pathogenic Candida species.

Pathogenic microbes exist in dynamic niches and have evolved robust adaptive responses to promote survival in their hosts. The major fungal pathogens of humans, Candida albicans and Candida glabrata, are exposed to a range of environmental stresses in their hosts including osmotic, oxidative and nitrosative stresses. Significant efforts have been devoted to the characterization of the adaptive responses to each of these stresses. In the wild, cells are frequently exposed simultaneously to combinations of these stresses and yet the effects of such combinatorial stresses have not been explored. We have developed a common experimental platform to facilitate the comparison of combinatorial stress responses in C. glabrata and C. albicans. This platform is based on the growth of cells in buffered rich medium at 30°C, and was used to define relatively low, medium and high doses of osmotic (NaCl), oxidative (H(2)O(2)) and nitrosative stresses (e.g., dipropylenetriamine (DPTA)-NONOate). The effects of combinatorial stresses were compared with the corresponding individual stresses under these growth conditions. We show for the first time that certain combinations of combinatorial stress are especially potent in terms of their ability to kill C. albicans and C. glabrata and/or inhibit their growth. This was the case for combinations of osmotic plus oxidative stress and for oxidative plus nitrosative stress. We predict that combinatorial stresses may be highly significant in host defences against these pathogenic yeasts.

A max-plus model of ribosome dynamics during mRNA translation.

We examine the dynamics of the translation stage of cellular protein production, in which ribosomes move uni-directionally along an mRNA strand, building amino acid chains as they go. We describe the system using a timed event graph-a class of Petri net useful for studying discrete events, which have to satisfy constraints. We use max-plus algebra to describe a deterministic version of the model, where the constraints represent steric effects which prevent more than one ribosome reading a given codon at a given time and delays associated with the availability of the different tRNAs. We calculate the protein production rate and density of ribosomes on the mRNA and find exact agreement between these analytical results and numerical simulations of the deterministic model, even in the case of heterogeneous mRNAs.

Recovery from stress - a cell cycle perspective.

We develop a Boolean model to explore the dynamical behaviour of budding yeast in response to osmotic and pheromone stress. Our model predicts that osmotic stress halts the cell cycle progression in either of four possible arrest points. The state of the cell at the onset of the stress dictates which arrest point is finally reached. According to our study and consistent with biological data, these cells can return to the cell cycle after removal of the stress. Moreover, the Boolean model illustrates how osmotic stress alters the state transitions of the cell. Furthermore, we investigate the influence of a particular pheromone based method for the synchronisation of the cell cycles in a population of cells. We show this technique is not a suitable method to study one of the arrest points under osmotic stress. Finally, we discuss how an osmotic stress can cause some of the so called frozen cells to divide. In this case the stress can move these cells to the cell cycle trajectory, such that they will replicate again.

Inference of Granger causal time-dependent influences in noisy multivariate time series.

Inferring Granger-causal interactions between processes promises deeper insights into mechanisms underlying network phenomena, e.g. in the neurosciences where the level of connectivity in neural networks is of particular interest. Renormalized partial directed coherence has been introduced as a means to investigate Granger causality in such multivariate systems. A major challenge in estimating respective coherences is a reliable parameter estimation of vector autoregressive processes. We discuss two shortcomings typical in relevant applications, i.e. non-stationarity of the processes generating the time series and contamination with observational noise. To overcome both, we present a new approach by combining renormalized partial directed coherence with state space modeling. A numerical efficient way to perform both the estimation as well as the statistical inference will be presented.

The dynamics of supply and demand in mRNA translation.

We study the elongation stage of mRNA translation in eukaryotes and find that, in contrast to the assumptions of previous models, both the supply and the demand for tRNA resources are important for determining elongation rates. We find that increasing the initiation rate of translation can lead to the depletion of some species of aa-tRNA, which in turn can lead to slow codons and queueing. Particularly striking "competition" effects are observed in simulations of multiple species of mRNA which are reliant on the same pool of tRNA resources. These simulations are based on a recent model of elongation which we use to study the translation of mRNA sequences from the Saccharomyces cerevisiae genome. This model includes the dynamics of the use and recharging of amino acid tRNA complexes, and we show via Monte Carlo simulation that this has a dramatic effect on the protein production behaviour of the system.

Theoretical basis of the community effect in development.

BACKGROUND: Genetically identical cells often show significant variation in gene expression profile and behaviour even in the same physiological condition. Notably, embryonic cells destined to the same tissue maintain a uniform transcriptional regulatory state and form a homogeneous cell group. One mechanism to keep the homogeneity within embryonic tissues is the so-called community effect in animal development. The community effect is an interaction among a group of many nearby precursor cells, and is necessary for them to maintain tissue-specific gene expression and differentiate in a coordinated manner. Although it has been shown that the cell-cell communication by a diffusible factor plays a crucial role, it is not immediately obvious why a community effect needs many cells. RESULTS: In this work, we propose a model of the community effect in development, which consists in a linear gene cascade and cell-cell communication. We examined the properties of the model theoretically using a combination of stochastic and deterministic modelling methods. We have derived the analytical formula for the threshold size of a cell population that is necessary for a community effect, which is in good agreement with stochastic simulation results. CONCLUSIONS: Our theoretical analysis indicates that a simple model with a linear gene cascade and cell-cell communication is sufficient to reproduce the community effect in development. The model explains why a community needs many cells. It suggests that the community's long-term behaviour is independent of the initial induction level, although the initiation of a community effect requires a sufficient amount of inducing signal. The mechanism of the community effect revealed by our theoretical analysis is analogous to that of quorum sensing in bacteria. The community effect may underlie the size control in animal development and also the genesis of autosomal dominant diseases including tumorigenesis.

Collective response of self-organized clusters of mechanosensitive channels.

Mechanosensitive channels are ion channels activated by membrane tension. We investigate the influence of the spatial distribution of bacterial mechanosensitive channels on activation (gating). Based on elastic short-range interactions we map this physical process onto an Ising-like model, which enables us to predict the clustering of channels and the effects of clustering on their gating. We conclude that the aggregation of channels and the consequent interactions among them leads to a global cooperative gating behavior with potentially dramatic consequences for the cell.

Multivariate analysis of dynamical processes with applications to the neurosciences.

Nowadays, data are recorded with increasing spatial and temporal resolution. Commonly these data are analyzed using univariate or bivariate approaches. Most of the analysis techniques assume stationarity of the underlying dynamical processes. Here, we present an approach that is capable of analyzing multivariate data, the so-called renormalized partial directed coherence. It utilizes the concept of Granger causality and is applicable to non-stationary data. We discuss its abilities and limitations, and demonstrate its usefulness in an application to murine electroencephalography (EEG) data during sleep transitions.