Measuring specialization in species interaction networks

BACKGROUND: Network analyses of plant-animal interactions hold valuable biological information. They are often used to quantify the degree of specialization between partners, but usually based on qualitative indices such as 'connectance' or number of links. These measures ignore interaction frequencies or sampling intensity, and strongly depend on network size. RESULTS: Here we introduce two quantitative indices using interaction frequencies to describe the degree of specialization, based on information theory. The first measure (d') describes the degree of interaction specialization at the species level, while the second measure (H(2)') characterizes the degree of specialization or partitioning among two parties in the entire network. Both indices are mathematically related and derived from Shannon entropy. The species-level index d' can be used to analyze variation within networks, while H(2)' as a network-level index is useful for comparisons across different interaction webs. Analyses of two published pollinator networks identified differences and features that have not been detected with previous approaches. For instance, plants and pollinators within a network differed in their average degree of specialization (weighted mean d'), and the correlation between specialization of pollinators and their relative abundance also differed between the webs. Rarefied sampling effort in both networks and null model simulations suggest that H(2)' is not affected by network size or sampling intensity. CONCLUSION: Quantitative analyses reflect properties of interaction networks more appropriately than previous qualitative attempts, and are robust against variation in sampling intensity, network size and symmetry. These measures will improve our understanding of patterns of specialization within and across networks from a broad spectrum of biological interactions

Mathematical models in mammalian cell biology

A report on the Conference on Systems Biology of Mammalian Cells, Dresden, Germany, 22-24 May 2008

Identifiability and experimental design in perturbation studies

Motivation A common strategy to infer and quantify interactions between components of a biological system is to deduce them from the network’s response to targeted perturbations. Such perturbation experiments are often challenging and costly. Therefore, optimizing the experimental design is essential to achieve a meaningful characterization of biological networks. However, it remains difficult to predict which combination of perturbations allows to infer specific interaction strengths in a given network topology. Yet, such a description of identifiability is necessary to select perturbations that maximize the number of inferable parameters. Results We show analytically that the identifiability of network parameters can be determined by an intuitive maximum-flow problem. Furthermore, we used the theory of matroids to describe identifiability relationships between sets of parameters in order to build identifiable effective network models. Collectively, these results allowed to device strategies for an optimal design of the perturbation experiments. We benchmarked these strategies on a database of human pathways. Remarkably, full network identifiability was achieved, on average, with less than a third of the perturbations that are needed in a random experimental design. Moreover, we determined perturbation combinations that additionally decreased experimental effort compared to single-target perturbations. In summary, we provide a framework that allows to infer a maximal number of interaction strengths with a minimal number of perturbation experiments. Availability and implementation IdentiFlow is available at github.com/GrossTor/IdentiFlow. Supplementary information Supplementary data are available at Bioinformatics online.Peer Reviewe

Mathematical modelling identifies conditions for maintaining and escaping feedback control in the intestinal epithelium

The intestinal epithelium is one of the fastest renewing tissues in mammals. It shows a hierarchical organisation, where intestinal stem cells at the base of crypts give rise to rapidly dividing transit amplifying cells that in turn renew the pool of short-lived differentiated cells. Upon injury and stem-cell loss, cells can also de-differentiate. Tissue homeostasis requires a tightly regulated balance of differentiation and stem cell proliferation, and failure can lead to tissue extinction or to unbounded growth and cancerous lesions. Here, we present a two-compartment mathematical model of intestinal epithelium population dynamics that includes a known feedback inhibition of stem cell differentiation by differentiated cells. The model shows that feedback regulation stabilises the number of differentiated cells as these become invariant to changes in their apoptosis rate. Stability of the system is largely independent of feedback strength and shape, but specific thresholds exist which if bypassed cause unbounded growth. When dedifferentiation is added to the model, we find that the system can recover faster after certain external perturbations. However, dedifferentiation makes the system more prone to losing homeostasis. Taken together, our mathematical model shows how a feedback-controlled hierarchical tissue can maintain homeostasis and can be robust to many external perturbations

Mathematical Modeling Identifies Inhibitors of Apoptosis as Mediators of Positive Feedback and Bistability

The intrinsic, or mitochondrial, pathway of caspase activation is essential for apoptosis induction by various stimuli including cytotoxic stress. It depends on the cellular context, whether cytochrome c released from mitochondria induces caspase activation gradually or in an all-or-none fashion, and whether caspase activation irreversibly commits cells to apoptosis. By analyzing a quantitative kinetic model, we show that inhibition of caspase-3 (Casp3) and Casp9 by inhibitors of apoptosis (IAPs) results in an implicit positive feedback, since cleaved Casp3 augments its own activation by sequestering IAPs away from Casp9. We demonstrate that this positive feedback brings about bistability (i.e., all-or-none behaviour), and that it cooperates with Casp3-mediated feedback cleavage of Casp9 to generate irreversibility in caspase activation. Our calculations also unravel how cell-specific protein expression brings about the observed qualitative differences in caspase activation (gradual versus all-or-none and reversible versus irreversible). Finally, known regulators of the pathway are shown to efficiently shift the apoptotic threshold stimulus, suggesting that the bistable caspase cascade computes multiple inputs into an all-or-none caspase output. As cellular inhibitory proteins (e.g., IAPs) frequently inhibit consecutive intermediates in cellular signaling cascades (e.g., Casp3 and Casp9), the feedback mechanism described in this paper is likely to be a widespread principle on how cells achieve ultrasensitivity, bistability, and irreversibility

Robust network inference using response logic

Motivation A major challenge in molecular and cellular biology is to map out the regulatory networks of cells. As regulatory interactions can typically not be directly observed experimentally, various computational methods have been proposed to disentangling direct and indirect effects. Most of these rely on assumptions that are rarely met or cannot be adapted to a given context. Results We present a network inference method that is based on a simple response logic with minimal presumptions. It requires that we can experimentally observe whether or not some of the system’s components respond to perturbations of some other components, and then identifies the directed networks that most accurately account for the observed propagation of the signal. To cope with the intractable number of possible networks, we developed a logic programming approach that can infer networks of hundreds of nodes, while being robust to noisy, heterogeneous or missing data. This allows to directly integrate prior network knowledge and additional constraints such as sparsity. We systematically benchmark our method on KEGG pathways, and show that it outperforms existing approaches in DREAM3 and DREAM4 challenges. Applied to a novel perturbation dataset on PI3K and MAPK pathways in isogenic models of a colon cancer cell line, it generates plausible network hypotheses that explain distinct sensitivities toward various targeted inhibitors due to different PI3K mutants. Availability and implementation A Python/Answer Set Programming implementation can be accessed at github.com/GrossTor/response-logic. Data and analysis scripts are available at github.com/GrossTor/response-logic-projects. Supplementary information Supplementary data are available at Bioinformatics online.Peer Reviewe

Recurrent design patterns in the feedback regulation of the mammalian signalling network

Biochemical networks are characterized by recurrent patterns and motifs, but the design principles underlying the dynamics of the mammalian intracellular signalling network remain unclear. We systematically analysed decay rates of 134 signalling proteins and investigated their gene expression profiles in response to stimulation to get insights into transcriptional feedback regulation. We found a clear separation of the signalling pathways into flexible and static parts: for each pathway a subgroup of unstable signal inhibitors is transcriptionally induced upon stimulation, while the other constitutively expressed signalling proteins are long-lived. Kinetic modelling suggests that this design principle allows for swift feedback regulation and establishes latency phases after signalling, and that it might be an optimal design due to a trade-off between energy efficiency and flexibility

Discovering Causal Signaling Pathways Through Gene-Expression Patterns

High-throughput gene-expression studies result in lists of differentially expressed genes. Most current meta-analyses of these gene lists include searching for significant membership of the translated proteins in various signaling pathways. However, such membership enrichment algorithms do not provide insight into which pathways caused the genes to be differentially expressed in the first place. Here, we present an intuitive approach for discovering upstream signaling pathways responsible for regulating these differentially expressed genes. We identify consistently regulated signature genes specific for signal transduction pathways from a panel of single-pathway perturbation experiments. An algorithm that detects overrepresentation of these signature genes in a gene group of interest is used to infer the signaling pathway responsible for regulation. We expose our novel resource and algorithm through a web server called SPEED: Signaling Pathway Enrichment using Experimental Data sets. SPEED can be freely accessed at http://speed.sys-bio.net/