Andrei Todor

Probabilistic Biological Network Alignment

Interactions between molecules are probabilistic events. An interaction may or may not happen with some probability, depending on a variety of factors such as the size, abundance, or proximity of the interacting molecules. In this paper, we consider the problem of aligning two biological networks. Unlike existing methods, we allow one of the two networks to contain probabilistic interactions. Allowing interaction probabilities makes the alignment more biologically relevant at the expense of explosive growth in the number of alternative topologies that may arise from different subsets of interactions that take place. We develop a novel method that efficiently and precisely characterizes this massive search space. We represent the topological similarity between pairs of aligned molecules (i.e., proteins) with the help of random variables and compute their expected values. We validate our method showing that, without sacrificing the running time performance, it can produce novel alignments. Our results also demonstrate that our method identifies biologically meaningful mappings under a comprehensive set of criteria used in the literature as well as the statistical coherence measure that we developed to analyze the statistical significance of the similarity of the functions of the aligned protein pairs.

Blood transcriptomics and metabolomics for personalized medicine

Molecular analysis of blood samples is pivotal to clinical diagnosis and has been intensively investigated since the rise of systems biology. Recent developments have opened new opportunities to utilize transcriptomics and metabolomics for personalized and precision medicine. Efforts from human immunology have infused into this area exquisite characterizations of subpopulations of blood cells. It is now possible to infer from blood transcriptomics, with fine accuracy, the contribution of immune activation and of cell subpopulations. In parallel, high-resolution mass spectrometry has brought revolutionary analytical capability, detecting > 10,000 metabolites, together with environmental exposure, dietary intake, microbial activity, and pharmaceutical drugs. Thus, the re-examination of blood chemicals by metabolomics is in order. Transcriptomics and metabolomics can be integrated to provide a more comprehensive understanding of the human biological states. We will review these new data and methods and discuss how they can contribute to personalized medicine.

mTOR regulates metabolic adaptation of APCs in the lung and controls the outcome of allergic inflammation.

Metabolic programming of tissue APCs Antigen-presenting cells (APCs) are scattered throughout the body in lymphoid organs and at the portals of pathogen entry, where they act as sentinels of the immune system. Sinclair et al. demonstrate that APCs at different sites have distinctive metabolic signatures and that the development and function of these cells are determined not only by their transcriptional program, but also by their metabolic state (see the Perspective by Wiesner and Klein). The authors identified a central role for mTOR in mediating the metabolic adaptation of such tissue-resident APCs by influencing the immunological character of allergic inflammation. Thus, tissues endow resident APCs with distinctive metabolic characteristics that control APC development and function. Science, this issue p. 1014; see also p. 973 Metabolic adaptation of antigen-presenting cells in the lung reprograms lung dendritic cells and modulates allergic inflammation. Antigen-presenting cells (APCs) occupy diverse anatomical tissues, but their tissue-restricted homeostasis remains poorly understood. Here, working with mouse models of inflammation, we found that mechanistic target of rapamycin (mTOR)–dependent metabolic adaptation was required at discrete locations. mTOR was dispensable for dendritic cell (DC) homeostasis in secondary lymphoid tissues but necessary to regulate cellular metabolism and accumulation of CD103+ DCs and alveolar macrophages in lung. Moreover, while numbers of mTOR-deficient lung CD11b+ DCs were not changed, they were metabolically reprogrammed to skew allergic inflammation from eosinophilic T helper cell 2 (TH2) to neutrophilic TH17 polarity. The mechanism for this change was independent of translational control but dependent on inflammatory DCs, which produced interleukin-23 and increased fatty acid oxidation. mTOR therefore mediates metabolic adaptation of APCs in distinct tissues, influencing the immunological character of allergic inflammation.

Large scale analysis of signal reachability

Motivation: Major disorders, such as leukemia, have been shown to alter the transcription of genes. Understanding how gene regulation is affected by such aberrations is of utmost importance. One promising strategy toward this objective is to compute whether signals can reach to the transcription factors through the transcription regulatory network (TRN). Due to the uncertainty of the regulatory interactions, this is a #P-complete problem and thus solving it for very large TRNs remains to be a challenge. Results: We develop a novel and scalable method to compute the probability that a signal originating at any given set of source genes can arrive at any given set of target genes (i.e., transcription factors) when the topology of the underlying signaling network is uncertain. Our method tackles this problem for large networks while providing a provably accurate result. Our method follows a divide-and-conquer strategy. We break down the given network into a sequence of non-overlapping subnetworks such that reachability can be computed autonomously and sequentially on each subnetwork. We represent each interaction using a small polynomial. The product of these polynomials express different scenarios when a signal can or cannot reach to target genes from the source genes. We introduce polynomial collapsing operators for each subnetwork. These operators reduce the size of the resulting polynomial and thus the computational complexity dramatically. We show that our method scales to entire human regulatory networks in only seconds, while the existing methods fail beyond a few tens of genes and interactions. We demonstrate that our method can successfully characterize key reachability characteristics of the entire transcriptions regulatory networks of patients affected by eight different subtypes of leukemia, as well as those from healthy control samples. Availability: All the datasets and code used in this article are available at bioinformatics.cise.ufl.edu/PReach/scalable.htm. Contact: atodor@cise.ufl.edu Supplementary information: Supplementary data are available at Bioinformatics online.

PReach: Reachability in Probabilistic Signaling Networks

Extracellular molecules trigger a response inside the cell by initiating a signal at special membrane receptors (i.e., sources) which is then transmitted to reporters (i.e., targets) through various chains of interactions among proteins. Understanding whether such a signal can reach from membrane receptors to reporters is essential in studying the cell response to extracellular events. This problem is drastically complicated due to the unreliability of the interaction data. In this paper, we develop a novel method, called PReach (Probabilistic Reachability), that precisely computes the probability that a signal can reach from a given collection of receptors to a given collection of reporters when the underlying signaling network is uncertain. This is a very difficult computational problem with no known polynomial-time solution. PReach represents each uncertain interaction as a bivariate polynomial. It transforms the reachability problem to a polynomial multiplication problem. We introduce novel polynomial collapsing operators that associate polynomial terms with possible paths between sources and targets as well as the cuts that separate sources from targets. These operators significantly shrink the number of polynomial terms and thus the running time. PReach has much better time complexity than the recent solutions for this problem. Our experimental results on real datasets demonstrate that this improvement leads to orders of magnitude of reduction in the running time over the most recent methods.

Uncertain interactions affect degree distribution of biological networks

Biological interactions are often uncertain events, that may or may not take place under different scenarios. Existing studies analyze the degree distribution of biological networks by assuming that all the given interactions take place under all circumstances. This strong and often incorrect assumption can have misleading results. Here, we address this problem and develop sound mathematical basis to analyze degree distribution of biological networks in the presence of uncertain interactions. We present a comparative study of node degree distributions in two types of biological networks: the classical deterministic networks and the more flexible probabilistic networks. We extend this comparison to joint degree distributions of nodes connected by edges. The number of possible network topologies grows exponentially with the number of uncertain interactions. However, the mathematical apparatus we develop allows us to compute these degree distributions quickly even for entire protein protein interaction networks. It also helps us find an adequate mathematical model using maximum likelihood estimation. l Our results confirm that power law and log-normal models best describe degree distributions for both probabilistic and deterministic networks. Moreover, the inverse correlation of degrees of neighboring nodes shows that, in probabilistic networks, nodes with large number of interactions prefer to interact with those with small number of interactions more frequently than expected.

Reachability analysis in probabilistic biological networks

Extra-cellular molecules trigger a response inside the cell by initiating a signal at special membrane receptors (i.e., sources), which is then transmitted to reporters (i.e., targets) through various chains of interactions among proteins. Understanding whether such a signal can reach from membrane receptors to reporters is essential in studying the cell response to extra-cellular events. This problem is drastically complicated due to the unreliability of the interaction data. In this paper, we develop a novel method, called PReach (Probabilistic Reachability), that precisely computes the probability that a signal can reach from a given collection of receptors to a given collection of reporters when the underlying signaling network is uncertain. This is a very difficult computational problem with no known polynomial-time solution. PReach represents each uncertain interaction as a bi-variate polynomial. It transforms the reachability problem to a polynomial multiplication problem. We introduce novel polynomial collapsing operators that associate polynomial terms with possible paths between sources and targets as well as the cuts that separate sources from targets. These operators significantly shrink the number of polynomial terms and thus the running time. PReach has much better time complexity than the recent solutions for this problem. Our experimental results on real data sets demonstrate that this improvement leads to orders of magnitude of reduction in the running time over the most recent methods. Availability: All the data sets used, the software implemented and the alignments found in this paper are available at http://bioinformatics.cise.ufl.edu/PReach/.

Characterizing the Topology of Probabilistic Biological Networks

Biological interactions are often uncertain events, that may or may not take place with some probability. This uncertainty leads to a massive number of alternative interaction topologies for each such network. The existing studies analyze the degree distribution of biological networks by assuming that all the given interactions take place under all circumstances. This strong and often incorrect assumption can lead to misleading results. In this paper, we address this problem and develop a sound mathematical basis to characterize networks in the presence of uncertain interactions. Using our mathematical representation, we develop a method that can accurately describe the degree distribution of such networks. We also take one more step and extend our method to accurately compute the joint-degree distributions of node pairs connected by edges. The number of possible network topologies grows exponentially with the number of uncertain interactions. However, the mathematical model we develop allows us to compute these degree distributions in polynomial time in the number of interactions. Our method works quickly even for entire protein-protein interaction (PPI) networks. It also helps us find an adequate mathematical model using MLE. We perform a comparative study of node-degree and joint-degree distributions in two types of biological networks: the classical deterministic networks and the more flexible probabilistic networks. Our results confirm that power-law and log-normal models best describe degree distributions for both probabilistic and deterministic networks. Moreover, the inverse correlation of degrees of neighboring nodes shows that, in probabilistic networks, nodes with large number of interactions prefer to interact with those with small number of interactions more frequently than expected. We also show that probabilistic networks are more robust for node-degree distribution computation than the deterministic ones. Availability: all the data sets used, the software implemented and the alignments found in this paper are available at >http://bioinformatics.cise.ufl.edu/projects/probNet/.

Counting motifs in probabilistic biological networks

Studying the distribution of motifs in biological networks provides valuable insights about the key functions of these networks. Finding motifs in networks is however a computationally challenging task. This task is further complicated by the fact that inherently, biological networks have uncertain topologies. Such uncertainty is often described using probabilistic network models. In this study we tackle this challenge. We present the exact computation of the expected value and variance of the number of occurrences of key motifs in probabilistic networks, as well as a specialized sampling approximate method for computing the variance for very large networks. Our method is generic, and easily extends to arbitrary motif topologies. Our experiments demonstrate that our method scales to large protein interaction networks as well as synthetically generated networks with different connectivity patterns. Using our method, we identify over-represented motifs in protein-protein interaction networks of five different organisms, as well as in human transcription regulatory networks of different human cells with different lineages.

Reachability analysis in large probabilistic biological networks

Extra-cellular molecules trigger a response inside the cell by initiating a signal at special membrane receptors (i.e., sources), which is then transmitted to reporters (i.e., targets) through various chains of interactions among proteins. Understanding whether such a signal can reach from membrane receptors to reporters is essential in studying the cell response to extra-cellular events. This problem is drastically complicated due to the unreliability of the interaction data. In this paper, we develop a novel method, called PReach (Probabilistic Reachability), that precisely computes the probability that a signal can reach from a given collection of receptors to a given collection of reporters when the underlying signaling network is uncertain. This is a very difficult computational problem with no known polynomial-time solution. PReach represents each uncertain interaction as a bi-variate polynomial. It transforms the reachability problem to a polynomial multiplication problem. We introduce novel polynomial collapsing operators that associate polynomial terms with possible paths between sources and targets as well as the cuts that separate sources from targets. These operators significantly shrink the number of polynomial terms and thus the running time. PReach has much better time complexity than the recent solutions for this problem. Our experimental results on real data sets demonstrate that this improvement leads to orders of magnitude of reduction in the running time over the most recent methods. Availability: All the data sets used, the software implemented and the alignments found in this paper are available at http://bioinformatics.cise.ufl.edu/PReach/.