An efficient biological pathway layout algorithm combining grid-layout and spring embedder for complicated cellular location information

<p>Abstract</p> <p>Background</p> <p>Graph drawing is one of the important techniques for understanding biological regulations in a cell or among cells at the pathway level. Among many available layout algorithms, the spring embedder algorithm is widely used not only for pathway drawing but also for circuit placement and www visualization and so on because of the harmonized appearance of its results. For pathway drawing, location information is essential for its comprehension. However, complex shapes need to be taken into account when torus-shaped location information such as nuclear inner membrane, nuclear outer membrane, and plasma membrane is considered. Unfortunately, the spring embedder algorithm cannot easily handle such information. In addition, crossings between edges and nodes are usually not considered explicitly.</p> <p>Results</p> <p>We proposed a new grid-layout algorithm based on the spring embedder algorithm that can handle location information and provide layouts with harmonized appearance. In grid-layout algorithms, the mapping of nodes to grid points that minimizes a cost function is searched. By imposing positional constraints on grid points, location information including complex shapes can be easily considered. Our layout algorithm includes the spring embedder cost as a component of the cost function. We further extend the layout algorithm to enable dynamic update of the positions and sizes of compartments at each step.</p> <p>Conclusions</p> <p>The new spring embedder-based grid-layout algorithm and a spring embedder algorithm are applied to three biological pathways; endothelial cell model, Fas-induced apoptosis model, and <it>C. elegans </it>cell fate simulation model. From the positional constraints, all the results of our algorithm satisfy location information, and hence, more comprehensible layouts are obtained as compared to the spring embedder algorithm. From the comparison of the number of crossings, the results of the grid-layout-based algorithm tend to contain more crossings than those of the spring embedder algorithm due to the positional constraints. For a fair comparison, we also apply our proposed method without positional constraints. This comparison shows that these results contain less crossings than those of the spring embedder algorithm. We also compared layouts of the proposed algorithm with and without compartment update and verified that latter can reach better local optima.</p

An efficient grid layout algorithm for biological networks utilizing various biological attributes

BACKGROUND: Clearly visualized biopathways provide a great help in understanding biological systems. However, manual drawing of large-scale biopathways is time consuming. We proposed a grid layout algorithm that can handle gene-regulatory networks and signal transduction pathways by considering edge-edge crossing, node-edge crossing, distance measure between nodes, and subcellular localization information from Gene Ontology. Consequently, the layout algorithm succeeded in drastically reducing these crossings in the apoptosis model. However, for larger-scale networks, we encountered three problems: (i) the initial layout is often very far from any local optimum because nodes are initially placed at random, (ii) from a biological viewpoint, human layouts still exceed automatic layouts in understanding because except subcellular localization, it does not fully utilize biological information of pathways, and (iii) it employs a local search strategy in which the neighborhood is obtained by moving one node at each step, and automatic layouts suggest that simultaneous movements of multiple nodes are necessary for better layouts, while such extension may face worsening the time complexity. RESULTS: We propose a new grid layout algorithm. To address problem (i), we devised a new force-directed algorithm whose output is suitable as the initial layout. For (ii), we considered that an appropriate alignment of nodes having the same biological attribute is one of the most important factors of the comprehension, and we defined a new score function that gives an advantage to such configurations. For solving problem (iii), we developed a search strategy that considers swapping nodes as well as moving a node, while keeping the order of the time complexity. Though a naïve implementation increases by one order, the time complexity, we solved this difficulty by devising a method that caches differences between scores of a layout and its possible updates. CONCLUSION: Layouts of the new grid layout algorithm are compared with that of the previous algorithm and human layout in an endothelial cell model, three times as large as the apoptosis model. The total cost of the result from the new grid layout algorithm is similar to that of the human layout. In addition, its convergence time is drastically reduced (40% reduction)

Identifying regulational alterations in gene regulatory networks by state space representation of vector autoregressive models and variational annealing

Background: In the analysis of effects by cell treatment such as drug dosing, identifying changes on gene network structures between normal and treated cells is a key task. A possible way for identifying the changes is to compare structures of networks estimated from data on normal and treated cells separately. However, this approach usually fails to estimate accurate gene networks due to the limited length of time series data and measurement noise. Thus, approaches that identify changes on regulations by using time series data on both conditions in an efficient manner are demanded. Methods: We propose a new statistical approach that is based on the state space representation of the vector autoregressive model and estimates gene networks on two different conditions in order to identify changes on regulations between the conditions. In the mathematical model of our approach, hidden binary variables are newly introduced to indicate the presence of regulations on each condition. The use of the hidden binary variables enables an efficient data usage; data on both conditions are used for commonly existing regulations, while for condition specific regulations corresponding data are only applied. Also, the similarity of networks on two conditions is automatically considered from the design of the potential function for the hidden binary variables. For the estimation of the hidden binary variables, we derive a new variational annealing method that searches the configuration of the binary variables maximizing the marginal likelihood. Results: For the performance evaluation, we use time series data from two topologically similar synthetic networks, and confirm that our proposed approach estimates commonly existing regulations as well as changes on regulations with higher coverage and precision than other existing approaches in almost all the experimental settings. For a real data application, our proposed approach is applied to time series data from normal Human lung cells and Human lung cells treated by stimulating EGF-receptors and dosing an anticancer drug termed Gefitinib. In the treated lung cells, a cancer cell condition is simulated by the stimulation of EGF-receptors, but the effect would be counteracted due to the selective inhibition of EGF-receptors by Gefitinib. However, gene expression profiles are actually different between the conditions, and the genes related to the identified changes are considered as possible off-targets of Gefitinib. Conclusions: From the synthetically generated time series data, our proposed approach can identify changes on regulations more accurately than existing methods. By applying the proposed approach to the time series data on normal and treated Human lung cells, candidates of off-target genes of Gefitinib are found. According to the published clinical information, one of the genes can be related to a factor of interstitial pneumonia, which is known as a side effect of Gefitinib

A Simple Axiomatization of Neo-Additive Choquet Expected Utility Theory on a Finite State Space

By assuming that a state space is finite, we provide an easy-to-understand axiomatization of neo-additive Choquet expected utility theory (CEU) following Chateauneuf et al. (2007). Our axiomatization based on Möbius inversions sheds new light on their usefulness for our understanding of the behaviors of decision makers and enables us to provide new interpretations for neo-additive CEU from uncertainty aversion (uncertainty lovingness) and certainty equivalent, respectively. Furthermore, our approach enables us to understand the relationship between existing contributions by Chateauneuf et al. (2007), Kajii et al. (2009), and Asano and Kojima (2022) in a clearer and more unified way