It is well known that an important step toward understanding the functions of a protein is to determine its subcellular location. Although numerous prediction algorithms have been developed, most of them typically focused on the proteins with only one location. In recent years, researchers have begun to pay attention to the subcellular localization prediction of the proteins with multiple sites. However, almost all the existing approaches have failed to take into account the correlations among the locations caused by the proteins with multiple sites, which may be the important information for improving the prediction accuracy of the proteins with multiple sites. In this paper, a new algorithm which can effectively exploit the correlations among the locations is proposed by using Gaussian process model. Besides, the algorithm also can realize optimal linear combination of various feature extraction technologies and could be robust to the imbalanced data set. Experimental results on a human protein data set show that the proposed algorithm is valid and can achieve better performance than the existing approaches. Over the past years, the research on determining the subcellular locations of proteins has attracted more attention from academia due to its important roles in understanding protein functions, identifying drug targets, annotating genomes and so on. The approaches for determining the subcellular locations of proteins can be divided into two categories: experimental and computational methods Since the pioneering efforts were provided As mentioned above, through the continuing efforts of researchers, many computational methods which can achieve superior performance have been developed. However, all these studies In order to deal with the protein with multiple sites, the common idea of the existing approaches is to train one or more single-label classifiers by transforming the original multi-label data into single-label ones and classify the query protein to the locations whose score outputted by the single-label classifiers satisfying some conditions. Three strategies were mainly used to transform the original multi-label data into single-label data. The first category such as Chou and Shen’s work In addition, to improve the whole performance of protein subcellular localization prediction approaches, another important factor is to represent the proteins with an effective feature extraction technology. Although the proteins may contain all the information such that they can be transported to the due subcellular compartments exactly, to establish a quality feature extraction technology that can mine this information is still a challenging problem. However, with the efforts of researchers, various types of feature extraction technologies based on the different local information of proteins such as N-terminus, sequence motifs, amino acid composition, and gene ontology terms have been proposed. Thus, we can try to improve the prediction performance by incorporating multiple local feature information of proteins. In fact, researchers have already done some work in this aspect. However, in many cases, different types of feature information were included in one predictor based on the subjective understanding of researchers, and it is hardly to realize the optimal combination of them. Thus, the second research context of our work is to optimally combine multiple feature extraction technologies in the predictor.Furthermore, the subcellular distribution of proteins is usually extremely imbalanced. For example, in the data set of eukaryotic proteins In order to consider aforementioned three problems simultaneously, a new classifier is proposed in this paper by using Gaussian process model. The basic idea of the proposed algorithm is to define multiple latent functions on the feature spaces, then the correlations among the locations can be identified by the covariance matrix between these latent functions, the optimal linear combination of different feature extraction technologies can be realized by defining a likelihood function and the imbalance of data can be coped with by the weighting coefficient of the likelihood on each sample. Since it can deal with the problems possessing the following properties: (1) the distribution of data on different classes may be imbalanced, (2) the data are represented in multiple feature spaces, and (3) each datum may associate with multiple labels simultaneously, the machine learning framework described in this paper is named imbalanced multi-modal multi-label learning (IMMML). we also call the proposed algorithm imbalanced multi-modal multi-label Gaussian process (IMMMLGP).According to a recent comprehensive review D and Q is the number of subcellular locations. Let m feature extraction technologies used to extract the feature information of the proteins. Thus, each protein X associated with n proteins with known sites, where, ith protein, iX and iX, iY can be represented by a vector iX belongs to ky, otherwise S which can correctly predict the subcellular locations of a new protein h is a set of the locations.Let Due to the desirable properties such as the natural Bayesian interpretation, explicit probabilistic formulation, and the ability to infer model parameters, Gaussian process model (GP) has received extensive attentions in recent years and become an important tool for many machine learning technologies. We will omit an introduction to it and refer the readers to the excellent books on this topic ky on the feature space X belongs to subcellular location ky can be obtained by the combination of latent functions ky. In IMMMLGP, the correlations among the subcellular locations can be identified by the covariance matrix of the latent functions; the optimal linear combination of different feature extraction technologies can be realized by defining a likelihood function and the combination coefficient of the jth feature extraction technology is just a parameter of the kernel function over feature space To represent our uncertainty over subcellular locations for a protein, a better method is to output a probability for each subcellular location. As shown in jth feature extraction technology. jk is a covariance function over feature space jk, i.e., The basic idea behind Gaussian process model is to place a Gaussian process prior over the latent functions. In this paper, we place the Gaussian process priors with zero mean and the following covariance function over the latent functions C and We assume that all the parameters can be given except According to (1), the joint distribution Let In this paper, we also would like to realize the optimal linear combination of various feature extraction technologies. It can be seen from (1) that the scale of F for given C and a becomesBy using Bayes’s rule, the posterior distribution over By using the approximation Thus, the probability C, a and C, a and Appendix S1.Until now, we have presented the whole IMMMLGP algorithm under the assumption that In this section, we test the proposed algorithm on a human protein data set collected from the Swiss-Prot database by Shen and Chou In statistical prediction, the following three cross-validation methods are often used to examine a predictor for its effectiveness in practical application: independent data set test, subsampling test, and jackknife test iX; y to be a proper label of iX; y derived from Since the performance evaluation of multi-label problems is much more complicated than the traditional single-label ones, the following popular multi-label evaluation metrics are used to comprehensively evaluate the performance of the proposed approach. Here, Average precision: Coverage: Ranking loss: Recall: F1-score: Absolute true success rate: The more detailed definitions of the first five metrics can be found in C. In order to justify the fact that the superior performance of the proposed algorithm benefits by considering the correlations among labels, we firstly investigate the performance difference between the proposed approach and its variation in which the covariance matrix C is assumed to be an identity matrix . As shown in the Section “Methods”, a main contribution of the proposed approach is that the correlations among the locations are exploited by using a covariance matrix In order to evaluate the relative performance of the proposed algorithm, it is compared with an existing algorithm named Hum-mPLoc 2.0 In order to understand why the proposed algorithm can achieve superior performance than Hum-mPLoc 2.0 on the proteins with multiple sites, we analysis the difference of the results outputted by the two algorithm. Finally, it should be pointed out that although the proposed algorithm can achieve superior performance than the existing ones, it mainly benefits by the novel classifier but not the feature information. In the future, we will try to improve the algorithm by using more feature information such as FunD  representation and SeqEvo  representation. Moreover, since user-friendly and publicly accessible web-servers represent the future direction for developing practically more useful models, simulated methods, or predictors Appendix S1(PDF)Click here for additional data file.


Cyanobacteria possess multiple mechanisms for regulating the pathways of photosynthetic and respiratory electron transport. Electron transport may be regulated indirectly by controlling the transfer of excitation energy from the light-harvesting complexes, or it may be more directly regulated by controlling the stoichiometry, localization, and interactions of photosynthetic and respiratory electron transport complexes. Regulation of the extent of linear vs. cyclic electron transport is particularly important for controlling the redox balance of the cell. This review discusses what is known of the regulatory mechanisms and the timescales on which they occur, with particular regard to the structural reorganization needed and the constraints imposed by the limited mobility of membrane-integral proteins in the crowded thylakoid membrane. Switching mechanisms requiring substantial movement of integral thylakoid membrane proteins occur on slower timescales than those that require the movement only of cytoplasmic or extrinsic membrane proteins. This difference is probably due to the restricted diffusion of membrane-integral proteins. Multiple switching mechanisms may be needed to regulate electron transport on different timescales. The thylakoid membranes of cyanobacteria are a complex intracytoplasmic membrane system that houses the photosynthetic electron transport chain, and also most of the respiratory electron transport complexes. Thylakoid membrane pairs separate a lumenal space from the cytoplasm: electron transport results in proton translocation across the membrane and into the lumen, and the resultant proton motive force is used to power ATP synthesis. Structural studies by cryo-electron tomography suggest that there may be limited connections between the thylakoid and plasma membranes: the nature of these connections remains unclear , 2012. MLike other photosynthetic membranes , cyanobaEscherichia coli plasma membrane proteins, for example  measurements show that Photosystem II centers are almost immobile under normal conditions . Another example . Restric example . In cont example . Therefo example . The ele2 fixation. Additionally, energy is stored in the form of a proton gradient across the thylakoid membrane, with the proton-motive force used to power the synthesis of ATP from ADP and phosphate. The ATP is required for energy input into the Calvin–Benson cycle, but can also be employed in many other cell processes. Absorbed light energy can also be dissipated as heat, via a variety of direct and indirect routes. Figure 1 summarizes, in highly simplified form, some of the alternative pathways of energy conversion in and around cyanobacterial thylakoid membranes, with their outputs of reducing power, proton-motive force or heat. The balance of photosynthetic outputs is critically important for the physiology of the cell. In particular, the cell has to maintain an appropriate redox balance, with sufficient reducing power available for CO2 fixation and other anabolic reactions, but without over-reduction of the electron transport chain, which can lead to dangerous side-reactions with oxygen . The redox trigger for state transitions allows the switch to be controlled by the redox status of the cell.In most cyanobacteria, the principal light-harvesting complexes are phycobilisomes, large protein assemblies anchored to the cytoplasmic surface of the thylakoid . PhycobiFigure 2). The reversal of OCP-induced energy quenching depends on a second cytoplasmic protein, the fluorescence recovery protein (FRP), which binds to the OCP and weakens its association with the phycobilisomes (A second light-harvesting switch in cyanobacteria involves the orange carotenoid protein (OCP), a photoactive cytoplasmic protein whose conformation is switched by exposure to blue light . Another cyanobacterial electron valve is the bidirectional hydrogenase (Hox), which can take electrons from the acceptor side of Photosystem I and use them to reduce protons to produce hydrogen . Hox is inhibited by oxygen but active under anaerobic conditions: it may be important primarily as an anaerobic alternative to Flv1/3, able to remove electrons from the system when oxygen is unavailable to act as a sink for electrons from Flv1/3. Unlike the Flv proteins, Hox activity is very variable on short timescales, suggesting that it could be acting as a rapid electron-transport switch. Hox activity is observed as a short burst of hydrogen evolution when dark-adapted anaerobic cells are illuminated  have obvious, but indirect, effects on photosynthetic electron transport. Another set of switches in cyanobacteria directly influence the pathways of electron transport by controlling the stoichiometry, interactions or proximity of different electron transport components in and around the thylakoid membrane. These switches can act to control the balance of linear and cyclic electron transport, and therefore the balance of proton-motive force and reducing power as photosynthetic outputs. Electron transport switches can also serve to generate heat at the expense of other photosynthetic products. For example, diverting electrons from the photosynthetic electron transport chain back to oxygen as an electron acceptor will generate proton-motive force and/or heat at the expense of reducing power. Switches that remove electrons from the photosynthetic electron transport chain are also known as “electron valves”: they apparently serve to prevent dangerous over-reduction of the electron transport chain. The flavodiiron proteins Flv1–4 are examples of cyanobacterial electron valves: they are cytoplasmic proteins that take electrons from the photosynthetic electron transport chain and divert them to alternative acceptors. Flv1 and Flv3 form a heterodimer that takes electrons from the acceptor side of PSI and uses them to reduce oxygen . An Flv2hydrogen . Diffusiuminated . Hydrogeuminated . It remanated . Cyanobacteria have multiple routes for cyclic electron transport around Photosystem I  shows a similar change in distribution under the same conditions. This switch in the distribution of the complexes correlates with a major change of the probability that electrons from the respiratory complexes are transferred to a Photosystem I rather than to a terminal oxidase . This is triggered by a change in the redox state of plastoquinone, similarly to state transitions. However, the redistribution, and associated changes in electron transport, occur on a slower timescale of 10–30 min , as compThe slowest switching mechanisms involve changes in gene expression. For example, changes in the cellular content of Photosystem I occur in response to a redox trigger  similarlFigure 2 summarizes some known photosynthetic switches in cyanobacteria, and the timescales on which they occur. It is intriguing that cyanobacteria have so many mechanisms to control photosynthetic electron transport, including multiple redox-triggered mechanisms to control the production of reducing power vs. proton motive force . The reason for this multiplicity of mechanisms may lie in the different timescales on which the different switches operate. Cyanobacteria can be exposed to changes in their light environment on multiple timescales, therefore need a suite of acclimation mechanisms ranging from rapid emergency responses to more optimal long-term changes in membrane protein content. Restricted protein mobility in the thylakoid membrane means that the fastest responses are always likely to involve membrane-extrinsic proteins.The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


S. cerevisiae.Tau-leaping is a stochastic simulation algorithm that efficiently reconstructs the temporal evolution of biological systems, modeled according to the stochastic formulation of chemical kinetics. The analysis of dynamical properties of these systems in physiological and perturbed conditions usually requires the execution of a large number of simulations, leading to high computational costs. Since each simulation can be executed independently from the others, a massive parallelization of tau-leaping can bring to relevant reductions of the overall running time. The emerging field of General Purpose Graphic Processing Units (GPGPU) provides power-efficient high-performance computing at a relatively low cost. In this work we introduce cuTauLeaping, a stochastic simulator of biological systems that makes use of GPGPU computing to execute multiple parallel tau-leaping simulations, by fully exploiting the Nvidia's Fermi GPU architecture. We show how a considerable computational speedup is achieved on GPU by partitioning the execution of tau-leaping into multiple separated phases, and we describe how to avoid some implementation pitfalls related to the scarcity of memory resources on the GPU streaming multiprocessors. Our results show that cuTauLeaping largely outperforms the CPU-based tau-leaping implementation when the number of parallel simulations increases, with a break-even directly depending on the size of the biological system and on the complexity of its emergent dynamics. In particular, cuTauLeaping is exploited to investigate the probability distribution of bistable states in the Schlögl model, and to carry out a bidimensional parameter sweep analysis to study the oscillatory regimes in the Ras/cAMP/PKA pathway in  In this context, mathematical modeling tools, simulation algorithms and analysis techniques simplify the predictions on the way these complex systems behave in normal conditions and how they react to genetic, chemical or environmental perturbations; moreover, they can facilitate the verification of specific dynamical properties, which can be characterized by non linear or multistable phenomena Nowadays, the use of computational methods represents a valuable and integrative tool to conventional experimental biology, thanks to the promising capability to gain a global-level understanding of the emergent dynamics of biological systems and to elucidate the mechanisms governing their functionality, that most of the times can be hardly determined by laboratory experiments only. Indeed, the computational study of biological systems can present many advantages in terms of cost, ease to use and rapidity, and can support laboratory work by suggesting in silico a wide spectrum of emergent phenomena; in particular, simulation algorithms are an essential tool to study the temporal evolution of biological systems. Anyway, the shift from the reproduction of the experimental observations to the capability of making predictions on the behavior of the system in unexplored conditions can be limited by the lack or the inaccuracy of available quantitative data , which are indispensable to settle a good model parameterization. To cope with these problems, several computational methods can be exploited Given a mathematical model describing the interactions between the components of a biological system, computer algorithms allow to validate and analyze the model, giving the possibility to recreate An additional aspect that should be considered when defining mathematical models of biological systems is related to the experimental evidences that most of the cellular regulation networks, especially those involving few amounts of some molecular species, are affected by noise Stochastic modeling of biological systems can rely on the definition of stochastic differential equations (SDEs), like the Langevin equation Despite the computational improvements brought by the tau-leaping algorithm, a typical task for the analysis of stochastic models can still be affected by high computational costs: as a matter of fact, besides requiring many different simulations to explore the space of all possible model parameterizations with PE, SA, PI or PSA analysis, the application of stochastic simulation algorithms needs a congruous number of repetitions of the simulations, under the same conditions, in order to deal with the effects of noise due to stochastic fluctuations and to obtain statistically significant results about the system behavior. Therefore, for the analysis of biological systems based on stochastic modeling approaches, an efficient strategy for the parallelization of multiple tau-leaping executions is necessary to obtain a consistent reduction of the computational costs, and to provide scientists with a powerful tool that may speed up the achievement of new insights into the functioning of biological systems.http://www.green500.org/lists/green201306). Both machines are based on NVIDIA Tesla K20 GPU.The traditional methods to perform parallel executions of an algorithm consist in multithreading ad hoc data structures that are necessary for an appropriate memory allocation on the GPU: this is a particularly tricky issue in GPGPU computing, since GPU memories need to be properly used to achieve good computational performances. Another drawback of GPU computing is related to the choice of efficient, parallel and statistically sound random number generators (RNGs). Like any other Monte Carlo-based algorithm, tau-leaping heavily relies on high-quality pseudorandom sequences. In this work, we discuss how to obtain good computational performances by exploiting a proper RNG among the available and out-of-the-box solutions.Previous works presented the parallelization on Graphics Processing Units (GPU) of multiple SSA simulations S. cerevisiae. In addition, we exploit synthetic systems of increasing size, randomly generated as described in In order to compare the computational costs of cuTauLeaping with respect to a standard CPU-based implementation of the original tau-leaping algorithm, we carry out different batches of simulations of four stochastic models of real biological systems: the Michaelis-Menten kinetics We show that even with a limited number of parallel simulations , then it is possible to evaluate a good approximation of Given a state critical: a reaction Note that the execution of many reactions per step could lead to negative amounts of the molecular species in The length of the step ex novo.If the execution of a tau-leaping step would lead to negative amounts of some species, then the Finally, if The emerging field of GPGPU computing allows developers to exploit the great computational power of modern multi-core GPUs, by giving access to the underlying parallel architecture that was conceived for speeding up real-time three-dimensional computer graphics. The GPU implementation of tau-leaping that we propose in this work was developed and optimized for Nvidia's Compute Unified Device Architecture (CUDA), a cross-platform GPGPU library that combines the Single Instruction Multiple Data (SIMD) architecture and multi-threading. CUDA automatically handles the control flow divergence, that is, threads can take different execution paths in a transparent way for the programmer. Nevertheless, conditional branches should be avoided whenever possible as they cause a reduction of performances, due to the serialization of the execution until reconvergence. For this reason, the tau-leaping algorithm required a major reconstruction in order to reduce the need for conditional branches, as will be described in the Using CUDA's naming conventions, the programmer implements a kernel  loaded from the host (the CPU) to the devices (one or more GPUs), replicated in many copies named threads. Threads can be organized in three-dimensional structures named blocks which, in turn, are contained in three-dimensional grids. Whenever the host runs a kernel, the GPU creates the corresponding grid and automatically schedules each block on one streaming multiprocessor (SM) available on the GPU, a solution that allows a transparent scaling of performances on different devices , but suffers from high access latencies, whilst the shared memory is faster but much smaller (tens of thousands KBs for each SM). Being a very small resource on each multiprocessor, the shared memory poses constraints on the blocks size, thus limiting the number of simultaneous threads that can be executed at once. However, in order to achieve the best performances, the shared memory represents a precious resource that must be exploited as much as possible. These considerations are central in our implementation of tau-leaping and will be described in more detail in the Since the introduction of the Fermi architecture, the global memory features a small amount of cache, which makes the use of the texture memory counterproductive Stochastic simulation algorithms exploit random numbers generators (RNGs). Nvidia's software development kit CURAND from CUDA toolkit v5.0 XORWOW is faster than MRG32K3A, but it is known to present statistical flaws In this section we describe the development of cuTauLeaping and its application to perform parallel stochastic simulations in a massively parallel way, by running multiple independent simulations as parallel CUDA threads. We introduce our GPU-oriented design of tau-leaping, consisting in a four phases workflow, and present the data structures, the memory allocation strategies and the advanced functions exploited on the Fermi architecture.We compare the computational performances of cuTauLeaping with the CPU implementation of tau-leaping provided in the software COPASI, a well known application for the simulation and the analysis of biochemical networks Finally, we show the advantages of using cuTauLeaping to investigate the effects of systematic perturbations on the system dynamics. To this aim, we performed different parameter sweep analyses (PSA) on the Schlögl and Ras/cAMP/PKA models, in which one (PSA-1D), two (PSA-2D) or three (PSA-3D) parameters were simultaneously varied within given sweep intervals . Within these ranges, the numerical values of each varied parameter were determined with a linear sampling for the amounts of molecular species; a logarithmic sampling was instead considered for stochastic constants (if not stated otherwise), in order to uniformly span over many orders of magnitude. All PSA were performed by generating a set of different initial conditions – corresponding to different parameterizations of the model under investigation – and then automatically executing the parallel stochastic simulations with cuTauLeaping.In cuTauLeaping, the workflow of the traditional tau-leaping algorithm is partitioned in different phases, which altogether allow a better exploitation of the parallel architecture of the GPU than a monolithic implementation. The rationale behind this choice is that the resources on each SM are limited, thus they would be quickly consumed by the data structures employed by tau-leaping, causing a low occupancy of the GPU that would then result in worse performances. Moreover, since tau-leaping embeds the potential execution of SSA simulation steps, a “fat” kernel responsible for both simulation algorithms would not be convenient, because of the following issues: In this section we describe in detail the design and the implementation of the different CUDA kernels that stand at the basis of cuTauLeaping. The four phases that constitute cuTauLeaping, schematized in Each thread proceeds by applying tau-leaping or SSA steps, which are mutually exclusive, according to the value of a vector In cuTauLeaping the first two phases are implemented in a single kernel, so that the tau-leaping step can be executed right after the calculation of the kernel If The four phases are implemented in the following kernels, which are executed in a sequential manner by each thread kernel kernel synchronizations with predicate evaluation and atomic functions. Synchronization functions are generally used to coordinate the communication between threads, but CUDA allows to exploit these functions to evaluate a predicate for all threads in a block; atomic functions allow to perform read-modify-write operations without any interference from any other thread, therefore avoiding the race condition. A combination of these functionalities allows to determine whether all threads have terminated their execution . This CUDA optimization technique, known as branch splitting, was shown to achieve a relevant gain in performances In order to further increase the performances of cuTauLeaping, we also optimized the CUDA code to better exploit the GPU architecture. The first optimization consists in keeping the register pressure low, in order to avoid the Another typical optimization of CUDA is to ensure coalesced access to data, i.e., an aligned and sequential organization of the memory, for all data structures that are updated by each thread. In our implementation we granted coalescence to all data structures that are private to each thread, that is, the system state the stoichiometric flattened vectors the vector the vector The data structures used to store the stoichiometric information  To analyze the performances of cuTauLeaping, the same simulations executed on GPU were carried out on a CPU architecture by exploiting the tau-leaping algorithm implemented in the software COPASI  The GPU used for the tests is a Nvidia GeForce GTX 590, a dual-GPU video card equipped with In all simulations, the total simulation time The results of the comparison between cuTauLeaping and COPASI CPU tau-leaping are summarized in For the sake of completeness, we also plot in et al.Finally, in order to investigate the influence of the size of the simulated system on cuTauLeaping performances, we executed several tests on randomly generated synthetic models (RGSM). In particular, we analyzed six distinct parameterizations of 100 different RGSM, each one consisting of 35 reactions and 33 species. The rationale behind the choice of this model size and various initial conditions was to compare the computational costs of cuTauLeaping for the simulation of RGSM on the one side, and the Ras/cAMP/PKA model on the other side. RGSM were generated according to the methodology proposed by Komarov In tests 1 and 2 we randomly selected the values of stochastic constants of the RGSM with a uniform probability in In tests 3 to 6 we exploited a modified strategy to select the values of stochastic constants, which were logarithmically sampled in the given range in order to uniformly span over different orders of magnitude. To obtain more realistic parameterizations, in tests 3 and 4 this range was defined according to the smallest and to the highest values of stochastic constants appearing in the Ras/cAMP/PKA model  determine the probability of reaching a particular state during the dynamical evolution of the system itself.To this aim, we performed In Finally, in S. cerevisiae, this pathway plays a major role in the regulation of metabolism, in stress resistance and to control the cell cycle progression In this section we present the results of a PSA carried out on the stochastic model of the Ras/cAMP/PKA pathway In To deeply investigate the role played by guanine nucleotides and Cdc25, in this work we further analyzed the extended version of the Ras/cAMP/PKA model presented in In These computational results can suggest possible interesting behaviors of the biological system under investigation. In this case, for instance, the establishment of oscillatory regimes in the above mentioned conditions can be due to the fact that Ras proteins are more frequently in their inactive state  when the ratio GTP/GDP decreases. Since in normal growth conditions the concentration of GTP is 3 to 5 times higher than GDP, the decreased activity of Ras proteins in the considered perturbed conditions – which are characterized by a favored unproductive binding/unbinding with GDP – can induce the establishment of an oscillatory regime ; on the other hand, the running time of each simulation can be larger than the overhead requested for server-node communication.An alternative methodology to perform multiple and massively parallel simulations consists in exploiting the GPGPU architecture. The modern GPU of mid-range price contains thousands of cores that – as long as the computational task can be subdivided and optimized for a SIMD architecture – allow an impressive peak of computational power, and also a higher energetic efficiency with respect to an equivalent CPU-based solution.Taking into account all these aspects, we developed cuTauLeaping, an implementation of tau-leaping algorithm as a set of strongly optimized CUDA kernels, able to simultaneously execute multiple independent simulations on a single machine. The specific design of cuTauLeaping presents some additional advantages: it avoids any memory transfer to and from the host, thus reducing the overall running time, and it can be embedded into the GPU-based software framework that we developed for PE To achieve even better performances, the tau-leaping algorithm was redesigned to Specifically, according to the memory structures described in In order to analyze the boost of performances of cuTauLeaping, we compared it with a standard CPU implementation , consisting of a few tens of reactions and species, defined according to a bottom-up modeling approach whereby a mechanistic description of the most relevant molecular interactions is provided Despite all these possible optimizations, stochastic simulations of complex biological systems still remain a computationally intensive task, especially when some molecular species occur in very low amounts and other in very large amounts – or also when the values of reaction constants span over different orders of magnitude – possibly inducing a slowdown of running time because of stiffness and multi-scale problems. Therefore, future efforts need to be focused on the implementation of GPU-based hybrid simulation algorithms The cuTauLeaping software is available from the authors upon request.Text S1Stochastic biological models.(PDF)Click here for additional data file.Text S2Comparison of the computational costs of cuTauLeaping using the random numbers generators XORWOW and MRG32K3A.(PDF)Click here for additional data file.


Abnormal electrical activity from the boundaries of ischemic cardiac tissue is recognized as one of the major causes in generation of ischemia-reperfusion arrhythmias. Here we present theoretical analysis of the waves of electrical activity that can rise on the boundary of cardiac cell network upon its recovery from ischaemia-like conditions. The main factors included in our analysis are macroscopic gradients of the cell-to-cell coupling and cell excitability and microscopic heterogeneity of individual cells. The interplay between these factors allows one to explain how spirals form, drift together with the moving boundary, get transiently pinned to local inhomogeneities, and finally penetrate into the bulk of the well-coupled tissue where they reach macroscopic scale. The asymptotic theory of the drift of spiral and scroll waves based on response functions provides explanation of the drifts involved in this mechanism, with the exception of effects due to the discreteness of cardiac tissue. In particular, this asymptotic theory allows an extrapolation of 2D events into 3D, which has shown that cells within the border zone can give rise to 3D analogues of spirals, the scroll waves. When and if such scroll waves escape into a better coupled tissue, they are likely to collapse due to the positive filament tension. However, our simulations have shown that such collapse of newly generated scrolls is not inevitable and that under certain conditions filament tension becomes negative, leading to scroll filaments to expand and multiply leading to a fibrillation-like state within small areas of cardiac tissue. Such recovery can be more dangerous then ischemia itself and often leads to ventricular fibrillation and sudden cardiac death in vitro experimental preparations or on computer modeling.Heart is a remarkably reliable machine whose function is to pump the blood as required by the organism. An important part of its work is the orderly propagation of electrical signal, that is the wave of excitation passing through cardiac muscle, which subsequently triggers its ordered contraction. Abnormalities of the excitation wave propagation, known as arrhythmias, are precursors of sudden cardiac arrest and other life-threatening pathologies. This paper focuses on mathematical analysis of arrhythmogenic conditions associated with cardiac tissue recovery from acute ischemia, also known as in silico modelling provided an explanation to several experimental findings, including the dependence of drift of boundary-bound spirals on their chirality, pin-drift-pin type of spiral tip motion and the effect of boundary movement on spiral detachment Our work builds on the experimental data acquired from monolayers of cardiac myocytes under conditions that mimicked the ischaemic boundary in silico approach. Yet, numerical modelling of cellular behaviour has its limitations, and there is a need to understand how much of the phenomena observed in the simulations are generic and how much of it depends on the specifics of the model. Further still, cardiac tissue is three-dimensional, whereas our experiments and simulations reported previously were conducted using two-dimensional cell networks. Extrapolation of the two dimensional data into three dimensions requires additional theoretical understanding.The rotating waves of activity to be discussed in this paper, occur on a much smaller spatial scale as compared to classical cardiac reentry In the present paper, we use an asymptotic theory of spiral and scroll waves' drift together with the recently developed numerical technique to compute the response functions of spiral waves Specifically, we address the following questions:In both experiments and numerical simulations, spiral waves were not static within the border zone. What determines the components of the drift velocity, and why the spiral cores can be dragged together with the moving border zone?In both experiments and numerical simulations, the drift of the spirals was interrupted by their “pinning” to clusters of cells. We have shown numerically that these can be cell clusters of either elevated or suppressed excitability. What is the mechanism of such pinning?In both experiments and numerical simulations, the episodes of spiral drift and pinning alternated. What is the mechanism by which pinning can give way to further drift?One of arrhythmogenic scenarios proposed in The mathematical model mimicking the conditions when tissue recoveres from acute ischaemia, and its experimental foundations are described in detail in our previous works We assume that the cells are arranged in a rectangular grid of The excitable dynamics of cells is described by the Beeler-Reuter-Pumir The maximum permeability of the fast inward current i.e. makes them automatic in silico network behaviour closely matching the behaviour of neonatal cardiomyocyte layers. The excitability of the latter cells was increased using beta-adrenergic stimulation with isoproterenol We also have altered the balance between inward and outward currents by inhibiting the inward potassium rectifier current, Heterogeneity of individual cells' excitability is described asSpace-time variations of Thus, the recovering ischaemic tissue is modelled as layers with imposed excitability and coupling profiles as shown in Finally, we also made simulations with deliberately arranged parametric distributions not exploiting random number generators. The details of those are given where the results are described.The asymptotic theory of spiral and scroll dynamics under small perturbations The theory assumes that spiral wave solutions to equations (5) for i.e. the velocity of the drift of the position of the core of the spiral, is defined, in the first order in In presence of a small perturbation, A more detailed exposition of the theory and description of the method of calculating the response functions are given in filaments, as spiral waves rotate around points called centres. In general, scroll filaments are not fixed in space but move, typically on a slow timescale relative to the rotation period. Hence, in addition to whatever dynamics 2D spiral waves might have, scroll waves exhibit additional dynamics associated with filament motion Scroll waves are three-dimensional analogues of spiral waves. They rotate around curves called Then, the motion equation for the filament, in the assumption of small filament curvature, filament tension of the scroll wave. The coefficient binormal drift coefficient and describes the drift of a scroll ring filament perpendicular to the plane of the ring, or more generally, the velocity component orthogonal to the local plane of the filament.Following Since the right-hand side of (7) is linear in i.e. in the negative It had been shown This equivalence of We suppose that the excitability kinetic parameter As can be seen from To elucidate possible role of the localised inhomogeneities, let us consider the case when the continuous limit is still applicable, but the spiral core size is comparable with the size of a localized inhomogeneity, or the magnitude of such inhomogeneity is so significant it affects the spiral dynamics despite the small geometry size. This can happen when the random distribution of properties produces relatively large lumps of cells with local average excitability deviating from the overall average. Let's consider an idealized situation when the parametric inhomogeneity is localized in a disk of radius We also deal with the drift caused by a gradient of the diffusivity, so thatBased on the response functions shown in binormal drift coefficientbinormal drift coefficiente.g. the drift of scroll rings along their axis. The filament tension As discussed above, the drift caused by the curvature of the filament is equivalent to the drift caused by the gradient of the diffusion coefficient, so the same coefficients, though taken with the opposite sign, will describe the drift of the spiral core or scroll filament in response to gradient of diffusivity. Namely, coefficient e.g. in The constant sign of the inhomogeneity specific force We shall now use the superposition principle to analyse the 2D drift of a spiral wave subject to a combination of forces caused by a smooth gradient of diffusivity, a smooth gradient of the excitability parameter i.e. both for attracting and repelling inhomogeneities.Following (29) , for every i.e. repelling inhomogeneity with excitability higher than i.e. attracting inhomogeneity with excitability lower than i.e. the red minimum was to the left of the blue maximum, it would create a paradoxical possibility of a stable equilibrium occuring due to interaction with a repelling inhomogeneity. We are not aware of any reasons why this could not happen in some models, but it does not happen in our present model in the range of parameters that we are interested in.Standard calculations give that an equilibrium at a distance Thus, these theoretical predictions based on the response functions of the vortices suggest that stable pinning of a spiral wave in our model may be to lowered-excitability sites only, while in the experimental and simulations described in Firstly, the pinning observed in experiments and simulations was not permanent but temporary. An explanation for that could be that the pinning persisted only until the gradient force exceeded the tear-off threshold (30). However, it is also possible that the pinning was temporary because it was really a slow-down near an unstable equilibrium in the vicinity of a repelling inhomogeneity. Panel (a) in Secondly, a certain mutual allocation of repelling heterogeneities may cause ‘permanent’ pinning, again until the parameters change. This is illustrated in in front of the inhomogeneity, and for the latter, behind it.Panel (d) in There are several factors responsible for the quantitative discrepancies seen in Naturally, with the random distribution of heterogeneity, as present in the experiments and the numerical simulations of the ischaemic border zone, all of the above scenarios with pinning to inhomogeneities of either sign could take place from time to time. In some experiments the pinning locations subsequently became sources of ectopic waves of excitation and therefore were associated with points of higher excitability. In other experiments, the pinning locations never produced the ectopic waves, which suggested that the pinning inhomogeneity had the lowered excitability. Understanding that there are different mechanisms of pinning to attractive inhomogeneity with lowered excitability and to a (group of) repelling inhomogeneity(s) with elevated excitability provides an explanation for these seemingly contradicting experimental observations.The asymptotic theory of spiral and scroll drift is valid for PDEs, describing continuous media. The theory might not be applicable if the discreteness of the cell structure is significant when the diffusivity is small. Thus our findings here are purely empirical, based on direct numerical simulations. The role of discreteness in 2D dynamics was extensively analysed in i.e. it can hinder the drift caused by the smooth parametric or diffusivity gradient. This is illustrated in The effect of dicreteness is to a certain extent similar to that of heterogeneities, It can be seen that in Note that change of filament tension due to relatively small discreteness is a generic feature of excitable media, and has been reported in FitzHugh-Nagumo Another important effect of the tissue discreteness is due to the role of microscopic heterogeneities of parameter We performed numerical simulations of the 3D tissue slab with diffusivity and excitability profiles shown in The first, “toy” set of parameters  and 12 wThe two “more realistic” sets of parameters  were , ,Simple escape into the well-coupled upper layer is not enough for the scrolls to cause fibrillation in 3D. Scroll waves are typically born as “scroll rings” with closed filaments. As shown above, in our model, negative filament tension is predicted by the theory for the smaller values of excitability parameter This main conclusion is supported and reinforced by simulations at larger, more realistic values of ments cf . The uppWe have considered the quantitative predictions of the asymptotic theory for the forces acting on rotating waves of activity that can form within a recovering ischaemic border. The direct numerical simulations with deliberately arranged conditions confirmed the theoretical predictions for the evolution of the vortices. Now, we can answer the specific questions posed in the “In both experiments and numerical simulations, spiral waves were not static within the border zone. What determines the components of the drift velocity, and why the spiral cores can be dragged together with the moving border zone?”1. - The theoretical analysis of the acting forces shows that regions with suppressed excitability - At the relatively low values of excitability i.e. towards the poor coupled bottom layer. This case corresponds to the simulation with At the relatively high values of excitability two reasons: the gradient of excitability will prevent the cores of spirals or filaments of scrolls from escaping into the more excitable outer zone; and at higher excitability, the gradient of coupling will also drag them away from the better coupled outer zone.Hence, a relatively high excitability in the upper layer will suppress the transition to fibrillatory-like state for “In both experiments and numerical simulations, the drift of the spirals was interrupted by their “pinning” to clusters of cells. We have shown numerically that these can be cell clusters of either elevated or suppressed excitability. What is the mechanism of such pinning?”2. i.e. locally increased or decreased excitability).- The theoretical analysis shows that a combination of acting forces generated by smooth gradients of tissue properties and a localized inhomogeneity in excitability parameter - There is more than one mechanism of pinning. Apart from pinning to an attracting inhomogeneity, the drift can also be stopped by a certain spatial arrangement of repelling inhomogeneities. Even if “permanent” pinning is not achieved, a temporary pinning still may be observed for some finite time if the trajectory of the spiral core passes near an unstable equilibrium. There is also a theoretical possibility of “orbital motion” which however is not realized in the present model at interesting values of parameters.“In both experiments and numerical simulations, the episodes of spiral drift and pinning alternated. What is the mechanism by which pinning can give way to further drift?”3. - Correspondingly, there is more than one mechanism of unpinning. One is that due to the border zone dynamics, parameters of the tissue may change in such a way that gradient-induced force exceeds the tear-off threshold. The other is that the spiral wave core drifts away from the pinning site because its position there was unstable in the first place.“One of arrhythmogenic scenarios proposed in  involved pinning of a spiral wave to a local heterogeneity which persists long enough until the border zone passes and the spiral gets into the better coupled tissue. Is this scenario viable in 3D?”4. filament tension and the binormal drift coefficient. In the considered tissue model, the filament tension is small compared to the binormal drift coefficient, and changes sign in the relevant range of excitability parameter. This means that scroll waves that managed to escape into the well coupled upper zone, might not necessarily immediately collapse.- In 3D, in addition to whatever dynamics 2D spiral waves might have, scroll waves exhibit additional dynamics associated with the motion of filament, and characterized by the third reason a relatively high excitability in the outer layer is “anti-arrhythmic”: at higher excitability, the scrolls in the outer layer are less likely to survive due to 3D effects.- The scroll filaments that managed to stay until the tissue is recovered, may not collapse but survive, if the filament tension is negative. These filaments may subsequently generate scroll wave turbulence. Note a nontrivial coincidence following from the asymptotic theory: excitability of the upper layer at the lower range of parameter - Further, there are some features revealed by the 2D simulations which are beyond direct applicability of the asymptotic theory. That is the effect of the dicreteness of the medium, which particularly matters at low values of diffusivity. The discretness of the medium can arrest the drift of spiral cores, and when applied to 3D scrolls, the filaments can freeze as long as their curvature is not too high, and the “filament tension” component of their drift freezes sooner than the “lateral binormal drift” component. Therefore, the scroll filaments that managed to stay until the tissue is recovered, may not collapse but survive, as their filament tension is frozen due to low diffusivity. In that case of the “frozen”, zero filament tension, the regime might rather look like a persistent tachycardia similar to the pinned 2D spiral regime.To summarize, we explored a biophysically plausible mechanism as to how ectopic beats and spreading scrolls of abnormal activity can be generated from the recovering boundary of acutely ischaemic tissue. Complex boundary behaviour in heterogeneous cell network was modeled with certain assumptions and simplifications, extensively discussed in our previous publications in vitro and in silico data from our previous publications and the current study. First, the data suggested that the combination of the two gradients  ensured that somewhere within the border zone there was a region where multiple ectopic sources were continuously being formed. They were highly localized focal points of activity, with activation spreading only to a few surrounding cells. Number of ectopic sources and specific window of conditions when they occured were affected by the degree of the network heterogeneity. Secondly, the data argued that if the ectopically active layer was sufficiently wide and/or the overall cell automaticity rose, ectopic sources developed into target-like waves. If coupling gradient and automaticity levels remained spatiotemporally fixed, the pattern of target-like sources persisted and no spiral activity was observed. However, when cell automaticity rose and/or border zone moved in space, the propagation patterns became non-stationary. This led to multiple wavebreaks resulting in spiral generation activity. The spiral waves typically demonstrated start-stop drifting behaviour, as a result of competing forces between pinning force due to local heterogeneity and a gradient-induced directional drift. The likelihood of a spiral escape into the better coupled upper tissue zone depend on the speed at which the border zone moves in space.With all the assumptions and limitations, the following combined conclusions can be made based on the Our extrapolation of 2D events into 3D is more theoretical, as tissue culture experiments similar to those described in In this study, we considered the asymptotic theory's quantitative predictions for the forces acting on a cardiac re-entry, and causing its drift, in the vicinity of the ischaemic border zone. The theoretical predictions allow to tell apart and highlight different mechanisms of arrythmogenesis by the ischaemic boder zone in three-dimentiontional settings. The direct numerical simulations with deliberately arranged conditions confirmed the theoretical predictions for the drift.We fully realize that in vivo, the above considered scenarios will be affected by multiple additional factors. These might include excitability kinetics different from the simplified generic model we used here, presence of highly excitable Purkinje fibers, macroscopic myofiber orientation, coronary vessels, fibrous or fat deposits, transmural differences in myocytes metabolic activity and their sensitivity to ischaemia. Yet, with all its limitations, this study represents one of the first attempts to theoretically explore a very complex set of highly arrhythmogenic conditions that can occur on the boundary of the recovering ischaemic tissue.Appendix S1Describing details of the Beeler-Reuter-Pumir kinetic model, and of our numerical scheme.(PDF)Click here for additional data file.Video S1Movie illustration to (MPG)Click here for additional data file.Video S2Movie illustration to (MOV)Click here for additional data file.


Cooperative breeding is generally associated with increased philopatry and sedentariness, presumably because short-distance dispersal facilitates the maintenance of kin groups. There are, however, few data on long-distance dispersal in cooperative breeders—the variable likely to be important for genetic diversification and speciation. We tested the hypothesis that cooperative breeders are less likely to engage in long-distance dispersal events by comparing records of vagrants outside their normal geographic range for matched pairs (cooperatively vs. non-cooperatively breeding) of North American species of birds. Results failed to support the hypothesis of reduced long-distance dispersal among cooperative breeders. Thus, our results counter the conclusion that the lower rate of speciation among cooperative breeding taxa found in recent analyses is a consequence of reduced vagility. In cooperatively breeding species of birds, grown offspring typically delay dispersal and remain at the nest to help raise non-descendant offspring Evidence thus supports the hypothesis that the frequency of philopatry and short-distance dispersal is relatively high in cooperative breeders. It does not necessarily follow, however, that cooperative breeders experience fewer or shorter long-distance dispersal events, the metric likely to be more important in terms of speciation and diversification rates Here we conduct a comparative analysis testing the hypothesis that cooperative breeders engage in relatively fewer or shorter long-distance dispersal events than non-cooperative breeders. We do this by focusing on vagrant records—records of individuals detected outside their normal geographic range—of North American cooperatively breeding species of birds and matched non-cooperatively breeding species. To our knowledge, vagrant records have not been used previously as a measure of long-distance dispersal, although Veit Aphelocoma) and the nuthatches (genus Sitta). In the case of the anis (genus Crotophaga), records were combined for the two cooperatively breeding species for comparison with the single non-cooperative species.We compiled vagrant records of seven species of cooperatively breeding birds paired with six species of non-cooperatively breeding birds . Each coAmerican Birds) for a ten-year period that included fall 1998 to summer 2007, inclusive. For each record of the species of interest, we noted the location and date. We then determined latitude and longitude coordinates using the searchable database provided by the Geographic Names Information System Vagrant records, defined as birds recorded outside their expected geographic range, were compiled from the regional reports published in North American Birds .Ranges were reprojected from their source North American 1983 datum , vagrants from October through March were compared to the wintering range, and those from April through September were compared to the breeding range The number of vagrants recorded for each species was compared to ensure that our results were not biased due to sample size. We deemed the number of vagrants to not be a useful comparative measure, however, because of non-congruence in geographic distribution and population size among species.Thus, our primary focus was on the relative distances of vagrant records; that is, how far away from their normal geographic range were vagrants recorded. Only vagrant records collected in the United States and Canada were included in order to restrict records to those representing approximately equal levels of vigilance among the birding community and likelihood of publication. Records of vagrant sightings in Mexico and southward were largely unavailable or not maintained in a manner consistent with North American records and so were excluded from analysis.In order to compare a measure of the tendency for long-distance dispersal, we also calculated an index of the relative frequency of vagrancy by the different species. Because the proportion of each species' geographic range that was within the United States and Canada varied across species, from less than 1% to 100%, the index normalized the frequency of vagrancy by dividing the number of vagrants by the area that was within the United States from a buffer drawn around the complete range polygon at the distance from the range to the farthest vagrant . This gaP = 0.9; records >100 kms: P = 1). Thus, the number of records we analyzed was comparable for cooperative and non-cooperative breeding species.The number of vagrant records per species varied from 4 to 163, with a mean of 54 per taxon . RestricOf the six overall paired comparisons, only the one between the two bluebird species supported the hypothesis that non-cooperative species exhibit greater vagrancy than cooperative species . In contFor the bluebird species, which are mostly migratory, additional comparisons were made by time of year. These seasonal results also showed greater vagrancy in the non-cooperative species, similar to the results from the comparison of all vagrants combined.P>0.05); that is, there was no detectable difference between cooperative and non-cooperative species in their mean vagrant distances. Second, we compared the maximum vagrant distances across all pairs of species; the difference was not significant (P = 0.7). Third, we compared the ratio of the density of vagrants in the U.S. and Canada to their estimated population densities within their normal ranges. Again, there was no significant difference between the cooperative and non-cooperative species (P = 0.5).Three comparisons were made across all pairs of species combined. First, we tested the mean distance of vagrants from the edge of the range. This test was repeated for all vagrants and for those records >100 km. Neither comparison was statistically significant .Measuring long-distance dispersal events will undoubtedly be easier in the future as GPS, genetic, and other technologies become more refined for use on smaller taxa. At this point, however, the only feasible way to accomplish a comparison of this scope is to use records of vagrant sightings, a resource largely overlooked until now. Ultimately, our results demonstrate the degree to which we do not yet understand the role of dispersal in the evolution of cooperation and point to the necessity for further investigation in this field.


Foreign bodies may be deposited in the oral cavity either by traumatic injury or iatrogenically. Among the commonly encountered iatrogenic foreign bodies are restorative materials like amalgam, obturation materials, broken instruments, needles, and so forth. The discovery of foreign bodies in the teeth is a special situation, which is often diagnosed accidentally. Detailed case history, clinical and radiographic examinations are necessary to come to a conclusion about the nature, size, location of the foreign body, and the difficulty involved in its retrieval. It is more common to find this situation in children as it is a well-known fact that children often tend to have the habit of placing foreign objects in the mouth. Sometimes the foreign objects get stuck in the root canals of the teeth, which the children do not reveal to their parents due to fear. These foreign objects may act as a potential source of infection and may later lead to a painful condition. This paper discusses the presence of unusual foreign bodies—a tip of the metallic compass, stapler pin, copper strip, and a broken sewing needle impregnated in the gingiva and their management. Self-inflicted injuries are not uncommon , 2 and rAn 8-year-old boy presented to the Department of Pedodontics of Dr. HSJIDS with the chief complaint of swelling and pain in the lower right posterior region since 3-4 days. Intraoral examination revealed a fractured filling, grade 1 mobility of the tooth, tenderness on percussion, and abscess in relation to tooth 85. An intraoral periapical radiograph was advised; it revealed the presence of a sharp radiopaque material present in relation to the external surface of the mesial root .Extraction of the involved tooth was done, and the foreign object was removed that was found out to be a sharp tip of the metallic compass . On furtAn 11-year-old boy was brought to the Department of Pediatric Dentistry with the chief complaint of pain and swelling in the maxillary anterior region. He had suffered dental trauma a year back. Intraoral examination revealed fractured 11 with the slit-like opening involving the pulp chamber of tooth 11 . The tooAn 28-year-old male patient reported to the Department of Oral Medicine and Radiology with a complaint of dull pain in upper right back region. The patient was an air conditioner mechanic and had met with an accident two months back; while repairing the air conditioner, it suddenly burst and he got severe injuries on his face and one of the fragments of the air conditioner got embedded in oral cavity. On examination, there was a fibrous swelling palpable in the vestibular area of the upper right premolars. An OPG radiograph was advised . The radAn 20-year-old male patient reported to the department with a history of breaking a sewing needle in upper right back area two days back while trying to remove the food debris . An IOPASelf-inflicted oral injuries can be premeditated or accidental or can result from an uncommon habit. These injuries usually result from a foreign object or a patient's fingernail that habitually causes injury to the teeth or the gingival tissue. There are varying degrees of self-injurious behavior from simple fingernail biting to the extremes in self-mutilation –11. The Various foreign objects were reported to be lodged in the root canals and the pulp chamber, which ranged from pencil leads , darningZillich and Picken  and TurnA conventional practice employed during emergency root canal treatment involves leaving the pulp chamber open where pus continues to discharge through the canal and cannot be dried within a reasonable period of time. Weine  recommenA radiograph can be of diagnostic significance especially if the foreign body is radiopaque. Hunter and Taljanovic  summarizIn patients who have had a penetrating injury, the nature of the foreign body determines the clinical behaviour; inert objects such as steel and glass may not cause significant inflammation to warrant their removal. Removal of organic foreign bodies is, however, mandatory, since these objects usually lead to secondary infection, with abscess and fistula formation. In our case, the various foreign bodies were the tip of the metallic compass, stapler pin, air conditioner copper chip, and fragments of broken needle that were removed timely and proper treatment plan could be carried out.


A new algorithm for feature and contrast enhancement of mammographic images is proposed in this paper. The approach bases on multiscale transform and mathematical morphology. First of all, the Laplacian Gaussian pyramid operator is applied to transform the mammography into different scale subband images. In addition, the detail or high frequency subimages are equalized by contrast limited adaptive histogram equalization (CLAHE) and low-pass subimages are processed by mathematical morphology. Finally, the enhanced image of feature and contrast is reconstructed from the Laplacian Gaussian pyramid coefficients modified at one or more levels by contrast limited adaptive histogram equalization and mathematical morphology, respectively. The enhanced image is processed by global nonlinear operator. The experimental results show that the presented algorithm is effective for feature and contrast enhancement of mammogram. The performance evaluation of the proposed algorithm is measured by contrast evaluation criterion for image, signal-noise-ratio (SNR), and contrast improvement index (CII). Breast cancer has been a significant public health problem for women in the world and early detection of breast cancer is very essential in the field of medicine before the means to prevent breast cancer have not yet been found. However, there are new cases 234580 and death rate 17.1% from the National Cancer Institute in the United States in 2013  introducIn recent years, there are many researchers that proposed all kinds of contrast enhancement algorithms to solve these problems produced by poor contrast images. Sundaram et al.  proposedWe compare the suitability of these methods for enhancement of mammographic images in general. We propose the approach which seems to be suitable for contrast enhancement of mammograms. Traditional multiscale analysis methods only enhance the high frequency components of mammogram. The proposed approach decomposes the image by the Laplacian Gaussian pyramid transform, firstly. Secondly, the CLAHE is adopted to enhance contrast and detail information of each level high frequency subimage decomposed by Laplacian pyramid transform and Gaussian filter is used to restrain the CLAHE to enlarge the noise of each subimage. Furthermore, mathematical morphology is applied to enhance local features and contrast at each pyramid level's subimage. Finally, the inverse Laplacian Gaussian pyramid transform is applied to reconstruct the decomposed subimages to obtain the features and contrast enhancement image. The enhanced image was adjusted the entire contrast by a global non-linear operator for nature visualization.The rest of this paper is organized as follows. Theory of the Laplacian Gaussian pyramid transform and the key characteristics of the CLAHE and mathematical morphology are detailed in Traditional image enhancement techniques cannot adapt to the varying characteristic of images. The application of a global transform or a fixed operator to an entire image often yields poor result at least in some parts of the given image . In ordeTo begin with, the original image is decomposed by the Laplacian Gaussian pyramid transform to obtain low frequency subband images and different scale coefficients of the high frequency components. At present, all kinds of filter techniques, including gray-scale operator, median filtering, edge enhancement operator, frequency enhancement operator, spatial-frequency filtering, and anisotropic adaptive filtering, are applied to reduce the noises of image for achieving image enhancement. However, these techniques are suitable for features enhancement of the whole image. In fact, we do need to enhance the local features and edges of medical image in some practical clinical application. Mathematical morphology operations fit these requirements. The morphology operators can enrich the low frequency information of the image and enhance this part contrast in terms of the principle of mathematical morphology. Therefore, noise in different multiscale subimages can be suppressed by morphology operations. Vessels, fibroglandular tissues, masses, and calcification points are reinforced at each pyramid level. Furthermore, morphology operators can make the feature details become smoother and the edges sharper. Most essential image processing algorithm can be represented in the form of morphological operations. In addition, the low frequency subbands contain basic information and parts contrast of image. Therefore, the processing of low frequency data is important and cannot be ignored. For the low-pass filtered subband images, we apply the mathematical morphological operations, combining opening operation with closing operation, to enrich the basic information and enhance image contrast.Secondly, histogram equalization is used for enriching detail information and sharping edges of the whole image. The detail information and image edges belong to the high frequency components. Furthermore, the high frequency subbands contain noises. We adopt the CLAHE to enhance the high frequency subbands coefficients, which can not only enhance the features and image contrast and enrich the detail information and image edges but also effectively suppresses the enlarged noise. Comparing with the AHE, the CLAHE can reduce computational time and effectively suppress the enlarged noise. Comparing with the traditional histogram equalization and the modified histogram equalization, the CLAHE can effectively enhance the local features, edges, and image contrast.Finally, we can reconstruct an enhanced image, and its size is the same as the original image. We apply the contrast low frequency coefficients adjusted through mathematical morphology and the high frequency subbands processed by the CLAHE to extract the enhanced feature and contrast image due to the Laplacian Gaussian pyramid transform is of the property of reversal. Besides, a global gain operation is used to adjust the contrast of reconstructed image in order to make the enhanced image more natural and smoother. The flowchart of the proposed algorithm is shown in g1. The image g1is then interpolated or made the convolution operations with kernel width 5 to reproduce the original array size and subtracted pixelwise from the original image to produce b0. This subband image b0, which is produced by an equivalent process of high-pass filter, is the finest level of the Laplacian Gaussian pyramid. The decimated low-pass filtering image g1 is further filtered by the Gaussian low-pass filter and subsampled producing g2. The g2 is interpolated or made the convolution operations with kernel width 5 and subtracted from the g1, which results in the second pyramid layer b1. All subsequent layers of the Laplacian Gaussian pyramid are computed by repeating these operations to the subsampled Gaussian low-pass filtering images from the previous iteration, until the setting pyramid level image bL−1 and the last level pyramid image gL are obtained. The flowchart of the reconstruction process is drawn on the right hand of the gL is interpolated or made the convolution operations with kernel width 5 to the array size of the next finer pyramid level bL−1, and the enhanced bL−1′ is added in this pixelwise to produce gL−1′. Interpolation, contrast enhancement, convolution, and addition operations are repeated until the reconstructed image at the original resolution level is obtained. The reconstruction is completely reversible if the interpolation filters used in decomposition and reconstruction are identical , the gray transfer function is expressed as follows:w is an integral dummy variable.Let According to the properties of integral, we can make the derivation of formula  to get aFurther, we can put the formula  into 2)2) and obAccording to  and the In generally,  is the gComparing with the whole histogram equalization, the adaptive histogram equalization (AHE) has the advantage of good local contrast enhancement. But the AHE needs to compute the local histogram and accumulate distribution function of every pixel; it is extremely computational intensive. Besides, the AHE is sensitive to noise.The AHE enhances the image contrast and enlarges the noise. In some cases, enhancement process results in image distortion in some detail area, which affects the visual diagnosis of clinicians for the enhanced image , 21. We Mathematical morphology originated in set theory, geometry, and topology establishes the relationship between the geometry of physical system and some of its property. Most essential image processing algorithms can be represented in the form of morphological operations. For example, morphology offers a unified and powerful approach to different image processing problems , 11, 22.I by a structural element SE is defined as follows [The erosion of a gray-scale digital image  follows , 9, 11. The gray-scale dilation can be described asI, using the structure elements SE, is defined as erosion followed by dilation and expressed as  is defined as dilation followed by erosion and given by  in a region that are smaller than the structure element. For the corresponding opposite sequence, the closing can fill in holes and concavities smaller than the structure element. The two operations can remove the noise in the image and cannot make the image distortion.In practical application morphological opening and closing pairs are combined in sequence for various image processing operations. There are two morphological operations known as top-hat (TH) and bottom-hat (BH) transformations. The top-hat transformation by opening is defined as the difference between the original image and its gray scale opening using structuring element SE and it is defined asSimilarly dual bottom-hat transformation by closing is the difference between the gray-scale closing image and original image as described byBased on the previous theoretical analysis, the TH transformation is an effective technique for enhancing small bright details from the background. Conversely, the dark features can be extracted from a brighter background by the BH transformation. In order to enhance the local contrast of the mammograms, the processing procedure is adding original image to the top-hat transformed image, and subtracting the bottom-hat image. Furthermore, its efficiency in image contrast enhancement has been proved by . The calEquation  has beena = (1/(sigm(c(1 − b)) − sigm(−c(1 + b)))) subject to 0 < b < 1, b and c are ratio coefficients of enhancement and can be set different values according to the practical testing experiment to adaptively adjust.We adopt a global gain adjustment technique in our investigation for histogram equalization enhancing part pixels uniformly at each pyramid level, which makes the visualization of the enhanced image to become more natural. We employ the mean introduced in , 22 to az) is described as follows:The sigm, AHE, the algorithm of nonlinear multiscale processing based on Laplace pyramid proposed in [M and N are height and width of the image, respectively, and f′ is the enhanced image. The larger the value of /(Xmax + Xmin) in its local window size. We applied a version of the optimized definition of contrast demonstrated in [C of an image is described as follows:mf is the mean luminance value of the foreground and the corresponding mb is equal to the mean luminance value of background. In our experiment, we use the 5∗5 local windows. The greater value of CII indicates that the given image quality is better.A quantization measure of contrast enhancement can be defined by a contrast improvement index, and its formula can be expressed by the following , 15, 23rated in . The conAs shown in Figures In Tables A method based on the Laplacian Gaussian pyramid transform, mathematical morphology, and contrast limited adaptive histogram equalization is proposed for features and contrast enhancement of mammographic images, which employs the penalty terms to adjust the various aspects of contrast enhancement. Thus, the proposed method enhances the image contrast at the same time as it effectively restricts the enlarged noise. The proposed method has been tested on mammograms and compared with the existing popular approaches of histogram equalization and adaptive histogram equalization, nonlinear multiscale processing based on Laplace pyramid, and the method based on wavelet transform and morphology. Furthermore, the experimental results show that the proposed method seems more suitable for mammographic images enhancement in both visual quality and qualitative measurements. Besides, the experimental results yielded by the proposed method still have a little unnatural in visualization. Therefore, the next step we will improve the proposed method and test it using mammographic images from the standard Database Mammographic Image Analysis Society (MIAS). For performance evaluation of the proposed algorithm, SNR, contrast evaluation criterion and contrast improvement index are adopted. The experimental results and metric data tables show that the proposed method seems to yield significantly the enhanced images. Comparing with other tested methods, the results of the proposed method are more suitable for clinic application.


The continuously increasing amount of RNA sequence and experimentally determined 3D structure data drives the development of computational methods supporting exploration of these data. Contemporary functional analysis of RNA molecules, such as ribozymes or riboswitches, covers various issues, among which tertiary structure modeling becomes more and more important. A growing number of tools to model and predict RNA structure calls for an evaluation of these tools and the quality of outcomes their produce. Thus, the development of reliable methods designed to meet this need is relevant in the context of RNA tertiary structure analysis and can highly influence the quality and usefulness of RNA tertiary structure prediction in the nearest future. Here, we present RNAlyzer—a computational method for comparison of RNA 3D models with the reference structure and for discrimination between the correct and incorrect models. Our approach is based on the idea of local neighborhood, defined as a set of atoms included in the sphere centered around a user-defined atom. A unique feature of the RNAlyzer is the simultaneous visualization of the model-reference structure distance at different levels of detail, from the individual residues to the entire molecules. RNA is one of the leading actors in all life processes. Its catalytic prowess, biological importance and ability to form complex structures have made this molecule an important subject of research in recent years. A variety of biological functions carried out by RNAs comes, inter alia, from their three dimensional structures. Thus, determination of the RNA structure is an important step in RNA analysis ,2. UnforThe growing number of RNA sequences and experimentally determined 3D structure data has prompted the development of new methods and software for RNA modeling . Only reThe assessment of the applicability of RNA models requires the development of reliable computational methods to compare them with the experimentally determined structures and thereby evaluate the accuracy of predictions. Correct identification of accurate models and recognition of methods that are likely to generate accurate models is an important aspect of model evaluation. Several metrics are currently used to evaluate 3D models of macromolecules. The most common metric to describe the mutual global deviation of two structures is the root mean square deviation (RMSD) calculated for pairs of corresponding atoms, following the optimal superposition of the two compared structures. Another common metric is the global distance test (GDT) originally invented for the comparison of protein structures ,23. MetrIn this article, we present a new computational method designed to support comparison of RNA structure models to a reference structure. The method is able to discriminate between correct and incorrect predictions in entire spectrum of detail . Our method is equipped with an advanced visualization function, and allows the user to compare tertiary structures simultaneously at different levels of accuracy.RNAlyzer allows the user to evaluate the agreement between a model of RNA molecule and a reference structure by comparisons between sets of atoms located inside a series of spheres. A sphere with a strictly defined radius is built around an atom selected by the user , which represents the center of the sphere of every nucleotide that is part of the reference structure. As a result of the sphere-building process, a set of all atoms included in a particular sphere from reference structure is obtained (no atoms from reference structure are omitted). In the next stage, for every sphere built on a particular atom belonging to nucleotide residue from the reference structure, a corresponding set of atoms from the analyzed model is identified. The alignment is done by matching atom numbers from reference and structure and model. Finally, substructures inside corresponding spheres are superimposed, and the RMSD between corresponding superimposed sets is calculated. Kabsch and McLachlan techniques ,25 have This module is responsible for checking the correctness of the input file and reporting all inconsistencies (e.g. violations of the PDB file format) to the user. Moreover, it contains functions to compute the RMSD between the model and the reference structure (for every sphere radius identified in input radii vector) based on atoms taken from spheres with different radii. The user can adjust the analysis and set initial values of several input parameters, such as a vector of radii or a type of atom that is positioned in the center of the sphere. The user can also decide whether all atoms of each particular nucleotide or only the central atom in a sphere will be considered. Following the calculations at this stage, the user can save results or proceed with visualization.The visualization module includes a tool that enables generation of five types of plots that represent different views focusing on different levels of detail. The current version of RNAlyzer is based on third-party secondary structure annotation tools such as RNAView or Annotate3D ,15,26,27The plots presented below were generated for models submitted to the RNA Puzzles competition by three groups  . These ghttp:\\rnalyzer.cs.put.poznan.pl.RNAlyzer is a standalone program written in JAVA programming language, and uses Java3D and Jmol libraries. The software runs on any modern Windows or UNIX system (including Mac OS X). RNAlyzer is free of charge for academic and commercial users. Executable version of RNAlyzer is available at Multi-model plot is presented in An example of Multi-model plot visualizes how accurate is the prediction of atoms located in the neighborhood of every nucleotide, taking into consideration current accuracy level (ie. sphere radius). Each line describes exactly one structural model—different colors correspond to different models. With a low radius , the quality of local structural neighborhood of analyzed models is correct for almost all nucleotide residues of the model, because accurate modeling of chemical structures of nucleotide residues is relatively easy. With the increasing value of radius, we can easily identify the parts of models that exhibit different accuracies of prediction, from low values of RMSD that indicate correct predictions, to important structural errors  that should be widely and carefully analyzed and refined. If the sphere radius reached the radius of the whole molecule, then the RMSD computed for each nucleotide is equal to the global RMSD computed for a whole structure  on the Multi-model plot can be confusing because the RMSD value for the worse model may dominate the visualization of errors for the model with a better accuracy. Hence, the user can analyze each model separately.The main feature of the RMSD averaged plot is shown in Multi-model plot and RMSD averaged plot is that in the latter case, the Y-axis represents values of RMSD calculated as the averaged sum of RMSD of spheres built with fixed radius for all nucleotides of the analyzed RNA molecule. This plot visualizes how averaged RMSD values change with an increasing sphere radius (ie. decreasing accuracy level). In general, this plot describes the changes of quality of prediction in entire spectrum of accuracy levels from local to global point of view.An example of 2D map plot is presented in spheres radii vector defined by the user. This plot shows where the prediction is inaccurate and allows the user to identify if prediction errors are similar for different analyzed models.An example of a 3D plot is presented in spheres radii vector defined by the user; and the Y-axis represents the RMSD values. The value of RMSD is also presented with the colored scale. Both plots (2D map plot and 3D plot) describe the accuracy of structural fragments of a predicted model around certain nucleotides.An example of a Cutoff plot is presented in Cutoff plot shows how accurate is the prediction of a particular model from a local point of view or, in other words, which part of the model structure is predicted correctly. The calculation is performed based on the fixed precision value (cutoff threshold) for each sphere radius, defined by the user in the spheres radii vector. As a result, the user receives information about the percentage of nucleotides predicted with the quality below specified cutoff (%). The value of cutoff threshold can be changed interactively by the user.An example of a http://paradise-ibmc.u-strasbg.fr/rnapuzzles/problems_past.html), compared them with the experimentally determined structures and analyzed the results in the context of model evaluation carried out within the RNA Puzzles experiment. The goal of the analysis presented below is to show benefits using RNAlyzer during quality evaluation process, but not to reevaluate results of RNA Puzzles.To show the advantages of the presented approach, we analyzed models of three different RNA molecules, submitted by eight research groups within the first ‘RNA Puzzles’ challenge that took place in November 2010 . We downMulti-model plot  is the best for Bujnicki_model_1 and Bujnicki_model_3 models  with very high accuracy, while the accuracy of other fragments and of the entire structure may be less important. On the other hand, in some other applications, the focus on the global structure may be more relevant. By analyzing models submitted to the RNA Puzzles challenge, we have demonstrated the utility of the proposed approach.Validation of RNA tertiary structure models is a crucial issue in a structural biology. The presented method meets this challenge. RNAlyzer uses RMSD as the quality indicator for comparisons on all accuracy levels; however, any other metric can be used to calculate local structural distances between the extracted set of atoms. In the current version of the program, only RMSD is available, but other metrics will be added to that approach in the future. We showed that our method may be used to evaluate structures simultaneously at different levels of accuracy, to identify predictions that have locally correct tertiary structure even if they are less accurate globally, and vice versa. In the case of RNA structures, such comparison is important, as the Supplementary Data are available at NAR Online: Supplementary Figures 1–4.EU Regional Development Fund [POIG.02.02.00-30-009/09]; European Regional Development Fund within Innovative Economy Programme [POIG.02.03.00-00-018/08 POWIEW]; National Science Center Poland [2012/06/A/ST6/00384 (to R.W.A.)]; National Science Center Poland [2012/05/B/ST6/03026]; Foundation for Polish Science . Funding for open access charge: National Science Center Poland [2012/06/A/ST6/00384].Conflict of interest statement. None declared.