The construction of a simultaneous functional order in nervous systems

The functional order of a collection of nervous elements is available to the system itself, as opposed to the anatomical geometrical order which exists only for external observers. It has been shown before (Part I) that covariances or coincidences in the signal activity of a neural net can be used in the construction of a simultaneous functional order in which a modality is represented as a concatenation of districts with a lattice structure. In this paper we will show how the resulting functional order in a nervous net can be related to the geometry of the underlying detector array. In particular, we will present an algorithm to construct an abstract geometrical complex from this functional order. The algebraic structure of this complex reflects the topological and geometrical structure of the underlying detector array. We will show how the activated subcomplexes of a complex can be related to segments of the detector array that are activated by the projection of a stimulus pattern. The homology of an abstract complex (and therefore of all of its subcomplexes) can be obtained from simple combinatorial operations on its coincidence scheme. Thus, both the geometry of a detector array and the topology of projections of stimulus patterns may have an objective existence for the neural system itself.     

The construction of a simultaneous functional order in nervous systems

The signal activity in a neural net will be constrained both by its physical structure and by environmental constraints. By monitoring its signal activity a neural system can build up a simultaneous functional order that encodes these constraints. We have previously (Part I) presented two models that construct a simultaneous functional order in a collection of neural elements using either signal-covariances or signal-coincides. In this paper we present the results of simulation experiments that were performed to study the influence of the physical constraints of a neural system on the simultaneous functional order produced by both models. In the simulation experiments we used a one-dimensional detector array. We delineate the physical constraints such an array has to satisfy in order to induce a functional order relation that allows an isomorphism with a geometrical order. We show that for an appropriate choice of the system parameters both models can produce a simultaneous functional order with sufficient internal coherence to allow isomorphisms with a triangulation. In this case the dimensionality and the coherence of the detector array are objectively available to the system itself.     

Geometrical structures determined by the functional order in nervous nets

The functional order of a collection of neural elements may be defined as the order induced through the total of covariances of signals carried by the members of the collection. Thus functional order differs from geometrical order (e.g. somatotopy) in that geometrical order is only available to external observers, whereas functional order is available to the system itself. It has been shown before that the covariances can be used to construct a partially ordered set that explicitely represents the functional order. It is demonstrated that certain constraints, if satisfied, make this set isomorphic with certain geometrical entities such as triangulations. For instance there may exist a set of hyperspheres in a n-dimensional space with overlap relations that are described with the same partially ordered set as that which describes the simultaneous/successive order of signals in a nerve. Thus it is logically possible that the optic nerve carries (functionally) two-dimensional signals, quite apart from anatomical considerations (e.g. the geometrically two-dimensional structure of the retina which exists only to external observers). The dimension of the modality defined by a collection of nervous elements can in principle be obtained from a cross-correlation analysis of multi-unit recordings without any resort to geometrical data such as somatotopic mappings.     

A high-order graph generating self-organizing structure

A large class of neural network models have their units organized in a lattice with fixed topology or generate their topology during the learning process. These network models can be used as neighborhood preserving map of the input manifold, but such a structure is difficult to manage since these maps are graphs with a number of nodes that is just one or two orders of magnitude less than the number of input points (i.e., the complexity of the map is comparable with the complexity of the manifold) and some hierarchical algorithms were proposed in order to obtain a high-level abstraction of these structures. In this paper a general structure capable to extract high order information from the graph generated by a large class of self-organizing networks is presented. This algorithm will allow to build a two layers hierarchical structure starting from the results obtained by using the suitable neural network for the distribution of the input data. Moreover the proposed algorithm is also capable to build a topology preserving map if it is trained using a graph that is also a topology preserving map.     

Evaluating functional network inference using simulations of complex biological systems

MOTIVATION: Although many network inference algorithms have been presented in the bioinformatics literature, no suitable approach has been formulated for evaluating their effectiveness at recovering models of complex biological systems from limited data. To overcome this limitation, we propose an approach to evaluate network inference algorithms according to their ability to recover a complex functional network from biologically reasonable simulated data. RESULTS: We designed a simulator to generate data representing a complex biological system at multiple levels of organization: behaviour, neural anatomy, brain electrophysiology, and gene expression of songbirds. About 90% of the simulated variables are unregulated by other variables in the system and are included simply as distracters. We sampled the simulated data at intervals as one would sample from a biological system in practice, and then used the sampled data to evaluate the effectiveness of an algorithm we developed for functional network inference. We found that our algorithm is highly effective at recovering the functional network structure of the simulated system-including the irrelevance of unregulated variables-from sampled data alone. To assess the reproducibility of these results, we tested our inference algorithm on 50 separately simulated sets of data and it consistently recovered almost perfectly the complex functional network structure underlying the simulated data. To our knowledge, this is the first approach for evaluating the effectiveness of functional network inference algorithms at recovering models from limited data. Our simulation approach also enables researchers a priori to design experiments and data-collection protocols that are amenable to functional network inference.     

A fully continuous individual-based model of tumor cell evolution

The aim of this work is to develop and study a fully continuous individual-based model (IBM) for cancer tumor invasion into a spatial environment of surrounding tissue. The IBM improves previous spatially discrete models, because it is continuous in all variables (including spatial variables), and thus not constrained to lattice frameworks. The IBM includes four types of individual elements: tumor cells, extracellular macromolecules (MM), a matrix degradative enzyme (MDE), and oxygen. The algorithm underlying the IBM is based on the dynamic interaction of these four elements in the spatial environment, with special consideration of mutation phenotypes. A set of stochastic differential equations is formulated to describe the evolution of the IBM in an equivalent way. The IBM is scaled up to a system of partial differential equations (PDE) representing the limiting behavior of the IBM as the number of cells and molecules approaches infinity. Both models (IBM and PDE) are numerically simulated with two kinds of initial conditions: homogeneous MM distribution and heterogeneous MM distribution. With both kinds of initial MM distributions spatial fingering patterns appear in the tumor growth. The output of both simulations is quite similar.     

Division of labor during trunk neural crest development

Neural crest cells, the migratory precursors of numerous cell types including the vertebrate peripheral nervous system, arise in the dorsal neural tube and follow prescribed routes into the embryonic periphery. While the timing and location of neural crest migratory pathways has been well documented in the trunk, a comprehensive collection of signals that guides neural crest migration along these paths has only recently been established. In this review, we outline the molecular cascade of events during trunk neural crest development. After describing the sequential routes taken by trunk neural crest cells, we consider the guidance cues that pattern these neural crest trajectories. We pay particular attention to segmental neural crest development and the steps and signals that generate a metameric peripheral nervous system, attempting to reconcile conflicting observations in chick and mouse. Finally, we compare cranial and trunk neural crest development in order to highlight common themes.     

The full EM algorithm for the MLEs of QTL effects and positions and their estimated variances in multiple-interval mapping

The advent of complete genetic linkage maps of DNA markers has made systematic studies of mapping quantitative trait loci (QTL) in experimental organisms feasible. The method of multiple-interval mapping provides an appropriate way for mapping QTL using genetic markers. However, efficient algorithms for the computation involved remain to be developed. In this article, a full EM algorithm for the simultaneous computation of the MLEs of QTL effects and positions is developed. EM-based formulas are derived for computing the observed Fisher information matrix. The full EM algorithm is compared with an ECM algorithm developed by Kao and Zeng (1997, Biometrics 53, 653-665). The validity of the inverted observed Fisher information matrix as an estimate of the variance matrix of the MLEs is demonstrated by a simulation study.     

The construction of a simultaneous functional order in nervous systems

In a previous paper (Part I) we introduced a model that constructs a simultaneous functional order in a set of neuronal elements by monitoring the coincidences in their signal activities (the so-called coincidence-model). The simultaneous signal activity in a neural net will be constrained both by its physical restrictions and by environmental constraints. In this paper we present the results of simulation experiments that were performed to study the influence of environmental constraits on the resulting functional order in a set of neural elements corresponding to a onedimensional detector array. We show that the coincidence-model produces a functional order that encodes the physical constraints of the environment. Moreover, we demonstrate that the signal activity in the neural net (the perceptions) can be related to events in the outer world. We provide some examples to demonstrate that our model may prove useful to gain insight into certain developmental disorders.     

Functional nodes in dynamic neural networks for bioprocess modelling

This contribution presents a novel method for the direct integration of a-priori knowledge in a neural network and its application for the online determination of a secondary metabolite during industrial yeast fermentation. Hereby, existing system knowledge is integrated in an artificial neural network (ANN) by means of 'functional nodes'. A generalized backpropagation algorithm is presented. For illustration, a set of ordinary differential equations describing the diacetyl formation and degradation during the cultivation is incorporated in a functional node and integrated in a dynamic feedforward neural network in a hybrid manner. The results show that a hybrid modelling approach exploiting available a-priori knowledge and experimental data can considerably outperform a pure data-based modelling approach with respect to robustness, generalization and necessary amount of training data. The number of training sets were decreased by 50%, obtaining the same accuracy as in a conventional approach. All incorrect decisions, according to defined cost criteria obtained with the conventional ANN, were avoided.     

Protein folding on the hexagonal lattice in the HP model

In this paper, we introduce the 2D hexagonal lattice as a biologically meaningful alternative to the standard square lattice for the study of protein folding in the HP model. We show that the hexagonal lattice alleviates the "sharp turn" problem and models certain aspects of the protein secondary structure more realistically. We present a 1/6-approximation and a clustering heuristic for protein folding on the hexagonal lattice. In addition to these two algorithms, we also implement a Monte Carlo Metropolis algorithm and a branch-and-bound partial enumeration algorithm, and conduct experiments to compare their effectiveness.     

Ensemble non-negative matrix factorization methods for clustering protein-protein interactions

MOTIVATION: When working with large-scale protein interaction data, an important analysis task is the assignment of pairs of proteins to groups that correspond to higher order assemblies. Previously a common approach to this problem has been to apply standard hierarchical clustering methods to identify such a groups. Here we propose a new algorithm for aggregating a diverse collection of matrix factorizations to produce a more informative clustering, which takes the form of a 'soft' hierarchy of clusters. RESULTS: We apply the proposed Ensemble non-negative matrix factorization (NMF) algorithm to a high-quality assembly of binary protein interactions derived from two proteome-wide studies in yeast. Our experimental evaluation demonstrates that the algorithm lends itself to discovering small localized structures in this data, which correspond to known functional groupings of complexes. In addition, we show that the algorithm also supports the assignment of putative functions for previously uncharacterized proteins, for instance the protein YNR024W, which may be an uncharacterized component of the exosome.     

Benchmarking protein classification algorithms via supervised cross-validation

Development and testing of protein classification algorithms are hampered by the fact that the protein universe is characterized by groups vastly different in the number of members, in average protein size, similarity within group, etc. Datasets based on traditional cross-validation (k-fold, leave-one-out, etc.) may not give reliable estimates on how an algorithm will generalize to novel, distantly related subtypes of the known protein classes. Supervised cross-validation, i.e., selection of test and train sets according to the known subtypes within a database has been successfully used earlier in conjunction with the SCOP database. Our goal was to extend this principle to other databases and to design standardized benchmark datasets for protein classification. Hierarchical classification trees of protein categories provide a simple and general framework for designing supervised cross-validation strategies for protein classification. Benchmark datasets can be designed at various levels of the concept hierarchy using a simple graph-theoretic distance. A combination of supervised and random sampling was selected to construct reduced size model datasets, suitable for algorithm comparison. Over 3000 new classification tasks were added to our recently established protein classification benchmark collection that currently includes protein sequence (including protein domains and entire proteins), protein structure and reading frame DNA sequence data. We carried out an extensive evaluation based on various machine-learning algorithms such as nearest neighbor, support vector machines, artificial neural networks, random forests and logistic regression, used in conjunction with comparison algorithms, BLAST, Smith-Waterman, Needleman-Wunsch, as well as 3D comparison methods DALI and PRIDE. The resulting datasets provide lower, and in our opinion more realistic estimates of the classifier performance than do random cross-validation schemes. A combination of supervised and random sampling was used to construct model datasets, suitable for algorithm comparison.

The datasets are available at http://hydra.icgeb.trieste.it/benchmark.     

Global stability in a delayed partial differential equation describing cellular replication

Here we consider the dynamics of a population of cells that are capable of simultaneous proliferation and maturation. The equations describing the cellular population numbers are first order partial differential equations (transport equations) in which there is an explicit temporal retardation as well as a nonlocal dependence in the maturation variable due to cell replication. The behavior of this system may be considered along the characteristics, and a global stability condition is proved.     

An Approximation Algorithm for the Minimum Breakpoint Linearization Problem

In the recent years, there has been a growing interest in inferring the total order of genes or markers on a chromosome, since current genetic mapping efforts might only suffice to produce a partial order. Many interesting optimization problems were thus formulated in the framework of genome rearrangement. As an important one among them, the minimum breakpoint linearization (MBL) problem is to find the total order of a partially ordered genome that minimizes its breakpoint distance to a reference genome whose genes are already totally ordered. It was previously shown to be NP-hard, and the algorithms proposed so far are all heuristic. In this paper, we present an {m^2+mover 2}-approximation algorithm for the MBL problem, where m is the number of gene maps that are combined together to form a partial order of the genome under investigation.     

Z-line formins promote contractile lattice growth and maintenance in striated muscles of C. elegans

Muscle contraction depends on interactions between actin and myosin filaments organized into sarcomeres, but the mechanism by which actin filaments incorporate into sarcomeres remains unclear. We have found that, during larval development in Caenorhabditis elegans, two members of the actin-assembling formin family, CYK-1 and FHOD-1, are present in striated body wall muscles near or on sarcomere Z lines, where barbed ends of actin filaments are anchored. Depletion of either formin during this period stunted growth of the striated contractile lattice, whereas their simultaneous reduction profoundly diminished lattice size and number of striations per muscle cell. CYK-1 persisted at Z lines in adulthood, and its near complete depletion from adults triggered phenotypes ranging from partial loss of Z line-associated filamentous actin to collapse of the contractile lattice. These results are, to our knowledge, the first genetic evidence implicating sarcomere-associated formins in the in vivo organization of the muscle cytoskeleton.     

FaST linear mixed models for genome-wide association studies

We describe factored spectrally transformed linear mixed models (FaST-LMM), an algorithm for genome-wide association studies (GWAS) that scales linearly with cohort size in both run time and memory use. On Wellcome Trust data for 15,000 individuals, FaST-LMM ran an order of magnitude faster than current efficient algorithms. Our algorithm can analyze data for 120,000 individuals in just a few hours, whereas current algorithms fail on data for even 20,000 individuals (http://mscompbio.codeplex.com/).     

A minor subspace algorithm based on neural Stiefel dynamics

In the present paper we investigate iterative minor subspace analysis computation by describing a neural approach based on weight flow on Stiefel manifold and by discussing four neural algorithms and a purely algebraic algorithm known from the scientific literature. A comparison of numerical experimental results and computational complexity estimates confirms the effectiveness and efficiency of the proposed approach.