Decomposing complex reaction networks using random sampling,principal component analysis and basis rotation

Background  

Metabolism and its regulation constitute a large fraction of the molecular activity within cells. The control of cellular metabolic state is mediated by numerous molecular mechanisms, which in effect position the metabolic network flux state at specific locations within a mathematically-definable steady-state flux space. Post-translational regulation constitutes a large class of these mechanisms, and decades of research indicate that achieving a network flux state through post-translational metabolic regulation is both a complex and complicated regulatory problem. No analysis method for the objective, top-down assessment of such regulation problems in large biochemical networks has been presented and demonstrated.     

Inference of signaling and gene regulatory networks by steady-state perturbation experiments: structure and accuracy

One of the fundamental problems of cell biology is the understanding of complex regulatory networks. Such networks are ubiquitous in cells and knowledge of their properties is essential for the understanding of cellular behavior. In earlier work (Kholodenko et al. (PNAS 99: 12841), it was shown how the structure of biological networks can be quantified from experimental measurements of steady-state concentrations of key intermediates as a result of perturbations using a simple algorithm called "unravelling". Here, we study the effect of experimental uncertainty on the accuracy of the inferred structure (i.e. whether interactions are excitatory or inhibitory) of the networks determined using the unravelling algorithm. We show that the accuracy of the network structure depends not only on the noise level but on the strength of the interactions within the network. In particular, both very small and very large values of the connection strengths lead to large uncertainty in the inferred network. We describe a powerful geometric tool for the intuitive understanding of the effect of experimental error on the qualitative accuracy of the inferred network. In addition, we show that the use of additional data beyond that needed to minimally constrain the network not only improves the accuracy of the inferred network, but also may allow the detection of situations in which the initial assumptions of unravelling with respect to the network and the perturbations have been violated. Our ideas are illustrated using the mitogen-activated protein kinase (MAPK) signaling network as an example.     

Identification of phytoplankton from flow cytometry data by using radial basis function neural networks.

We describe here the application of a type of artificial neural network, the Gaussian radial basis function (RBF) network, in the identification of a large number of phytoplankton strains from their 11-dimensional flow cytometric characteristics measured by the European Optical Plankton Analyser instrument. The effect of network parameters on optimization is examined. Optimized RBF networks recognized 34 species of marine and freshwater phytoplankton with 91. 5% success overall. The relative importance of each measured parameter in discriminating these data and the behavior of RBF networks in response to data from "novel" species (species not present in the training data) were analyzed.     

Neutral phenotypes as network keystone species

The concept of network keystone species is proposed. A set of phenotypes constitute a network that acts as a functional keystone. When an ecosystem forms a large, complex network that changes temporally, it is generally difficult to tell which will become a keystone species. Based on simulations of abstract ecosystems, phenotypes were classified to show that neutral phenotypes, or slowly reproducing phenotypes, are candidates for keystone species. I show that the removal of neutral phenotypes breaks up an attractor state and produces significant impacts on the stability of an attractor, in spite of small population size. The effect of partial removal of neutral phenotypes, and the combinatorial effects of keystone species, are reported in detail.     

Predicting the effect of competition on secondary plant extinctions in plant–pollinator networks

What are the limitations of models that predict the behavior of an ecological community based on a single type of species interaction? Using plant–pollinator network models as an example, we contrast the predicted vulnerability of a community to secondary extinctions under the assumption of purely mutualistic interactions versus mutualistic and competitive interactions. We find that competition among plant species increases the risk of secondary extinctions and extinction cascades. Simulations over a number of different network structures indicate that this effect is stronger in larger networks, more strongly connected networks and networks with higher plant:pollinator ratios. We conclude that efforts to model plant–pollinator communities will systematically over‐estimate community robustness to species loss if plant competition is ignored. However, because the effect of plant competition depends on network architecture, and because characterization of plant competition is work intensive, we suggest that efforts to account for plant competition in plant–pollinator network models should be focused on large, strongly connected networks with high plant:pollinator ratios.     

Identification of Phytoplankton from Flow Cytometry Data by Using Radial Basis Function Neural Networks

We describe here the application of a type of artificial neural network, the Gaussian radial basis function (RBF) network, in the identification of a large number of phytoplankton strains from their 11-dimensional flow cytometric characteristics measured by the European Optical Plankton Analyser instrument. The effect of network parameters on optimization is examined. Optimized RBF networks recognized 34 species of marine and freshwater phytoplankton with 91.5% success overall. The relative importance of each measured parameter in discriminating these data and the behavior of RBF networks in response to data from “novel” species (species not present in the training data) were analyzed.     

Stress Heterogeneities in Sheared Type-I Collagen Networks Revealed by Boundary Stress Microscopy

Disordered fiber networks provide structural support to a wide range of important materials, and the combination of spatial and dynamic complexity may produce large inhomogeneities in mechanical properties, an effect that is largely unexplored experimentally. In this work, we introduce Boundary Stress Microscopy to quantify the non-uniform surface stresses in sheared collagen gels. We find local stresses exceeding average stresses by an order of magnitude, with variations over length scales much larger than the network mesh size. The strain stiffening behavior observed over a wide range of network mesh sizes can be parameterized by a single characteristic strain and associated stress, which describes both the strain stiffening regime and network yielding. The characteristic stress is approximately proportional to network density, but the peak boundary stress at both the characteristic strain and at yielding are remarkably insensitive to concentration.     

A discrete fully recurrent network of max product units for associative memory and classification

This paper defines the truncated normalized max product operation for the transformation of states of a network and provides a method for solving a set of equations based on this operation. The operation serves as the transformation for the set of fully connected units in a recurrent network that otherwise might consist of linear threshold units. Component values of the state vector and outputs of the units take on the values in the set [0, 0.1,..., 0.9, 1]. The result is a much larger state space given a particular number of units and size of connection matrix than for a network based on threshold units. Since the operation defined here can form the basis of transformations in a recurrent network with a finite number of states, fixed points or cycles are possible and the network based on this operation for transformations can be used as an associative memory or pattern classifier with fixed points taking on the role of prototypes. Discrete fully recurrent networks have proven themselves to be very useful as associative memories and as classifiers. However they are often based on units that have binary states. The effect of this is that the data to be processed consisting of vectors in R(n) have to be converted to vectors in [0, 1]m with m much larger than n since binary encoding based on positional notation is not feasible. This implies a large increase in the number of components. The effect can be lessened by allowing more states for each unit in our network. The network proposed demonstrates those properties that are desirable in an associative memory very well as the simulations show.     

Random main effects of treatment: A case study with a network meta‐analysis

If the number of treatments in a network meta‐analysis is large, it may be possible and useful to model the main effect of treatment as random, that is to say as random realizations from a normal distribution of possible treatment effects. This then constitutes a third sort of random effect that may be considered in connection with such analyses. The first and most common models treatment‐by‐trial interaction as being random and the second, rather rarer, models the main effects of trial as being random and thus permits the recovery of intertrial information. Taking the example of a network meta‐analysis of 44 similar treatments in 10 trials, we illustrate how a hierarchical approach to modeling a random main effect of treatment can be used to produce shrunk (toward the overall mean) estimates of effects for individual treatments. As a related problem, we also consider the issue of using a random‐effect model for the within‐trial variances from trial to trial. We provide a number of possible graphical representations of the results and discuss the advantages and disadvantages of such an approach.     

Role of microtubules versus myosin heavy chain isoforms in contractile dysfunction of hypertrophied murine cardiocytes

In large mammals there is a correlation between microtubule network densification and contractile dysfunction in severe pressure-overload hypertrophy. In small mammals there is a similar correlation for the shift to beta-myosin heavy chain (MHC), a MHC isoform having a slower ATPase Vmax. In this study, murine left ventricular (LV) pressure overload invoked both mechanisms: microtubule network densification and beta-MHC expression. Cardiac beta-MHC was also augmented without altering tubulin levels by two load-independent means, chemical thyroidectomy and transgenesis. In hypertrophy, contractile function of the LV and its cardiocytes decreased proportionally; microtubule depolymerization restored normal cellular contraction. In hypothyroid mice having a complete shift from alpha-MHC to beta-MHC, contractile function of the LV and its cardiocytes also decreased, but microtubule depolymerization had no effect on cellular contraction. In transgenic mice having a cardiac beta-MHC increase similar to that in hypertrophy, contractile function of the LV and its cardiocytes was normal, and microtubule depolymerization had no effect. Thus, although both mechanisms may cause contractile dysfunction, for the extent of MHC isoform switching seen even in severe murine LV pressure-overload hypertrophy, microtubule network densification appears to have the more important role.     

A Three-Dimensional Computational Model of Collagen Network Mechanics

Extracellular matrix (ECM) strongly influences cellular behaviors, including cell proliferation, adhesion, and particularly migration. In cancer, the rigidity of the stromal collagen environment is thought to control tumor aggressiveness, and collagen alignment has been linked to tumor cell invasion. While the mechanical properties of collagen at both the single fiber scale and the bulk gel scale are quite well studied, how the fiber network responds to local stress or deformation, both structurally and mechanically, is poorly understood. This intermediate scale knowledge is important to understanding cell-ECM interactions and is the focus of this study. We have developed a three-dimensional elastic collagen fiber network model (bead-and-spring model) and studied fiber network behaviors for various biophysical conditions: collagen density, crosslinker strength, crosslinker density, and fiber orientation (random vs. prealigned). We found the best-fit crosslinker parameter values using shear simulation tests in a small strain region. Using this calibrated collagen model, we simulated both shear and tensile tests in a large linear strain region for different network geometry conditions. The results suggest that network geometry is a key determinant of the mechanical properties of the fiber network. We further demonstrated how the fiber network structure and mechanics evolves with a local formation, mimicking the effect of pulling by a pseudopod during cell migration. Our computational fiber network model is a step toward a full biomechanical model of cellular behaviors in various ECM conditions.     

Spike independency in feed-forward networks

A cortical neuron puts thousands of synaptic contacts on other neurons. The effect of the spike event spreads over a large number of neurons. So it is possible for spike timings to be correlated to each other. But there have not been so many reports of spike timing correlations, while there have been many reports of somewhat longer time range correlations through mean spike rates. Can independent firings be preserved in spite of a number of connections? The present study attempts to determine whether independent firings can be propagated through a simple feed-forward neural network. It is assumed that each unit obeys a threshold mechanism at each discrete time and that connections are statistically uniform with the excitation balanced to the inhibition and delay distributed. It is found that the independent firings can be stably propagated through the feed-forward network at a network parameter region, which contains the physiologically reasonable range. Another interesting result is that the independency-stable spike probability has a lower limit 0.0323.     

The mechanical behavior of mutant K14-R125P keratin bundles and networks in NEB-1 keratinocytes

Epidermolysis bullosa simplex (EBS) is an inherited skin-blistering disease that is caused by dominant mutations in the genes for keratin K5 or K14 proteins. While the link between keratin mutations and keratinocyte fragility in EBS patients is clear, the exact biophysical mechanisms underlying cell fragility are not known. In this study, we tested the hypotheses that mutant K14-R125P filaments and/or networks in human keratinocytes are mechanically defective in their response to large-scale deformations. We found that mutant filaments and networks exhibit no obvious defects when subjected to large uniaxial strains and have no negative effects on the ability of human keratinocytes to survive large strains. We also found that the expression of mutant K14-R125P protein has no effect on the morphology of the F-actin or microtubule networks or their responses to large strains. Disassembly of the F-actin network with Latrunculin A unexpectedly led to a marked decrease in stretch-induced necrosis in both WT and mutant cells. Overall, our results contradict the hypotheses that EBS mutant keratin filaments and/or networks are mechanically defective. We suggest that future studies should test the alternative hypothesis that keratinocytes in EBS cells are fragile because they possess a sparser keratin network.     

Finding quasi-optimal network topologies for information transmission in active networks

This work clarifies the relation between network circuit (topology) and behaviour (information transmission and synchronization) in active networks, e.g. neural networks. As an application, we show how one can find network topologies that are able to transmit a large amount of information, possess a large number of communication channels, and are robust under large variations of the network coupling configuration. This theoretical approach is general and does not depend on the particular dynamic of the elements forming the network, since the network topology can be determined by finding a Laplacian matrix (the matrix that describes the connections and the coupling strengths among the elements) whose eigenvalues satisfy some special conditions. To illustrate our ideas and theoretical approaches, we use neural networks of electrically connected chaotic Hindmarsh-Rose neurons.     

Finite-size and correlation-induced effects in mean-field dynamics

The brain’s activity is characterized by the interaction of a very large number of neurons that are strongly affected by noise. However, signals often arise at macroscopic scales integrating the effect of many neurons into a reliable pattern of activity. In order to study such large neuronal assemblies, one is often led to derive mean-field limits summarizing the effect of the interaction of a large number of neurons into an effective signal. Classical mean-field approaches consider the evolution of a deterministic variable, the mean activity, thus neglecting the stochastic nature of neural behavior. In this article, we build upon two recent approaches that include correlations and higher order moments in mean-field equations, and study how these stochastic effects influence the solutions of the mean-field equations, both in the limit of an infinite number of neurons and for large yet finite networks. We introduce a new model, the infinite model, which arises from both equations by a rescaling of the variables and, which is invertible for finite-size networks, and hence, provides equivalent equations to those previously derived models. The study of this model allows us to understand qualitative behavior of such large-scale networks. We show that, though the solutions of the deterministic mean-field equation constitute uncorrelated solutions of the new mean-field equations, the stability properties of limit cycles are modified by the presence of correlations, and additional non-trivial behaviors including periodic orbits appear when there were none in the mean field. The origin of all these behaviors is then explored in finite-size networks where interesting mesoscopic scale effects appear. This study leads us to show that the infinite-size system appears as a singular limit of the network equations, and for any finite network, the system will differ from the infinite system.     

Robustness elasticity in complex networks

Network robustness refers to a network's resilience to stress or damage. Given that most networks are inherently dynamic, with changing topology, loads, and operational states, their robustness is also likely subject to change. However, in most analyses of network structure, it is assumed that interaction among nodes has no effect on robustness. To investigate the hypothesis that network robustness is not sensitive or elastic to the level of interaction (or flow) among network nodes, this paper explores the impacts of network disruption, namely arc deletion, over a temporal sequence of observed nodal interactions for a large Internet backbone system. In particular, a mathematical programming approach is used to identify exact bounds on robustness to arc deletion for each epoch of nodal interaction. Elasticity of the identified bounds relative to the magnitude of arc deletion is assessed. Results indicate that system robustness can be highly elastic to spatial and temporal variations in nodal interactions within complex systems. Further, the presence of this elasticity provides evidence that a failure to account for nodal interaction can confound characterizations of complex networked systems.     

Reconstructing pathways in large genetic networks from genetic perturbations.

I present an algorithm that determines the longest path between every gene pair in an arbitrarily large genetic network from large scale gene perturbation data. The algorithm's computational complexity is O(nk(2)), where n is the number of genes in the network and k is the average number of genes affected by a genetic perturbation. The algorithm is able to distinguish a large fraction of direct regulatory interactions from indirect interactions, even if the accuracy of its input data is substantially compromised.     

Relation between complexity and stability in food webs with adaptive behavior

We investigate the influence of functional responses (Lotka-Volterra or Holling type), initial topological web structure (randomly connected or niche model), adaptive behavior (adaptive foraging and predator avoidance) and the type of constraints on the adaptive behavior (linear or nonlinear) on the stability and structure of food webs. Two kinds of stability are considered: one is the network robustness (i.e., the proportion of species surviving after population dynamics) and the other is the species deletion stability. When evaluating the network structure, we consider link density as well as the trophic level structure. We show that the types of functional responses and initial web structure do not have a large effect on the stability of food webs, but foraging behavior has a large stabilizing effect. It leads to a positive complexity-stability relationship whenever higher "complexity" implies more potential prey per species. The other type of adaptive behavior, predator avoidance behavior, makes food webs only slightly more stable. The observed link density after population dynamics depends strongly on the presence or absence of adaptive foraging, and on the type of constraints used. We also show that the trophic level structure is preserved under population dynamics with adaptive foraging.     

AIM: A network model of attention in auditory cortex

Attentional modulation of cortical networks is critical for the cognitive flexibility required to process complex scenes. Current theoretical frameworks for attention are based almost exclusively on studies in visual cortex, where attentional effects are typically modest and excitatory. In contrast, attentional effects in auditory cortex can be large and suppressive. A theoretical framework for explaining attentional effects in auditory cortex is lacking, preventing a broader understanding of cortical mechanisms underlying attention. Here, we present a cortical network model of attention in primary auditory cortex (A1). A key mechanism in our network is attentional inhibitory modulation (AIM) of cortical inhibitory neurons. In this mechanism, top-down inhibitory neurons disinhibit bottom-up cortical circuits, a prominent circuit motif observed in sensory cortex. Our results reveal that the same underlying mechanisms in the AIM network can explain diverse attentional effects on both spatial and frequency tuning in A1. We find that a dominant effect of disinhibition on cortical tuning is suppressive, consistent with experimental observations. Functionally, the AIM network may play a key role in solving the cocktail party problem. We demonstrate how attention can guide the AIM network to monitor an acoustic scene, select a specific target, or switch to a different target, providing flexible outputs for solving the cocktail party problem.