Energy in functional brain states correlates with cognition in adolescent-onset schizophrenia and healthy persons

Adolescent-onset schizophrenia (AOS) is a relatively rare and under-studied form of schizophrenia with more severe cognitive impairments and poorer outcome compared to adult-onset schizophrenia. Several neuroimaging studies have reported alterations in regional activations that account for activity in individual regions (first-order model) and functional connectivity that reveals pairwise co-activations (second-order model) in AOS compared to controls. The pairwise maximum entropy model, also called the Ising model, can integrate both first-order and second-order terms to elucidate a comprehensive picture of neural dynamics and captures both individual and pairwise activity measures into a single quantity known as energy, which is inversely related to the probability of state occurrence. We applied the MEM framework to task functional MRI data collected on 23 AOS individuals in comparison with 53 healthy control subjects while performing the Penn Conditional Exclusion Test (PCET), which measures executive function that has been repeatedly shown to be more impaired in AOS compared to adult-onset schizophrenia. Accuracy of PCET performance was significantly reduced among AOS compared to controls as expected. Average cumulative energy achieved for a participant over the course of the fMRI negatively correlated with task performance, and the association was stronger than any first-order associations. The AOS subjects spent more time in higher energy states that represent lower probability of occurrence and were associated with impaired executive function and greater severity of psychopathology suggesting that the neural dynamics may be less efficient compared to controls who spent more time in lower energy states occurring with higher probability and hence are more stable and efficient. The energy landscapes in both conditions featured attractors that corresponded to two distinct subnetworks, namely fronto-temporal and parieto-motor. Attractor basins were larger in the controls than in AOS; moreover, fronto-temporal basin size was significantly correlated with cognitive performance in controls but not among the AOS. The single trial trajectories for the AOS group also showed higher variability in concordance with shallow attractor basins among AOS. These findings suggest that the neural dynamics of AOS features more frequent occurrence of less probable states with shallower attractors, which lack the relation to executive function associated with attractors in control subjects suggesting a diminished capacity of AOS to generate task-effective brain states.

Temporal Mapper: Transition networks in simulated and real neural dynamics

Characterizing large-scale dynamic organization of the brain relies on both data-driven and mechanistic modeling, which demands a low versus high level of prior knowledge and assumptions about how constituents of the brain interact. However, the conceptual translation between the two is not straightforward. The present work aims to provide a bridge between data-driven and mechanistic modeling. We conceptualize brain dynamics as a complex landscape that is continuously modulated by internal and external changes. The modulation can induce transitions between one stable brain state (attractor) to another. Here, we provide a novel method-Temporal Mapper-built upon established tools from the field of topological data analysis to retrieve the network of attractor transitions from time series data alone. For theoretical validation, we use a biophysical network model to induce transitions in a controlled manner, which provides simulated time series equipped with a ground-truth attractor transition network. Our approach reconstructs the ground-truth transition network from simulated time series data better than existing time-varying approaches. For empirical relevance, we apply our approach to fMRI data gathered during a continuous multitask experiment. We found that occupancy of the high-degree nodes and cycles of the transition network was significantly associated with subjects' behavioral performance. Taken together, we provide an important first step toward integrating data-driven and mechanistic modeling of brain dynamics.

Collective computational intelligence in biology - Emergence of memory in somatic tissues

Role of memory in the function of biological tissues, organs and organisms remains unexplored with many unanswered questions. In this study, the emergence of associative memory in somatic (non-neural) tissues and its potential relation to tissue function was explored using a number of biologically plausible network topologies in in silico tissues with computing cells. These topologies were local cooperation; complete system-wide cooperation or inhibition; and local cooperation and short- or long-range inhibition. These were tested with and without self-feedback on two-dimensional (2D) three-dimensional (3D) cell networks, resulting in various forms of fully and partially connected networks. Further, both binary inputs with threshold processing and real-valued inputs with nonlinear processing were considered. Results revealed the emergence of diverse forms of tissue memory. In full cooperation, networks produced one fixed attractor indicating the propensity towards a stable memory pattern which in a real tissue could correspond to an invariable physiological state, such as bioelectric homeostasis. The local neighbourhood cooperation produced both a fixed and a limit cycle attractor that could be beneficial for a tissue to hold few associative memories including circadian rhythms. Most interesting results were found for the local cooperation with short- or long-range inhibition topologies that produced a cluster of fixed and limit cycle attractors offering diverse memories. Fixed attractors could correspond to inactive tissue states and active nonrhythmic functional states and limit cycles could correspond to circadian rhythms such as pumping in heart, kidney or liver in various oscillatory regimes. In all topologies, self-feedback abolished or drastically reduced the limit cycles in favour of fixed stable state. These attractor patterns were found to be largely invariant to scale (2D or 3D) and type of inputs and processing. We also explored the self-optimising ability of the 'local cooperation with global (short- or long-range) inhibition' 2D topologies with Hebbian learning with fixed and flexible topologies. The fixed topology learned to self-model to consolidate memory towards fewer more stable attractors. The flexible topology even formed new connections to bring the system to a single fixed state. Thus local cooperation with global inhibition topology can offer greater freedom to create diverse memory pattens that can be tempered by learning, self-feedback, and to some extent continuous processing to simplify and consolidate memory towards manageable forms.

Dissecting cell fate dynamics in pediatric glioblastoma through the lens of complex systems and cellular cybernetics

Cancers are complex dynamic ecosystems. Reductionist approaches to science are inadequate in characterizing their self-organized patterns and collective emergent behaviors. Since current approaches to single-cell analysis in cancer systems rely primarily on single time-point multiomics, many of the temporal features and causal adaptive behaviors in cancer dynamics are vastly ignored. As such, tools and concepts from the interdisciplinary paradigm of complex systems theory are introduced herein to decode the cellular cybernetics of cancer differentiation dynamics and behavioral patterns. An intuition for the attractors and complex networks underlying cancer processes such as cell fate decision-making, multiscale pattern formation systems, and epigenetic state-transitions is developed. The applications of complex systems physics in paving targeted therapies and causal pattern discovery in precision oncology are discussed. Pediatric high-grade gliomas are discussed as a model-system to demonstrate that cancers are complex adaptive systems, in which the emergence and selection of heterogeneous cellular states and phenotypic plasticity are driven by complex multiscale network dynamics. In specific, pediatric glioblastoma (GBM) is used as a proof-of-concept model to illustrate the applications of the complex systems framework in understanding GBM cell fate decisions and decoding their adaptive cellular dynamics. The scope of these tools in forecasting cancer cell fate dynamics in the emerging field of computational oncology and patient-centered systems medicine is highlighted.

Capturing the non-stationarity of whole-brain dynamics underlying human brain states

Brain dynamics depicts an extremely complex energy landscape that changes over time, and its characterisation is a central unsolved problem in neuroscience. We approximate the non-stationary landscape sustained by the human brain through a novel mathematical formalism that allows us characterise the attractor structure, i.e. the stationary points and their connections. Due to its time-varying nature, the structure of the global attractor and the corresponding number of energy levels changes over time. We apply this formalism to distinguish quantitatively between the different human brain states of wakefulness and different stages of sleep, as a step towards future clinical applications.

The Effects of Graded Levels of Calorie Restriction XV: Phase Space Attractors Reveal Distinct Behavioral Phenotypes

Calorie restriction (CR) has a positive impact on health and life span. Previous work, however, does not reveal the whole underlying mechanism of behavioral phenotypes under CR. We propose a new approach based on phase space reconstruction (PSR) to analyze the behavioral responses of mice to graded CR. This involved reconstructing high-dimensional attractors which topologically represent the intrinsic dynamics of mice based on low-dimensional time series of movement counts observed during the 90-day time course of restriction. PSR together with correlation dimensions (CD), Kolmogorov entropy (KE), and multifractal spectra builds a map from internal attractors to the phenotype of mice and reveals the mice with increasing CR levels undergo significant changes from a normal to a new state. Features of the attractors (CD and KE) were significantly associated with gene expression profiles in the hypothalamus of the same individuals.

Attractor-state itinerancy in neural circuits with synaptic depression

Neural populations with strong excitatory recurrent connections can support bistable states in their mean firing rates. Multiple fixed points in a network of such bistable units can be used to model memory retrieval and pattern separation. The stability of fixed points may change on a slower timescale than that of the dynamics due to short-term synaptic depression, leading to transitions between quasi-stable point attractor states in a sequence that depends on the history of stimuli. To better understand these behaviors, we study a minimal model, which characterizes multiple fixed points and transitions between them in response to stimuli with diverse time- and amplitude-dependencies. The interplay between the fast dynamics of firing rate and synaptic responses and the slower timescale of synaptic depression makes the neural activity sensitive to the amplitude and duration of square-pulse stimuli in a nontrivial, history-dependent manner. Weak cross-couplings further deform the basins of attraction for different fixed points into intricate shapes. We find that while short-term synaptic depression can reduce the total number of stable fixed points in a network, it tends to strongly increase the number of fixed points visited upon repetitions of fixed stimuli. Our analysis provides a natural explanation for the system's rich responses to stimuli of different durations and amplitudes while demonstrating the encoding capability of bistable neural populations for dynamical features of incoming stimuli.

In search of sports biomechanics' holy grail: Can athlete-specific optimum sports techniques be identified?

The development of methods that can identify athlete-specific optimum sports techniques-arguably the holy grail of sports biomechanics-is one of the greatest challenges for researchers in the field. This 'perspectives article' critically examines, from a dynamical systems theoretical standpoint, the claim that athlete-specific optimum sports techniques can be identified through biomechanical optimisation modelling. To identify athlete-specific optimum sports techniques, dynamical systems theory suggests that a representative set of organismic constraints, along with their non-linear characteristics, needs to be identified and incorporated into the mathematical model of the athlete. However, whether the athlete will be able to adopt, and reliably reproduce, his/her predicted optimum technique will largely be dependent on his/her intrinsic dynamics. If the attractor valley corresponding to the existing technique is deep, or if the attractor valleys corresponding to the existing technique and the predicted optimum technique are in different topographical regions of the dynamic landscape, technical modifications may be challenging or impossible to reliably implement even after extended practice. The attractor layout defining the intrinsic dynamics of the athlete, therefore, needs to be determined to establish the likelihood of the predicted optimum technique being reliably attainable by the athlete. Given the limited set of organismic constraints typically used in mathematical models of athletes, combined with the methodological challenges associated with mapping the attractor layout of an athlete, it seems unlikely that athlete-specific optimum sports techniques will be identifiable through biomechanical optimisation modelling for the majority of sports skills in the near future.

Spatiotemporal discrimination in attractor networks with short-term synaptic plasticity

We demonstrate that a randomly connected attractor network with dynamic synapses can discriminate between similar sequences containing multiple stimuli suggesting such networks provide a general basis for neural computations in the brain. The network contains units representing assemblies of pools of neurons, with preferentially strong recurrent excitatory connections rendering each unit bi-stable. Weak interactions between units leads to a multiplicity of attractor states, within which information can persist beyond stimulus offset. When a new stimulus arrives, the prior state of the network impacts the encoding of the incoming information, with short-term synaptic depression ensuring an itinerancy between sets of active units. We assess the ability of such a network to encode the identity of sequences of stimuli, so as to provide a template for sequence recall, or decisions based on accumulation of evidence. Across a range of parameters, such networks produce the primacy (better final encoding of the earliest stimuli) and recency (better final encoding of the latest stimuli) observed in human recall data and can retain the information needed to make a binary choice based on total number of presentations of a specific stimulus. Similarities and differences in the final states of the network produced by different sequences lead to predictions of specific errors that could arise when an animal or human subject generalizes from training data, when the training data comprises a subset of the entire stimulus repertoire. We suggest that such networks can provide the general purpose computational engines needed for us to solve many cognitive tasks.

Evolutionary framework of the human interactome: Unicellular and multicellular giant clusters

The main contradiction of multicellularity (MCM) is between the unicellular (UC) and multicellular (MC) levels. In human interactome we revealed two giant clusters with MC and UC medians (and several smaller ones with MC medians). The enrichment of these clusters by phylostrata and by functions support the MC versus UC division. The total interactome and the giant clusters show a core-periphery evolutionary growth. From viewpoint of the MCM, the most important is the placement of genes, appearing at UC evolutionary stage, in the MC clusters. Thus, genes involved in vesicle-mediated transport, cell cycle, cellular responses to stress, post-translational modifications and many diseases appeared at UC evolutionary stage but are placed mostly in MC clusters. Genes downregulated with age are enriched in UC cluster, whereas the upregulated genes are preferentially placed in MC giant cluster. The tumor suppressor and pluripotency regulating pathways are also enriched in MC giant cluster. Therefore, this cluster probably operates as 'internal manager' constraining runaway unicellularity. The clusters have denser interactions within than between them, therefore they can serve as attractors (stable states of dynamic systems) of cellular programs. Importantly, the UC cluster have a higher inside/outside connection ratio compared with MC clusters, which suggests a stronger attractor effect and may explain why cells of MC organisms are prone to oncogenesis. The evolutionary clustering of human interactome elucidates the MC control over functions appearing at UC evolutionary stage and can build a framework for biosystems studies focusing on the interplay between UC and MC levels.

A nonlinear mathematical model of cell-mediated immune response for tumor phenotypic heterogeneity

Human cancers display intra-tumor heterogeneity in many phenotypic features, such as expression of cell surface receptors, growth, and angiogenic, proliferative, and immunogenic factors, which represent obstacles to a successful immune response. In this paper, we propose a nonlinear mathematical model of cancer immunosurveillance that takes into account some of these features based on cell-mediated immune responses. The model describes phenomena that are seen in vivo, such as tumor dormancy, robustness, immunoselection over tumor heterogeneity (also called "cancer immunoediting") and strong sensitivity to initial conditions in the composition of tumor microenvironment. The results framework has as common element the tumor as an attractor for abnormal cells. Bifurcation analysis give us as tumor attractors fixed-points, limit cycles and chaotic attractors, the latter emerging from period-doubling cascade displaying Feigenbaum's universality. Finally, we simulated both elimination and escape tumor scenarios by means of a stochastic version of the model according to the Doob-Gillespie algorithm.

Modeling the Epigenetic Landscape in Plant Development

Computational mechanistic models enable a systems-level understanding of plant development by integrating available molecular experimental data and simulating their collective dynamical behavior. Boolean gene regulatory network dynamical models have been extensively used as a qualitative modeling framework for such purpose. More recently, network modeling protocols have been extended to model the epigenetic landscape associated with gene regulatory networks. In addition to understanding the concerted action of interconnected genes, epigenetic landscape models aim to uncover the patterns of cell state transition events that emerge under diverse genetic and environmental background conditions. In this chapter we present simple protocols that naturally extend gene regulatory network modeling and demonstrate their use in modeling plant developmental processes under the epigenetic landscape framework. We focus on conceptual clarity and practical implementation, providing directions to the corresponding technical literature. The protocols presented here can be applied to any well-characterized gene regulatory network in plants, animals, or human disease.

ASP-based method for the enumeration of attractors in non-deterministic synchronous and asynchronous multi-valued networks

BACKGROUND

This paper addresses the problem of finding attractors in biological regulatory networks. We focus here on non-deterministic synchronous and asynchronous multi-valued networks, modeled using automata networks (AN). AN is a general and well-suited formalism to study complex interactions between different components (genes, proteins,...). An attractor is a minimal trap domain, that is, a part of the state-transition graph that cannot be escaped. Such structures are terminal components of the dynamics and take the form of steady states (singleton) or complex compositions of cycles (non-singleton). Studying the effect of a disease or a mutation on an organism requires finding the attractors in the model to understand the long-term behaviors.

RESULTS

We present a computational logical method based on answer set programming (ASP) to identify all attractors. Performed without any network reduction, the method can be applied on any dynamical semantics. In this paper, we present the two most widespread non-deterministic semantics: the asynchronous and the synchronous updating modes. The logical approach goes through a complete enumeration of the states of the network in order to find the attractors without the necessity to construct the whole state-transition graph. We realize extensive computational experiments which show good performance and fit the expected theoretical results in the literature.

CONCLUSION

The originality of our approach lies on the exhaustive enumeration of all possible (sets of) states verifying the properties of an attractor thanks to the use of ASP. Our method is applied to non-deterministic semantics in two different schemes (asynchronous and synchronous). The merits of our methods are illustrated by applying them to biological examples of various sizes and comparing the results with some existing approaches. It turns out that our approach succeeds to exhaustively enumerate on a desktop computer, in a large model (100 components), all existing attractors up to a given size (20 states). This size is only limited by memory and computation time.

Sepsis reconsidered: Identifying novel metrics for behavioral landscape characterization with a high-performance computing implementation of an agent-based model

OBJECTIVES

Sepsis affects nearly 1 million people in the United States per year, has a mortality rate of 28-50% and requires more than $20 billion a year in hospital costs. Over a quarter century of research has not yielded a single reliable diagnostic test or a directed therapeutic agent for sepsis. Central to this insufficiency is the fact that sepsis remains a clinical/physiological diagnosis representing a multitude of molecularly heterogeneous pathological trajectories. Advances in computational capabilities offered by High Performance Computing (HPC) platforms call for an evolution in the investigation of sepsis to attempt to define the boundaries of traditional research (bench, clinical and computational) through the use of computational proxy models. We present a novel investigatory and analytical approach, derived from how HPC resources and simulation are used in the physical sciences, to identify the epistemic boundary conditions of the study of clinical sepsis via the use of a proxy agent-based model of systemic inflammation.

DESIGN

Current predictive models for sepsis use correlative methods that are limited by patient heterogeneity and data sparseness. We address this issue by using an HPC version of a system-level validated agent-based model of sepsis, the Innate Immune Response ABM (IIRBM), as a proxy system in order to identify boundary conditions for the possible behavioral space for sepsis. We then apply advanced analysis derived from the study of Random Dynamical Systems (RDS) to identify novel means for characterizing system behavior and providing insight into the tractability of traditional investigatory methods.

RESULTS

The behavior space of the IIRABM was examined by simulating over 70 million sepsis patients for up to 90 days in a sweep across the following parameters: cardio-respiratory-metabolic resilience; microbial invasiveness; microbial toxigenesis; and degree of nosocomial exposure. In addition to using established methods for describing parameter space, we developed two novel methods for characterizing the behavior of a RDS: Probabilistic Basins of Attraction (PBoA) and Stochastic Trajectory Analysis (STA). Computationally generated behavioral landscapes demonstrated attractor structures around stochastic regions of behavior that could be described in a complementary fashion through use of PBoA and STA. The stochasticity of the boundaries of the attractors highlights the challenge for correlative attempts to characterize and classify clinical sepsis.

CONCLUSIONS

HPC simulations of models like the IIRABM can be used to generate approximations of the behavior space of sepsis to both establish "boundaries of futility" with respect to existing investigatory approaches and apply system engineering principles to investigate the general dynamic properties of sepsis to provide a pathway for developing control strategies. The issues that bedevil the study and treatment of sepsis, namely clinical data sparseness and inadequate experimental sampling of system behavior space, are fundamental to nearly all biomedical research, manifesting in the "Crisis of Reproducibility" at all levels. HPC-augmented simulation-based research offers an investigatory strategy more consistent with that seen in the physical sciences (which combine experiment, theory and simulation), and an opportunity to utilize the leading advances in HPC, namely deep machine learning and evolutionary computing, to form the basis of an iterative scientific process to meet the full promise of Precision Medicine (right drug, right patient, right time).

Mathematical models of cell phenotype regulation and reprogramming: Make cancer cells sensitive again!

A cell's phenotype is the observable actualization of complex interactions between its genome, epigenome, and local environment. While traditional views in cancer have held that cellular and tumor phenotypes are largely functions of genomic instability, increasing attention has recently been given to epigenetic and microenvironmental influences. Such non-genetic factors allow cancer cells to experience intrinsic diversity and plasticity, and at the tumor level can result in phenotypic heterogeneity and treatment evasion. In 2006, Takahashi and Yamanaka exploited the epigenome's plasticity by "reprogramming" differentiated cells into a pluripotent state by inducing expression of a cocktail of four transcription factors. Recent advances in cancer biology have shown not only that cellular reprogramming is possible for malignant cells, but it may provide a foundation for future therapies. Nevertheless, cell reprogramming experiments are frequently plagued by low efficiency, activation of aberrant transcriptional programs, instability, and often rely on expertise gathered from systems which may not translate directly to cancer. Here, we review a theoretical framework tracing back to Waddington's epigenetic landscape which may be used to derive quantitative and qualitative understanding of cellular reprogramming. Implications for tumor heterogeneity, evolution and adaptation are discussed in the context of designing new treatments to re-sensitize recalcitrant tumors. This article is part of a Special Issue entitled: Evolutionary principles - heterogeneity in cancer?, edited by Dr. Robert A. Gatenby.

Systematic expression profiling analysis mines dys-regulated modules in active tuberculosis based on re-weighted protein-protein interaction network and attract algorithm

About 90% of tuberculosis (TB) patients latently infected with Mycobacterium tuberculosis (Mtb) show no symptoms, yet have a 10% chance in lifetime to progress active TB. Nevertheless, current diagnosis approaches need improvement in efficiency and sensitivity. The objective of this work was to detect potential signatures for active TB to further improve the understanding of the biological roles of functional modules involved in this disease. First, targeted networks of active TB and control groups were established via re-weighting protein-protein interaction (PPI) networks using Pearson's correlation coefficient (PCC). Candidate modules were detected from the targeted networks, and the modules with Jaccard score >0.7 were defined as attractors. After that, identification of dys-regulated modules was conducted from the attractors using attract method, Subsequently, gene oncology (GO) enrichment analyses were implemented for genes in the dys-regulated modules. We obtained 33 and 65 candidate modules from the targeted networks of control and active TB groups, respectively. Overall, 13 attractors were identified. Using the cut-off criteria of false discovery rate <0.05, there were 4 dys-regulated modules (Module 1, 2, 3, and 4). Based on the GO annotation results, genes in Modules 1, 2 and 4 were only involved in translation. Most genes in Module 1, 2 and 4 were associated with ribosomes. Accordingly, these dys-regulated modules might serve as potential biomarkers of active TB, facilitating the development for a more efficient, and sensitive diagnostic assay for active TB.

Fixed-points in random Boolean networks: The impact of parallelism in the Barabási-Albert scale-free topology case

Fixed points are fundamental states in any dynamical system. In the case of gene regulatory networks (GRNs) they correspond to stable genes profiles associated to the various cell types. We use Kauffman's approach to model GRNs with random Boolean networks (RBNs). In this paper we explore how the topology affects the distribution of the number of fixed points in randomly generated networks. We also study the size of the basins of attraction of these fixed points if we assume the α-asynchronous dynamics (where every node is updated independently with probability 0≤α≤1). It is well-known that asynchrony avoids the cyclic attractors into which parallel dynamics tends to fall. We observe the remarkable property that, in all our simulations, if for a given RBN with Barabási-Albert topology and α-asynchronous dynamics an initial configuration reaches a fixed point, then every configuration also reaches a fixed point. By contrast, in the parallel regime, the percentage of initial configurations reaching a fixed point (for the same networks) is dramatically smaller. We contrast the results of the simulations on Barabási-Albert networks with the classical Erdös-Rényi model of random networks. Everything indicates that Barabási-Albert networks are extremely robust. Finally, we study the mean and maximum time/work needed to reach a fixed point when starting from randomly chosen initial configurations.

An efficient algorithm for identifying primary phenotype attractors of a large-scale Boolean network

Background

Boolean network modeling has been widely used to model large-scale biomolecular regulatory networks as it can describe the essential dynamical characteristics of complicated networks in a relatively simple way. When we analyze such Boolean network models, we often need to find out attractor states to investigate the converging state features that represent particular cell phenotypes. This is, however, very difficult (often impossible) for a large network due to computational complexity.

Results

There have been some attempts to resolve this problem by partitioning the original network into smaller subnetworks and reconstructing the attractor states by integrating the local attractors obtained from each subnetwork. But, in many cases, the partitioned subnetworks are still too large and such an approach is no longer useful. So, we have investigated the fundamental reason underlying this problem and proposed a novel efficient way of hierarchically partitioning a given large network into smaller subnetworks by focusing on some attractors corresponding to a particular phenotype of interest instead of considering all attractors at the same time. Using the definition of attractors, we can have a simplified update rule with fixed state values for some nodes. The resulting subnetworks were small enough to find out the corresponding local attractors which can be integrated for reconstruction of the global attractor states of the original large network.

Conclusions

The proposed approach can substantially extend the current limit of Boolean network modeling for converging state analysis of biological networks.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0338-4) contains supplementary material, which is available to authorized users.

Tracking the flow of hippocampal computation: Pattern separation, pattern completion, and attractor dynamics

Classic computational theories of the mnemonic functions of the hippocampus ascribe the processes of pattern separation to the dentate gyrus (DG) and pattern completion to the CA3 region. Until the last decade, the large majority of single-unit studies of the hippocampus in behaving animals were from the CA1 region. The lack of data from the DG, CA3, and the entorhinal inputs to the hippocampus severely hampered the ability to test these theories with neurophysiological techniques. The past ten years have seen a major increase in the recordings from the CA3 region and the medial entorhinal cortex (MEC), with an increasing (but still limited) number of experiments from the lateral entorhinal cortex (LEC) and DG. This paper reviews a series of studies in a local-global cue mismatch (double-rotation) experiment in which recordings were made from cells in the anterior thalamus, MEC, LEC, DG, CA3, and CA1 regions. Compared to the standard cue environment, the change in the DG representation of the cue-mismatch environment was greater than the changes in its entorhinal inputs, providing support for the theory of pattern separation in the DG. In contrast, the change in the CA3 representation of the cue-mismatch environment was less than the changes in its entorhinal and DG inputs, providing support for a pattern completion/error correction function of CA3. The results are interpreted in terms of continuous attractor network models of the hippocampus and the relationship of these models to pattern separation and pattern completion theories. Whereas DG may perform an automatic pattern separation function, the attractor dynamics of CA3 allow it to perform a pattern separation or pattern completion function, depending on the nature of its inputs and the relative strength of the internal attractor dynamics.

Endogenous molecular-cellular hierarchical modeling of prostate carcinogenesis uncovers robust structure

We explored endogenous molecular-cellular network hypothesis for prostate cancer by constructing relevant endogenous interaction network model and analyzing its dynamical properties. Molecular regulations involved in cell proliferation, apoptosis, differentiation and metabolism are included in a hierarchical mathematical modeling scheme. This dynamical network organizes into multiple robust functional states, including physiological and pathological ones. Some states have characteristics of cancer: elevated metabolic and immune activities, high concentration of growth factors and different proliferative, apoptotic and adhesive behaviors. The molecular profile of calculated cancer state agrees with existing experiments. The modeling results have additional predictions which may be validated by further experiment: 1) Prostate supports both stem cell like and liver style proliferation; 2) While prostate supports multiple cell types, including basal, luminal and endocrine cell type differentiated from its stem cell, luminal cell is most likely to be transformed malignantly into androgen independent type cancer; 3) Retinoic acid pathway and C/EBPα are possible therapeutic targets.

Dynamics of neural networks over undirected graphs

In this paper we study the dynamical behavior of neural networks such that their interconnections are the incidence matrix of an undirected finite graph G=(V,E) (i.e., the weights belong to {0,1}). The network may be updated synchronously (every node is updated at the same time), sequentially (nodes are updated one by one in a prescribed order) or in a block-sequential way (a mixture of the previous schemes). We characterize completely the attractors (fixed points or cycles). More precisely, we establish the convergence to fixed points related to a parameter α(G), taking into account the number of loops, edges, vertices as well as the minimum number of edges to remove from E in order to obtain a maximum bipartite graph. Roughly, α(G')<0 for any G' subgraph of G implies the convergence to fixed points. Otherwise, cycles appear. Actually, for very simple networks (majority functions updated in a block-sequential scheme such that each block is of minimum cardinality two) we exhibit cycles with non-polynomial periods.

An in silico target identification using Boolean network attractors: Avoiding pathological phenotypes

Target identification aims at identifying biomolecules whose function should be therapeutically altered to cure the considered pathology. An algorithm for in silico target identification using Boolean network attractors is proposed. It assumes that attractors correspond to phenotypes produced by the modeled biological network. It identifies target combinations which allow disturbed networks to avoid attractors associated with pathological phenotypes. The algorithm is tested on a Boolean model of the mammalian cell cycle and its applications are illustrated on a Boolean model of Fanconi anemia. Results show that the algorithm returns target combinations able to remove attractors associated with pathological phenotypes and then succeeds in performing the proposed in silico target identification. However, as with any in silico evidence, there is a bridge to cross between theory and practice. Nevertheless, it is expected that the algorithm is of interest for target identification.

Multistate network model for the pathfinding problem with a self-recovery property

In this study, we propose a continuous model for a pathfinding system. We consider acyclic graphs whose vertices are connected by unidirectional edges. The proposed model autonomously finds a path connecting two specified vertices, and the path is represented by a stable solution of the proposed model. The system has a self-recovery property, i.e., the system can find a path when one of the connections in the existing path is suddenly terminated. Further, we demonstrate that the appropriate installation of inhibitory interaction improves the search time.

Template-based intervention in Boolean network models of biological systems

MOTIVATION

A grand challenge in the modeling of biological systems is the identification of key variables which can act as targets for intervention. Boolean networks are among the simplest of models, yet they have been shown to adequately model many of the complex dynamics of biological systems. In our recent work, we utilized a logic minimization approach to identify quality single variable targets for intervention from the state space of a Boolean network. However, as the number of variables in a network increases, the more likely it is that a successful intervention strategy will require multiple variables. Thus, for larger networks, such an approach is required in order to identify more complex intervention strategies while working within the limited view of the network's state space. Specifically, we address three primary challenges for the large network arena: the first challenge is how to consider many subsets of variables, the second is to design clear methods and measures to identify the best targets for intervention in a systematic way, and the third is to work with an intractable state space through sampling.

RESULTS

We introduce a multiple variable intervention target called a template and show through simulation studies of random networks that these templates are able to identify top intervention targets in increasingly large Boolean networks. We first show that, when other methods show drastic loss in performance, template methods show no significant performance loss between fully explored and partially sampled Boolean state spaces. We also show that, when other methods show a complete inability to produce viable intervention targets in sampled Boolean state spaces, template methods maintain significantly consistent success rates even as state space sizes increase exponentially with larger networks. Finally, we show the utility of the template approach on a real-world Boolean network modeling T-LGL leukemia.

CONCLUSIONS

Overall, these results demonstrate how template-based approaches now effectively take over for our previous single variable approaches and produce quality intervention targets in larger networks requiring sampled state spaces.

Attractor Structures of Signaling Networks: Consequences of Different Conformational Barcode Dynamics and Their Relations to Network-Based Drug Design

Conformational barcodes tag functional sites of proteins and are decoded by interacting molecules transmitting the incoming signal. Conformational barcodes are modified by all co-occurring allosteric events induced by post-translational modifications, pathogen, drug binding, etc. We argue that fuzziness (plasticity) of conformational barcodes may be increased by disordered protein structures, by integrative plasticity of multi-phosphorylation events, by increased intracellular water content (decreased molecular crowding) and by increased action of molecular chaperones. This leads to increased plasticity of signaling and cellular networks. Increased plasticity is both substantiated by and inducing an increased noise level. Using the versatile network dynamics tool, Turbine (www.turbine.linkgroup.hu), here we show that the 10 % noise level expected in cellular systems shifts a cancer-related signaling network of human cells from its proliferative attractors to its largest, apoptotic attractor representing their health-preserving response in the carcinogen containing and tumor suppressor deficient environment modeled in our study. Thus, fuzzy conformational barcodes may not only make the cellular system more plastic, and therefore more adaptable, but may also stabilize the complex system allowing better access to its largest attractor.

Multi-dimensional coordination in cross-country skiing analyzed using self-organizing maps

This study sought to ascertain how multi-dimensional coordination patterns changed with five poling speeds for 12 National Standard cross-country skiers during roller skiing on a treadmill. Self-organizing maps (SOMs), a type of artificial neural network, were used to map the multi-dimensional time series data on to a two-dimensional output grid. The trajectories of the best-matching nodes of the output were then used as a collective variable to train a second SOM to produce attractor diagrams and attractor surfaces to study coordination stability. Although four skiers had uni-modal basins of attraction that evolved gradually with changing speed, the other eight had two or three basins of attraction as poling speed changed. Two skiers showed bi-modal basins of attraction at some speeds, an example of degeneracy. What was most clearly evident was that different skiers showed different coordination dynamics for this skill as poling speed changed: inter-skier variability was the rule rather than an exception. The SOM analysis showed that coordination was much more variable in response to changing speeds compared to outcome variables such as poling frequency and cycle length.

A REDUCTION METHOD FOR BOOLEAN NETWORK MODELS PROVEN TO CONSERVE ATTRACTORS

Boolean models, wherein each component is characterized with a binary (ON or OFF) variable, have been widely employed for dynamic modeling of biological regulatory networks. However, the exponential dependencse of the size of the state space of these models on the number of nodes in the network can be a daunting prospect for attractor analysis of large-scale systems. We have previously proposed a network reduction technique for Boolean models and demonstrated its applicability on two biological systems, namely, the abscisic acid signal transduction network as well as the T-LGL leukemia survival signaling network. In this paper, we provide a rigorous mathematical proof that this method not only conserves the fixed points of a Boolean network, but also conserves the complex attractors of general asynchronous Boolean models wherein at each time step a randomly selected node is updated. This method thus allows one to infer the long-term dynamic properties of a large-scale system from those of the corresponding reduced model.