Boolean analysis reveals systematic interactions among low-abundance species in the human gut microbiome.

The analysis of microbiome compositions in the human gut has gained increasing interest due to the broader availability of data and functional databases and substantial progress in data analysis methods, but also due to the high relevance of the microbiome in human health and disease. While most analyses infer interactions among highly abundant species, the large number of low-abundance species has received less attention. Here we present a novel analysis method based on Boolean operations applied to microbial co-occurrence patterns. We calibrate our approach with simulated data based on a dynamical Boolean network model from which we interpret the statistics of attractor states as a theoretical proxy for microbiome composition. We show that for given fractions of synergistic and competitive interactions in the model our Boolean abundance analysis can reliably detect these interactions. Analyzing a novel data set of 822 microbiome compositions of the human gut, we find a large number of highly significant synergistic interactions among these low-abundance species, forming a connected network, and a few isolated competitive interactions.

A Thalamocortical Neural Mass Model of the EEG during NREM Sleep and Its Response to Auditory Stimulation.

Few models exist that accurately reproduce the complex rhythms of the thalamocortical system that are apparent in measured scalp EEG and at the same time, are suitable for large-scale simulations of brain activity. Here, we present a neural mass model of the thalamocortical system during natural non-REM sleep, which is able to generate fast sleep spindles (12-15 Hz), slow oscillations (<1 Hz) and K-complexes, as well as their distinct temporal relations, and response to auditory stimuli. We show that with the inclusion of detailed calcium currents, the thalamic neural mass model is able to generate different firing modes, and validate the model with EEG-data from a recent sleep study in humans, where closed-loop auditory stimulation was applied. The model output relates directly to the EEG, which makes it a useful basis to develop new stimulation protocols.

RNAi revised--target mRNA-dependent enhancement of gene silencing.

The discovery of RNA interference (RNAi) gave rise to the development of new nucleic acid-based technologies as powerful investigational tools and potential therapeutics. Mechanistic key details of RNAi in humans need to be deciphered yet, before such approaches take root in biomedicine and molecular therapy. We developed and validated an in silico-based model of siRNA-mediated RNAi in human cells in order to link in vitro-derived pre-steady state kinetic data with a quantitative and time-resolved understanding of RNAi on the cellular level. The observation that product release by Argonaute 2 is accelerated in the presence of an excess of target RNA in vitro inspired us to suggest an associative mechanism for the RNA slicer reaction where incoming target mRNAs actively promote dissociation of cleaved mRNA fragments. This novel associative model is compatible with high multiple turnover rates of RNAi-based gene silencing in living cells and accounts for target mRNA concentration-dependent enhancement of the RNAi machinery.

Modeling the effect of sleep regulation on a neural mass model.

In mammals, sleep is categorized by two main sleep stages, rapid eye movement (REM) and non-REM (NREM) sleep that are known to fulfill different functional roles, the most notable being the consolidation of memory. While REM sleep is characterized by brain activity similar to wakefulness, the EEG activity changes drastically with the emergence of K-complexes, sleep spindles and slow oscillations during NREM sleep. These changes are regulated by circadian and ultradian rhythms, which emerge from an intricate interplay between multiple neuronal populations in the brainstem, forebrain and hypothalamus and the resulting varying levels of neuromodulators. Recently, there has been progress in the understanding of those rhythms both from a physiological as well as theoretical perspective. However, how these neuromodulators affect the generation of the different EEG patterns and their temporal dynamics is poorly understood. Here, we build upon previous work on a neural mass model of the sleeping cortex and investigate the effect of those neuromodulators on the dynamics of the cortex and the corresponding transition between wakefulness and the different sleep stages. We show that our simplified model is sufficient to generate the essential features of human EEG over a full day. This approach builds a bridge between sleep regulatory networks and EEG generating neural mass models and provides a valuable tool for model validation.

Characterization of K-complexes and slow wave activity in a neural mass model.

NREM sleep is characterized by two hallmarks, namely K-complexes (KCs) during sleep stage N2 and cortical slow oscillations (SOs) during sleep stage N3. While the underlying dynamics on the neuronal level is well known and can be easily measured, the resulting behavior on the macroscopic population level remains unclear. On the basis of an extended neural mass model of the cortex, we suggest a new interpretation of the mechanisms responsible for the generation of KCs and SOs. As the cortex transitions from wake to deep sleep, in our model it approaches an oscillatory regime via a Hopf bifurcation. Importantly, there is a canard phenomenon arising from a homoclinic bifurcation, whose orbit determines the shape of large amplitude SOs. A KC corresponds to a single excursion along the homoclinic orbit, while SOs are noise-driven oscillations around a stable focus. The model generates both time series and spectra that strikingly resemble real electroencephalogram data and points out possible differences between the different stages of natural sleep.

Novel Insights into Guide RNA 5'-Nucleoside/Tide Binding by Human Argonaute 2.

The human Argonaute 2 (hAgo2) protein is a key player of RNA interference (RNAi). Upon complex formation with small non-coding RNAs, the protein initially interacts with the 5'-end of a given guide RNA through multiple interactions within the MID domain. This interaction has been reported to show a strong bias for U and A over C and G at the 5'-position. Performing molecular dynamics simulations of binary hAgo2/OH-guide-RNA complexes, we show that hAgo2 is a highly flexible protein capable of binding to guide strands with all four possible 5'-bases. Especially, in the case of C and G this is associated with rather large individual conformational rearrangements affecting the MID, PAZ and even the N-terminal domains to different degrees. Moreover, a 5'-G induces domain motions in the protein, which trigger a previously unreported interaction between the 5'-base and the L2 linker domain. Combining our in silico analyses with biochemical studies of recombinant hAgo2, we find that, contrary to previous observations, hAgo2 is capable of functionally accommodating guide strands regardless of the 5'-base.

Source imaging of deep-brain activity using the regional spatiotemporal Kalman filter.

BACKGROUND AND OBJECTIVE: The human brain displays rich and complex patterns of interaction within and among brain networks that involve both cortical and subcortical brain regions. Due to the limited spatial resolution of surface electroencephalography (EEG), EEG source imaging is used to reconstruct brain sources and investigate their spatial and temporal dynamics. The majority of EEG source imaging methods fail to detect activity from subcortical brain structures. The reconstruction of subcortical sources is a challenging task because the signal from these sources is weakened and mixed with artifacts and other signals from cortical sources. In this proof-of-principle study we present a novel EEG source imaging method, the regional spatiotemporal Kalman filter (RSTKF), that can detect deep brain activity. METHODS: The regional spatiotemporal Kalman filter (RSTKF) is a generalization of the spatiotemporal Kalman filter (STKF), which allows for the characterization of different regional dynamics in the brain. It is based on state-space modeling with spatially heterogeneous dynamical noise variances, since models with spatial and temporal homogeneity fail to describe the dynamical complexity of brain activity. First, RSTKF is tested using simulated EEG data from sources in the frontal lobe, putamen, and thalamus. After that, it is applied to non-averaged interictal epileptic spikes from a presurgical epilepsy patient with focal epileptic activity in the amygdalo-hippocampal complex. The results of RSTKF are compared to those of low-resolution brain electromagnetic tomography (LORETA) and of standard STKF. RESULTS: Only RSTKF is successful in consistently and accurately localizing the sources in deep brain regions. Additionally, RSTKF shows improved spatial resolution compared to LORETA and STKF. CONCLUSIONS: RSTKF is a generalization of STKF that allows for accurate, focal, and consistent localization of sources, especially in the deeper brain areas. In contrast to standard source imaging methods, RSTKF may find application in the localization of the epileptogenic zone in deeper brain structures, such as mesial frontal and temporal lobe epilepsies, especially in EEG recordings for which no reliable averaged spike shape can be obtained due to lack of the necessary number of spikes required to reach a certain signal-to-noise ratio level after averaging.

Stochastic gain in finite populations.

Flexible learning rates can lead to increased payoffs under the influence of noise. In a previous paper [Traulsen, Phys. Rev. Lett. 93, 028701 (2004)], we have demonstrated this effect based on a replicator dynamics model which is subject to external noise. Here, we utilize recent advances on finite population dynamics and their connection to the replicator equation to extend our findings and demonstrate the stochastic gain effect in finite population systems. Finite population dynamics is inherently stochastic, depending on the population size and the intensity of selection, which measures the balance between the deterministic and the stochastic parts of the dynamics. This internal noise can be exploited by a population using an appropriate microscopic update process, even if learning rates are constant.

Coevolutionary dynamics in large, but finite populations.

Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form of a Fokker-Planck equation was derived for frequency-dependent selection with two strategies in finite populations based on microscopic processes [A. Traulsen, J. C. Claussen, and C. Hauert, Phys. Rev. Lett. 95, 238701 (2005)]. Here we generalize this approach in a twofold way: First, we extend the framework to an arbitrary number of strategies and second, we allow for mutations in the evolutionary process. The deterministic limit of infinite population size of the frequency-dependent Moran process yields the adjusted replicator-mutator equation, which describes the combined effect of selection and mutation. For finite populations, we provide an extension taking random drift into account. In the limit of neutral selection, i.e., whenever the process is determined by random drift and mutations, the stationary strategy distribution is derived. This distribution forms the background for the coevolutionary process. In particular, a critical mutation rate uc is obtained separating two scenarios: above uc the population predominantly consists of a mixture of strategies whereas below uc the population tends to be in homogeneous states. For one of the fundamental problems in evolutionary biology, the evolution of cooperation under Darwinian selection, we demonstrate that the analytical framework provides excellent approximations to individual based simulations even for rather small population sizes. This approach complements simulation results and provides a deeper, systematic understanding of coevolutionary dynamics.

Role of inhibitory feedback for information processing in thalamocortical circuits.

The information transfer in the thalamus is blocked dynamically during sleep, in conjunction with the occurrence of spindle waves. In order to describe the dynamic mechanisms which control the sensory transfer of information, it is necessary to have a qualitative model for the response properties of thalamic neurons. As the theoretical understanding of the mechanism remains incomplete, we analyze two modeling approaches for a recent experiment by Le Masson et al. [Nature (London) 417, 854 (2002)] on the thalamocortical loop. We use a conductance based model in order to motivate an extension of the Hindmarsh-Rose model, which mimics experimental observations of Le Masson et al. Typically, thalamic neurons possess two different firing modes, depending on their membrane potential. At depolarized potentials, the cells fire in a single spike mode and relay synaptic inputs in a one-to-one manner to the cortex. If the cell gets hyperpolarized, T-type calcium currents generate burst-mode firing which leads to a decrease in the spike transfer. In thalamocortical circuits, the cell membrane gets hyperpolarized by recurrent inhibitory feedback loops. In the case of reciprocally coupled excitatory and inhibitory neurons, inhibitory feedback leads to metastable self-sustained oscillations, which mask the incoming input, and thereby reduce the information transfer significantly.

Chimera patterns under the impact of noise.

We investigate two types of chimera states, patterns consisting of coexisting spatially separated domains with coherent and incoherent dynamics, in ring networks of Stuart-Landau oscillators with symmetry-breaking coupling, under the influence of noise. Amplitude chimeras are characterized by temporally periodic dynamics throughout the whole network, but spatially incoherent behavior with respect to the amplitudes in a part of the system; they are long-living transients. Chimera death states generalize chimeras to stationary inhomogeneous patterns (oscillation death), which combine spatially coherent and incoherent domains. We analyze the impact of random perturbations, addressing the question of robustness of chimera states in the presence of white noise. We further consider the effect of symmetries applied to random initial conditions.

Non-Gaussian fluctuations arising from finite populations: Exact results for the evolutionary Moran process.

The appropriate description of fluctuations within the framework of evolutionary game theory is a fundamental unsolved problem in the case of finite populations. The Moran process recently introduced into this context in Nowak, [Nature (London) 428, 646 (2004)] defines a promising standard model of evolutionary game theory in finite populations for which analytical results are accessible. In this paper, we derive the stationary distribution of the Moran process population dynamics for arbitrary 2 x 2 games for the finite-size case. We show that a nonvanishing background fitness can be transformed to the vanishing case by rescaling the payoff matrix. In contrast to the common approach to mimic finite-size fluctuations by Gaussian distributed noise, the finite-size fluctuations can deviate significantly from a Gaussian distribution.

1/f(alpha) spectra in elementary cellular automata and fractal signals.

We systematically compute the power spectra of the one-dimensional elementary cellular automata introduced by Wolfram. On the one hand our analysis reveals that one automaton displays 1/f spectra though considered as trivial, and on the other hand that various automata classified as chaotic or complex display no 1/f spectra. We model the results generalizing the recently investigated Sierpinski signal to a class of fractal signals that are tailored to produce 1/f(alpha) spectra. From the widespread occurrence of (elementary) cellular automata patterns in chemistry, physics, and computer sciences, there are various candidates to show spectra similar to our results.

Evolutionary dynamics for persistent cooperation in structured populations.

The emergence and maintenance of cooperative behavior is a fascinating topic in evolutionary biology and social science. The public goods game (PGG) is a paradigm for exploring cooperative behavior. In PGG, the total resulting payoff is divided equally among all participants. This feature still leads to the dominance of defection without substantially magnifying the public good by a multiplying factor. Much effort has been made to explain the evolution of cooperative strategies, including a recent model in which only a portion of the total benefit is shared by all the players through introducing a new strategy named persistent cooperation. A persistent cooperator is a contributor who is willing to pay a second cost to retrieve the remaining portion of the payoff contributed by themselves. In a previous study, this model was analyzed in the framework of well-mixed populations. This paper focuses on discussing the persistent cooperation in lattice-structured populations. The evolutionary dynamics of the structured populations consisting of three types of competing players (pure cooperators, defectors, and persistent cooperators) are revealed by theoretical analysis and numerical simulations. In particular, the approximate expressions of fixation probabilities for strategies are derived on one-dimensional lattices. The phase diagrams of stationary states, and the evolution of frequencies and spatial patterns for strategies are illustrated on both one-dimensional and square lattices by simulations. Our results are consistent with the general observation that, at least in most situations, a structured population facilitates the evolution of cooperation. Specifically, here we find that the existence of persistent cooperators greatly suppresses the spreading of defectors under more relaxed conditions in structured populations compared to that obtained in well-mixed populations.

Stability borders of feedback control of delayed measured systems.

When stabilization of unstable periodic orbits or fixed points by the method given by Ott, Grebogi, and Yorke (OGY) must be based on a measurement delayed by tau orbit lengths, the performance of unmodified OGY method is expected to decline. For experimental considerations, it is desired to know the range of stability with minimal knowledge of the system. We find that unmodified OGY control fails beyond a maximal Lyapunov number of lambda(max) =1+ ( 1/tau ) . In this paper the area of stability is investigated both for OGY control of known fixed points and for difference control of unknown or inaccurately known fixed points. An estimated value of the control gain is given. Finally we outline what extensions must be considered if one wants to stabilize fixed points with Lyapunov numbers above lambda(max) .

Similarity-based cooperation and spatial segregation.

We analyze a cooperative game, where the cooperative act is not based on the previous behavior of the coplayer, but on the similarity between the players. This system has been studied in a mean-field description recently [Phys. Rev. E 68, 046129 (2003)]]. Here, the spatial extension to a two-dimensional lattice is studied, where each player interacts with eight players in a Moore neighborhood. The system shows a strong segregation independent of parameters. The introduction of a local conversion mechanism towards tolerance allows for four-state cycles and the emergence of spiral waves in the spatial game. In the case of asymmetric costs of cooperation a rich variety of complex behavior is observed depending on both cooperation costs. Finally, we study the stabilization of a cooperative fixed point of a forecast rule in the symmetric game, which corresponds to cooperation across segregation borders. This fixed point becomes unstable for high cooperation costs, but can be stabilized by a linear feedback mechanism.

Improved control of delayed measured systems.

In this paper, we address the question of how the control of delayed measured chaotic systems can be improved. Both unmodified Ott-Grebogi-Yorke control and difference control can be successfully applied only for a certain range of Lyapunov numbers depending on the delay time. We show that this limitation can be overcome by at least two classes of methods, namely, by rhythmic control and by the memory methods of linear predictive logging control and memory difference control.

Sierpinski signal generates 1/f alpha spectra.

We investigate the row sum of the binary pattern generated by the Sierpinski automaton: Interpreted as a time series we calculate the power spectrum of this Sierpinski signal analytically and obtain a unique rugged fine structure with underlying power law decay with an exponent of approximately 1.15. Despite the simplicity of the model, it can serve as a model for 1/f(alpha) spectra in a certain class of experimental and natural systems such as catalytic reactions and mollusc patterns.

Desynchronizing effect of high-frequency stimulation in a generic cortical network model.

Transcranial electrical stimulation (TCES) and deep brain stimulation are two different applications of electrical current to the brain used in different areas of medicine. Both have a similar frequency dependence of their efficiency, with the most pronounced effects around 100 Hz. We apply superthreshold electrical stimulation, specifically depolarizing DC current, interrupted at different frequencies, to a simple model of a population of cortical neurons which uses phenomenological descriptions of neurons by Izhikevich and synaptic connections on a similar level of sophistication. With this model, we are able to reproduce the optimal desynchronization around 100 Hz, as well as to predict the full frequency dependence of the efficiency of desynchronization, and thereby to give a possible explanation for the action mechanism of TCES.

The phase response of the cortical slow oscillation.

Cortical slow oscillations occur in the mammalian brain during deep sleep and have been shown to contribute to memory consolidation, an effect that can be enhanced by electrical stimulation. As the precise underlying working mechanisms are not known it is desired to develop and analyze computational models of slow oscillations and to study the response to electrical stimuli. In this paper we employ the conductance based model of Compte et al. (J Neurophysiol 89:2707-2725, 2003) to study the effect of electrical stimulation. The population response to electrical stimulation depends on the timing of the stimulus with respect to the state of the slow oscillation. First, we reproduce the experimental results of electrical stimulation in ferret brain slices by Shu et al. (Nature 423:288-293, 2003) from the conductance based model. We then numerically obtain the phase response curve for the conductance based network model to quantify the network's response to weak stimuli. Our results agree with experiments in vivo and in vitro that show that sensitivity to stimulation is weaker in the up than in the down state. However, we also find that within the up state stimulation leads to a shortening of the up state, or phase advance, whereas during the up-down transition a prolongation of up states is possible, resulting in a phase delay. Finally, we compute the phase response curve for the simple mean-field model by Ngo et al. (EPL Europhys Lett 89:68002, 2010) and find that the qualitative shape of the PRC is preserved, despite its different mechanism for the generation of slow oscillations.