Differential control of active and silent phases in relaxation models of neuronal rhythms

Rhythmic bursting activity, found in many biological systems, serves a variety of important functions. Such activity is composed of episodes, or bursts (the active phase, AP) that are separated by quiescent periods (the silent phase, SP). Here, we use mean field, firing rate models of excitatory neural network activity to study how AP and SP durations depend on two critical network parameters that control network connectivity and cellular excitability. In these models, the AP and SP correspond to the network's underlying bistability on a fast time scale due to rapid recurrent excitatory connectivity. Activity switches between the AP and SP because of two types of slow negative feedback: synaptic depression—which has a divisive effect on the network input/output function, or cellular adaptation—a subtractive effect on the input/output function. We show that if a model incorporates the divisive process (regardless of the presence of the subtractive process), then increasing cellular excitability will speed up the activity, mostly by decreasing the silent phase. Reciprocally, if the subtractive process is present, increasing the excitatory connectivity will slow down the activity, mostly by lengthening the active phase. We also show that the model incorporating both slow processes is less sensitive to parameter variations than the models with only one process. Finally, we note that these network models are formally analogous to a type of cellular pacemaker and thus similar results apply to these cellular pacemakers. Action Editor: Misha Tsodyks     

Determining the contributions of divisive and subtractive feedback in the Hodgkin-Huxley model

The Hodgkin-Huxley (HH) model is the basis for numerous neural models. There are two negative feedback processes in the HH model that regulate rhythmic spiking. The first is an outward current with an activation variable n that has an opposite influence to the excitatory inward current and therefore provides subtractive negative feedback. The other is the inactivation of an inward current with an inactivation variable h that reduces the amount of positive feedback and therefore provides divisive feedback. Rhythmic spiking can be obtained with either negative feedback process, so we ask what is gained by having two feedback processes. We also ask how the different negative feedback processes contribute to spiking. We show that having two negative feedback processes makes the HH model more robust to changes in applied currents and conductance densities than models that possess only one negative feedback variable. We also show that the contributions made by the subtractive and divisive feedback variables are not static, but depend on time scales and conductance values. In particular, they contribute differently to the dynamics in Type I versus Type II neurons.     

Feedback-induced gain control in stochastic spiking networks

The joint influence of recurrent feedback and noise on gain control in a network of globally coupled spiking leaky integrate-and-fire neurons is studied theoretically and numerically. The context of our work is the origin of divisive versus subtractive gain control, as mixtures of these effects are seen in a variety of experimental systems. We focus on changes in the slope of the mean firing frequency-versus-input bias (f –I) curve when the gain control signal to the cells comes from the cells’ output spikes. Feedback spikes are modeled as alpha functions that produce an additive current in the current balance equation. For generality, they occur after a fixed minimum delay. We show that purely divisive gain control, i.e. changes in the slope of the f –I curve, arises naturally with this additive negative or positive feedback, due to a linearizing actions of feedback. Negative feedback alone lowers the gain, accounting in particular for gain changes in weakly electric fish upon pharmacological opening of the feedback loop as reported by Bastian (J Neurosci 6:553–562, 1986). When negative feedback is sufficiently strong it further causes oscillatory firing patterns which produce irregularities in the f –I curve. Small positive feedback alone increases the gain, but larger amounts cause abrupt jumps to higher firing frequencies. On the other hand, noise alone in open loop linearizes the f –I curve around threshold, and produces mixtures of divisive and subtractive gain control. With both noise and feedback, the combined gain control schemes produce a primarily divisive gain control shift, indicating the robustness of feedback gain control in stochastic networks. Similar results are found when the “input” parameter is the contrast of a time-varying signal rather than the bias current. Theoretical results are derived relating the slope of the f –I curve to feedback gain and noise strength. Good agreement with simulation results are found for inhibitory and excitatory feedback. Finally, divisive feedback is also found for conductance-based feedback (shunting or excitatory) with and without noise. This article is part of a special issue on Neuronal Dynamics of Sensory Coding.     

Noise-induced transitions in slow wave neuronal dynamics

Many neuronal systems exhibit slow random alternations and sudden switches in activity states. Models with noisy relaxation dynamics (oscillatory, excitable or bistable) account for these temporal, slow wave, patterns and the fluctuations within states. The noise-induced transitions in a relaxation dynamics are analogous to escape by a particle in a slowly changing double-well potential. In this formalism, we obtain semi-analytically the first and second order statistical properties: the distributions of the slow process at the transitions and the temporal correlations of successive switching events. We find that the temporal correlations can be used to help distinguish among biophysical mechanisms for the slow negative feedback, such as divisive or subtractive. We develop our results in the context of models for cellular pacemaker neurons; they also apply to mean-field models for spontaneously active networks with slow wave dynamics.     

The effect of negative feedback loops on the dynamics of boolean networks

Feedback loops play an important role in determining the dynamics of biological networks. To study the role of negative feedback loops, this article introduces the notion of distance-to-positive-feedback which, in essence, captures the number of independent negative feedback loops in the network, a property inherent in the network topology. Through a computational study using Boolean networks, it is shown that distance-to-positive-feedback has a strong influence on network dynamics and correlates very well with the number and length of limit cycles in the phase space of the network. To be precise, it is shown that, as the number of independent negative feedback loops increases, the number (length) of limit cycles tends to decrease (increase). These conclusions are consistent with the fact that certain natural biological networks exhibit generally regular behavior and have fewer negative feedback loops than randomized networks with the same number of nodes and same connectivity.     

The principle of homeostasis in the hypothalamus-pituitary-adrenal system: new insight from positive feedback

Feedback control, both negative and positive, is a fundamental feature of biological systems. Some of these systems strive to achieve a state of equilibrium or "homeostasis". The major endocrine systems are regulated by negative feedback, a process believed to maintain hormonal levels within a relatively narrow range. Positive feedback is often thought to have a destabilizing effect. Here, we present a "principle of homeostasis," which makes use of both positive and negative feedback loops. To test the hypothesis that this homeostatic concept is valid for the regulation of cortisol, we assessed experimental data in humans with different conditions (gender, obesity, endocrine disorders, medication) and analyzed these data by a novel computational approach. We showed that all obtained data sets were in agreement with the presented concept of homeostasis in the hypothalamus-pituitary-adrenal axis. According to this concept, a homeostatic system can stabilize itself with the help of a positive feedback loop. The brain mineralocorticoid and glucocorticoid receptors-with their known characteristics-fulfill the key functions in the homeostatic concept: binding cortisol with high and low affinities, acting in opposing manners, and mediating feedback effects on cortisol. This study supports the interaction between positive and negative feedback loops in the hypothalamus-pituitary-adrenal system and in this way sheds new light on the function of dual receptor regulation. Current knowledge suggests that this principle of homeostasis could also apply to other biological systems.     

Novel Atomic Force Microscopy Based Biopanning for Isolation of Morphology Specific Reagents against TDP-43 Variants in Amyotrophic Lateral Sclerosis

Because protein variants play critical roles in many diseases including TDP-43 in Amyotrophic Lateral Sclerosis (ALS), alpha-synuclein in Parkinson’s disease and beta-amyloid and tau in Alzheimer’s disease, it is critically important to develop morphology specific reagents that can selectively target these disease-specific protein variants to study the role of these variants in disease pathology and for potential diagnostic and therapeutic applications. We have developed novel atomic force microscopy (AFM) based biopanning techniques that enable isolation of reagents that selectively recognize disease-specific protein variants. There are two key phases involved in the process, the negative and positive panning phases. During the negative panning phase, phages that are reactive to off-target antigens are eliminated through multiple rounds of subtractive panning utilizing a series of carefully selected off-target antigens. A key feature in the negative panning phase is utilizing AFM imaging to monitor the process and confirm that all undesired phage particles are removed. For the positive panning phase, the target antigen of interest is fixed on a mica surface and bound phages are eluted and screened to identify phages that selectively bind the target antigen. The target protein variant does not need to be purified providing the appropriate negative panning controls have been used. Even target protein variants that are only present at very low concentrations in complex biological material can be utilized in the positive panning step. Through application of this technology, we acquired antibodies to protein variants of TDP-43 that are selectively found in human ALS brain tissue. We expect that this protocol should be applicable to generating reagents that selectively bind protein variants present in a wide variety of different biological processes and diseases.     

Reconstructing feedback representations in the ventral visual pathway with a generative adversarial autoencoder

While vision evokes a dense network of feedforward and feedback neural processes in the brain, visual processes are primarily modeled with feedforward hierarchical neural networks, leaving the computational role of feedback processes poorly understood. Here, we developed a generative autoencoder neural network model and adversarially trained it on a categorically diverse data set of images. We hypothesized that the feedback processes in the ventral visual pathway can be represented by reconstruction of the visual information performed by the generative model. We compared representational similarity of the activity patterns in the proposed model with temporal (magnetoencephalography) and spatial (functional magnetic resonance imaging) visual brain responses. The proposed generative model identified two segregated neural dynamics in the visual brain. A temporal hierarchy of processes transforming low level visual information into high level semantics in the feedforward sweep, and a temporally later dynamics of inverse processes reconstructing low level visual information from a high level latent representation in the feedback sweep. Our results append to previous studies on neural feedback processes by presenting a new insight into the algorithmic function and the information carried by the feedback processes in the ventral visual pathway.     

Is the balance between competition and facilitation a driver of the patch dynamics in arid vegetation mosaics?

In most arid ecosystems, the vegetation is organized into two‐phase mosaics, where high‐cover vegetation patches are interspersed in a matrix of low plant cover. We studied the role of the biotic interaction balance (competition/facilitation) between shrubs and grasses as a driver of patch dynamics and maintenance of two‐phase vegetation mosaics. Following Watt's seminal model, we conducted two field experiments in which we manipulated different vegetation patches to obtain the different stages along the building and degradation dynamics of high‐cover patches. In addition we applied two possible belowground competition treatments (natural and experimentally reduced). We measured plant variables (emergence, survival, height, flower culms) on grass seedlings and transplants. We integrated all plant measurements into a single positive and negative component, to calculate the net balance along three stages of the patch dynamics proposed. The net biotic interaction balance was negative during the early and mature stages of high‐cover patches because the average standardized effect from the negative component was below ?0.44, while the positive component was not different from zero. However, the net biotic interaction balance was positive during the degraded stages of high‐cover patches because the negative average component was ?0.37, while the positive component reached 0.58. The negative net effects during early and mature stages of high‐cover patches can be explained by the occurrence of wet years, because high rainfalls hide the aboveground facilitation. Our findings point out the importance of complementary mechanisms to the interaction balance in the mosaic maintenance (e.g. trapping of seeds by shrubs) according to the inter‐annual rainfall variability.     

System-level feedbacks control cell cycle progression

Repetitive cell cycles, which are essential to the perpetuation of life, are orchestrated by an underlying biochemical reaction network centered around cyclin-dependent protein kinases (Cdks) and their regulatory subunits (cyclins). Oscillations of Cdk1/CycB activity between low and high levels during the cycle trigger DNA replication and mitosis in the correct order. Based on computational modeling, we proposed that the low and the high kinase activity states are alternative stable steady states of a bistable Cdk-control system. Bistability is a consequence of system-level feedback (positive and double-negative feedback signals) in the underlying control system. We have also argued that bistability underlies irreversible transitions between low and high Cdk activity states and thereby ensures directionality of cell cycle progression.     

An Evolutionary Firefly Algorithm for the Estimation of Nonlinear Biological Model Parameters

The development of accurate computational models of biological processes is fundamental to computational systems biology. These models are usually represented by mathematical expressions that rely heavily on the system parameters. The measurement of these parameters is often difficult. Therefore, they are commonly estimated by fitting the predicted model to the experimental data using optimization methods. The complexity and nonlinearity of the biological processes pose a significant challenge, however, to the development of accurate and fast optimization methods. We introduce a new hybrid optimization method incorporating the Firefly Algorithm and the evolutionary operation of the Differential Evolution method. The proposed method improves solutions by neighbourhood search using evolutionary procedures. Testing our method on models for the arginine catabolism and the negative feedback loop of the p53 signalling pathway, we found that it estimated the parameters with high accuracy and within a reasonable computation time compared to well-known approaches, including Particle Swarm Optimization, Nelder-Mead, and Firefly Algorithm. We have also verified the reliability of the parameters estimated by the method using an a posteriori practical identifiability test.     

Resonant spatiotemporal learning in large random recurrent networks

 Taking a global analogy with the structure of perceptual biological systems, we present a system composed of two layers of real-valued sigmoidal neurons. The primary layer receives stimulating spatiotemporal signals, and the secondary layer is a fully connected random recurrent network. This secondary layer spontaneously displays complex chaotic dynamics. All connections have a constant time delay. We use for our experiments a Hebbian (covariance) learning rule. This rule slowly modifies the weights under the influence of a periodic stimulus. The effect of learning is twofold: (i) it simplifies the secondary-layer dynamics, which eventually stabilizes to a periodic orbit; and (ii) it connects the secondary layer to the primary layer, and realizes a feedback from the secondary to the primary layer. This feedback signal is added to the incoming signal, and matches it (i.e., the secondary layer performs a one-step prediction of the forthcoming stimulus). After learning, a resonant behavior can be observed: the system resonates with familiar stimuli, which activates a feedback signal. In particular, this resonance allows the recognition and retrieval of partial signals, and dynamic maintenence of the memory of past stimuli. This resonance is highly sensitive to the temporal relationships and to the periodicity of the presented stimuli. When we present stimuli which do not match in time or space, the feedback remains silent. The number of different stimuli for which resonant behavior can be learned is analyzed. As with Hopfield networks, the capacity is proportional to the size of the second, recurrent layer. Moreover, the high capacity displayed allows the implementation of our model on real-time systems interacting with their environment. Such an implementation is reported in the case of a simple behavior-based recognition task on a mobile robot. Finally, we present some functional analogies with biological systems in terms of autonomy and dynamic binding, and present some hypotheses on the computational role of feedback connections. Received: 27 April 2001 / Accepted in revised form: 15 January 2002     

Noise Propagation in Gene Regulation Networks Involving Interlinked Positive and Negative Feedback Loops

It is well known that noise is inevitable in gene regulatory networks due to the low-copy numbers of molecules and local environmental fluctuations. The prediction of noise effects is a key issue in ensuring reliable transmission of information. Interlinked positive and negative feedback loops are essential signal transduction motifs in biological networks. Positive feedback loops are generally believed to induce a switch-like behavior, whereas negative feedback loops are thought to suppress noise effects. Here, by using the signal sensitivity (susceptibility) and noise amplification to quantify noise propagation, we analyze an abstract model of the Myc/E2F/MiR-17-92 network that is composed of a coupling between the E2F/Myc positive feedback loop and the E2F/Myc/miR-17-92 negative feedback loop. The role of the feedback loop on noise effects is found to depend on the dynamic properties of the system. When the system is in monostability or bistability with high protein concentrations, noise is consistently suppressed. However, the negative feedback loop reduces this suppression ability (or improves the noise propagation) and enhances signal sensitivity. In the case of excitability, bistability, or monostability, noise is enhanced at low protein concentrations. The negative feedback loop reduces this noise enhancement as well as the signal sensitivity. In all cases, the positive feedback loop acts contrary to the negative feedback loop. We also found that increasing the time scale of the protein module or decreasing the noise autocorrelation time can enhance noise suppression; however, the systems sensitivity remains unchanged. Taken together, our results suggest that the negative/positive feedback mechanisms in coupled feedback loop dynamically buffer noise effects rather than only suppressing or amplifying the noise.     

Strong Isotope Effects on Melting Dynamics and Ice Crystallisation Processes in Cryo Vitrification Solutions

The nucleation and growth of crystalline ice during cooling, and further crystallization processes during re-warming are considered to be key processes determining the success of low temperature storage of biological objects, as used in medical, agricultural and nature conservation applications. To avoid these problems a method, termed vitrification, is being developed to inhibit ice formation by use of high concentration of cryoprotectants and ultra-rapid cooling, but this is only successful across a limited number of biological objects and in small volume applications. This study explores physical processes of ice crystal formation in a model cryoprotective solution used previously in trials on vitrification of complex biological systems, to improve our understanding of the process and identify limiting biophysical factors. Here we present results of neutron scattering experiments which show that even if ice crystal formation has been suppressed during quench cooling, the water molecules, mobilised during warming, can crystallise as detectable ice. The crystallisation happens right after melting of the glass phase formed during quench cooling, whilst the sample is still transiting deep cryogenic temperatures. We also observe strong water isotope effects on ice crystallisation processes in the cryoprotectant mixture. In the neutron scattering experiment with a fully protiated water component, we observe ready crystallisation occurring just after the glass melting transition. On the contrary with a fully deuteriated water component, the process of crystallisation is either completely or substantially supressed. This behaviour might be explained by nuclear quantum effects in water. The strong isotope effect, observed here, may play an important role in development of new cryopreservation strategies.     

Roles of positive and negative feedback in biological systems

We discuss the influence of positive and negative feedback on the stability of a system, which is not clear-cut, and involves complex, mathematical problems. We show in particular that positive feedback can have a stabilising effect on some systems. We also point out the role that positive feedback plays in the digital treatment of signals required by cellular signalling, drawing on analogies from electronics, and the role that negative feedback plays in making a system robust against alteration of its parameters. Both positive and negative feedback can be seen as important enhancers of the properties of biological systems.     

ZPS: visualization of recent adaptive evolution of proteins

Background  

Detection of adaptive amino acid changes in proteins under recent short-term selection is of great interest for researchers studying microevolutionary processes in microbial pathogens or any other biological species. However, independent occurrence of such point mutations within genetically diverse haplotypes makes it difficult to detect the selection footprint by using traditional molecular evolutionary analyses. The recently developed Zonal Phylogeny (ZP) has been shown to be a useful analytic tool for identifying the footprints of short-term positive selection. ZP separates protein-encoding genes into evolutionarily long-term (with silent diversity) and short-term (without silent diversity) categories, or zones, followed by statistical analysis to detect signs of positive selection in the short-term zone. However, successful broad application of ZP for analysis of large haplotype datasets requires automation of the relatively labor-intensive computational process.     

Coralline algal maerl frameworks-Islands within the phaeophytic kelp belt

Summary In the subtropical belt highly productive ecosystems are formed by coral reefs in oligotrophic seas. Towards more eutrophic conditions, coral reefs diminish and are subsequently replaced by highly productive kelp forests. In high latitudes framework constructing carbonate production is enhanced by the growth of branching coralline algae which predominantly generate maerl-type deposits. On a global view, these coralline algal ecosystems show an island-like distribution pattern within the phaeophytic kelp belt. Compared to kelp ecosystems, coralline-algaldominated ecosystems have low rates of productivity. Therefore, it is reasonable to seek the pronounced competitive value of the extremely slow-growing corallines. Due to their low annual growth increment, the coralline algae studied are very endangered by abiotic physical disturbances and by overgrowth of rapidly growing filamentous algae or sessile invertebrates. To overcome fouling pressure and storm-triggered physical disturbances, coralline algae thrive well in wave-sheltered headlands or skerry areas and generate characteristic ‘denuded areas’ by intense herbivory. This general distributional pattern is also true for high-boreal to subarctic coralline algal bioherms in northern Norway. Such a complex biological feedback maintains a high potential of self-regulation or self-organization in the algal reef bioherms. The different proponents involved in feedback processes include bacterial colonization, diatom microfouling and selective induction of larval metamorphosis. The negative impact of diatom microfouling and the important role of herbivores are relevant activities in the feedback system on a microscopic scale. Macroscopically, intense herbivory on coralline algae create denuded conditions, which are a widespread phenomenon in coralline algal ecosystems.