Bistable networks

For the brain to function properly, its neurons must make the right connections during neural development. A key aspect of this process is the tight regulation of axon growth as axons navigate towards their targets. Neuronal growth cones at the tips of developing axons switch between growth and paused states during axonal pathfinding, and this switching behaviour determines the heterogeneous axon growth rates observed during brain development. The mechanisms controlling this switching behaviour, however, remain largely unknown...

Single-cell analysis is pivotal to deciphering complex phenomena like heterogeneity, bistability, and asynchronous oscillations, where a population ensemble cannot represent individual behaviors. Bulk cell-free systems, despite having unique advantages of manipulation and characterization of biochemical networks, lack the essential single-cell information to understand a class of out-of-steady-state dynamics including cell cycles. Here, by encapsulating Xenopus egg extracts in water-in-oil microemulsions, we developed artificial cells that are adjustable in sizes and periods, sustain mitotic oscillations for over 30 cycles, and function in forms from the simplest cytoplasmic-only to the more complicated ones involving nuclear dynamics, mimicking real cells...

Stoichiometric network analysis (SNA) is a method for studying the stability of steady states of stoichiometric systems by decomposing the corresponding network into elementary subnetworks (also known as extreme currents) and identifying those that may cause loss of a network's stability via interplay of positive and negative feedback. Experimentally studied complex (bio)chemical reactions often display dynamical instabilities leading to oscillations or bistable switches. When modelling such systems, a frequently met case is that an assumed detailed mechanism in terms of power law kinetics is available, but some of the rate coefficients are unknown and obtaining them by traditional kinetic methods based on a least-square fit is cumbersome or unfeasible...

Artificial neural networks (ANNs) are known to be a powerful tool for data analysis. They are used in social science, robotics, and neurophysiology for solving tasks of classification, forecasting, pattern recognition, etc. In neuroscience, ANNs allow the recognition of specific forms of brain activity from multichannel EEG or MEG data. This makes the ANN an efficient computational core for brain-machine systems. However, despite significant achievements of artificial intelligence in recognition and classification of well-reproducible patterns of neural activity, the use of ANNs for recognition and classification of patterns in neural networks still requires additional attention, especially in ambiguous situations...

Phase synchronization drives connectivity between neural oscillators, providing a flexible mechanism through which information can be effectively and selectively routed between task-relevant cortical areas. The ability to keep track of objects moving between the left and right visual hemifields, for example, requires the integration of information between the two cerebral hemispheres. Both animal and human studies have suggested that coherent (or phase-locked) gamma oscillations (30-80 Hz) might underlie this ability...

A hallmark of cortical circuits is their versatility. They can perform multiple fundamental computations such as normalization, memory storage, and rhythm generation. Yet it is far from clear how such versatility can be achieved in a single circuit, given that specialized models are often needed to replicate each computation. Here, we show that the stabilized supralinear network (SSN) model, which was originally proposed for sensory integration phenomena such as contrast invariance, normalization, and surround suppression, can give rise to dynamic cortical features of working memory, persistent activity, and rhythm generation...

Ostreococcus tauri is the smallest free-living unicellular organism with one copy of each core cell cycle genes in its genome. There is a growing interest in this green algae due to its evolutionary origin. Since O. tauri is diverged early in the green lineage, relatively close to the ancestral eukaryotic cell, it might hold a key phylogenetic position in the eukaryotic tree of life. In this study, we focus on the regulatory network of its cell division cycle. We propose a mathematical modelling framework to integrate the existing knowledge of cell cycle network of O...

Posttranslational modification of proteins is important for signal transduction, and hence significant effort has gone toward understanding how posttranslational modification networks process information. This involves, on the theory side, analyzing the dynamical systems arising from such networks. Which networks are, for instance, bistable? Which networks admit sustained oscillations? Which parameter values enable such behaviors? In this Biophysical Perspective, we highlight recent progress in this area and point out some important future directions...

In this paper, we study through mathematical modelling the combined effect of transcriptional and translational regulation by proteins and small noncoding RNAs (sRNA) in a genetic feedback motif that has an important role in the survival of E. coli under stress associated with oxygen and energy availability. We show that subtle changes in this motif can bring in drastically different effects on the gene expression. In particular, we show that a threshold response in the gene expression changes to a bistable response as the regulation on sRNA synthesis or degradation is altered...

We analyze the dynamics of two coupled identical populations of quadratic integrate-and-fire neurons, which represent the canonical model for class I neurons near the spiking threshold. The populations are heterogeneous; they include both inherently spiking and excitable neurons. The coupling within and between the populations is global via synapses that take into account the finite width of synaptic pulses. Using a recently developed reduction method based on the Lorentzian ansatz, we derive a closed system of equations for the neuron's firing rates and the mean membrane potentials in both populations...

Nanocarrier-mediated mRNA delivery and release into the cells with subsequent translation to protein is of interest in the context of the development of a new generation of drugs. In particular, this protein can play a role of a transcription factor and be used as a tool to regulate temporarily the genetic networks. The corresponding transient kinetics of gene expression are expected to depend on the mechanism and duration of mRNA release. Assuming the release to be rapid on the time scale of other steps, the author shows theoretically the mRNA-related transient features of gene expression occurring in stable, bistable, and oscillatory regimes in a single cell...

The mechanistic Target of Rapamycin (mTOR) signalling network is an evolutionarily conserved network that controls key cellular processes, including cell growth and metabolism. Consisting of the major kinase complexes mTOR Complex 1 and 2 (mTORC1/2), the mTOR network harbours complex interactions and feedback loops. The DEP domain-containing mTOR-interacting protein (DEPTOR) was recently identified as an endogenous inhibitor of both mTORC1 and 2 through direct interactions, and is in turn degraded by mTORC1/2, adding an extra layer of complexity to the mTOR network...

Reciprocal inhibition is a common motif exploited by neuronal networks; an intuitive and tractable way to examine the behaviors produced by reciprocal inhibition is to consider a pair of neurons that synaptically inhibit each other and receive constant or noisy excitatory driving currents. In this work, we examine reciprocal inhibition using two models (a voltage-based and a current-based integrate-and-fire model with instantaneous or temporally structured input), and we use analytic and computational tools to examine the bifurcations that occur and study the various possible monostable, bistable, and tristable regimes that can exist; we find that, depending on system parameters (and on choice of neuron model), there can exist up to 3 distinct monostable regimes (denoted M0, M1, M2), 3 distinct bistable regimes (denoted B, B1, B2), and a single tristable regime (denoted T)...

In response to developmental and environmental conditions, cells exit the mitotic cell cycle and enter the meiosis program to generate haploid gametes from diploid germ cells. Once cells decide to enter the meiosis program they become irreversibly committed to the completion of meiosis irrespective of the presence of cue signals. How meiotic entry and commitment occur due to the dynamics of the regulatory network is not well understood. Therefore, we constructed a mathematical model of the regulatory network that controls the transition from mitosis to meiosis in Schizosaccharomyces pombe...

Stochastic reaction networks that exhibit bistable behavior are common in systems biology, materials science, and catalysis. Sampling of stationary distributions is crucial for understanding and characterizing the long-time dynamics of bistable stochastic dynamical systems. However, simulations are often hindered by the insufficient sampling of rare transitions between the two metastable regions. In this paper, we apply the parallel replica method for a continuous time Markov chain in order to improve sampling of the stationary distribution in bistable stochastic reaction networks...

Life is sustained by a variety of cyclic processes such as cell division, muscle contraction, and neuron firing. The periodic signals powering these processes often direct a variety of other downstream systems, which operate at different time scales and must have the capacity to divide or multiply the period of the master clock. Period modulation is also an important challenge in synthetic molecular systems, where slow and fast components may have to be coordinated simultaneously by a single oscillator whose frequency is often difficult to tune...

Motivation: Metabolism can exhibit dynamic phenomena like bistability due to the presence of regulatory motifs like the positive feedback loop. As cell factories, microorganisms with bistable metabolism can have a high and a low product flux at the two stable steady states, respectively. The exclusion of metabolic regulation and network dynamics limits the ability of pseudo-steady state stoichiometric models to detect the presence of bistability, and reliably assess the outcomes of design perturbations to metabolic networks...

Cellular differentiations are often regulated by bistable switches resulting from specific arrangements of multiple positive feedback loops (PFL) fused to one another. Although bistability generates digital responses at the cellular level, stochasticity in chemical reactions causes population heterogeneity in terms of its differentiated states. We hypothesized that the specific arrangements of PFLs may have evolved to minimize the cellular heterogeneity in differentiation. In order to test this we investigated variability in cellular differentiation controlled either by parallel or serial arrangements of multiple PFLs having similar average properties under extrinsic and intrinsic noises...

The precise regulation of cell life division is indispensable to the reliable inheritance of genetic material, i.e. DNA, in successive generations of cells. This is governed by dedicated biochemical networks which ensure that all requirements are met before transition from one phase to the next. The Spindle Assembly Checkpoint (SAC) is an evolutionarily mechanism that delays mitotic progression until all chromosomes are properly linked to the mitotic spindle. During some asymmetric cell divisions, such as those observed in budding yeast, an additional mechanism, the Spindle Position Checkpoint (SPOC), is required to delay exit from mitosis until the mitotic spindle is correctly aligned...

In this article, the dynamic structure of complex supramolecular polymers composed of bistable [c2]daisy chain rotaxanes as molecular machines that are linked by ureidopyrimidinones (Upy) as recognition moieties was studied. pH actuation of the integrated mechanically active rotaxanes controls the contraction/extension of the polymer chains as well as their physical reticulation. Small-angle neutron and X-ray scattering were used to study in-depth the nanostructure of the contracted and extended polymer aggregates in toluene solution...