Using sensitivity analyses to understand bistable system behavior.

BACKGROUND: Bistable systems, i.e., systems that exhibit two stable steady states, are of particular interest in biology. They can implement binary cellular decision making, e.g., in pathways for cellular differentiation and cell cycle regulation. The onset of cancer, prion diseases, and neurodegenerative diseases are known to be associated with malfunctioning bistable systems. Exploring and characterizing parameter spaces in bistable systems, so that they retain or lose bistability, is part of a lot of therapeutic research such as cancer pharmacology. RESULTS: We use eigenvalue sensitivity analysis and stable state separation sensitivity analysis to understand bistable system behaviors, and to characterize the most sensitive parameters of a bistable system. While eigenvalue sensitivity analysis is an established technique in engineering disciplines, it has not been frequently used to study biological systems. We demonstrate the utility of these approaches on a published bistable system. We also illustrate scalability and generalizability of these methods to larger bistable systems. CONCLUSIONS: Eigenvalue sensitivity analysis and separation sensitivity analysis prove to be promising tools to define parameter design rules to make switching decisions between either stable steady state of a bistable system and a corresponding monostable state after bifurcation. These rules were applied to the smallest two-component bistable system and results were validated analytically. We showed that with multiple parameter settings of the same bistable system, we can design switching to a desirable state to retain or lose bistability when the most sensitive parameter is varied according to our parameter perturbation recommendations. We propose eigenvalue and stable state separation sensitivity analyses as a framework to evaluate large and complex bistable systems.

An Early Cortical Progenitor-Specific Mechanism Regulates Thalamocortical Innervation.

The cortical subplate is critical in regulating the entry of thalamocortical sensory afferents into the cortex. These afferents reach the subplate at embryonic day (E)15.5 in the mouse, but "wait" for several days, entering the cortical plate postnatally. We report that when transcription factor LHX2 is lost in E11.5 cortical progenitors, which give rise to subplate neurons, thalamocortical afferents display premature, exuberant ingrowth into the E15.5 cortex. Embryonic mutant subplate neurons are correctly positioned below the cortical plate, but they display an altered transcriptome and immature electrophysiological properties during the waiting period. The sensory thalamus in these cortex-specific Lhx2 mutants displays atrophy and by postnatal day (P) 7, sensory innervation to the cortex is nearly eliminated leading to a loss of the somatosensory barrels. Strikingly, these phenotypes do not manifest if LHX2 is lost in postmitotic subplate neurons, and the transcriptomic dysregulation in the subplate resulting from postmitotic loss of LHX2 is vastly distinct from that seen when LHX2 is lost in progenitors. These results demonstrate a mechanism operating in subplate progenitors that has profound consequences on the growth of thalamocortical axons into the cortex.SIGNIFICANCE STATEMENT Thalamocortical nerves carry sensory information from the periphery to the cortex. When they first grow into the embryonic cortex, they "wait" at the subplate, a structure critical for the guidance and eventual connectivity of thalamic axons with their cortical targets. How the properties of subplate neurons are regulated is unclear. We report that transcription factor LHX2 is required in the progenitor "mother" cells of the cortical primordium when they are producing their "daughter" subplate neurons, in order for the thalamocortical pathway to wait at the subplate. Without LHX2 function in subplate progenitors, thalamocortical axons grow past the subplate, entering the cortical plate prematurely. This is followed by their eventual attrition and, consequently, a profound loss of sensory innervation of the mature cortex.

HillTau: A fast, compact abstraction for model reduction in biochemical signaling networks.

Signaling networks mediate many aspects of cellular function. The conventional, mechanistically motivated approach to modeling such networks is through mass-action chemistry, which maps directly to biological entities and facilitates experimental tests and predictions. However such models are complex, need many parameters, and are computationally costly. Here we introduce the HillTau form for signaling models. HillTau retains the direct mapping to biological observables, but it uses far fewer parameters, and is 100 to over 1000 times faster than ODE-based methods. In the HillTau formalism, the steady-state concentration of signaling molecules is approximated by the Hill equation, and the dynamics by a time-course tau. We demonstrate its use in implementing several biochemical motifs, including association, inhibition, feedforward and feedback inhibition, bistability, oscillations, and a synaptic switch obeying the BCM rule. The major use-cases for HillTau are system abstraction, model reduction, scaffolds for data-driven optimization, and fast approximations to complex cellular signaling.

Dendrites, deep learning, and sequences in the hippocampus.

The hippocampus places us both in time and space. It does so over remarkably large spans: milliseconds to years, and centimeters to kilometers. This works for sensory representations, for memory, and for behavioral context. How does it fit in such wide ranges of time and space scales, and keep order among the many dimensions of stimulus context? A key organizing principle for a wide sweep of scales and stimulus dimensions is that of order in time, or sequences. Sequences of neuronal activity are ubiquitous in sensory processing, in motor control, in planning actions, and in memory. Against this strong evidence for the phenomenon, there are currently more models than definite experiments about how the brain generates ordered activity. The flip side of sequence generation is discrimination. Discrimination of sequences has been extensively studied at the behavioral, systems, and modeling level, but again physiological mechanisms are fewer. It is against this backdrop that I discuss two recent developments in neural sequence computation, that at face value share little beyond the label "neural." These are dendritic sequence discrimination, and deep learning. One derives from channel physiology and molecular signaling, the other from applied neural network theory - apparently extreme ends of the spectrum of neural circuit detail. I suggest that each of these topics has deep lessons about the possible mechanisms, scales, and capabilities of hippocampal sequence computation.

Discovery biology of neuropsychiatric syndromes (DBNS): a center for integrating clinical medicine and basic science.

BACKGROUND: There is emerging evidence that there are shared genetic, environmental and developmental risk factors in psychiatry, that cut across traditional diagnostic boundaries. With this background, the Discovery biology of neuropsychiatric syndromes (DBNS) proposes to recruit patients from five different syndromes (schizophrenia, bipolar disorder, obsessive compulsive disorder, Alzheimer's dementia and substance use disorders), identify those with multiple affected relatives, and invite these families to participate in this study. The families will be assessed: 1) To compare neuro-endophenotype measures between patients, first degree relatives (FDR) and healthy controls., 2) To identify cellular phenotypes which differentiate the groups., 3) To examine the longitudinal course of neuro-endophenotype measures., 4) To identify measures which correlate with outcome, and 5) To create a unified digital database and biorepository. METHODS: The identification of the index participants will occur at well-established specialty clinics. The selected individuals will have a strong family history (with at least another affected FDR) of mental illness. We will also recruit healthy controls without family history of such illness. All recruited individuals (N = 4500) will undergo brief clinical assessments and a blood sample will be drawn for isolation of DNA and peripheral blood mononuclear cells (PBMCs). From among this set, a subset of 1500 individuals (300 families and 300 controls) will be assessed on several additional assessments [detailed clinical assessments, endophenotype measures (neuroimaging- structural and functional, neuropsychology, psychophysics-electroencephalography, functional near infrared spectroscopy, eye movement tracking)], with the intention of conducting repeated measurements every alternate year. PBMCs from this set will be used to generate lymphoblastoid cell lines, and a subset of these would be converted to induced pluripotent stem cell lines and also undergo whole exome sequencing. DISCUSSION: We hope to identify unique and overlapping brain endophenotypes for major psychiatric syndromes. In a proportion of subjects, we expect these neuro-endophenotypes to progress over time and to predict treatment outcome. Similarly, cellular assays could differentiate cell lines derived from such groups. The repository of biomaterials as well as digital datasets of clinical parameters, will serve as a valuable resource for the broader scientific community who wish to address research questions in the area.

Multirate method for co-simulation of electrical-chemical systems in multiscale modeling.

Multiscale modeling by means of co-simulation is a powerful tool to address many vital questions in neuroscience. It can for example be applied in the study of the process of learning and memory formation in the brain. At the same time the co-simulation technique makes it possible to take advantage of interoperability between existing tools and multi-physics models as well as distributed computing. However, the theoretical basis for multiscale modeling is not sufficiently understood. There is, for example, a need of efficient and accurate numerical methods for time integration. When time constants of model components are different by several orders of magnitude, individual dynamics and mathematical definitions of each component all together impose stability, accuracy and efficiency challenges for the time integrator. Following our numerical investigations in Brocke et al. (Frontiers in Computational Neuroscience, 10, 97, 2016), we present a new multirate algorithm that allows us to handle each component of a large system with a step size appropriate to its time scale. We take care of error estimates in a recursive manner allowing individual components to follow their discretization time course while keeping numerical error within acceptable bounds. The method is developed with an ultimate goal of minimizing the communication between the components. Thus it is especially suitable for co-simulations. Our preliminary results support our confidence that the multirate approach can be used in the class of problems we are interested in. We show that the dynamics ofa communication signal as well as an appropriate choice of the discretization order between system components may have a significant impact on the accuracy of the coupled simulation. Although, the ideas presented in the paper have only been tested on a single model, it is likely that they can be applied to other problems without loss of generality. We believe that this work may significantly contribute to the establishment of a firm theoretical basis and to the development of an efficient computational framework for multiscale modeling and simulations.

Role of DARPP-32 and ARPP-21 in the Emergence of Temporal Constraints on Striatal Calcium and Dopamine Integration.

In reward learning, the integration of NMDA-dependent calcium and dopamine by striatal projection neurons leads to potentiation of corticostriatal synapses through CaMKII/PP1 signaling. In order to elicit the CaMKII/PP1-dependent response, the calcium and dopamine inputs should arrive in temporal proximity and must follow a specific (dopamine after calcium) order. However, little is known about the cellular mechanism which enforces these temporal constraints on the signal integration. In this computational study, we propose that these temporal requirements emerge as a result of the coordinated signaling via two striatal phosphoproteins, DARPP-32 and ARPP-21. Specifically, DARPP-32-mediated signaling could implement an input-interval dependent gating function, via transient PP1 inhibition, thus enforcing the requirement for temporal proximity. Furthermore, ARPP-21 signaling could impose the additional input-order requirement of calcium and dopamine, due to its Ca2+/calmodulin sequestering property when dopamine arrives first. This highlights the possible role of phosphoproteins in the temporal aspects of striatal signal transduction.

Laterality and symmetry in rat olfactory behavior and in physiology of olfactory input.

Many species use bilateral sampling for odor-guided navigation. Bilateral localization strategies typically involve balanced and lateralized sensory input and early neuronal processing. For example, if gradient direction is estimated by differential sampling, then any asymmetry could bias the perceived direction. Subsequent neuronal processing can compensate for this asymmetry but requires the presence of mechanisms to track changes in asymmetry. A high degree of laterality is also important for differential sampling because spillover of signals will dilute the perceived odor gradient. In apparent contradiction to this model, both symmetry and laterality of nasal air flow have been reported to be incomplete in rats. Here, we measured symmetry and laterality in early olfactory processing in the rat. We first established behavioral readouts of precisely controlled bilateral odorant stimuli. We found that rats could rapidly and accurately report the direction of a wide range of odor gradients, presented in random sequence. We then showed that nasal air flow was symmetric over an entire day in awake rats. Furthermore, odor sampling from the two nostrils in the behavioral task was highly lateralized. This lateralization extended to the receptor epithelium responses as measured by electro-olfactograms. We finally observed strong lateralization of intrinsic signal responses from the glomerular layer of the olfactory bulb. We confirmed that a differential comparison of glomerular responses was sufficient to localize odorants. Together, these results suggest that the rat olfactory system is symmetric, with highly lateralized odor flow and neuronal responses. In combination, these attributes support odor localization by differential comparison.

Synthetic Data Resource and Benchmarks for Time Cell Analysis and Detection Algorithms.

Hippocampal CA1 cells take part in reliable, time-locked activity sequences in tasks that involve an association between temporally separated stimuli, in a manner that tiles the interval between the stimuli. Such cells have been termed time cells. Here, we adopt a first-principles approach to comparing diverse analysis and detection algorithms for identifying time cells. We generated synthetic activity datasets using calcium signals recorded in vivo from the mouse hippocampus using two-photon (2-P) imaging, as template response waveforms. We assigned known, ground truth values to perturbations applied to perfect activity signals, including noise, calcium event width, timing imprecision, hit trial ratio and background (untuned) activity. We tested a range of published and new algorithms and their variants on this dataset. We find that most algorithms correctly classify over 80% of cells, but have different balances between true and false positives, and different sensitivity to the five categories of perturbation. Reassuringly, most methods are reasonably robust to perturbations, including background activity, and show good concordance in classification of time cells. The same algorithms were also used to analyze and identify time cells in experimental physiology datasets recorded in vivo and most show good concordance.

A computational view of short-term plasticity and its implications for E-I balance.

Short-term plasticity (STP) and excitatory-inhibitory balance (EI balance) are both ubiquitous building blocks of brain circuits across the animal kingdom. The synapses involved in EI are also subject to short-term plasticity, and several experimental studies have shown that their effects overlap. Recent computational and theoretical work has begun to highlight the functional implications of the intersection of these motifs. The findings are nuanced: while there are general computational themes, such as pattern tuning, normalization, and gating, much of the richness of these interactions comes from region- and modality specific tuning of STP properties. Together these findings point towards the STP-EI balance combination as being a versatile and highly efficient neural building block for a wide range of pattern-specific responses.

NeuroML: a language for describing data driven models of neurons and networks with a high degree of biological detail.

Biologically detailed single neuron and network models are important for understanding how ion channels, synapses and anatomical connectivity underlie the complex electrical behavior of the brain. While neuronal simulators such as NEURON, GENESIS, MOOSE, NEST, and PSICS facilitate the development of these data-driven neuronal models, the specialized languages they employ are generally not interoperable, limiting model accessibility and preventing reuse of model components and cross-simulator validation. To overcome these problems we have used an Open Source software approach to develop NeuroML, a neuronal model description language based on XML (Extensible Markup Language). This enables these detailed models and their components to be defined in a standalone form, allowing them to be used across multiple simulators and archived in a standardized format. Here we describe the structure of NeuroML and demonstrate its scope by converting into NeuroML models of a number of different voltage- and ligand-gated conductances, models of electrical coupling, synaptic transmission and short-term plasticity, together with morphologically detailed models of individual neurons. We have also used these NeuroML-based components to develop an highly detailed cortical network model. NeuroML-based model descriptions were validated by demonstrating similar model behavior across five independently developed simulators. Although our results confirm that simulations run on different simulators converge, they reveal limits to model interoperability, by showing that for some models convergence only occurs at high levels of spatial and temporal discretisation, when the computational overhead is high. Our development of NeuroML as a common description language for biophysically detailed neuronal and network models enables interoperability across multiple simulation environments, thereby improving model transparency, accessibility and reuse in computational neuroscience.

Physiology and Therapeutic Potential of SK, H, and M Medium AfterHyperPolarization Ion Channels.

SK, HCN, and M channels are medium afterhyperpolarization (mAHP)-mediating ion channels. The three channels co-express in various brain regions, and their collective action strongly influences cellular excitability. However, significant diversity exists in the expression of channel isoforms in distinct brain regions and various subcellular compartments, which contributes to an equally diverse set of specific neuronal functions. The current review emphasizes the collective behavior of the three classes of mAHP channels and discusses how these channels function together although they play specialized roles. We discuss the biophysical properties of these channels, signaling pathways that influence the activity of the three mAHP channels, various chemical modulators that alter channel activity and their therapeutic potential in treating various neurological anomalies. Additionally, we discuss the role of mAHP channels in the pathophysiology of various neurological diseases and how their modulation can alleviate some of the symptoms.

Patterned Optogenetic Stimulation Using a DMD Projector.

Optical manipulation is a powerful way to control neural activity in vitro and in vivo with millisecond precision. Patterning of light provides the remarkable ability to simultaneously target spatially segregated neurons from a population. Commercially available projectors provide one of the simplest and most economical ways of achieving spatial light modulation at millisecond timescales. Here, we describe the protocol for constructing a projector-based spatio-temporal light patterning system integrated with a microscope on a typical electrophysiology rig. The set-up is well suited for applications requiring rapid, distinct, and combinatorial inputs, akin to brain activity. This equipment involved is fairly economical (<$5000 including all optical and mechanical components), and the set-up is easy to assemble and program.

Computation, wiring, and plasticity in synaptic clusters.

Synaptic clusters on dendrites are extraordinarily compact computational building blocks. They contribute to key local computations through biophysical and biochemical signaling that utilizes convergence in space and time as an organizing principle. However, these computations can only arise in very special contexts. Dendritic cluster computations, their highly organized input connectivity, and the mechanisms for their formation are closely linked, yet these have not been analyzed as parts of a single process. Here, we examine these linkages. The sheer density of axonal and dendritic arborizations means that there are far more potential connections (close enough for a spine to reach an axon) than actual ones. We see how dendritic clusters draw upon electrical, chemical, and mechano-chemical signaling to implement the rules for formation of connections and subsequent computations. Crucially, the same mechanisms that underlie their functions also underlie their formation.

Signaling logic of activity-triggered dendritic protein synthesis: an mTOR gate but not a feedback switch.

Changes in synaptic efficacy are believed to form the cellular basis for memory. Protein synthesis in dendrites is needed to consolidate long-term synaptic changes. Many signals converge to regulate dendritic protein synthesis, including synaptic and cellular activity, and growth factors. The coordination of these multiple inputs is especially intriguing because the synthetic and control pathways themselves are among the synthesized proteins. We have modeled this system to study its molecular logic and to understand how runaway feedback is avoided. We show that growth factors such as brain-derived neurotrophic factor (BDNF) gate activity-triggered protein synthesis via mammalian target of rapamycin (mTOR). We also show that bistability is unlikely to arise from the major protein synthesis pathways in our model, even though these include several positive feedback loops. We propose that these gating and stability properties may serve to suppress runaway activation of the pathway, while preserving the key role of responsiveness to multiple sources of input.

How to record a million synaptic weights in a hippocampal slice.

A key step toward understanding the function of a brain circuit is to find its wiring diagram. New methods for optical stimulation and optical recording of neurons make it possible to map circuit connectivity on a very large scale. However, single synapses produce small responses that are difficult to measure on a large scale. Here I analyze how single synaptic responses may be detectable using relatively coarse readouts such as optical recording of somatic calcium. I model a network consisting of 10,000 input axons and 100 CA1 pyramidal neurons, each represented using 19 compartments with voltage-gated channels and calcium dynamics. As single synaptic inputs cannot produce a measurable somatic calcium response, I stimulate many inputs as a baseline to elicit somatic action potentials leading to a strong calcium signal. I compare statistics of responses with or without a single axonal input riding on this baseline. Through simulations I show that a single additional input shifts the distribution of the number of output action potentials. Stochastic resonance due to probabilistic synaptic release makes this shift easier to detect. With approximately 80 stimulus repetitions this approach can resolve up to 35% of individual activated synapses even in the presence of 20% recording noise. While the technique is applicable using conventional electrical stimulation and extracellular recording, optical methods promise much greater scaling, since the number of synapses scales as the product of the number of inputs and outputs. I extrapolate from current high-speed optical stimulation and recording methods, and show that this approach may scale up to the order of a million synapses in a single two-hour slice-recording experiment.

Memory switches in chemical reaction space.

Just as complex electronic circuits are built from simple Boolean gates, diverse biological functions, including signal transduction, differentiation, and stress response, frequently use biochemical switches as a functional module. A relatively small number of such switches have been described in the literature, and these exhibit considerable diversity in chemical topology. We asked if biochemical switches are indeed rare and if there are common chemical motifs and family relationships among such switches. We performed a systematic exploration of chemical reaction space by generating all possible stoichiometrically valid chemical configurations up to 3 molecules and 6 reactions and up to 4 molecules and 3 reactions. We used Monte Carlo sampling of parameter space for each such configuration to generate specific models and checked each model for switching properties. We found nearly 4,500 reaction topologies, or about 10% of our tested configurations, that demonstrate switching behavior. Commonly accepted topological features such as feedback were poor predictors of bistability, and we identified new reaction motifs that were likely to be found in switches. Furthermore, the discovered switches were related in that most of the larger configurations were derived from smaller ones by addition of one or more reactions. To explore even larger configurations, we developed two tools: the "bistabilizer," which converts almost-bistable systems into bistable ones, and frequent motif mining, which helps rank untested configurations. Both of these tools increased the coverage of our library of bistable systems. Thus, our systematic exploration of chemical reaction space has produced a valuable resource for investigating the key signaling motif of bistability.

Impaired Reliability and Precision of Spiking in Adults But Not Juveniles in a Mouse Model of Fragile X Syndrome.

Fragile X syndrome (FXS) is the most common source of intellectual disability and autism. Extensive studies have been performed on the network and behavioral correlates of the syndrome, but our knowledge about intrinsic conductance changes is still limited. In this study, we show a differential effect of FMRP knockout in different subsections of hippocampus using whole-cell patch clamp in mouse hippocampal slices. We observed no significant change in spike numbers in the CA1 region of hippocampus, but a significant increase in CA3, in juvenile mice. However, in adult mice we see a reduction in spike number in the CA1 with no significant difference in CA3. In addition, we see increased variability in spike numbers in CA1 cells following a variety of steady and modulated current step protocols. This effect emerges in adult mice (8 weeks) but not juvenile mice (4 weeks). This increased spiking variability was correlated with reduced spike number and with elevated AHP. The increased AHP arose from elevated SK currents (small conductance calcium-activated potassium channels), but other currents involved in medium AHP, such as Ih and M, were not significantly different. We obtained a partial rescue of the cellular variability phenotype when we blocked SK current using the specific blocker apamin. Our observations provide a single-cell correlate of the network observations of response variability and loss of synchronization, and suggest that the elevation of SK currents in FXS may provide a partial mechanistic explanation for this difference.

Models of cell signaling pathways.

Cellular signaling circuits handle an enormous range of computations. Beyond the housekeeping, replicating and other functions of individual cells, signaling circuits must implement the immensely complex logic of development and function of multicellular organisms. Computer models are useful tools to understand this complexity. Recent studies have extended such models to include electrical, mechanical and spatial details of signaling, and to address the stochastic effects that arise when small numbers of molecules interact. Increasing numbers of models have been developed in close conjunction with experiments, and this interplay gives a deeper and more reliable insight into signaling function.

Minimum information requested in the annotation of biochemical models (MIRIAM).

Most of the published quantitative models in biology are lost for the community because they are either not made available or they are insufficiently characterized to allow them to be reused. The lack of a standard description format, lack of stringent reviewing and authors' carelessness are the main causes for incomplete model descriptions. With today's increased interest in detailed biochemical models, it is necessary to define a minimum quality standard for the encoding of those models. We propose a set of rules for curating quantitative models of biological systems. These rules define procedures for encoding and annotating models represented in machine-readable form. We believe their application will enable users to (i) have confidence that curated models are an accurate reflection of their associated reference descriptions, (ii) search collections of curated models with precision, (iii) quickly identify the biological phenomena that a given curated model or model constituent represents and (iv) facilitate model reuse and composition into large subcellular models.