Signaling in small subcellular volumes. II. Stochastic and diffusion effects on synaptic network properties

Spine apparatus modulates Ca 2+ in spines through spatial localization of sources and sinks

Dendritic spines are small protrusions on dendrites in neurons and serve as sites of postsynaptic activity. Some of these spines contain smooth endoplasmic reticulum (SER), and sometimes an even further specialized SER known as the spine apparatus (SA). In this work, we developed a stochastic spatial model to investigate the role of the SER and the SA in modulating Ca 2+ dynamics. Using this model, we investigated how ryanodine receptor (RyR) localization, spine membrane geometry, and SER geometry can impact Ca 2+ transients in the spine and in the dendrite. Our simulations found that RyR opening is dependent on where it is localized in the SER and on the SER geometry. In order to maximize Ca 2+ in the dendrites (for activating clusters of spines and spine-spine communication), a laminar SA was favorable with RyRs localized in the neck region, closer to the dendrite. We also found that the presence of the SER without the laminar structure, coupled with RyR localization at the head, leads to higher Ca 2+ presence in the spine. These predictions serve as design principles for understanding how spines with an ER can regulate Ca 2+ dynamics differently from spines without ER through a combination of geometry and receptor localization.

Highlights

1RyR opening in dendritic spine ER is location dependent and spine geometry dependent. Ca 2+ buffers and SERCA can buffer against runaway potentiation of spines even when CICR is activated. RyRs located towards the ER neck allow for more Ca 2+ to reach the dendrites. RyRs located towards the spine head are favorable for increased Ca 2+ in spines.

A stochastic model of hippocampal synaptic plasticity with geometrical readout of enzyme dynamics

Discovering the rules of synaptic plasticity is an important step for understanding brain learning. Existing plasticity models are either (1) top-down and interpretable, but not flexible enough to account for experimental data, or (2) bottom-up and biologically realistic, but too intricate to interpret and hard to fit to data. To avoid the shortcomings of these approaches, we present a new plasticity rule based on a geometrical readout mechanism that flexibly maps synaptic enzyme dynamics to predict plasticity outcomes. We apply this readout to a multi-timescale model of hippocampal synaptic plasticity induction that includes electrical dynamics, calcium, CaMKII and calcineurin, and accurate representation of intrinsic noise sources. Using a single set of model parameters, we demonstrate the robustness of this plasticity rule by reproducing nine published ex vivo experiments covering various spike-timing and frequency-dependent plasticity induction protocols, animal ages, and experimental conditions. Our model also predicts that in vivo-like spike timing irregularity strongly shapes plasticity outcome. This geometrical readout modelling approach can be readily applied to other excitatory or inhibitory synapses to discover their synaptic plasticity rules.

Close agreement between deterministic versus stochastic modeling of first-passage time to vesicle fusion

Ca2+-dependent cell processes, such as neurotransmitter or endocrine vesicle fusion, are inherently stochastic due to large fluctuations in Ca2+ channel gating, Ca2+ diffusion, and Ca2+ binding to buffers and target sensors. However, previous studies revealed closer-than-expected agreement between deterministic and stochastic simulations of Ca2+ diffusion, buffering, and sensing if Ca2+ channel gating is not Ca2+ dependent. To understand this result more fully, we present a comparative study complementing previous work, focusing on Ca2+ dynamics downstream of Ca2+ channel gating. Specifically, we compare deterministic (mean-field/mass-action) and stochastic simulations of vesicle exocytosis latency, quantified by the probability density of the first-passage time (FPT) to the Ca2+-bound state of a vesicle fusion sensor, following a brief Ca2+ current pulse. We show that under physiological constraints, the discrepancy between FPT densities obtained using the two approaches remains small even if as few as ∼50 Ca2+ ions enter per single channel-vesicle release unit. Using a reduced two-compartment model for ease of analysis, we illustrate how this close agreement arises from the smallness of correlations between fluctuations of the reactant molecule numbers, despite the large magnitude of fluctuation amplitudes. This holds if all relevant reactions are heteroreaction between molecules of different species, as is the case for bimolecular Ca2+ binding to buffers and downstream sensor targets. In this case, diffusion and buffering effectively decorrelate the state of the Ca2+ sensor from local Ca2+ fluctuations. Thus, fluctuations in the Ca2+ sensor's state underlying the FPT distribution are only weakly affected by the fluctuations in the local Ca2+ concentration around its average, deterministically computable value.

Stochastic reaction-diffusion modeling of calcium dynamics in 3D dendritic spines of Purkinje cells

Calcium (Ca²⁺) is a second messenger assumed to control changes in synaptic strength in the form of both long-term depression and long-term potentiation at Purkinje cell dendritic spine synapses via inositol trisphosphate (IP₃)-induced Ca²⁺ release. These Ca²⁺ transients happen in response to stimuli from parallel fibers (PFs) from granule cells and climbing fibers (CFs) from the inferior olivary nucleus. These events occur at low numbers of free Ca²⁺, requiring stochastic single-particle methods when modeling them. We use the stochastic particle simulation program MCell to simulate Ca²⁺ transients within a three-dimensional Purkinje cell dendritic spine. The model spine includes the endoplasmic reticulum, several Ca²⁺ transporters, and endogenous buffer molecules. Our simulations successfully reproduce properties of Ca²⁺ transients in different dynamical situations. We test two different models of the IP₃ receptor (IP₃R). The model with nonlinear concentration response of binding of activating Ca²⁺ reproduces experimental results better than the model with linear response because of the filtering of noise. Our results also suggest that Ca²⁺-dependent inhibition of the IP₃R needs to be slow to reproduce experimental results. Simulations suggest the experimentally observed optimal timing window of CF stimuli arises from the relative timing of CF influx of Ca²⁺ and IP₃ production sensitizing IP₃R for Ca²⁺-induced Ca²⁺ release. We also model ataxia, a loss of fine motor control assumed to be the result of malfunctioning information transmission at the granule to Purkinje cell synapse, resulting in a decrease or loss of Ca²⁺ transients. Finally, we propose possible ways of recovering Ca²⁺ transients under ataxia.

Binding of Filamentous Actin to CaMKII as Potential Regulation Mechanism of Bidirectional Synaptic Plasticity by β CaMKII in Cerebellar Purkinje Cells

Calcium-calmodulin dependent protein kinase II (CaMKII) regulates many forms of synaptic plasticity, but little is known about its functional role during plasticity induction in the cerebellum. Experiments have indicated that the β isoform of CaMKII controls the bidirectional inversion of plasticity at parallel fibre (PF)-Purkinje cell (PC) synapses in cerebellar cortex. Because the cellular events that underlie these experimental findings are still poorly understood, we developed a simple computational model to investigate how β CaMKII regulates the direction of plasticity in cerebellar PCs. We present the first model of AMPA receptor phosphorylation that simulates the induction of long-term depression (LTD) and potentiation (LTP) at the PF-PC synapse. Our simulation results suggest that the balance of CaMKII-mediated phosphorylation and protein phosphatase 2B (PP2B)-mediated dephosphorylation of AMPA receptors can determine whether LTD or LTP occurs in cerebellar PCs. The model replicates experimental observations that indicate that β CaMKII controls the direction of plasticity at PF-PC synapses, and demonstrates that the binding of filamentous actin to CaMKII can enable the β isoform of the kinase to regulate bidirectional plasticity at these synapses.

Mathematical Modelling of Nitric Oxide/Cyclic GMP/Cyclic AMP Signalling in Platelets

Platelet activation contributes to normal haemostasis but also to pathologic conditions like stroke and cardiac infarction. Signalling by cGMP and cAMP inhibit platelet activation and are therefore attractive targets for thrombosis prevention. However, extensive cross-talk between the cGMP and cAMP signalling pathways in multiple tissues complicates the selective targeting of their activities. We have used mathematical modelling based on experimental data from the literature to quantify the steady state behaviour of nitric oxide (NO)/cGMP/cAMP signalling in platelets. The analysis provides an assessment of NO-induced cGMP synthesis and PKG activation as well as cGMP-mediated cAMP and PKA activation though modulation of phosphodiesterase (PDE2 and 3) activities. Both one- and two-compartment models of platelet cyclic nucleotide signalling are presented. The models provide new insight for understanding how NO signalling to cGMP and indirectly cAMP, can inhibit platelet shape-change, the initial step of platelet activation. Only the two-compartment models could account for the experimental observation that NO-mediated PKA activation can occur when the bulk platelet cAMP level is unchanged. The models revealed also a potential for hierarchical interplay between the different platelet phosphodiesterases. Specifically, the models predict, unexpectedly, a strong effect of pharmacological inhibitors of cGMP-specific PDE5 on the cGMP/cAMP cross-talk. This may explain the successful use of weak PDE5-inhibitors, such as dipyridamole, in anti-platelet therapy. In conclusion, increased NO signalling or PDE5 inhibition are attractive ways of increasing cGMP-cAMP cross-talk selectively in platelets.

Development of computational models of cAMP signaling

Despite the growing evidence defining the cAMP signaling network as a master regulator of cellular function in a number of tissues, regulatory feedback loops, signal compartmentalization, as well as cross-talk with other signaling pathways make understanding the emergent properties of cAMP cellular action a daunting task. Dynamical models of signaling that combine quantitative rigor with molecular details can contribute valuable mechanistic insight into the complexity of intracellular cAMP signaling by complementing and guiding experimental efforts. In this chapter, we review the development of cAMP computational models. We describe how features of the cAMP network can be represented and review the types of experimental data useful in modeling cAMP signaling. We also compile a list of published cAMP models that can aid in the development of novel dynamical models of cAMP signaling.

Multiscale model of dynamic neuromodulation integrating neuropeptide-induced signaling pathway activity with membrane electrophysiology

We developed a multiscale model to bridge neuropeptide receptor-activated signaling pathway activity with membrane electrophysiology. Typically, the neuromodulation of biochemical signaling and biophysics have been investigated separately in modeling studies. We studied the effects of Angiotensin II (AngII) on neuronal excitability changes mediated by signaling dynamics and downstream phosphorylation of ion channels. Experiments have shown that AngII binding to the AngII receptor type-1 elicits baseline-dependent regulation of cytosolic Ca(2+) signaling. Our model simulations revealed a baseline Ca(2+)-dependent response to AngII receptor type-1 activation by AngII. Consistent with experimental observations, AngII evoked a rise in Ca(2+) when starting at a low baseline Ca(2+) level, and a decrease in Ca(2+) when starting at a higher baseline. Our analysis predicted that the kinetics of Ca(2+) transport into the endoplasmic reticulum play a critical role in shaping the Ca(2+) response. The Ca(2+) baseline also influenced the AngII-induced excitability changes such that lower Ca(2+) levels were associated with a larger firing rate increase. We examined the relative contributions of signaling kinases protein kinase C and Ca(2+)/Calmodulin-dependent protein kinase II to AngII-mediated excitability changes by simulating activity blockade individually and in combination. We found that protein kinase C selectively controlled firing rate adaptation whereas Ca(2+)/Calmodulin-dependent protein kinase II induced a delayed effect on the firing rate increase. We tested whether signaling kinetics were necessary for the dynamic effects of AngII on excitability by simulating three scenarios of AngII-mediated KDR channel phosphorylation: (1), an increased steady state; (2), a step-change increase; and (3), dynamic modulation. Our results revealed that the kinetics emerging from neuromodulatory activation of the signaling network were required to account for the dynamical changes in excitability. In summary, our integrated multiscale model provides, to our knowledge, a new approach for quantitative investigation of neuromodulatory effects on signaling and electrophysiology.

MAP kinase modules: the excursion model and the steps that count

MAP kinase modules propagate diverse extracellular signals to downstream effectors. The two dual phosphorylation reactions catalyzed by the modules are thought to control the switch behavior of the pathway. Here we review recent approaches to understand these pathways through signal-to-response studies in cells and in vitro. These data are reconciled with physical models as well as predictions made on mathematical and theoretical grounds. Biochemical analysis has shown recently that the dual phosphorylation reactions catalyzed by MAP kinase modules are sequential at both levels of the cascade. The observed order of phosphorylation events suggests an excursion from the Ser/Thr kinase activity of the MAP3K into Tyr kinase activity of the central dual specificity MAP2K. How the order of events might be encoded in the structures and interactions is discussed. The ordered mechanism confirms predictions that reactions should be sequential to generate the steep signal-to-response curves and delayed responses observed in cells.

Modeling maintenance of long-term potentiation in clustered synapses: long-term memory without bistability

Memories are stored, at least partly, as patterns of strong synapses. Given molecular turnover, how can synapses maintain strong for the years that memories can persist? Some models postulate that biochemical bistability maintains strong synapses. However, bistability should give a bimodal distribution of synaptic strength or weight, whereas current data show unimodal distributions for weights and for a correlated variable, dendritic spine volume. Thus it is important for models to simulate both unimodal distributions and long-term memory persistence. Here a model is developed that connects ongoing, competing processes of synaptic growth and weakening to stochastic processes of receptor insertion and removal in dendritic spines. The model simulates long-term (>1 yr) persistence of groups of strong synapses. A unimodal weight distribution results. For stability of this distribution it proved essential to incorporate resource competition between synapses organized into small clusters. With competition, these clusters are stable for years. These simulations concur with recent data to support the “clustered plasticity hypothesis” which suggests clusters, rather than single synaptic contacts, may be a fundamental unit for storage of long-term memory. The model makes empirical predictions and may provide a framework to investigate mechanisms maintaining the balance between synaptic plasticity and stability of memory.

Stochasticity in Ca2+ increase in spines enables robust and sensitive information coding

A dendritic spine is a very small structure (∼0.1 µm³) of a neuron that processes input timing information. Why are spines so small? Here, we provide functional reasons; the size of spines is optimal for information coding. Spines code input timing information by the probability of Ca²⁺ increases, which makes robust and sensitive information coding possible. We created a stochastic simulation model of input timing-dependent Ca²⁺ increases in a cerebellar Purkinje cell's spine. Spines used probability coding of Ca²⁺ increases rather than amplitude coding for input timing detection via stochastic facilitation by utilizing the small number of molecules in a spine volume, where information per volume appeared optimal. Probability coding of Ca²⁺ increases in a spine volume was more robust against input fluctuation and more sensitive to input numbers than amplitude coding of Ca²⁺ increases in a cell volume. Thus, stochasticity is a strategy by which neurons robustly and sensitively code information.

Multiscale modeling and synaptic plasticity

Synaptic plasticity is a major convergence point for theory and computation, and the process of plasticity engages physiology, cell, and molecular biology. In its many manifestations, plasticity is at the hub of basic neuroscience questions about memory and development, as well as more medically themed questions of neural damage and recovery. As an important cellular locus of memory, synaptic plasticity has received a huge amount of experimental and theoretical attention. If computational models have tended to pick specific aspects of plasticity, such as STDP, and reduce them to an equation, some experimental studies are equally guilty of oversimplification each time they identify a new molecule and declare it to be the last word in plasticity and learning. Multiscale modeling begins with the acknowledgment that synaptic function spans many levels of signaling, and these are so tightly coupled that we risk losing essential features of plasticity if we focus exclusively on any one level. Despite the technical challenges and gaps in data for model specification, an increasing number of multiscale modeling studies have taken on key questions in plasticity. These have provided new insights, but importantly, they have opened new avenues for questioning. This review discusses a wide range of multiscale models in plasticity, including their technical landscape and their implications.

Modeling intracellular signaling underlying striatal function in health and disease

Striatum, which is the input nucleus of the basal ganglia, integrates cortical and thalamic glutamatergic inputs with dopaminergic afferents from the substantia nigra pars compacta. The combination of dopamine and glutamate strongly modulates molecular and cellular properties of striatal neurons and the strength of corticostriatal synapses. These actions are performed via intracellular signaling networks, containing several intertwined feedback loops. Understanding the role of dopamine and other neuromodulators requires the development of quantitative dynamical models for describing the intracellular signaling, in order to provide precise unambiguous descriptions and quantitative predictions. Building such models requires integration of data from multiple data sources containing information regarding the molecular interactions, the strength of these interactions, and the subcellular localization of the molecules. Due to the uncertainty, variability, and sparseness of these data, parameter estimation techniques are critical for inferring or constraining the unknown parameters, and sensitivity analysis evaluates which parameters are most critical for a given observed macroscopic behavior. Here, we briefly review the modeling approaches and tools that have been used to investigate biochemical signaling in the striatum, along with some of the models built around striatum. We also suggest a future direction for the development of such models from the, now becoming abundant, high-throughput data.

A stochastic signaling network mediates the probabilistic induction of cerebellar long-term depression

Many cellular processes involve a small number of molecules and undergo stochastic fluctuations in their levels of activity. Cerebellar long-term depression (LTD) is a form of synaptic plasticity expressed as a reduction in the number of synaptic AMPA receptors (AMPARs) in Purkinje cells. We developed a stochastic model of the LTD signaling network, including a PKC-ERK-cPLA(2) positive feedback loop and mechanisms of AMPAR trafficking, and tuned the model to replicate calcium uncaging experiments. The signaling network activity in single synapses switches between two discrete stable states (LTD and non-LTD) in a probabilistic manner. The stochasticity of the signaling network causes threshold dithering and allows at the macroscopic level for many different and stable mean magnitudes of depression. The probability of LTD occurrence in a single spine is only modulated by the concentration and duration of the signal used to trigger it, and inputs with the same magnitude can give rise to two different responses; there is no threshold for the input signal. The stochasticity is intrinsic to the signaling network and not mostly dependent on noise in the calcium input signal, as has been suggested previously. The activities of the ultrasensitive ERK and of cPLA(2) undergo strong stochastic fluctuations. Conversely, PKC, which acts as a noise filter, is more constantly activated. Systematic variation of the biochemical population size demonstrates that threshold dithering and the absence of spontaneous LTD depend critically on the number of molecules in a spine, indicating constraints on spine size in Purkinje cells.

Molecular constraints on synaptic tagging and maintenance of long-term potentiation: a predictive model

Protein synthesis-dependent, late long-term potentiation (LTP) and depression (LTD) at glutamatergic hippocampal synapses are well characterized examples of long-term synaptic plasticity. Persistent increased activity of protein kinase M ζ (PKMζ) is thought essential for maintaining LTP. Additional spatial and temporal features that govern LTP and LTD induction are embodied in the synaptic tagging and capture (STC) and cross capture hypotheses. Only synapses that have been “tagged” by a stimulus sufficient for LTP and learning can “capture” PKMζ. A model was developed to simulate the dynamics of key molecules required for LTP and LTD. The model concisely represents relationships between tagging, capture, LTD, and LTP maintenance. The model successfully simulated LTP maintained by persistent synaptic PKMζ, STC, LTD, and cross capture, and makes testable predictions concerning the dynamics of PKMζ. The maintenance of LTP, and consequently of at least some forms of long-term memory, is predicted to require continual positive feedback in which PKMζ enhances its own synthesis only at potentiated synapses. This feedback underlies bistability in the activity of PKMζ. Second, cross capture requires the induction of LTD to induce dendritic PKMζ synthesis, although this may require tagging of a nearby synapse for LTP. The model also simulates the effects of PKMζ inhibition, and makes additional predictions for the dynamics of CaM kinases. Experiments testing the above predictions would significantly advance the understanding of memory maintenance.

A fundamental problem in neurobiology is to understand how memories are maintained for up to years. Long-term potentiation (LTP), an enduring increase in the strength of specific connections (synapses) between neurons, is thought to comprise, at least in part, the substrate of learning and memory. What processes transduce brief stimuli into persistent LTP? Persistent increased activity of an enzyme denoted protein kinase M ζ (PKMζ) is thought essential for maintaining LTP. Only synapses that have been “tagged” by a stimulus, such as stimuli needed for LTP and learning, can “capture” PKMζ. We developed a model simulating dynamics of key molecules required for LTP and its opposite, long-term depression (LTD). The model concisely represents relationships between tagging, capture, LTD, and LTP maintenance. It makes testable predictions concerning the dynamics of PKMζ. The maintenance of LTP and memory is predicted to require positive feedback in which PKMζ enhances its own synthesis at potentiated synapses. Without synaptic capture of PKMζ, no positive feedback would occur. LTD induction is also predicted to increase PKMζ synthesis. The model also makes predictions about regulation of PKMζ synthesis. Experiments testing the above predictions would advance the understanding of memory maintenance.

Subcellular location of PKA controls striatal plasticity: stochastic simulations in spiny dendrites

Dopamine release in the striatum has been implicated in various forms of reward dependent learning. Dopamine leads to production of cAMP and activation of protein kinase A (PKA), which are involved in striatal synaptic plasticity and learning. PKA and its protein targets are not diffusely located throughout the neuron, but are confined to various subcellular compartments by anchoring molecules such as A-Kinase Anchoring Proteins (AKAPs). Experiments have shown that blocking the interaction of PKA with AKAPs disrupts its subcellular location and prevents LTP in the hippocampus and striatum; however, these experiments have not revealed whether the critical function of anchoring is to locate PKA near the cAMP that activates it or near its targets, such as AMPA receptors located in the post-synaptic density. We have developed a large scale stochastic reaction-diffusion model of signaling pathways in a medium spiny projection neuron dendrite with spines, based on published biochemical measurements, to investigate this question and to evaluate whether dopamine signaling exhibits spatial specificity post-synaptically. The model was stimulated with dopamine pulses mimicking those recorded in response to reward. Simulations show that PKA colocalization with adenylate cyclase, either in the spine head or in the dendrite, leads to greater phosphorylation of DARPP-32 Thr34 and AMPA receptor GluA1 Ser845 than when PKA is anchored away from adenylate cyclase. Simulations further demonstrate that though cAMP exhibits a strong spatial gradient, diffusible DARPP-32 facilitates the spread of PKA activity, suggesting that additional inactivation mechanisms are required to produce spatial specificity of PKA activity.

The striatum is a part of the basal ganglia which plays a role in addiction and reward learning. Its importance is underscored by pathologies such as Parkinson's disease and Huntington's disease in which degeneration of the dopamine inputs to the striatum or degeneration of neurons in the striatum, respectively, produces motor dysfunction. Dopamine in the striatum activates cascades of signaling molecules, ultimately producing an activity dependent change in the strength of connections between neurons. However, the dispersive movement of signaling molecules seems incompatible with the strengthening of specific subsets of connections, which is required for formation of distinct memories. Anchoring proteins, which restrict molecules to particular compartments within the neuron, are proposed to achieve specificity. We develop a reaction-diffusion model of dopamine activated signaling pathways to explore mechanisms whereby anchoring proteins can produce specificity. We use an efficient Monte-Carlo simulator to implement the cascades of signaling molecules in a neuronal dendrite with multiple dendritic spines. Simulations demonstrate that spatial specificity requires both anchoring proteins and inactivation mechanisms that limit the diffusion of signaling molecules.

Computational study of noise in a large signal transduction network

BACKGROUND

Biochemical systems are inherently noisy due to the discrete reaction events that occur in a random manner. Although noise is often perceived as a disturbing factor, the system might actually benefit from it. In order to understand the role of noise better, its quality must be studied in a quantitative manner. Computational analysis and modeling play an essential role in this demanding endeavor.

RESULTS

We implemented a large nonlinear signal transduction network combining protein kinase C, mitogen-activated protein kinase, phospholipase A2, and β isoform of phospholipase C networks. We simulated the network in 300 different cellular volumes using the exact Gillespie stochastic simulation algorithm and analyzed the results in both the time and frequency domain. In order to perform simulations in a reasonable time, we used modern parallel computing techniques. The analysis revealed that time and frequency domain characteristics depend on the system volume. The simulation results also indicated that there are several kinds of noise processes in the network, all of them representing different kinds of low-frequency fluctuations. In the simulations, the power of noise decreased on all frequencies when the system volume was increased.

CONCLUSIONS

We concluded that basic frequency domain techniques can be applied to the analysis of simulation results produced by the Gillespie stochastic simulation algorithm. This approach is suited not only to the study of fluctuations but also to the study of pure noise processes. Noise seems to have an important role in biochemical systems and its properties can be numerically studied by simulating the reacting system in different cellular volumes. Parallel computing techniques make it possible to run massive simulations in hundreds of volumes and, as a result, accurate statistics can be obtained from computational studies.

From the stochasticity of molecular processes to the variability of synaptic transmission

The variability of the postsynaptic response following a single action potential arises from two sources: the neurotransmitter release is probabilistic, and the postsynaptic response to neurotransmitter release has variable timing and amplitude. At individual synapses, the number of molecules of a given type that are involved in these processes is small enough that the stochastic (random) properties of molecular events cannot be neglected. How the stochasticity of molecular processes contributes to the variability of synaptic transmission, its sensitivity and its robustness to molecular fluctuations has important implications for our understanding of the mechanistic basis of synaptic transmission and of synaptic plasticity.

Stochastic amplification of calcium-activated potassium currents in Ca2+ microdomains

Small conductance (SK) calcium-activated potassium channels are found in many tissues throughout the body and open in response to elevations in intracellular calcium. In hippocampal neurons, SK channels are spatially co-localized with L-Type calcium channels. Due to the restriction of calcium transients into microdomains, only a limited number of L-Type Ca(2+) channels can activate SK and, thus, stochastic gating becomes relevant. Using a stochastic model with calcium microdomains, we predict that intracellular Ca(2+) fluctuations resulting from Ca(2+) channel gating can increase SK2 subthreshold activity by 1-2 orders of magnitude. This effectively reduces the value of the Hill coefficient. To explain the underlying mechanism, we show how short, high-amplitude calcium pulses associated with stochastic gating of calcium channels are much more effective at activating SK2 channels than the steady calcium signal produced by a deterministic simulation. This stochastic amplification results from two factors: first, a supralinear rise in the SK2 channel's steady-state activation curve at low calcium levels and, second, a momentary reduction in the channel's time constant during the calcium pulse, causing the channel to approach its steady-state activation value much faster than it decays. Stochastic amplification can potentially explain subthreshold SK2 activation in unified models of both sub- and suprathreshold regimes. Furthermore, we expect it to be a general phenomenon relevant to many proteins that are activated nonlinearly by stochastic ligand release.

Sequestration of CaMKII in dendritic spines in silico

Calcium calmodulin dependent kinase II (CaMKII) is sequestered in dendritic spines within seconds upon synaptic stimulation. The program Smoldyn was used to develop scenarios of single molecule CaMKII diffusion and binding in virtual dendritic spines. We first validated simulation of diffusion as a function of spine morphology. Additional cellular structures were then incorporated to simulate binding of CaMKII to the post-synaptic density (PSD); binding to cytoskeleton; or their self-aggregation. The distributions of GFP tagged native and mutant constructs in dissociated hippocampal neurons were measured to guide quantitative analysis. Intra-spine viscosity was estimated from fluorescence recovery after photo-bleach (FRAP) of red fluorescent protein. Intra-spine mobility of the GFP-CaMKIIα constructs was measured, with hundred-millisecond or better time resolution, from FRAP of distal spine tips in conjunction with fluorescence loss (FLIP) from proximal regions. Different FRAP \ FLIP profiles were predicted from our Scenarios and provided a means to differentiate binding to the PSDs from self-aggregation. The predictions were validated by experiments. Simulated fits of the Scenarios provided estimates of binding and rate constants. We utilized these values to assess the role of self-aggregation during the initial response of native CaMKII holoenzymes to stimulation. The computations revealed that self-aggregation could provide a concentration-dependent switch to amplify CaMKII sequestration and regulate its activity depending on its occupancy of the actin cytoskeleton.

Four-dimensional dynamics of MAPK information processing systems

Mitogen activated protein kinase (MAPK) cascades process a myriad of stimuli received by cell-surface receptors and generate precise spatio-temporal guidance for multiple target proteins, dictating receptor-specific cellular outcomes. Computational modelling reveals that the intrinsic topology of MAPK cascades enables them to amplify signal sensitivity and amplitude, reduce noise and display intricate dynamic properties, which include toggle switches, excitation pulses and oscillations. Specificity of signaling responses can be brought about by signal-induced feedback and feedforward wiring imposed on the MAPK cascade backbone. Intracellular gradients of protein activities arise from the spatial separation of opposing reactions in kinase-phosphatase cycles. The membrane confinement of the initiating kinase in MAPK cascades and cytosolic localization of phosphatases can result in precipitous gradients of phosphorylated signal-transducers if they spread solely by diffusion. Endocytotic trafficking of active kinases driven by molecular motors and traveling waves of protein phosphorylation can propagate phosphorylation signals from the plasma membrane to the nucleus, especially in large cells, such as Xenopus eggs.

Phosphoproteomics-based modeling defines the regulatory mechanism underlying aberrant EGFR signaling

Background

Mutation of the epidermal growth factor receptor (EGFR) results in a discordant cell signaling, leading to the development of various diseases. However, the mechanism underlying the alteration of downstream signaling due to such mutation has not yet been completely understood at the system level. Here, we report a phosphoproteomics-based methodology for characterizing the regulatory mechanism underlying aberrant EGFR signaling using computational network modeling.

Methodology/Principal Findings

Our phosphoproteomic analysis of the mutation at tyrosine 992 (Y992), one of the multifunctional docking sites of EGFR, revealed network-wide effects of the mutation on EGF signaling in a time-resolved manner. Computational modeling based on the temporal activation profiles enabled us to not only rediscover already-known protein interactions with Y992 and internalization property of mutated EGFR but also further gain model-driven insights into the effect of cellular content and the regulation of EGFR degradation. Our kinetic model also suggested critical reactions facilitating the reconstruction of the diverse effects of the mutation on phosphoproteome dynamics.

Conclusions/Significance

Our integrative approach provided a mechanistic description of the disorders of mutated EGFR signaling networks, which could facilitate the development of a systematic strategy toward controlling disease-related cell signaling.

Effects of ionizing radiation on cell-to-cell communication

Cell-to-cell signaling has become a significant issue in radiation biology due to experimental evidence, accumulated primarily since the early 1990s, of radiation-induced bystander effects. Several candidate mediators involved in cell-to-cell communication have been investigated and proposed as being responsible for this phenomenon, but the current investigation techniques (both theoretical and experimental) of the mechanisms involved, due to the particular set-up of each experiment, result in experimental data that often are not directly comparable. In this study, a comprehensive approach was adopted to describe cell-to-cell communication (focusing on cytokine signaling) and its modulation by external agents such as ionizing radiation. The aim was also to provide integrated theoretical instruments and experimental data to help in understanding the peculiarities of in vitro experiments. Theoretical/modeling activities were integrated with experimental measurements by (1) redesigning a cybernetic model (proposed in its original form in the 1950s) to frame cell-to-cell communication processes, (2) implementing and developing a mathematical model, and (3) designing and carrying out experiments to quantify key parameters involved in intercellular signaling (focusing as a pilot study on the release and decay of IL-6 molecules and their modulation by radiation). This formalization provides an interpretative framework for understanding the intercellular signaling and in particular for focusing on the study of cell-to-cell communication in a "step-by-step" approach. Under this model, the complex phenomenon of signal transmission was reduced where possible into independent processes to investigate them separately, providing an evaluation of the role of cell communication to guarantee and maintain the robustness of the in vitro experimental systems against the effects of perturbations.

Stochastic ion channel gating in dendritic neurons: morphology dependence and probabilistic synaptic activation of dendritic spikes

Neuronal activity is mediated through changes in the probability of stochastic transitions between open and closed states of ion channels. While differences in morphology define neuronal cell types and may underlie neurological disorders, very little is known about influences of stochastic ion channel gating in neurons with complex morphology. We introduce and validate new computational tools that enable efficient generation and simulation of models containing stochastic ion channels distributed across dendritic and axonal membranes. Comparison of five morphologically distinct neuronal cell types reveals that when all simulated neurons contain identical densities of stochastic ion channels, the amplitude of stochastic membrane potential fluctuations differs between cell types and depends on sub-cellular location. For typical neurons, the amplitude of membrane potential fluctuations depends on channel kinetics as well as open probability. Using a detailed model of a hippocampal CA1 pyramidal neuron, we show that when intrinsic ion channels gate stochastically, the probability of initiation of dendritic or somatic spikes by dendritic synaptic input varies continuously between zero and one, whereas when ion channels gate deterministically, the probability is either zero or one. At physiological firing rates, stochastic gating of dendritic ion channels almost completely accounts for probabilistic somatic and dendritic spikes generated by the fully stochastic model. These results suggest that the consequences of stochastic ion channel gating differ globally between neuronal cell-types and locally between neuronal compartments. Whereas dendritic neurons are often assumed to behave deterministically, our simulations suggest that a direct consequence of stochastic gating of intrinsic ion channels is that spike output may instead be a probabilistic function of patterns of synaptic input to dendrites.

The activity of neurons in the brain is mediated through changes in the probability of random transitions between open and closed states of ion channels. Since differences in morphology define distinct types of neuron and may underlie neurological disorders, it is important to understand how morphology influences the functional consequences of these random transitions. However, the complexities of neuronal morphology, together with the large number of ion channels expressed by a single neuron, have made this issue difficult to explore systematically. We introduce and validate new computational tools that enable efficient generation and simulation of models containing ion channels distributed across complex neuronal morphologies. Using these tools we demonstrate that the impact of random ion channel opening depends on neuronal morphology and ion channel kinetics. We show that in a realistic model of a neuron important for navigation and memory random gating of ion channels substantially modifies responses to synaptic input. Our results suggest a new and general perspective, whereby output from a neuron is a probabilistic rather than a fixed function of synaptic input to its dendrites. These results and new tools will contribute to the understanding of how intrinsic properties of neurons influence computations carried out within the brain.

The chemical biology of synapses and neuronal circuits

Excitatory synapses are located in confined chemical spaces called the dendritic spines. These are atypical femtoliter-order microdomains where the behavior of even single molecules may have important biological consequences. Powerful chemical biological techniques have now been developed to decipher the dynamic stability of the synapses and to further interrogate the complex properties of neuronal circuits.

The role of type 4 phosphodiesterases in generating microdomains of cAMP: large scale stochastic simulations

Cyclic AMP (cAMP) and its main effector Protein Kinase A (PKA) are critical for several aspects of neuronal function including synaptic plasticity. Specificity of synaptic plasticity requires that cAMP activates PKA in a highly localized manner despite the speed with which cAMP diffuses. Two mechanisms have been proposed to produce localized elevations in cAMP, known as microdomains: impeded diffusion, and high phosphodiesterase (PDE) activity. This paper investigates the mechanism of localized cAMP signaling using a computational model of the biochemical network in the HEK293 cell, which is a subset of pathways involved in PKA-dependent synaptic plasticity. This biochemical network includes cAMP production, PKA activation, and cAMP degradation by PDE activity. The model is implemented in NeuroRD: novel, computationally efficient, stochastic reaction-diffusion software, and is constrained by intracellular cAMP dynamics that were determined experimentally by real-time imaging using an Epac-based FRET sensor (H30). The model reproduces the high concentration cAMP microdomain in the submembrane region, distinct from the lower concentration of cAMP in the cytosol. Simulations further demonstrate that generation of the cAMP microdomain requires a pool of PDE4D anchored in the cytosol and also requires PKA-mediated phosphorylation of PDE4D which increases its activity. The microdomain does not require impeded diffusion of cAMP, confirming that barriers are not required for microdomains. The simulations reported here further demonstrate the utility of the new stochastic reaction-diffusion algorithm for exploring signaling pathways in spatially complex structures such as neurons.

Modelling the molecular mechanisms of synaptic plasticity using systems biology approaches

Synaptic plasticity is thought to underlie learning and memory, but the complexity of the interactions between the ion channels, enzymes and genes that are involved in synaptic plasticity impedes a deep understanding of this phenomenon. Computer modelling has been used to investigate the information processing that is performed by the signalling pathways involved in synaptic plasticity in principal neurons of the hippocampus, striatum and cerebellum. In the past few years, new software developments that combine computational neuroscience techniques with systems biology techniques have allowed large-scale, kinetic models of the molecular mechanisms underlying long-term potentiation and long-term depression. We highlight important advancements produced by these quantitative modelling efforts and introduce promising approaches that use advancements in live-cell imaging.

Toxicity testing in the 21st century: a vision and a strategy

With the release of the landmark report Toxicity Testing in the 21st Century: A Vision and a Strategy, the U.S. National Academy of Sciences, in 2007, precipitated a major change in the way toxicity testing is conducted. It envisions increased efficiency in toxicity testing and decreased animal usage by transitioning from current expensive and lengthy in vivo testing with qualitative endpoints to in vitro toxicity pathway assays on human cells or cell lines using robotic high-throughput screening with mechanistic quantitative parameters. Risk assessment in the exposed human population would focus on avoiding significant perturbations in these toxicity pathways. Computational systems biology models would be implemented to determine the dose-response models of perturbations of pathway function. Extrapolation of in vitro results to in vivo human blood and tissue concentrations would be based on pharmacokinetic models for the given exposure condition. This practice would enhance human relevance of test results, and would cover several test agents, compared to traditional toxicological testing strategies. As all the tools that are necessary to implement the vision are currently available or in an advanced stage of development, the key prerequisites to achieving this paradigm shift are a commitment to change in the scientific community, which could be facilitated by a broad discussion of the vision, and obtaining necessary resources to enhance current knowledge of pathway perturbations and pathway assays in humans and to implement computational systems biology models. Implementation of these strategies would result in a new toxicity testing paradigm firmly based on human biology.

Toxicity testing in the 21st century: a vision and a strategy

With the release of the landmark report Toxicity Testing in the 21st Century: A Vision and a Strategy, the U.S. National Academy of Sciences, in 2007, precipitated a major change in the way toxicity testing is conducted. It envisions increased efficiency in toxicity testing and decreased animal usage by transitioning from current expensive and lengthy in vivo testing with qualitative endpoints to in vitro toxicity pathway assays on human cells or cell lines using robotic high-throughput screening with mechanistic quantitative parameters. Risk assessment in the exposed human population would focus on avoiding significant perturbations in these toxicity pathways. Computational systems biology models would be implemented to determine the dose-response models of perturbations of pathway function. Extrapolation of in vitro results to in vivo human blood and tissue concentrations would be based on pharmacokinetic models for the given exposure condition. This practice would enhance human relevance of test results, and would cover several test agents, compared to traditional toxicological testing strategies. As all the tools that are necessary to implement the vision are currently available or in an advanced stage of development, the key prerequisites to achieving this paradigm shift are a commitment to change in the scientific community, which could be facilitated by a broad discussion of the vision, and obtaining necessary resources to enhance current knowledge of pathway perturbations and pathway assays in humans and to implement computational systems biology models. Implementation of these strategies would result in a new toxicity testing paradigm firmly based on human biology.

The effect of noise on CaMKII activation in a dendritic spine during LTP induction

Activation of calcium-calmodulin dependent protein kinase II (CaMKII) during induction of long-term potentiation (LTP) is a series of complicated stochastic processes that are affected by noise. There are two main sources of noise affecting CaMKII activation within a dendritic spine. One is the noise associated with stochastic opening of N-methyl-d-aspartate (NMDA) receptor channels and the other is the noise associated with the stochastic reaction-diffusion kinetics leading to CaMKII activation. Many models have been developed to simulate CaMKII activation, but there is no fully stochastic model that studies the effect of noise on CaMKII activation. Here we construct a fully stochastic model to study these effects. Our results show that noise has important effects on CaMKII activation variability, with the effect from stochastic opening of NMDA receptor channels being 5-10 times more significant than that from stochastic reactions involving CaMKII. In addition, CaMKII activation levels and the variability of activation are greatly affected by small changes in NMDA receptor channel number at the synapse. One reason LTP induction protocols may require tetanic or repeated burst stimulation is that there is a need to overcome inherent variability to provide sufficiently large calcium signals through NMDA receptor channels; with meaningful physiological stimuli, noise may allow the calcium signal to exceed threshold for CaMKII activation when it might not do so otherwise.

Hybrid stochastic simulations of intracellular reaction-diffusion systems

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.

Expression levels of the alpha4 subunit of the GABA(A) receptor in differentiated neuroblastoma cells are correlated with GABA-gated current

The alpha4 subunit of the GABA(A) receptor (GABAR) is capable of rapid plasticity, increased by chronic exposure to positive GABA modulators, such as the neurosteroid 3alpha-OH-5alpha[beta]-pregnan-20-one (THP). Here, we show that 48 h exposure of differentiated neuroblastoma cells (IMR-32) to 100 nM THP increases alpha4 expression, without changing the current density or the concentration-response curve. Increased expression of alpha4-containing GABAR was verified by a relative insensitivity of GABA (EC(20))-gated current to modulation by the benzodiazepine (BZ) lorazepam (0.01-100 microM), and potentiation of current by flumazenil and RO15-4513, characteristic of alpha4betagamma2 pharmacology. In contrast to THP, compounds which decrease GABA-gated current, such as the BZ inverse agonist DMCM, the GABAR antagonist gabazine and the open channel blocker penicillin, decreased alpha4 expression after a 48 h exposure, without changing BZ responsiveness. However, pentobarbital, another positive GABA modulator, increased alpha4 expression, while the BZ antagonist flumazenil had no effect. In order to test whether changes in current were responsible for increased alpha4 expression, decreases in the Cl(-) driving force were produced by chronic exposure to the NKCC1 blocker bumetanide (10 microM). When applied under these conditions of reduced GABA-gated current, THP failed to increase alpha4 expression. The results of this study suggest that alpha4 expression is correlated with changes in GABA-gated current, rather than simply through ligand-receptor interactions. These findings have relevance for GABAR subunit plasticity produced by fluctuations in endogenous steroids across the menstrual cycle, when altered BZ sensitivity is reported.

Interlinked dual-time feedback loops can enhance robustness to stochasticity and persistence of memory

Multiple interlinked positive feedback loops shape the stimulus responses of various biochemical systems, such as the cell cycle or intracellular Ca2+ release. Recent studies with simplified models have identified two advantages of coupling fast and slow feedback loops. This dual-time structure enables a fast response while enhancing resistances of responses and bistability to stimulus noise. We now find that (1) the dual-time structure similarly confers resistance to internal noise due to molecule number fluctuations, and (2) model variants with altered coupling, which better represent some specific biochemical systems, share all the above advantages. We also develop a similar bistable model with coupling of a fast autoactivation loop to a slow loop. This model's topology was suggested by positive feedback proposed to play a role in long-term synaptic potentiation (LTP). The advantages of fast response and noise resistance are also present in this autoactivation model. Empirically, LTP develops resistance to reversal over approximately 1h . The model suggests this resistance may result from increased amounts of synaptic kinases involved in positive feedback.

Spine neck geometry determines spino-dendritic cross-talk in the presence of mobile endogenous calcium binding proteins

Dendritic spines are thought to compartmentalize second messengers like Ca2+. The notion of isolated spine signaling, however, was challenged by the recent finding that under certain conditions mobile endogenous Ca(2+)-binding proteins may break the spine limit and lead to activation of Ca(2+)-dependent dendritic signaling cascades. Since the size of spines is variable, the spine neck may be an important regulator of this spino-dendritic crosstalk. We tested this hypothesis by using an experimentally defined, kinetic computer model in which spines of Purkinje neurons were coupled to their parent dendrite by necks of variable geometry. We show that Ca2+ signaling and calmodulin activation in spines with long necks is essentially isolated from the dendrite, while stubby spines show a strong coupling with their dendrite, mediated particularly by calbindin D28k. We conclude that the spine neck geometry, in close interplay with mobile Ca(2+)-binding proteins, regulates the spino-dendritic crosstalk.

IkappaB, NF-kappaB regulation model: simulation analysis of small number of molecules

The regulation of IkappaB, NF-kappaB is of foremost interest in biology as the transcription factor NF-kappaB has multiple target genes. We have modeled a previously published model by Hoffmann et al. (2002) of IkappaB, NF-kappaB mathematically as discrete reaction systems. We have used stochastic algorithm to compare the results when there are large and small numbers of molecules available in a finite volume for each protein. Our results for small number of molecules show that with continuous presence of stimulation, nuclear NF-kappaB oscillates continuously in every individual cell rather than damping, which was observed in cell population results. This characteristic of the system is missed when averaged behavior is studied.

Bistable MAP kinase activity: a plausible mechanism contributing to maintenance of late long-term potentiation

Bistability of MAP kinase (MAPK) activity has been suggested to contribute to several cellular processes, including differentiation and long-term synaptic potentiation. A recent model (Markevich NI, Hoek JB, Kholodenko BN. J Cell Biol 164: 353–359, 2004) predicts bistability due to interactions of the kinases and phosphatases in the MAPK pathway, without feedback from MAPK to earlier reactions. Using this model and enzyme concentrations appropriate for neurons, we simulated bistable MAPK activity, but bistability was present only within a relatively narrow range of activity of Raf, the first pathway kinase. Stochastic fluctuations in molecule numbers eliminated bistability for small molecule numbers, such as are expected in the volume of a dendritic spine. However, positive-feedback loops have been posited from MAPK up to Raf activation. One proposed loop in which MAPK directly activates Raf was incorporated into the model. We found that such feedback greatly enhanced the robustness of both stable states of MAPK activity to stochastic fluctuations and to parameter variations. Bistability was robust for molecule numbers plausible for a dendritic spine volume. The upper state of MAPK activity was resistant to inhibition of MEK activation for >1 h, which suggests that inhibitor experiments have not sufficed to rule out a role for persistent MAPK activity in the maintenance of long-term potentiation (LTP). These simulations suggest that persistent MAPK activity and consequent upregulation of translation may contribute to LTP maintenance and to long-term memory. Experiments using a fluorescent MAPK substrate may further test this hypothesis.

Insight or illusion? Seeing inside the cell with mesoscopic simulations

The expulsion of material from a cell by fusion of vesicles at the plasma membrane, and the entry of a virus by membrane invagination are complex membrane-associated processes whose control is crucial to cell survival. Our ability to visualize the dynamics of such processes experimentally is limited by spatial resolution and the speed of molecular rearrangements. The increase in computing power of the last few decades enables the construction of computational tools for observing cellular processes in silico. As experiments yield increasing amounts of data on the protein and lipid constituents of the cell, computer simulations parametrized using this data are beginning to allow models of cellular processes to be interrogated in ways unavailable in the laboratory. Mesoscopic simulations retain only those molecular features that are believed to be relevant to the processes of interest. This allows the dynamics of spatially heterogeneous membranes and the crowded cytoplasmic environment to be followed at a modest computational cost. The price for such power is that the atomic detail of the constituents is much lower than in atomistic Molecular Dynamics simulations. We argue that this price is worth paying because mesoscopic simulations can generate new insight into the complex, dynamic life of a cell.

Two independent positive feedbacks and bistability in the Bcl-2 apoptotic switch

Background

The complex interplay between B-cell lymphoma 2 (Bcl-2) family proteins constitutes a crucial checkpoint in apoptosis. Its detailed molecular mechanism remains controversial. Our former modeling studies have selected the ‘Direct Activation Model’ as a better explanation for experimental observations. In this paper, we continue to extend this model by adding interactions according to updating experimental findings.

Methodology/Principal Findings

Through mathematical simulation we found bistability, a kind of switch, can arise from a positive (double negative) feedback in the Bcl-2 interaction network established by anti-apoptotic group of Bcl-2 family proteins. Moreover, Bax/Bak auto-activation as an independent positive feedback can enforce the bistability, and make it more robust to parameter variations. By ensemble stochastic modeling, we also elucidated how intrinsic noise can change ultrasensitive switches into gradual responses. Our modeling result agrees well with recent experimental data where bimodal Bax activation distributions in cell population were found.

Conclusions/Significance

Along with the growing experimental evidences, our studies successfully elucidate the switch mechanism embedded in the Bcl-2 interaction network and provide insights into pharmacological manipulation of Bcl-2 apoptotic switch as further cancer therapies.

Simulation of networks of spiking neurons: a review of tools and strategies

We review different aspects of the simulation of spiking neural networks. We start by reviewing the different types of simulation strategies and algorithms that are currently implemented. We next review the precision of those simulation strategies, in particular in cases where plasticity depends on the exact timing of the spikes. We overview different simulators and simulation environments presently available (restricted to those freely available, open source and documented). For each simulation tool, its advantages and pitfalls are reviewed, with an aim to allow the reader to identify which simulator is appropriate for a given task. Finally, we provide a series of benchmark simulations of different types of networks of spiking neurons, including Hodgkin-Huxley type, integrate-and-fire models, interacting with current-based or conductance-based synapses, using clock-driven or event-driven integration strategies. The same set of models are implemented on the different simulators, and the codes are made available. The ultimate goal of this review is to provide a resource to facilitate identifying the appropriate integration strategy and simulation tool to use for a given modeling problem related to spiking neural networks.

A new principle for information storage in an enzymatic pathway model

Strong experimental evidence indicates that protein kinase and phosphatase (KP) cycles are critical to both the induction and maintenance of activity-dependent modifications in neurons. However, their contribution to information storage remains controversial, despite impressive modeling efforts. For instance, plasticity models based on KP cycles do not account for the maintenance of plastic modifications. Moreover, bistable KP cycle models that display memory fail to capture essential features of information storage: rapid onset, bidirectional control, graded amplitude, and finite lifetimes. Here, we show in a biophysical model that upstream activation of KP cycles, a ubiquitous mechanism, is sufficient to provide information storage with realistic induction and maintenance properties: plastic modifications are rapid, bidirectional, and graded, with finite lifetimes that are compatible with animal and human memory. The maintenance of plastic modifications relies on negligible reaction rates in basal conditions and thus depends on enzyme nonlinearity and activation properties of the activity-dependent KP cycle. Moreover, we show that information coding and memory maintenance are robust to stochastic fluctuations inherent to the molecular nature of activity-dependent KP cycle operation. This model provides a new principle for information storage where plasticity and memory emerge from a single dynamic process whose rate is controlled by neuronal activity. This principle strongly departs from the long-standing view that memory reflects stable steady states in biological systems, and offers a new perspective on memory in animals and humans.

A model of late long-term potentiation simulates aspects of memory maintenance

Late long-term potentiation (L-LTP) denotes long-lasting strengthening of synapses between neurons. L-LTP appears essential for the formation of long-term memory, with memories at least partly encoded by patterns of strengthened synapses. How memories are preserved for months or years, despite molecular turnover, is not well understood. Ongoing recurrent neuronal activity, during memory recall or during sleep, has been hypothesized to preferentially potentiate strong synapses, preserving memories. This hypothesis has not been evaluated in the context of a mathematical model representing ongoing activity and biochemical pathways important for L-LTP. In this study, ongoing activity was incorporated into two such models – a reduced model that represents some of the essential biochemical processes, and a more detailed published model. The reduced model represents synaptic tagging and gene induction simply and intuitively, and the detailed model adds activation of essential kinases by Ca²⁺. Ongoing activity was modeled as continual brief elevations of Ca²⁺. In each model, two stable states of synaptic strength/weight resulted. Positive feedback between synaptic weight and the amplitude of ongoing Ca²⁺ transients underlies this bistability. A tetanic or theta-burst stimulus switches a model synapse from a low basal weight to a high weight that is stabilized by ongoing activity. Bistability was robust to parameter variations in both models. Simulations illustrated that prolonged periods of decreased activity reset synaptic strengths to low values, suggesting a plausible forgetting mechanism. However, episodic activity with shorter inactive intervals maintained strong synapses. Both models support experimental predictions. Tests of these predictions are expected to further understanding of how neuronal activity is coupled to maintenance of synaptic strength. Further investigations that examine the dynamics of activity and synaptic maintenance can be expected to help in understanding how memories are preserved for up to a lifetime in animals including humans.

Intrinsic fluctuations, robustness, and tunability in signaling cycles

Covalent modification cycles (e.g., phosphorylation-dephosphorylation) underlie most cellular signaling and control processes. Low molecular copy number, arising from compartmental segregation and slow diffusion between compartments, potentially renders these cycles vulnerable to intrinsic chemical fluctuations. How can a cell operate reliably in the presence of this inherent stochasticity? How do changes in extrinsic parameters lead to variability of response? Can cells exploit these parameters to tune cycles to different ranges of stimuli? We study the dynamics of an isolated phosphorylation cycle. Our model shows that the cycle transmits information reliably if it is tuned to an optimal parameter range, despite intrinsic fluctuations and even for small input signal amplitudes. At the same time, the cycle is sensitive to changes in the concentration and activity of kinases and phosphatases. This sensitivity can lead to significant cell-to-cell response variability. It also provides a mechanism to tune the cycle to transmit signals in various amplitude ranges. Our results show that signaling cycles possess a surprising combination of robustness and tunability. This combination makes them ubiquitous in eukaryotic signaling, optimizing signaling in the presence of fluctuations using their inherent flexibility. On the other hand, cycles tuned to suppress intrinsic fluctuations can be vulnerable to changes in the number and activity of kinases and phosphatases. Such trade-offs in robustness to intrinsic and extrinsic fluctuations can influence the evolution of signaling cascades, making them the weakest links in cellular circuits.

Spino-dendritic cross-talk in rodent Purkinje neurons mediated by endogenous Ca2+-binding proteins

The range of actions of the second messenger Ca(2+) is a key determinant of neuronal excitability and plasticity. For dendritic spines, there is on-going debate regarding how diffusional efflux of Ca(2+) affects spine signalling. However, the consequences of spino-dendritic coupling for dendritic Ca(2+) homeostasis and downstream signalling cascades have not been explored to date. We addressed this question by four-dimensional computer simulations, which were based on Ca(2+)-imaging data from mice that either express or lack distinct endogenous Ca(2+)-binding proteins. Our simulations revealed that single active spines do not affect dendritic Ca(2+) signalling. Neighbouring, coactive spines, however, induce sizeable increases in dendritic [Ca(2+)](i) when they process slow synaptic Ca(2+) signals, such as those implicated in the induction of long-term plasticity. This spino-dendritic coupling is mediated by buffered diffusion, specifically by diffusing calbindin-bound Ca(2+). This represents a central mechanism for activating calmodulin in dendritic shafts and therefore a novel form of signal integration in spiny dendrites.

Constructing realistic neural simulations with GENESIS

The GEneral NEural SImulation System (GENESIS) is an open source simulation platform for realistic modeling of systems ranging from subcellular components and biochemical reactions to detailed models of single neurons, simulations of large networks of realistic neurons, and systems-level models. The graphical interface XODUS permits the construction of a wide variety of interfaces for the control and visualization of simulations. The object-oriented scripting language allows one to easily construct and modify simulations built from the GENESIS libraries of simulation components. Here, we present procedures for installing GENESIS and its supplementary tutorials, running GENESIS simulations, and creating new neural simulations.

Dendritic spine viscoelasticity and soft-glassy nature: balancing dynamic remodeling with structural stability

Neuronal dendritic spines are a key component of brain circuitry, implicated in many mechanisms for plasticity and long-term stability of synaptic communication. They can undergo rapid actin-based activity-dependent shape fluctuations, an intriguing biophysical property that is believed to alter synaptic transmission. Yet, because of their small size (approximately 1 microm or less) and metastable behavior, spines are inaccessible to most physical measurement techniques. Here we employ atomic force microscopy elasticity mapping and novel dynamic indentation methods to probe the biomechanics of dendritic spines in living neurons. We find that spines exhibit 1), a wide range of rigidities, correlated with morphological characteristics, axonal association, and glutamatergic stimulation, 2), a uniquely large viscosity, four to five times that of other cell types, consistent with a high density of solubilized proteins, and 3), weak power-law rheology, described by the soft-glassy model for cellular mechanics. Our findings provide a new perspective on spine functionality and identify key mechanical properties that govern the ability of spines to rapidly remodel and regulate internal protein trafficking but also maintain structural stability.