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

Understanding molecular signaling cascades in neural disease using multi-resolution models

If the genome defines the program for the operations of a cell, signaling networks execute it. These cascades of chemical, cell-biological, structural, and trafficking events span milliseconds (e.g., synaptic release) to potentially a lifetime (e.g., stabilization of dendritic spines). In principle almost every aspect of neuronal function, particularly at the synapse, depends on signaling. Thus dysfunction of these cascades, whether through mutations, local dysregulation, or infection, leads to disease. The sheer complexity of these pathways is matched by the range of diseases and the diversity of their phenotypes. In this review, we discuss how to build computational models, how these models are essential to tackle this complexity, and the benefits of using families of models at different levels of detail to understand signaling in health and disease.

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.

Chemical signals mediate many computations in cells, from housekeeping functions in all cells to memory and pattern selectivity in neurons. These signals form complex networks of interactions. Computer models are a powerful way to study how such networks behave, but it is hard to get all the chemical details for typical models, and it is slow to run them with standard numerical approaches to chemical kinetics. We introduce HillTau as a simplified way to model complex chemical networks. HillTau models condense multiple reaction steps into single steps defined by a small number of parameters for activation and settling time. As a result the models are simple, easy to find values for, and they run quickly. Remarkably, they fit the full chemical formulations rather well. We illustrate the utility of HillTau for modeling several signaling network functions, and for fitting complicated signaling networks.

Relationship Between mTOR Signaling Activation and Postoperative Neurocognitive Disorder in Aged Rats

BACKGROUND

Although incidence rates of postoperative neurocognitive disorder (PND) in aged individuals following noncardiac major surgery are rising as individuals are living longer, the mechanism of PND remains poorly understood. We wondered if mammalian target of rapamycin (mTOR) signaling might be associated with PND since mTOR controls some essential intracellular events.

OBJECTIVE

To investigate whether surgery activates the mTOR signaling pathway in aged rats, leading to PND, and whether the mTOR inhibitor, rapamycin, can be used to alleviate PND.

METHODS

We randomly assigned aged rats to four groups: normal control (C), isoflurane (I), surgery (S), and rapamycin (R). Then, we anesthetized Groups I, S, and R, following which, Groups S and R underwent a splenectomy. After surgery, Group R was administered rapamycin. We used the Morris water maze to test the rats' spatial learning and memory after surgery.

RESULTS

In Group S, escape latency (ie, the time to find the platform) was markedly higher, and the ratio of swimming time in the target quadrant was lower, compared to the other groups. In Group R, escape latency was markedly lower as compared with Group S, and the ratio of swimming time in the target quadrant was higher.

CONCLUSIONS

Our results indicate that an altered mTOR signaling pathway after a splenectomy causes PND in aged rats, which can be alleviated by rapamycin.

Dynamic modeling of signal transduction by mTOR complexes in cancer

Signal integration has a crucial role in the cell fate decision and dysregulation of the cellular signaling pathways is a primary characteristic of cancer. As a signal integrator, mTOR shows a complex dynamical behavior which determines the cell fate at different cellular processes levels, including cell cycle progression, cell survival, cell death, metabolic reprogramming, and aging. The dynamics of the complex responses to rapamycin in cancer cells have been attributed to its differential time-dependent inhibitory effects on mTORC1 and mTORC2, the two main complexes of mTOR. Two explanations were previously provided for this phenomenon: 1-Rapamycin does not inhibit mTORC2 directly, whereas it prevents mTORC2 formation by sequestering free mTOR protein (Le Chatelier's principle). 2-Components like Phosphatidic Acid (PA) further stabilize mTORC2 compared with mTORC1. To understand the mechanism by which rapamycin differentially inhibits the mTOR complexes in the cancer cells, we present a mathematical model of rapamycin mode of action based on the first explanation, i.e., Le Chatelier's principle. Translating the interactions among components of mTORC1 and mTORC2 into a mathematical model revealed the dynamics of rapamycin action in different doses and time-intervals of rapamycin treatment. This model shows that rapamycin has stronger effects on mTORC1 compared with mTORC2, simply due to its direct interaction with free mTOR and mTORC1, but not mTORC2, without the need to consider other components that might further stabilize mTORC2. Based on our results, even when mTORC2 is less stable compared with mTORC1, it can be less inhibited by rapamycin.

Switching On Depression and Potentiation in the Cerebellum

Long-term depression (LTD) and long-term potentiation (LTP) in the cerebellum are important for motor learning. However, the signaling mechanisms controlling whether LTD or LTP is induced in response to synaptic stimulation remain obscure. Using a unified model of LTD and LTP at the cerebellar parallel fiber-Purkinje cell (PF-PC) synapse, we delineate the coordinated pre- and postsynaptic signaling that determines the direction of plasticity. We show that LTP is the default response to PF stimulation above a well-defined frequency threshold. However, if the calcium signal surpasses the threshold for CaMKII activation, then an ultrasensitive "on switch" activates an extracellular signal-regulated kinase (ERK)-based positive feedback loop that triggers LTD instead. This postsynaptic feedback loop is sustained by another, trans-synaptic, feedback loop that maintains nitric oxide production throughout LTD induction. When full depression is achieved, an automatic "off switch" inactivates the feedback loops, returning the network to its basal state and demarcating the end of the early phase of LTD.

Short-term cellular memory tunes the signaling responses of the chemokine receptor CXCR4

The chemokine receptor CXCR4 regulates fundamental processes in development, normal physiology, and diseases, including cancer. Small subpopulations of CXCR4-positive cells drive the local invasion and dissemination of malignant cells during metastasis, emphasizing the need to understand the mechanisms controlling responses at the single-cell level to receptor activation by the chemokine ligand CXCL12. Using single-cell imaging, we discovered that short-term cellular memory of changes in environmental conditions tuned CXCR4 signaling to Akt and ERK, two kinases activated by this receptor. Conditioning cells with growth stimuli before CXCL12 exposure increased the number of cells that initiated CXCR4 signaling and the amplitude of Akt and ERK activation. Data-driven, single-cell computational modeling revealed that growth factor conditioning modulated CXCR4-dependent activation of Akt and ERK by decreasing extrinsic noise (preexisting cell-to-cell differences in kinase activity) in PI3K and mTORC1. Modeling established mTORC1 as critical for tuning single-cell responses to CXCL12-CXCR4 signaling. Our single-cell model predicted how combinations of extrinsic noise in PI3K, Ras, and mTORC1 superimposed on different driver mutations in the ERK and/or Akt pathways to bias CXCR4 signaling. Computational experiments correctly predicted that selected kinase inhibitors used for cancer therapy shifted subsets of cells to states that were more permissive to CXCR4 activation, suggesting that such drugs may inadvertently potentiate pro-metastatic CXCR4 signaling. Our work establishes how changing environmental inputs modulate CXCR4 signaling in single cells and provides a framework to optimize the development and use of drugs targeting this signaling pathway.

PIP3-Phldb2 is crucial for LTP regulating synaptic NMDA and AMPA receptor density and PSD95 turnover

The essential involvement of phosphoinositides in synaptic plasticity is well-established, but incomplete knowledge of the downstream molecular entities prevents us from understanding their signalling cascades completely. Here, we determined that Phldb2, of which pleckstrin-homology domain is highly sensitive to PIP₃, functions as a phosphoinositide-signalling mediator for synaptic plasticity. BDNF application caused Phldb2 recruitment toward postsynaptic membrane in dendritic spines, whereas PI3K inhibition resulted in its reduced accumulation. Phldb2 bound to postsynaptic scaffolding molecule PSD-95 and was crucial for localization and turnover of PSD-95 in the spine. Phldb2 also bound to GluA1 and GluA2. Phldb2 was indispensable for the interaction between NMDA receptors and CaMKII, and the synaptic density of AMPA receptors. Therefore, PIP₃-responsive Phldb2 is pivotal for induction and maintenance of LTP. Memory formation was impaired in our Phldb2^−/− mice.

From membrane receptors to protein synthesis and actin cytoskeleton: Mechanisms underlying long lasting forms of synaptic plasticity

Synaptic plasticity, the activity dependent change in synaptic strength, forms the molecular foundation of learning and memory. Synaptic plasticity includes structural changes, with spines changing their size to accomodate insertion and removal of postynaptic receptors, which are correlated with functional changes. Of particular relevance for memory storage are the long lasting forms of synaptic plasticity which are protein synthesis dependent. Due to the importance of spine structural plasticity and protein synthesis, this review focuses on the signaling pathways that connect synaptic stimulation with regulation of protein synthesis and remodeling of the actin cytoskeleton. We also review computational models that implement novel aspects of molecular signaling in synaptic plasticity, such as the role of neuromodulators and spatial microdomains, as well as highlight the need for computational models that connect activation of memory kinases with spine actin dynamics.

FindSim: A Framework for Integrating Neuronal Data and Signaling Models

Current experiments touch only small but overlapping parts of very complex subcellular signaling networks in neurons. Even with modern optical reporters and pharmacological manipulations, a given experiment can only monitor and control a very small subset of the diverse, multiscale processes of neuronal signaling. We have developed FindSim (Framework for Integrating Neuronal Data and SIgnaling Models) to anchor models to structured experimental datasets. FindSim is a framework for integrating many individual electrophysiological and biochemical experiments with large, multiscale models so as to systematically refine and validate the model. We use a structured format for encoding the conditions of many standard physiological and pharmacological experiments, specifying which parts of the model are involved, and comparing experiment outcomes with model output. A database of such experiments is run against successive generations of composite cellular models to iteratively improve the model against each experiment, while retaining global model validity. We suggest that this toolchain provides a principled and scalable way to tackle model complexity and diversity of data sources.

Cancerous perturbations within the ERK, PI3K/Akt, and Wnt/β-catenin signaling network constitutively activate inter-pathway positive feedback loops

Perturbations in molecular signaling pathways are a result of genetic or epigenetic alterations, which may lead to malignant transformation of cells. Despite cellular robustness, specific genetic or epigenetic changes of any gene can trigger a cascade of failures, which result in the malfunctioning of cell signaling pathways and lead to cancer phenotypes. The extent of cellular robustness has a link with the architecture of the network such as feedback and feedforward loops. Perturbation in components within feedback loops causes a transition from a regulated to a persistently activated state and results in uncontrolled cell growth. This work represents the mathematical and quantitative modeling of ERK, PI3K/Akt, and Wnt/β-catenin signaling crosstalk to show the dynamics of signaling responses during genetic and epigenetic changes in cancer. ERK, PI3K/Akt, and Wnt/β-catenin signaling crosstalk networks include both intra and inter-pathway feedback loops which function in a controlled fashion in a healthy cell. Our results show that cancerous perturbations of components such as EGFR, Ras, B-Raf, PTEN, and components of the destruction complex cause extreme fragility in the network and constitutively activate inter-pathway positive feedback loops. We observed that the aberrant signaling response due to the failure of specific network components is transmitted throughout the network via crosstalk, generating an additive effect on cancer growth and proliferation.

Dynamic modelling of the mTOR signalling network reveals complex emergent behaviours conferred by DEPTOR

The mechanistic Target of Rapamycin (mTOR) signalling network is an evolutionarily conserved network that controls key cellular processes, including cell growth and metabolism. Consisting of the major kinase complexes mTOR Complex 1 and 2 (mTORC1/2), the mTOR network harbours complex interactions and feedback loops. The DEP domain-containing mTOR-interacting protein (DEPTOR) was recently identified as an endogenous inhibitor of both mTORC1 and 2 through direct interactions, and is in turn degraded by mTORC1/2, adding an extra layer of complexity to the mTOR network. Yet, the dynamic properties of the DEPTOR-mTOR network and the roles of DEPTOR in coordinating mTORC1/2 activation dynamics have not been characterised. Using computational modelling, systems analysis and dynamic simulations we show that DEPTOR confers remarkably rich and complex dynamic behaviours to mTOR signalling, including abrupt, bistable switches, oscillations and co-existing bistable/oscillatory responses. Transitions between these distinct modes of behaviour are enabled by modulating DEPTOR expression alone. We characterise the governing conditions for the observed dynamics by elucidating the network in its vast multi-dimensional parameter space, and develop strategies to identify core network design motifs underlying these dynamics. Our findings provide new systems-level insights into the complexity of mTOR signalling contributed by DEPTOR.

Understanding the mTOR signaling pathway via mathematical modeling

The mechanistic target of rapamycin (mTOR) is a central regulatory pathway that integrates a variety of environmental cues to control cellular growth and homeostasis by intricate molecular feedbacks. In spite of extensive knowledge about its components, the molecular understanding of how these function together in space and time remains poor and there is a need for Systems Biology approaches to perform systematic analyses. In this work, we review the recent progress how the combined efforts of mathematical models and quantitative experiments shed new light on our understanding of the mTOR signaling pathway. In particular, we discuss the modeling concepts applied in mTOR signaling, the role of multiple feedbacks and the crosstalk mechanisms of mTOR with other signaling pathways. We also discuss the contribution of principles from information and network theory that have been successfully applied in dissecting design principles of the mTOR signaling network. We finally propose to classify the mTOR models in terms of the time scale and network complexity, and outline the importance of the classification toward the development of highly comprehensive and predictive models. WIREs Syst Biol Med 2017, 9:e1379. doi: 10.1002/wsbm.1379 For further resources related to this article, please visit the WIREs website.

In SilicoModel-driven Assessment of the Effects of Brain-derived Neurotrophic Factor Deficiency on Glutamate and Gamma-Aminobutyric Acid: Implications for Understanding Schizophrenia Pathophysiology

Objective

Deficient brain-derived neurotrophic factor (BDNF) is one of the important mechanisms underlying the neuroplasticity abnormalities in schizophrenia. Aberration in BDNF signaling pathways directly or circuitously influences neurotransmitters like glutamate and gamma-aminobutyric acid (GABA). For the first time, this study attempts to construct and simulate the BDNF-neurotransmitter network in order to assess the effects of BDNF deficiency on glutamate and GABA.

Methods

Using CellDesigner, we modeled BDNF interactions with calcium influx via N-methyl-D-aspartate receptor (NMDAR)- Calmodulin activation; synthesis of GABA via cell cycle regulators protein kinase B, glycogen synthase kinase and β-catenin; transportation of glutamate and GABA. Steady state stability, perturbation time-course simulation and sensitivity analysis were performed in COPASI after assigning the kinetic functions, optimizing the unknown parameters using random search and genetic algorithm.

Results

Study observations suggest that increased glutamate in hippocampus, similar to that seen in schizophrenia, could potentially be contributed by indirect pathway originated from BDNF. Deficient BDNF could suppress Glutamate decarboxylase 67-mediated GABA synthesis. Further, deficient BDNF corresponded to impaired transport via vesicular glutamate transporter, thereby further increasing the intracellular glutamate in GABAergic and glutamatergic cells. BDNF also altered calcium dependent neuroplasticity via NMDAR modulation. Sensitivity analysis showed that Calmodulin, cAMP response element-binding protein (CREB) and CREB regulated transcription coactivator-1 played significant role in this network.

Conclusion

The study presents in silicoquantitative model of biochemical network constituting the key signaling molecules implicated in schizophrenia pathogenesis. It provides mechanistic insights into putative contribution of deficient BNDF towards alterations in neurotransmitters and neuroplasticity that are consistent with current understanding of the disorder.

A systems study reveals concurrent activation of AMPK and mTOR by amino acids

Amino acids (aa) are not only building blocks for proteins, but also signalling molecules, with the mammalian target of rapamycin complex 1 (mTORC1) acting as a key mediator. However, little is known about whether aa, independently of mTORC1, activate other kinases of the mTOR signalling network. To delineate aa-stimulated mTOR network dynamics, we here combine a computational–experimental approach with text mining-enhanced quantitative proteomics. We report that AMP-activated protein kinase (AMPK), phosphatidylinositide 3-kinase (PI3K) and mTOR complex 2 (mTORC2) are acutely activated by aa-readdition in an mTORC1-independent manner. AMPK activation by aa is mediated by Ca²⁺/calmodulin-dependent protein kinase kinase β (CaMKKβ). In response, AMPK impinges on the autophagy regulators Unc-51-like kinase-1 (ULK1) and c-Jun. AMPK is widely recognized as an mTORC1 antagonist that is activated by starvation. We find that aa acutely activate AMPK concurrently with mTOR. We show that AMPK under aa sufficiency acts to sustain autophagy. This may be required to maintain protein homoeostasis and deliver metabolite intermediates for biosynthetic processes.

mTORC1 is known to mediate the signalling activity of amino acids. Here, the authors combine modelling with experiments and find that amino acids acutely stimulate mTORC2, IRS/PI3K and AMPK, independently of mTORC1. AMPK activation through CaMKKβ sustains autophagy under non-starvation conditions.

Computational model of a positive BDNF feedback loop in hippocampal neurons following inhibitory avoidance training

Inhibitory avoidance (IA) training in rodents initiates a molecular cascade within hippocampal neurons. This cascade contributes to the transition of short- to long-term memory (i.e., consolidation). Here, a differential equation-based model was developed to describe a positive feedback loop within this molecular cascade. The feedback loop begins with an IA-induced release of brain-derived neurotrophic factor (BDNF), which in turn leads to rapid phosphorylation of the cAMP response element-binding protein (pCREB), and a subsequent increase in the level of the β isoform of the CCAAT/enhancer binding protein (C/EBPβ). Increased levels of C/EBPβ lead to increased bdnf expression. Simulations predicted that an empirically observed delay in the BDNF-pCREB-C/EBPβ feedback loop has a profound effect on the dynamics of consolidation. The model also predicted that at least two independent self-sustaining signaling pathways downstream from the BDNF-pCREB-C/EBPβ feedback loop contribute to consolidation. Currently, the nature of these downstream pathways is unknown.

Systems Biology of Immunomodulation for Post-Stroke Neuroplasticity: Multimodal Implications of Pharmacotherapy and Neurorehabilitation

AIMS

Recent studies indicate that anti-inflammatory drugs, act as a double-edged sword, not only exacerbating secondary brain injury but also contributing to neurological recovery after stroke. Our aim is to explore whether there is a beneficial role for neuroprotection and functional recovery using anti-inflammatory drug along with neurorehabilitation therapy using transcranial direct current stimulation (tDCS) and repetitive transcranial magnetic stimulation (rTMS), so as to improve functional recovery after ischemic stroke.

METHODS

We develop a computational systems biology approach from preclinical data, using ordinary differential equations, to study the behavior of both phenotypes of microglia, such as M1 type (pro-inflammatory) vis-à-vis M2 type (anti-inflammatory) under anti-inflammatory drug action (minocycline). We explore whether pharmacological treatment along with cerebral stimulation using tDCS and rTMS is beneficial or not. We utilize the systems pathway analysis of minocycline in nuclear factor kappa beta (NF-κB) signaling and neurorehabilitation therapy using tDCS and rTMS that act through brain-derived neurotrophic factor (BDNF) and tropomyosin-related kinase B (TrkB) signaling pathways.

RESULTS

We demarcate the role of neuroinflammation and immunomodulation in post-stroke recovery, under minocycline activated-microglia and neuroprotection together with improved neurogenesis, synaptogenesis, and functional recovery under the action of rTMS or tDCS. We elucidate the feasibility of utilizing rTMS/tDCS to increase neuroprotection across the reperfusion stage during minocycline administration. We delineate that the signaling pathways of minocycline by modulation of inflammatory genes in NF-κB and proteins activated by tDCS and rTMS through BDNF, TrkB, and calmodulin kinase (CaMK) signaling. Utilizing systems biology approach, we show that the activation pathways for pharmacotherapy (minocycline) and neurorehabilitation (rTMS applied to ipsilesional cortex and tDCS) results into increased neuronal and synaptic activity that commonly occur through activation of N-methyl-d-aspartate receptors. We construe that considerable additive neuroprotection effect would be obtained and delayed reperfusion injury can be remedied, if one uses multimodal intervention of minocycline together with tDCS and rTMS.

CONCLUSION

Additive beneficial effect is, thus, noticed for pharmacotherapy along with neurorehabilitation therapy, by maneuvering the dynamics of immunomodulation using anti-inflammatory drug and cerebral stimulation for augmenting the functional recovery after stroke, which may engender clinical applicability for enhancing plasticity, rehabilitation, and neurorestoration.

Enabling surface dependent diffusion in spatial simulations using Smoldyn

Background

Spatial computer simulations are becoming more feasible and relevant for studies of signaling pathways due to technical advances in experimental techniques yielding better high resolution data. However, many common single particle simulation environments used in computational systems biology lack the functionality to easily implement spatially heterogeneous membrane environments.

Results

We introduce an extension to the single particle simulator Smoldyn that allows modeling of surface-dependent diffusion, without unnecessarily increasing molecular states or numbers, hence avoiding explosion of molecule and reaction definitions.

Conclusions

We demonstrate the usefulness of this approach studying AMPA receptor diffusion at the postsynaptic density and its spatial trapping without introducing hypothetical scaffold elements or membrane barriers.

Electronic supplementary material

The online version of this article (doi:10.1186/s13104-015-1723-6) contains supplementary material, which is available to authorized users.

Transcription control pathways decode patterned synaptic inputs into diverse mRNA expression profiles

Synaptic plasticity requires transcription and translation to establish long-term changes that form the basis for long term memory. Diverse stimuli, such as synaptic activity and growth factors, trigger synthesis of mRNA to regulate changes at the synapse. The palette of possible mRNAs is vast, and a key question is how the cell selects which mRNAs to synthesize. To address this molecular decision-making, we have developed a biochemically detailed model of synaptic-activity triggered mRNA synthesis. We find that there are distinct time-courses and amplitudes of different branches of the mRNA regulatory signaling pathways, which carry out pattern-selective combinatorial decoding of stimulus patterns into distinct mRNA subtypes. Distinct, simultaneously arriving input patterns that impinge on the transcriptional control network interact nonlinearly to generate novel mRNA combinations. Our model combines major regulatory pathways and their interactions connecting synaptic input to mRNA synthesis. We parameterized and validated the model by incorporating data from multiple published experiments. The model replicates outcomes of knockout experiments. We suggest that the pattern-selectivity mechanisms analyzed in this model may act in many cell types to confer the capability to decode temporal patterns into combinatorial mRNA expression.

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.

Approaches and tools for modeling signaling pathways and calcium dynamics in neurons

Signaling pathways are cascades of intracellular biochemical reactions that are activated by transmembrane receptors, and ultimately lead to transcription in the nucleus. In neurons, both calcium permeable synaptic and ionic channels as well as G protein coupled receptors initiate activation of signaling pathway molecules that interact with electrical activity at multiple spatial and time scales. At small temporal and spatial scales, calcium modifies the properties of ionic channels, whereas at larger temporal and spatial scales, various kinases and phosphatases modify the properties of ionic channels, producing phenomena such as synaptic plasticity and homeostatic plasticity. The elongated structure of neuronal dendrites and the organization of multi-protein complexes by anchoring proteins imply that the spatial dimension must be explicit. Therefore, modeling signaling pathways in neurons utilizes algorithms for both diffusion and reactions. The small size of spines coupled with small concentrations of some molecules implies that some reactions occur stochastically. The need for stochastic simulation of many reaction and diffusion events coupled with the multiple temporal and spatial scales makes modeling of signaling pathways a difficult problem. Several different software programs have achieved different aspects of these capabilities. This review explains some of the mathematical formulas used for modeling reactions and diffusion. In addition, it briefly presents the simulators used for modeling reaction-diffusion systems in neurons, together with scientific problems addressed.

Molecular mechanisms underlying neuronal synaptic plasticity: systems biology meets computational neuroscience in the wilds of synaptic plasticity

Interactions among signaling pathways that are activated by transmembrane receptors produce complex networks and emergent dynamical behaviors that are implicated in synaptic plasticity. Temporal dynamics and spatial aspects are critical determinants of cell responses such as synaptic plasticity, although the mapping between spatiotemporal activity pattern and direction of synaptic plasticity is not completely understood. Computational modeling of neuronal signaling pathways has significantly contributed to understanding signaling pathways underlying synaptic plasticity. Spatial models of signaling pathways in hippocampal neurons have revealed mechanisms underlying the spatial distribution of extracellular signal-related kinase (ERK) activation in hippocampal neurons. Other spatial models have demonstrated that the major role of anchoring proteins in striatal and hippocampal synaptic plasticity is to place molecules near their activators. Simulations of yet other models have revealed that the spatial distribution of synaptic plasticity may differ for potentiation versus depression. In general, the most significant advances have been made by interactive modeling and experiments; thus, an interdisciplinary approach should be applied to investigate critical issues in neuronal signaling pathways. These issues include identifying which transmembrane receptors are key for activating ERK in neurons, and the crucial targets of kinases that produce long-lasting synaptic plasticity. Although the number of computer programs for computationally efficient simulation of large reaction-diffusion networks is increasing, parameter estimation and sensitivity analysis in these spatial models remain more difficult than in single compartment models. Advances in live cell imaging coupled with further software development will continue to accelerate the development of spatial models of synaptic plasticity.

Computational modelling of the regulation of Insulin signalling by oxidative stress

Background

Existing models of insulin signalling focus on short term dynamics, rather than the longer term dynamics necessary to understand many physiologically relevant behaviours. We have developed a model of insulin signalling in rodent adipocytes that includes both transcriptional feedback through the Forkhead box type O (FOXO) transcription factor, and interaction with oxidative stress, in addition to the core pathway. In the model Reactive Oxygen Species are both generated endogenously and can be applied externally. They regulate signalling though inhibition of phosphatases and induction of the activity of Stress Activated Protein Kinases, which themselves modulate feedbacks to insulin signalling and FOXO.

Results

Insulin and oxidative stress combined produce a lower degree of activation of insulin signalling than insulin alone. Fasting (nutrient withdrawal) and weak oxidative stress upregulate antioxidant defences while stronger oxidative stress leads to a short term activation of insulin signalling but if prolonged can have other effects including degradation of the insulin receptor substrate (IRS1) and FOXO. At high insulin the protective effect of moderate oxidative stress may disappear.

Conclusion

Our model is consistent with a wide range of experimental data, some of which is difficult to explain. Oxidative stress can have effects that are both up- and down-regulatory on insulin signalling. Our model therefore shows the complexity of the interaction between the two pathways and highlights the need for such integrated computational models to give insight into the dysregulation of insulin signalling along with more data at the individual level.

A complete SBML model file can be downloaded from BIOMODELS (https://www.ebi.ac.uk/biomodels-main) with unique identifier MODEL1212210000.

Other files and scripts are available as additional files with this journal article and can be downloaded from https://github.com/graham1034/Smith2012_insulin_signalling.

A modelling-experimental approach reveals insulin receptor substrate (IRS)-dependent regulation of adenosine monosphosphate-dependent kinase (AMPK) by insulin

Mammalian target of rapamycin (mTOR) kinase responds to growth factors, nutrients and cellular energy status and is a central controller of cellular growth. mTOR exists in two multiprotein complexes that are embedded into a complex signalling network. Adenosine monophosphate-dependent kinase (AMPK) is activated by energy deprivation and shuts off adenosine 5'-triphosphate (ATP)-consuming anabolic processes, in part via the inactivation of mTORC1. Surprisingly, we observed that AMPK not only responds to energy deprivation but can also be activated by insulin, and is further induced in mTORC1-deficient cells. We have recently modelled the mTOR network, covering both mTOR complexes and their insulin and nutrient inputs. In the present study we extended the network by an AMPK module to generate the to date most comprehensive data-driven dynamic AMPK-mTOR network model. In order to define the intersection via which AMPK is activated by the insulin network, we compared simulations for six different hypothetical model structures to our observed AMPK dynamics. Hypotheses ranking suggested that the most probable intersection between insulin and AMPK was the insulin receptor substrate (IRS) and that the effects of canonical IRS downstream cues on AMPK would be mediated via an mTORC1-driven negative-feedback loop. We tested these predictions experimentally in multiple set-ups, where we inhibited or induced players along the insulin-mTORC1 signalling axis and observed AMPK induction or inhibition. We confirmed the identified model and therefore report a novel connection within the insulin-mTOR-AMPK network: we conclude that AMPK is positively regulated by IRS and can be inhibited via the negative-feedback loop.

A dynamic network model of mTOR signaling reveals TSC-independent mTORC2 regulation

The kinase mammalian target of rapamycin (mTOR) exists in two multiprotein complexes (mTORC1 and mTORC2) and is a central regulator of growth and metabolism. Insulin activation of mTORC1, mediated by phosphoinositide 3-kinase (PI3K), Akt, and the inhibitory tuberous sclerosis complex 1/2 (TSC1-TSC2), initiates a negative feedback loop that ultimately inhibits PI3K. We present a data-driven dynamic insulin-mTOR network model that integrates the entire core network and used this model to investigate the less well understood mechanisms by which insulin regulates mTORC2. By analyzing the effects of perturbations targeting several levels within the network in silico and experimentally, we found that, in contrast to current hypotheses, the TSC1-TSC2 complex was not a direct or indirect (acting through the negative feedback loop) regulator of mTORC2. Although mTORC2 activation required active PI3K, this was not affected by the negative feedback loop. Therefore, we propose an mTORC2 activation pathway through a PI3K variant that is insensitive to the negative feedback loop that regulates mTORC1. This putative pathway predicts that mTORC2 would be refractory to Akt, which inhibits TSC1-TSC2, and, indeed, we found that mTORC2 was insensitive to constitutive Akt activation in several cell types. Our results suggest that a previously unknown network structure connects mTORC2 to its upstream cues and clarifies which molecular connectors contribute to mTORC2 activation.

The protein kinase Mζ network as a bistable switch to store neuronal memory

Background

Protein kinase Mζ (PKMζ), the brain-specific, atypical protein kinase C isoform, plays a key role in long-term maintenance of memory. This molecule is essential for long-term potentiation of the neuron and various modalities of learning such as spatial memory and fear conditioning. It is unknown, however, how PKMζ stores information for long periods of time despite molecular turnover.

Results

We hypothesized that PKMζ forms a bistable switch because it appears to constitute a positive feedback loop (PKMζ induces its local synthesis) part of which is ultrasensitive (PKMζ stimulates its synthesis through dual pathways). To examine this hypothesis, we modeled the biochemical network of PKMζ with realistic kinetic parameters. Bifurcation analyses of the model showed that the system maintains either the up state or the down state according to previous inputs. Furthermore, the model was able to reproduce a variety of previous experimental results regarding synaptic plasticity and learning, which suggested that it captures the essential mechanism for neuronal memory. We proposed in vitro and in vivo experiments that would critically examine the validity of the model and illuminate the pivotal role of PKMζ in synaptic plasticity and learning.

Conclusions

This study revealed bistability of the PKMζ network and supported its pivotal role in long-term storage of memory.

Postsynaptic signal transduction models for long-term potentiation and depression

More than a hundred biochemical species, activated by neurotransmitters binding to transmembrane receptors, are important in long-term potentiation (LTP) and long-term depression (LTD). To investigate which species and interactions are critical for synaptic plasticity, many computational postsynaptic signal transduction models have been developed. The models range from simple models with a single reversible reaction to detailed models with several hundred kinetic reactions. In this study, more than a hundred models are reviewed, and their features are compared and contrasted so that similarities and differences are more readily apparent. The models are classified according to the type of synaptic plasticity that is modeled (LTP or LTD) and whether they include diffusion or electrophysiological phenomena. Other characteristics that discriminate the models include the phase of synaptic plasticity modeled (induction, expression, or maintenance) and the simulation method used (deterministic or stochastic). We find that models are becoming increasingly sophisticated, by including stochastic properties, integrating with electrophysiological properties of entire neurons, or incorporating diffusion of signaling molecules. Simpler models continue to be developed because they are computationally efficient and allow theoretical analysis. The more complex models permit investigation of mechanisms underlying specific properties and experimental verification of model predictions. Nonetheless, it is difficult to fully comprehend the evolution of these models because (1) several models are not described in detail in the publications, (2) only a few models are provided in existing model databases, and (3) comparison to previous models is lacking. We conclude that the value of these models for understanding molecular mechanisms of synaptic plasticity is increasing and will be enhanced further with more complete descriptions and sharing of the published models.

BDNF activates mTOR to regulate GluR1 expression required for memory formation

BACKGROUND

The mammalian target of Rapamycin (mTOR) kinase plays a key role in translational control of a subset of mRNAs through regulation of its initiation step. In neurons, mTOR is present at the synaptic region, where it modulates the activity-dependent expression of locally-translated proteins independently of mRNA synthesis. Indeed, mTOR is necessary for different forms of synaptic plasticity and long-term memory (LTM) formation. However, little is known about the time course of mTOR activation and the extracellular signals governing this process or the identity of the proteins whose translation is regulated by this kinase, during mnemonic processing.

METHODOLOGY/PRINCIPAL FINDINGS

Here we show that consolidation of inhibitory avoidance (IA) LTM entails mTOR activation in the dorsal hippocampus at the moment of and 3 h after training and is associated with a rapid and rapamycin-sensitive increase in AMPA receptor GluR1 subunit expression, which was also blocked by intra-hippocampal delivery of GluR1 antisense oligonucleotides (ASO). In addition, we found that pre- or post-training administration of function-blocking anti-BDNF antibodies into dorsal CA1 hampered IA LTM retention, abolished the learning-induced biphasic activation of mTOR and its readout, p70S6K and blocked GluR1 expression, indicating that BDNF is an upstream factor controlling mTOR signaling during fear-memory consolidation. Interestingly, BDNF ASO hindered LTM retention only when given into dorsal CA1 1 h after but not 2 h before training, suggesting that BDNF controls the biphasic requirement of mTOR during LTM consolidation through different mechanisms: an early one involving BDNF already available at the moment of training, and a late one, happening around 3 h post-training that needs de novo synthesis of this neurotrophin.

CONCLUSIONS/SIGNIFICANCE

IN CONCLUSION, OUR FINDINGS DEMONSTRATE THAT: 1) mTOR-mediated mRNA translation is required for memory consolidation during at least two restricted time windows; 2) this kinase acts downstream BDNF in the hippocampus and; 3) it controls the increase of synaptic GluR1 necessary for memory consolidation.