Michael Graupner

Calcium-based plasticity model explains sensitivity of synaptic changes to spike pattern, rate, and dendritic location

Multiple stimulation protocols have been found to be effective in changing synaptic efficacy by inducing long-term potentiation or depression. In many of those protocols, increases in postsynaptic calcium concentration have been shown to play a crucial role. However, it is still unclear whether and how the dynamics of the postsynaptic calcium alone determine the outcome of synaptic plasticity. Here, we propose a calcium-based model of a synapse in which potentiation and depression are activated above calcium thresholds. We show that this model gives rise to a large diversity of spike timing-dependent plasticity curves, most of which have been observed experimentally in different systems. It accounts quantitatively for plasticity outcomes evoked by protocols involving patterns with variable spike timing and firing rate in hippocampus and neocortex. Furthermore, it allows us to predict that differences in plasticity outcomes in different studies are due to differences in parameters defining the calcium dynamics. The model provides a mechanistic understanding of how various stimulation protocols provoke specific synaptic changes through the dynamics of calcium concentration and thresholds implementing in simplified fashion protein signaling cascades, leading to long-term potentiation and long-term depression. The combination of biophysical realism and analytical tractability makes it the ideal candidate to study plasticity at the synapse, neuron, and network levels.

STDP in a bistable synapse model based on CaMKII and associated signaling pathways.

The calcium/calmodulin-dependent protein kinase II (CaMKII) plays a key role in the induction of long-term postsynaptic modifications following calcium entry. Experiments suggest that these long-term synaptic changes are all-or-none switch-like events between discrete states. The biochemical network involving CaMKII and its regulating protein signaling cascade has been hypothesized to durably maintain the evoked synaptic state in the form of a bistable switch. However, it is still unclear whether experimental LTP/LTD protocols lead to corresponding transitions between the two states in realistic models of such a network. We present a detailed biochemical model of the CaMKII autophosphorylation and the protein signaling cascade governing the CaMKII dephosphorylation. As previously shown, two stable states of the CaMKII phosphorylation level exist at resting intracellular calcium concentration, and high calcium transients can switch the system from the weakly phosphorylated (DOWN) to the highly phosphorylated (UP) state of the CaMKII (similar to a LTP event). We show here that increased CaMKII dephosphorylation activity at intermediate Ca2+ concentrations can lead to switching from the UP to the DOWN state (similar to a LTD event). This can be achieved if protein phosphatase activity promoting CaMKII dephosphorylation activates at lower Ca2+ levels than kinase activity. Finally, it is shown that the CaMKII system can qualitatively reproduce results of plasticity outcomes in response to spike-timing dependent plasticity (STDP) and presynaptic stimulation protocols. This shows that the CaMKII protein network can account for both induction, through LTP/LTD-like transitions, and storage, due to its bistability, of synaptic changes.

Co-activation of VTA DA and GABA neurons mediates nicotine reinforcement

Smoking is the most important preventable cause of mortality and morbidity worldwide. This nicotine addiction is mediated through the nicotinic acetylcholine receptor (nAChR), expressed on most neurons, and also many other organs in the body. Even within the ventral tegmental area (VTA), the key brain area responsible for the reinforcing properties of all drugs of abuse, nicotine acts on several different cell types and afferents. Identifying the precise action of nicotine on this microcircuit, in vivo, is important to understand reinforcement, and finally to develop efficient smoking cessation treatments. We used a novel lentiviral system to re-express exclusively high-affinity nAChRs on either dopaminergic (DAergic) or γ-aminobutyric acid-releasing (GABAergic) neurons, or both, in the VTA. Using in vivo electrophysiology, we show that, contrary to widely accepted models, the activation of GABA neurons in the VTA plays a crucial role in the control of nicotine-elicited DAergic activity. Our results demonstrate that both positive and negative motivational values are transmitted through the dopamine (DA) neuron, but that the concerted activity of DA and GABA systems is necessary for the reinforcing actions of nicotine through burst firing of DA neurons. This work identifies the GABAergic interneuron as a potential target for smoking cessation drug development.

Mechanisms of induction and maintenance of spike-timing dependent plasticity in biophysical synapse models.

We review biophysical models of synaptic plasticity, with a focus on spike-timing dependent plasticity (STDP). The common property of the discussed models is that synaptic changes depend on the dynamics of the intracellular calcium concentration, which itself depends on pre- and postsynaptic activity. We start by discussing simple models in which plasticity changes are based directly on calcium amplitude and dynamics. We then consider models in which dynamic intracellular signaling cascades form the link between the calcium dynamics and the plasticity changes. Both mechanisms of induction of STDP (through the ability of pre/postsynaptic spikes to evoke changes in the state of the synapse) and of maintenance of the evoked changes (through bistability) are discussed.

Synaptic Input Correlations Leading to Membrane Potential Decorrelation of Spontaneous Activity in Cortex

Correlations in the spiking activity of neurons have been found in many regions of the cortex under multiple experimental conditions and are postulated to have important consequences for neural population coding. While there is a large body of extracellular data reporting correlations of various strengths, the subthreshold events underlying the origin and magnitude of signal-independent correlations (called noise or spike count correlations) are unknown. Here we investigate, using intracellular recordings, how synaptic input correlations from shared presynaptic neurons translate into membrane potential and spike-output correlations. Using a pharmacologically activated thalamocortical slice preparation, we perform simultaneous recordings from pairs of layer IV neurons in the auditory cortex of mice and measure synaptic potentials/currents, membrane potentials, and spiking outputs. We calculate cross-correlations between excitatory and inhibitory inputs to investigate correlations emerging from the network. We furthermore evaluate membrane potential correlations near resting potential to study how excitation and inhibition combine and affect spike-output correlations. We demonstrate directly that excitation is correlated with inhibition thereby partially canceling each other and resulting in weak membrane potential and spiking correlations between neurons. Our data suggest that cortical networks are set up to partially cancel correlations emerging from the connections between neurons. This active decorrelation is achieved because excitation and inhibition closely track each other. Our results suggest that the numerous shared presynaptic inputs do not automatically lead to increased spiking correlations.

Computational Approaches to the Neurobiology of Drug Addiction

To increase our understanding of drug addiction--notably its pharmacological and neurobiological determinants--researchers have begun to formulate computational models of drug self-administration. Currently, one can roughly distinguish between three classes of models which all have in common to attribute to brain dopamine signaling a key role in addiction. The first class of models contains quantitative pharmacological models that describe the influence of pharmacokinetic and pharmacodynamic factors on drug self-administration. These models fail, however, to explain how the drug self-administration behavior is acquired and how it eventually becomes rigid and compulsive with extended drug use. Models belonging to the second class circumvent some of these limitations by modeling how drug use usurps the function of dopamine in reinforcement learning and action selection. However, despite their behavioral plausibility, these latter models lack neurobiological plausibility and ignore the potential role of opponent processes in addiction. The third class of models attempts to surmount these pitfalls by providing a more realistic picture of the midbrain dopamine circuitry and of the complex action of drugs of abuse in the output of this circuitry. Here we provide a brief overview of these different models to illustrate the potential contribution of mathematical modeling to our understanding of the neurobiology of drug addiction.

Modeling nicotinic neuromodulation from global functional and network levels to nAChR based mechanisms

Neuromodulator action has received increasing attention in theoretical neuroscience. Yet models involving both neuronal populations dynamics at the circuit level and detailed receptor properties are only now being developed. Here we review recent computational approaches to neuromodulation, focusing specifically on acetylcholine (ACh) and nicotine. We discuss illustrative examples of models ranging from functional top-down to neurodynamical bottom-up. In the top-down approach, a computational theory views ACh as encoding the uncertainty expected in an environment. A different line of models accounts for neural population dynamics treating ACh as toggling neuronal networks between read-in of information and recall of memory. Building on the neurodynamics idea we discuss two models of nicotines action with increasing degree of biological realism. Both consider explicitly receptor-level mechanisms but with different scales of detail. The first is a large-scale model of nicotine-dependent modulation of dopaminergic signaling that is capable of simulating nicotine self-administration. The second is a novel approach where circuit-level neurodynamics of the ventral tegmental area (VTA) are combined with explicit models of the dynamics of specific nicotinic ACh receptor subtypes. We show how the model is constructed based on local anatomy, electrophysiology and receptor properties and provide an illustration of its potential. In particular, we show how the model can shed light on the specific mechanisms by which nicotine controls dopaminergic neurotransmission in the VTA. This model serves us to conclude that detailed accounts for neuromodulator action at the basis of behavioral and cognitive models are crucial to understand how neuromodulators mediate their functional properties.

Endogenous cholinergic inputs and local circuit mechanisms govern the phasic mesolimbic dopamine response to nicotine.

Nicotine exerts its reinforcing action by stimulating nicotinic acetylcholine receptors (nAChRs) and boosting dopamine (DA) output from the ventral tegmental area (VTA). Recent data have led to a debate about the principal pathway of nicotine action: direct stimulation of the DAergic cells through nAChR activation, or disinhibition mediated through desensitization of nAChRs on GABAergic interneurons. We use a computational model of the VTA circuitry and nAChR function to shed light on this issue. Our model illustrates that the α4β2-containing nAChRs either on DA or GABA cells can mediate the acute effects of nicotine. We account for in vitro as well as in vivo data, and predict the conditions necessary for either direct stimulation or disinhibition to be at the origin of DA activity increases. We propose key experiments to disentangle the contribution of both mechanisms. We show that the rate of endogenous acetylcholine input crucially determines the evoked DA response for both mechanisms. Together our results delineate the mechanisms by which the VTA mediates the acute rewarding properties of nicotine and suggest an acetylcholine dependence hypothesis for nicotine reinforcement.

A Theory of Plasma Membrane Calcium Pump Stimulation and Activity

The ATP-driven Plasma Membrane Calcium pump or Ca2+-ATPase (PMCA) is characterized by a high affinity for calcium and a low transport rate compared to other transmembrane calcium transport proteins. It plays a crucial role for calcium extrusion from cells. Calmodulin is an intracellular calcium buffering protein which is capable in its Ca2+ liganded form of stimulating the PMCA by increasing both the affinity to calcium and the maximum calcium transport rate. We introduce a new model of this stimulation process and derive analytical expressions for experimental observables in order to determine the model parameters on the basis of specific experiments. We furthermore develop a model for the pumping activity. The pumping description resolves the seeming contradiction of the Ca2+:ATP stoichiometry of 1:1 during a translocation step and the observation that the pump binds two calcium ions at the intracellular site. The combination of the calcium pumping and the stimulation model correctly describes PMCA function. We find that the processes of calmodulin-calcium complex attachment to the pump and of stimulation have to be separated. Other PMCA properties are discussed in the framework of the model. The presented model can serve as a tool for calcium dynamics simulations and provides the possibility to characterize different pump isoforms by different type-specific parameter sets.

Memory Maintenance in Synapses with Calcium-Based Plasticity in the Presence of Background Activity

Most models of learning and memory assume that memories are maintained in neuronal circuits by persistent synaptic modifications induced by specific patterns of pre- and postsynaptic activity. For this scenario to be viable, synaptic modifications must survive the ubiquitous ongoing activity present in neural circuits in vivo. In this paper, we investigate the time scales of memory maintenance in a calcium-based synaptic plasticity model that has been shown recently to be able to fit different experimental data-sets from hippocampal and neocortical preparations. We find that in the presence of background activity on the order of 1 Hz parameters that fit pyramidal layer 5 neocortical data lead to a very fast decay of synaptic efficacy, with time scales of minutes. We then identify two ways in which this memory time scale can be extended: (i) the extracellular calcium concentration in the experiments used to fit the model are larger than estimated concentrations in vivo. Lowering extracellular calcium concentration to in vivo levels leads to an increase in memory time scales of several orders of magnitude; (ii) adding a bistability mechanism so that each synapse has two stable states at sufficiently low background activity leads to a further boost in memory time scale, since memory decay is no longer described by an exponential decay from an initial state, but by an escape from a potential well. We argue that both features are expected to be present in synapses in vivo. These results are obtained first in a single synapse connecting two independent Poisson neurons, and then in simulations of a large network of excitatory and inhibitory integrate-and-fire neurons. Our results emphasise the need for studying plasticity at physiological extracellular calcium concentration, and highlight the role of synaptic bi- or multistability in the stability of learned synaptic structures.