Modelling Receptor-Induced Signalling Cascades (Corticostriatal Synapses)
- The first version of the model that was used to explore how transient dopamine, acetylcholine and adenosine signals affect the striatal cAMP/PKA signalling. BioModels database: MODEL1502200000 and MODEL1502200001.
- The second version of the model was expanded to include additional signalling elements to explain the temporal aspects of long-term potentiation (LTP) in stimulus and reward association at the molecular level. BioModels database: MODEL1603270000.
- The model building workflow can be found at: https://sites.google.com/scilifelab.se/workflow/home
A list of recent and relevant publications:
- Nair et al., J Neurosci. 2015, 35(41):14017-30
- Nair et al., PLoS Comput Biol., 2016, 12(9):e1005080
The ability of neurons to form new synapses and update the communication strength of existing synapses is considered to be central to learning and memory. Various types of synapses in the central nervous system exhibit activity-dependent plasticity, i.e. their strengths are reproducibly updated in response to a combination of pre- and post-synaptic activity. These activity-dependent synaptic updates result largely from the interaction of multiple neurotransmitters/neuromodulators, receptor-induced biochemical signalling, activated in the synaptic compartments. Thus, a quantitative understanding of how extracellular neurotransmitter/neuromodulator signals are translated, into and integrated by, intracellular molecular signalling is important to understand synaptic plasticity. Various individual receptor-triggered signalling pathways involved in this process have been experimentally characterised at different synapse types, but how these pathways interact with each other and act as a whole, to produce functionally important responses, is still less clear.
Case study: Corticostriatal synapse
We took corticostriatal synapse as a case study to investigate how the extracellular signal is translated, into and integrated by, the intracellular molecular signalling. These are the synapses formed between incoming cortical neurons (typically layer 5 pyramidal neurons) and striatal medium-sized spiny projection neurons (MSNs).
Why has the corticostriatal synapse been taken as the case study?
Corticostriatal synapses are glutamatergic in nature and are known to play a crucial role in striatal physiology, which in turn is involved in important behaviours, such as reward learning and motor control. These synapses also exhibit long-term synaptic plasticity that is dependent on intracellular calcium levels, and this is considered to be a molecular substrate for reward learning. Furthermore, they are known to be particularly sensitive to neuromodulators, such as dopamine and acetylcholine. These neuromodulators mainly act via metabotropic receptors, which exert a strong influence in synaptic plasticity and are believed to be connected to behavioural aspects, such as saliency and causality in reward learning. Thus, these synapses are ideal to investigate the effect of both activity-dependent synaptic plasticity and the effect of neuromodulators on this process.
Specific questions to be addressed in the HBP with regards to intracellular signalling?
The main objective is to understand the integration of different neuromodulators and synaptic activity patterns that could produce synaptic potentiation or depression. This will mainly be achieved by synthesising a reasonably correct quantitative description of synaptic molecular signalling involved in long-term plasticity. This will be undertaken by integrating existing data from the literature and via the Neuroinformatics Platform. In addition, molecular dynamics simulations will be able to predict model parameters.
What is our specific take?
We use ordinary differential equations (ODEs) to model molecular interactions, even though more fundamental, but slower methods such as Molecular Dynamics exist. Stochastic models are also used as they explicitly model the randomness of molecular reactions. Both require huge amounts of computation time and do not always improve prediction uncertainty.
Our understanding of the system can be expressed in a graph view with fluxes between molecular compounds (vertices) and the kinetic laws which determine the precise reaction rate (on the edges). Overall, these average rate ODEs are a compromise between system size and time needed to obtain a forward solution of the model (Initial Value Problem).
Whenever geometry seems to play a significant role, we attempt to model it via compartments. At this level of granularity this does not happen very often and the kinetic laws used to model the reactions are crucial. Whenever we can, we summarise several elementary (mass action) reactions into an effective flux between two points. Even though in principle one could decompose such reactions, the decomposition has more free parameters. They contribute almost nothing to our understanding and usually cannot be uniquely determined by experimental data. In some cases, a vast number of very similar molecules can be summarised into one type of reactant with a custom reaction dynamic, which improves the usability of the model.
The reaction rate coefficients vary in magnitude and are almost always very difficult to determine. Experimental data are coarse, sparse and not fully normalised. The parameter estimation in a given case might well be an ill-posed inverse problem. We tackle this difficulty by Bayesian model analysis and sampling. This results in some predictive power despite the remaining uncertainty in the parameter space.
This set of practices is by no means unique. But, of course other approaches to modelling exist in the field of systems biology.
- Our modelling efforts were started with a focus on the cAMP/PKA signalling in MSNs because this pathway is known to be crucial for long-term potentiation (LTP) and could be affected by various neuromodulators. In the first version of the intracellular signalling model, we investigated how transient dopamine and acetylcholine signals are integrated by MSNs, and how this in turn affects the cAMP/PKA signalling. This study and the associated models were published in 2015.
- The dopamine-dependent aspect of the signalling model was further improved to incorporate more recent data in the second version of the model. This version of the model was also expanded to include additional signalling pathways, such as calcium-dependent CaMKII signalling and phosphoproteins, such as ARPP-21. This version of the model was published in 2016. This study investigated how intracellular molecular mechanisms could produce an input-interval and order-dependent integration of calcium and dopamine-dependent signalling, which has been reported in the literature. This study presented a plausible molecular basis for the eligibility trace in the simple stimulus-reward association.
- Currently, the next model update is in the process of development and is expected to be released in late 2018. This update is primarily focused on the addition of long-term depression (LTD)-related pathways, mainly endocannabinoid signalling. In this version, we will also include the interaction between LTP-related (cAMP/PKA and CaMKII) and LTD-related (endocannabinoid) pathways to investigate how different stimulus patterns result in either LTP or LTD.
- In addition to the modelling, we are also streamlining and automating different parts of the model building process. Efforts on this workflow are actively moving forward and an early release is expected by mid-2018. The goal is to develop a series of reliable tools for model handling and conversion between specific mathematical forms of the model (an executable form) and a more descriptive, general, biological model, which is separate from the simulation framework. Furthermore, we are working on more efficient tools for parameter estimation, model reduction, sensitivity analysis, model validation and prediction that are to be released under a free license in the following years.
Jeanette Hellgren Kotaleski, KTH Royal Institute of Technology, Sweden
Olivia Eriksson, KTH Royal Institute of Technology, Sweden
Anu G. Nair, KTH Royal Institute of Technology, Sweden
Parul Tewatia, KTH Royal Institute of Technology, Sweden
João Pedro Santos, KTH Royal Institute of Technology, Sweden
Andrei Kramer-Miehe, KTH Royal Institute of Technology, Sweden
Benefits to the Community
- Besides addressing specific scientific questions, important resource outputs of this project are self-contained model description files that can be readily used by the wider neuroscience community:
- All the incremental versions of the intracellular signalling models described here are made available on various public platforms in standard SBML format. They can thus be reused to study the dynamics of striatal intracellular signalling.
- The models can also be extended by adding newer components or integrated into larger signalling networks, with some minor re-parameterisation (following the workflow discussed at https://sites.google.com/scilifelab.se/workflow/home), while taking into account the existing model constraints and emergent dynamics.
- The publicly available model SBML files can be used to integrate biochemical reactions into a single cell electrical model using the neuroML framework. One can thus study the effect of neuromodulation on the different channel expressions and conductances, and thereby the neuronal firing properties.
- The input-output relation of the modelled intracellular signalling can be abstracted as plasticity rules of phenomenological synaptic models in neuronal networks.
- The resources developed in relation to the semi-automated model building process will be made publicly available and these could be used directly in future modelling exercises.