Imbalanced pattern completion vs. separation in cognitive disease: network simulations of synaptic pathologies predict a personalized therapeutics strategy
© Hanson and Madison; licensee BioMed Central Ltd. 2010
Received: 20 January 2010
Accepted: 13 August 2010
Published: 13 August 2010
Diverse Mouse genetic models of neurodevelopmental, neuropsychiatric, and neurodegenerative causes of impaired cognition exhibit at least four convergent points of synaptic malfunction: 1) Strength of long-term potentiation (LTP), 2) Strength of long-term depression (LTD), 3) Relative inhibition levels (Inhibition), and 4) Excitatory connectivity levels (Connectivity).
To test the hypothesis that pathological increases or decreases in these synaptic properties could underlie imbalances at the level of basic neural network function, we explored each type of malfunction in a simulation of autoassociative memory. These network simulations revealed that one impact of impairments or excesses in each of these synaptic properties is to shift the trade-off between pattern separation and pattern completion performance during memory storage and recall. Each type of synaptic pathology either pushed the network balance towards intolerable error in pattern separation or intolerable error in pattern completion. Imbalances caused by pathological impairments or excesses in LTP, LTD, inhibition, or connectivity, could all be exacerbated, or rescued, by the simultaneous modulation of any of the other three synaptic properties.
Because appropriate modulation of any of the synaptic properties could help re-balance network function, regardless of the origins of the imbalance, we propose a new strategy of personalized cognitive therapeutics guided by assay of pattern completion vs. pattern separation function. Simulated examples and testable predictions of this theorized approach to cognitive therapeutics are presented.
Key Synaptic Phenotypes in Mouse Models of Diseased Cognition
Fragile × synd.
Tsc2 KO (rat)
Diverse disease models exhibit convergent synaptic and circuit alterations
Examples of neurodevelopmental diseases that can include memory deficits, where causative genes have been identified and mouse models have been created, include Angelman syndrome, Down syndrome, Fragile × syndrome, FRAXE Syndrome, Rett Syndrome, Neurofibromatosis, Tuberous Sclerosis, and various X-linked Mental Retardations (XLMR) (Table 1, top). Transgenic mouse models have also been created that are relevant to neuropsychiatric conditions including schizophrenia, a disease where memory impairment is an important endophenotype (Table 1, middle). In addition to Alzheimer's disease, other neurodegenerative diseases often more noted for their hallmark motor symptoms, also feature important cognitive phenotypes, and mouse models of neurodegenerative conditions with memory alterations include Amyotrophic Lateral Sclerosis (ALS), Huntington's disease, Parkinson's disease, and Spinocerebellar Ataxia (SCA) (Table 1, bottom). Together, these diverse mouse models provide a comparative window into potential substrates of memory impairment. In particular reoccurring points of pathological changes include: 1) Strength of LTP, 2) Strength of LTD, 3) Relative inhibition, and 4) Connectivity levels.
Neural Network Simulation of Autoassociation
The connectivity level of the recurrent excitatory synapses was set to a given value (for example 50%; Fig.3A), which was implemented by constraining the average number of randomly selected postsynaptic target neurons for each presynaptic neuron.
LTP and LTD
In the absence of any stored memories, all potential synaptic connections were silent with no AMPA receptor (AMPAR) conductance. LTP was implemented by potentiating synapses between presynaptic and postsynaptic neurons that both fired action potentials within the time window of a single gamma cycle during pattern storage. The strength of LTP was defined by the maximal excitatory synaptic conductance variable, gMaxAMPA. LTD was implemented by depressing synapses between presynaptic neurons and postsynaptic neurons that were active during storage of different stimulus patterns within a set of simultaneously stored patterns. The parameter, γLTD, defined the strength of LTD (see methods, Fig3B). The result of these plasticity mechanisms is that as larger numbers of patterns are simultaneously stored in the network, more silent synapses are potentiated, and more of those potentiated synapses are also reduced in strength by LTD due to accumulated overlap of the stimulus patterns (Fig.3C,D).
The strength of the feedback inhibitory conductance, gGABA, received by each pyramidal neuron was set relative to the average maximal excitatory conductance received by excitatory neurons, as defined by the Inhibition Ratio variable (see methods). Thus, the strength of LTP, LTD, connectivity, and inhibition could all be varied to simulate pathological conditions or therapeutic modulation via manipulation of single variables.
Measuring Pattern Completion and Pattern Separation
Wild-type Synaptic Properties
While biologically plausible values of each synaptic property serve as a good starting point for the baseline model, the necessary simplifications of the model make it difficult to predict exact wild-type values of synaptic properties. For example, relative inhibition is specified using the ratio of GABAA receptor (GABAAR) to AMPAR conductance in each spatially reduced neuron. However the dynamics of synaptic interaction in spatially complex neurons, can enhance the ability of inhibition to oppose excitation [21, 22], suggesting amplified GABAAR to AMPAR conductance ratios may be needed in the simplified simulation. Because of such considerations, we decided to determine wild-type network parameters via an empirical assessment of storage and recall performance. To avoid focusing on a non-unique set of optimal parameters we explored network performance over a broad range of parameter space by creating a database with 960,000 combinations of parameter values (gMaxAMPA, γLTD, Relative Inhibition, and Connectivity %) and memory storage conditions (see methods). While different metrics could be used to assess network performance, we defined optimal networks based on the maximal error rate, which was calculated as the greater of pattern completion or pattern separation error rates. Using this measure, pattern completion and pattern separation errors were equal in their ability to limit network performance.
Pattern Separation and Completion with Single Synaptic Pathologies
Interaction Between Multiple Synaptic Alterations
Discussion and Conclusions
Substrates of Imbalanced Network Performance
To intuitively understand the basis of the interactions between the different points of synaptic pathology it is important to appreciate that the underlying substrates of successful pattern completion (and failed separation) necessarily converge at action potential generation, while essential to pattern separation (and failed completion) is lack of inappropriate spiking. Thus while the effects of LTP, LTD, inhibition and connectivity levels all impinge on the ability of synaptic inputs to drive output spiking, other perturbations that also effect input-output coupling will also alter the balance between completion and separation. For example, while beyond the scope of the present analysis, neuromodulatory influences that alter intrinsic excitability are also aberrant in disease states and are expected to alter pattern separation and completion functions [19, 31].
Theory of Personalized Therapeutics
That the four examined points of synaptic pathology all further converge in causing one of two distinct network imbalances provides a potential point of therapeutic intervention (Fig.8B). In particular, a pattern completion bias predicts one direction of therapeutic manipulation for each synaptic property, while a separation bias predicts therapeutic value for the opposite directions of manipulation (Fig.8C). If pattern completion vs. pattern separation performance were to be extensively evaluated in cognitive disease, two general possibilities exist: 1) Some causes of disease will consistently involve a separation bias, while other causes will always involve a completion bias, 2) Even within the same disease, the complex interaction of genetics and environment with disease progression will result in some patients with a completion bias and others with a separation bias.
Example Cross-Therapeutic Predictions for Overall Averages of Disease Populations
Disease or model
Memory rescue observed with
Other predicted targets
↑ LTP, ↑ connectivity, ↓ LTD
Down synd. mouse
↓ LTP, ↓ connectivity, ↑ LTD
Fragile × mouse
↓ Inhibition, ↓ LTD, ↑ connectivity
How pattern separation and pattern completion deficits in neural networks will read out in indirect behavioral measurements such as tests of prospective interference may be complicated, but could be determined by experiments correlating behavior and read-outs of neural network separation/completion function. However, the promise for implementing such an approach of assay-based therapeutic prescription is good, since non-invasive touchscreen-based memory tests already exist, including explicit measurement of pattern separation function, in both mouse models  and human patients [42, 43]. While higher-order processing strategies could confound behavioral read-outs of basic network functions , direct assay of autoassociative function can be performed in rodent models using recordings of neuronal ensemble activity [4–6], and has been demonstrated in humans using functional imaging . Although the current simulations focused on autoassociative function in the key region of CA3, interactions across multiple neural circuits are known to underlie cognitive behaviors like learning and memory. Nonetheless, much of the cortex is organized in recurrent circuits, and could process and store information in a sparser but analogous manner to CA3. Therefore, especially in cases contributed to by genetic disruptions with potentially widespread effects, the predicted manipulations aimed at rebalancing function could be broadly beneficial across neural networks underlying a pathologically extreme cognitive style. Ultimately tests of the types of predictions outlined in Fig.8 and detailed above, will support or refute this theorized approach of personalized cognitive therapeutics.
Network simulations were constructed using NeuroConstruct  and simulations were run using Neuron . Custom Matlab (Mathworks) scripts were used to generate stimulus pattern sets, calculate synaptic plasticity, and analyze simulation output. Each neuron was modeled as an isopotential sphere with a radius of 10 μm and had a membrane capacitance of 1.0 μF/cm2 and contained a leak conductance with Eleak = -67 mV (GLeak = 0.1 μS/cm2), and Fast Na+ (GNa = 100 μS/cm2), and Delayed Rectifier K+ (GK = 80 μS/cm2) conductances, based on a reduced model of hippocampal rhythm generation  (see Fig.2). Na+ current was calculated as: INa = GNam3h(Vm-ENa), with ENa = 90 mV, K+ current was calculated as: IK = GKn4(Vm-EK), with EK = -100. AMPA conductances of excitatory synapses had time courses described by GAMPA = exp(-t/tau2) - exp(-t/tau1), with tau1 = 1 and tau2 = 4, EAMPA = 0 mV, and GABAA conductances had time courses described by: GGABA = exp(-t/tau2)-exp(-t/tau1), with tau1 = 2 and tau2 = 8, EGABA = -80 mV. Synaptic delays were 1 ms and axonal conduction times were considered negligible.
For each simulation of a given connectivity level, three different connectivity profiles were generated using different random seeds in NeuroConstruct. The average performance of simulations using 10 different random sets of memories in each connectivity profile was calculated. Error rates are presented as mean ± SEM of the average performance in three connectivity profiles.
The weight of associational connections (W) following synaptic plasticity was determined using an adaptation of the equation used in the model of autoassociation we based our simulations on : Wij = nij11/(nij11*γ11+nij10*γ10+nij01* γ01), where nij11 is the number of patterns where presynaptic(i) and postsynaptic(j) neurons fire together, and nij10 and nij01 are the number of patterns where presynaptic or postsynaptic neurons fire independently within a set of stored patterns. For simplicity in our implementation, γ11 was set to a value of 1, and γ10 and γ01 shared the same value, γLTD. This yielded the equation; Wij= gMaxAMPA *nij11/(nij11+(nij10+nij01)*γLTD), where the normalized strength of maximal potentiation, gMaxAMPA, defines the strength of LTP, and the single parameter, γLTD, defines the strength of LTD (Fig.3B).
The strength of the excitatory synapses onto the inhibitory neuron was set to 90% of gMaxAMPA. The strength of inhibitory synaptic conductances in the network was set relative to the maximal total excitation received by a pyramidal neuron during a stimulus pattern involving 10 neurons such that: gGABA = gMaxAMPA*10*Connectivity Level*Relative Inhibition.
Parameter permutations consisting of 20 connectivity levels spaced between 5 and 100%, 20 gMaxAMPA values spaced between 2.78 and 55.56 nS, 20 logarithmically spaced Inhibition Ratio values between 0.01 and 100 (corresponding to 1.83 fold increments), and γLTD values logarithmically spaced between 0.1 and 10 (corresponding to 1.27 fold increments) were evaluated. For each of these 160,000 permutations of synaptic properties, 6 different sized pattern sets were assessed using multiple connectivity and stimulus pattern random seed conditions (see connectivity), for a total of 180 simulations per parameter combination. To facilitate the required large number of simulations, an approximation was made, based on the fact that the presence or absence of a spike in each individual neuron (which determines pattern storage or pattern completion success or failure), is determined entirely by, 1) the total excitatory conductance resulting from the properties of synaptic plasticity in the context of connectivity, and 2) the strength of inhibition. Therefore, a table of spike thresholds as a function of both total excitatory and inhibitory conductance received by a neuron was generated from a set of simulations with systematic variations in these properties. During creation of the database, pattern separation and pattern completion errors were assessed based on neuronal firing patterns determined by comparing values of total excitatory and inhibitory conductances in each neuron to the table of firing thresholds. Validation of this efficiency measure was performed by directly comparing several key parameter combinations using the threshold-table approximation with full explicit simulations. Optimal balanced networks were defined as the parameter combinations with the lowest maximal error (the higher error in either pattern separation or pattern completion), thus reflecting an even breakdown of pattern separation and completion for a given number of stored patterns.
This work was supported by grants from the National Institute of Mental Health (MH065541) and by The G. Harold and Leila Y. Mathers Charitable Foundation.
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