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A compressed sensing perspective of hippocampal function.

Petrantonakis PC, Poirazi P - Front Syst Neurosci (2014)

Bottom Line: Input from the cortex passes through convergent axon pathways to the downstream hippocampal subregions and, after being appropriately processed, is fanned out back to the cortex.In this work, hippocampus related regions and their respective circuitry are presented as a CS-based system whose different components collaborate to realize efficient memory encoding and decoding processes.This proposition introduces a unifying mathematical framework for hippocampal function and opens new avenues for exploring coding and decoding strategies in the brain.

View Article: PubMed Central - PubMed

Affiliation: Computational Biology Lab, Institute of Molecular Biology and Biotechnology, Foundation for Research and Technology-Hellas Heraklion, Greece.

ABSTRACT
Hippocampus is one of the most important information processing units in the brain. Input from the cortex passes through convergent axon pathways to the downstream hippocampal subregions and, after being appropriately processed, is fanned out back to the cortex. Here, we review evidence of the hypothesis that information flow and processing in the hippocampus complies with the principles of Compressed Sensing (CS). The CS theory comprises a mathematical framework that describes how and under which conditions, restricted sampling of information (data set) can lead to condensed, yet concise, forms of the initial, subsampled information entity (i.e., of the original data set). In this work, hippocampus related regions and their respective circuitry are presented as a CS-based system whose different components collaborate to realize efficient memory encoding and decoding processes. This proposition introduces a unifying mathematical framework for hippocampal function and opens new avenues for exploring coding and decoding strategies in the brain.

No MeSH data available.


Related in: MedlinePlus

Processing scheme in hippocampus according to the CS theory. (A) The EC input causes the firing of a population of granule cells in DG (filled red cycles) and a subthreshold depolarization of a subset of CA3 pyramidal cells (empty green cycles). Source of excitation and corresponding activity are depicted with the same colors. Excited cells are depicted by filled cycles. Colored empty cycles represent near-thershold cells, which are depolarized but not active. Black cycles represent cells at rest. (B) In CA3, excited cells, the ones excited after the subthreshold depolarization and the ones directly excited by mossy fibers (filled red cycles in CA3), constitute the joint contribution of EC (matrix A) and DG (x′) to CA3 activation (Ax′). The noisy subset y′ of neurons is expressed by the subthreshold depolarized cells (green cycles in CA3). (C) The error term produced in CA3 (‖Ax′ ‒ y′‖L2) is fed back to DG in order to participate in the L1 minimization algorithm taking place in DG. DG's activity leads to the sparsest population (min ‖ x′‖L1) that meets the demands of the contextual information (green empty cycles in CA3) from which current activity of CA3 (filled cycles) diverges. (D) The algorithm evolves with the incorporation of the sparser projection from DG to CA3 causing a new Ax′ activity in CA3 (filled cycles).
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Figure 5: Processing scheme in hippocampus according to the CS theory. (A) The EC input causes the firing of a population of granule cells in DG (filled red cycles) and a subthreshold depolarization of a subset of CA3 pyramidal cells (empty green cycles). Source of excitation and corresponding activity are depicted with the same colors. Excited cells are depicted by filled cycles. Colored empty cycles represent near-thershold cells, which are depolarized but not active. Black cycles represent cells at rest. (B) In CA3, excited cells, the ones excited after the subthreshold depolarization and the ones directly excited by mossy fibers (filled red cycles in CA3), constitute the joint contribution of EC (matrix A) and DG (x′) to CA3 activation (Ax′). The noisy subset y′ of neurons is expressed by the subthreshold depolarized cells (green cycles in CA3). (C) The error term produced in CA3 (‖Ax′ ‒ y′‖L2) is fed back to DG in order to participate in the L1 minimization algorithm taking place in DG. DG's activity leads to the sparsest population (min ‖ x′‖L1) that meets the demands of the contextual information (green empty cycles in CA3) from which current activity of CA3 (filled cycles) diverges. (D) The algorithm evolves with the incorporation of the sparser projection from DG to CA3 causing a new Ax′ activity in CA3 (filled cycles).

Mentions: Figure 5 summarizes the different storage steps according to the L1 minimization concept. The reasoning adopted here is actually an enhanced version of the context-based model of episodic memory formation proposed by John Lisman (Lisman, 1999). Assume that the EC input to DG and CA3 via the perforant path causes the firing of a population of granule cells and a subthreshold depolarization of a subset of CA3 pyramidal cells (Figure 5A). Information conveyed to CA3 can be differentiated from that sent to DG. It is assumed to deliver contextual content that is not expressed by the explicit firing of the CA3 cells, but by the positively biased potential of the forthcoming excitation through the mossy fiber afferents (Lisman, 1999). Then, apart from the excitation of the positively biased pyramidal cells in CA3 (Figure 5B, green cycles), other CA3 cells may also fire due to the strong mossy fiber connections (Henze et al., 2002). These cells, the ones excited after the subthreshold depolarization and the directly excited ones, constitute the joint contribution of EC (matrix A) and DG (x′, where x′ is just an estimation of signal x) to CA3 activation. The noisy subset y′ of neurons (conceptually described in Figure 1B) is expressed by the subthreshold depolarized cells (green cycles, Figure 5A). Thus, the divergence of the joint EC-DG (Ax′) effect on CA3 from the subthreshold activated CA3 population (y′) stands for the error minimization term described by the second part of equation (Equation 3), i.e., ‖Ax′ − y′‖L2 ≤ ε.


A compressed sensing perspective of hippocampal function.

Petrantonakis PC, Poirazi P - Front Syst Neurosci (2014)

Processing scheme in hippocampus according to the CS theory. (A) The EC input causes the firing of a population of granule cells in DG (filled red cycles) and a subthreshold depolarization of a subset of CA3 pyramidal cells (empty green cycles). Source of excitation and corresponding activity are depicted with the same colors. Excited cells are depicted by filled cycles. Colored empty cycles represent near-thershold cells, which are depolarized but not active. Black cycles represent cells at rest. (B) In CA3, excited cells, the ones excited after the subthreshold depolarization and the ones directly excited by mossy fibers (filled red cycles in CA3), constitute the joint contribution of EC (matrix A) and DG (x′) to CA3 activation (Ax′). The noisy subset y′ of neurons is expressed by the subthreshold depolarized cells (green cycles in CA3). (C) The error term produced in CA3 (‖Ax′ ‒ y′‖L2) is fed back to DG in order to participate in the L1 minimization algorithm taking place in DG. DG's activity leads to the sparsest population (min ‖ x′‖L1) that meets the demands of the contextual information (green empty cycles in CA3) from which current activity of CA3 (filled cycles) diverges. (D) The algorithm evolves with the incorporation of the sparser projection from DG to CA3 causing a new Ax′ activity in CA3 (filled cycles).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4126371&req=5

Figure 5: Processing scheme in hippocampus according to the CS theory. (A) The EC input causes the firing of a population of granule cells in DG (filled red cycles) and a subthreshold depolarization of a subset of CA3 pyramidal cells (empty green cycles). Source of excitation and corresponding activity are depicted with the same colors. Excited cells are depicted by filled cycles. Colored empty cycles represent near-thershold cells, which are depolarized but not active. Black cycles represent cells at rest. (B) In CA3, excited cells, the ones excited after the subthreshold depolarization and the ones directly excited by mossy fibers (filled red cycles in CA3), constitute the joint contribution of EC (matrix A) and DG (x′) to CA3 activation (Ax′). The noisy subset y′ of neurons is expressed by the subthreshold depolarized cells (green cycles in CA3). (C) The error term produced in CA3 (‖Ax′ ‒ y′‖L2) is fed back to DG in order to participate in the L1 minimization algorithm taking place in DG. DG's activity leads to the sparsest population (min ‖ x′‖L1) that meets the demands of the contextual information (green empty cycles in CA3) from which current activity of CA3 (filled cycles) diverges. (D) The algorithm evolves with the incorporation of the sparser projection from DG to CA3 causing a new Ax′ activity in CA3 (filled cycles).
Mentions: Figure 5 summarizes the different storage steps according to the L1 minimization concept. The reasoning adopted here is actually an enhanced version of the context-based model of episodic memory formation proposed by John Lisman (Lisman, 1999). Assume that the EC input to DG and CA3 via the perforant path causes the firing of a population of granule cells and a subthreshold depolarization of a subset of CA3 pyramidal cells (Figure 5A). Information conveyed to CA3 can be differentiated from that sent to DG. It is assumed to deliver contextual content that is not expressed by the explicit firing of the CA3 cells, but by the positively biased potential of the forthcoming excitation through the mossy fiber afferents (Lisman, 1999). Then, apart from the excitation of the positively biased pyramidal cells in CA3 (Figure 5B, green cycles), other CA3 cells may also fire due to the strong mossy fiber connections (Henze et al., 2002). These cells, the ones excited after the subthreshold depolarization and the directly excited ones, constitute the joint contribution of EC (matrix A) and DG (x′, where x′ is just an estimation of signal x) to CA3 activation. The noisy subset y′ of neurons (conceptually described in Figure 1B) is expressed by the subthreshold depolarized cells (green cycles, Figure 5A). Thus, the divergence of the joint EC-DG (Ax′) effect on CA3 from the subthreshold activated CA3 population (y′) stands for the error minimization term described by the second part of equation (Equation 3), i.e., ‖Ax′ − y′‖L2 ≤ ε.

Bottom Line: Input from the cortex passes through convergent axon pathways to the downstream hippocampal subregions and, after being appropriately processed, is fanned out back to the cortex.In this work, hippocampus related regions and their respective circuitry are presented as a CS-based system whose different components collaborate to realize efficient memory encoding and decoding processes.This proposition introduces a unifying mathematical framework for hippocampal function and opens new avenues for exploring coding and decoding strategies in the brain.

View Article: PubMed Central - PubMed

Affiliation: Computational Biology Lab, Institute of Molecular Biology and Biotechnology, Foundation for Research and Technology-Hellas Heraklion, Greece.

ABSTRACT
Hippocampus is one of the most important information processing units in the brain. Input from the cortex passes through convergent axon pathways to the downstream hippocampal subregions and, after being appropriately processed, is fanned out back to the cortex. Here, we review evidence of the hypothesis that information flow and processing in the hippocampus complies with the principles of Compressed Sensing (CS). The CS theory comprises a mathematical framework that describes how and under which conditions, restricted sampling of information (data set) can lead to condensed, yet concise, forms of the initial, subsampled information entity (i.e., of the original data set). In this work, hippocampus related regions and their respective circuitry are presented as a CS-based system whose different components collaborate to realize efficient memory encoding and decoding processes. This proposition introduces a unifying mathematical framework for hippocampal function and opens new avenues for exploring coding and decoding strategies in the brain.

No MeSH data available.


Related in: MedlinePlus