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Calderini M, Thivierge JP. Estimating Fisher discriminant error in a linear integrator model of neural population activity. JOURNAL OF MATHEMATICAL NEUROSCIENCE 2021; 11:6. [PMID: 33606089 PMCID: PMC7895896 DOI: 10.1186/s13408-021-00104-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/14/2020] [Accepted: 02/03/2021] [Indexed: 06/12/2023]
Abstract
Decoding approaches provide a useful means of estimating the information contained in neuronal circuits. In this work, we analyze the expected classification error of a decoder based on Fisher linear discriminant analysis. We provide expressions that relate decoding error to the specific parameters of a population model that performs linear integration of sensory input. Results show conditions that lead to beneficial and detrimental effects of noise correlation on decoding. Further, the proposed framework sheds light on the contribution of neuronal noise, highlighting cases where, counter-intuitively, increased noise may lead to improved decoding performance. Finally, we examined the impact of dynamical parameters, including neuronal leak and integration time constant, on decoding. Overall, this work presents a fruitful approach to the study of decoding using a comprehensive theoretical framework that merges dynamical parameters with estimates of readout error.
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Affiliation(s)
- Matias Calderini
- School of Psychology, University of Ottawa, 136 Jean Jacques Lussier, Ottawa, ON, K1N 6N5, Canada
| | - Jean-Philippe Thivierge
- School of Psychology, University of Ottawa, 136 Jean Jacques Lussier, Ottawa, ON, K1N 6N5, Canada.
- Brain and Mind Research Institute, University of Ottawa, Ottawa, ON, K1N 6N5, Canada.
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Radosevic M, Willumsen A, Petersen PC, Lindén H, Vestergaard M, Berg RW. Decoupling of timescales reveals sparse convergent CPG network in the adult spinal cord. Nat Commun 2019; 10:2937. [PMID: 31270315 PMCID: PMC6610135 DOI: 10.1038/s41467-019-10822-9] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2018] [Accepted: 06/04/2019] [Indexed: 12/12/2022] Open
Abstract
During the generation of rhythmic movements, most spinal neurons receive an oscillatory synaptic drive. The neuronal architecture underlying this drive is unknown, and the corresponding network size and sparseness have not yet been addressed. If the input originates from a small central pattern generator (CPG) with dense divergent connectivity, it will induce correlated input to all receiving neurons, while sparse convergent wiring will induce a weak correlation, if any. Here, we use pairwise recordings of spinal neurons to measure synaptic correlations and thus infer the wiring architecture qualitatively. A strong correlation on a slow timescale implies functional relatedness and a common source, which will also cause correlation on fast timescale due to shared synaptic connections. However, we consistently find marginal coupling between slow and fast correlations regardless of neuronal identity. This suggests either sparse convergent connectivity or a CPG network with recurrent inhibition that actively decorrelates common input.
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Affiliation(s)
- Marija Radosevic
- Department of Neuroscience, Faculty of Health and Medical Sciences, University of Copenhagen, Blegdamsvej 3, DK-2200, Copenhagen N, Denmark
| | - Alex Willumsen
- Department of Neuroscience, Faculty of Health and Medical Sciences, University of Copenhagen, Blegdamsvej 3, DK-2200, Copenhagen N, Denmark
| | - Peter C Petersen
- Department of Neuroscience, Faculty of Health and Medical Sciences, University of Copenhagen, Blegdamsvej 3, DK-2200, Copenhagen N, Denmark
- Neuroscience Institute, New York University, New York, NY, 10016, USA
| | - Henrik Lindén
- Department of Neuroscience, Faculty of Health and Medical Sciences, University of Copenhagen, Blegdamsvej 3, DK-2200, Copenhagen N, Denmark
| | - Mikkel Vestergaard
- Department of Neuroscience, Faculty of Health and Medical Sciences, University of Copenhagen, Blegdamsvej 3, DK-2200, Copenhagen N, Denmark
- Department of Neuroscience, Max Delbrück Center for Molecular Medicine (MDC), 13125, Berlin-Buch, Germany
| | - Rune W Berg
- Department of Neuroscience, Faculty of Health and Medical Sciences, University of Copenhagen, Blegdamsvej 3, DK-2200, Copenhagen N, Denmark.
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Pena RFO, Zaks MA, Roque AC. Dynamics of spontaneous activity in random networks with multiple neuron subtypes and synaptic noise : Spontaneous activity in networks with synaptic noise. J Comput Neurosci 2018; 45:1-28. [PMID: 29923159 PMCID: PMC6061197 DOI: 10.1007/s10827-018-0688-6] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2017] [Revised: 05/19/2018] [Accepted: 05/23/2018] [Indexed: 12/18/2022]
Abstract
Spontaneous cortical population activity exhibits a multitude of oscillatory patterns, which often display synchrony during slow-wave sleep or under certain anesthetics and stay asynchronous during quiet wakefulness. The mechanisms behind these cortical states and transitions among them are not completely understood. Here we study spontaneous population activity patterns in random networks of spiking neurons of mixed types modeled by Izhikevich equations. Neurons are coupled by conductance-based synapses subject to synaptic noise. We localize the population activity patterns on the parameter diagram spanned by the relative inhibitory synaptic strength and the magnitude of synaptic noise. In absence of noise, networks display transient activity patterns, either oscillatory or at constant level. The effect of noise is to turn transient patterns into persistent ones: for weak noise, all activity patterns are asynchronous non-oscillatory independently of synaptic strengths; for stronger noise, patterns have oscillatory and synchrony characteristics that depend on the relative inhibitory synaptic strength. In the region of parameter space where inhibitory synaptic strength exceeds the excitatory synaptic strength and for moderate noise magnitudes networks feature intermittent switches between oscillatory and quiescent states with characteristics similar to those of synchronous and asynchronous cortical states, respectively. We explain these oscillatory and quiescent patterns by combining a phenomenological global description of the network state with local descriptions of individual neurons in their partial phase spaces. Our results point to a bridge from events at the molecular scale of synapses to the cellular scale of individual neurons to the collective scale of neuronal populations.
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Affiliation(s)
- Rodrigo F. O. Pena
- Department of Physics, Faculty of Philosophy, Sciences and Letters of Ribeirão Preto, University of São Paulo, Ribeirão Preto, SP Brazil
| | - Michael A. Zaks
- Department of Physics, Faculty of Mathematics and Natural Sciences, Humboldt University of Berlin, Berlin, Germany
| | - Antonio C. Roque
- Department of Physics, Faculty of Philosophy, Sciences and Letters of Ribeirão Preto, University of São Paulo, Ribeirão Preto, SP Brazil
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Calderini M, Zhang S, Berberian N, Thivierge JP. Optimal Readout of Correlated Neural Activity in a Decision-Making Circuit. Neural Comput 2018; 30:1573-1611. [PMID: 29652584 DOI: 10.1162/neco_a_01083] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Abstract
The neural correlates of decision making have been extensively studied with tasks involving a choice between two alternatives that is guided by visual cues. While a large body of work argues for a role of the lateral intraparietal (LIP) region of cortex in these tasks, this role may be confounded by the interaction between LIP and other regions, including medial temporal (MT) cortex. Here, we describe a simplified linear model of decision making that is adapted to two tasks: a motion discrimination and a categorization task. We show that the distinct contribution of MT and LIP may indeed be confounded in these tasks. In particular, we argue that the motion discrimination task relies on a straightforward visuomotor mapping, which leads to redundant information between MT and LIP. The categorization task requires a more complex mapping between visual information and decision behavior, and therefore does not lead to redundancy between MT and LIP. Going further, the model predicts that noise correlations within LIP should be greater in the categorization compared to the motion discrimination task due to the presence of shared inputs from MT. The impact of these correlations on task performance is examined by analytically deriving error estimates of an optimal linear readout for shared and unique inputs. Taken together, results clarify the contribution of MT and LIP to decision making and help characterize the role of noise correlations in these regions.
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Affiliation(s)
- Matias Calderini
- Center for Neural Dynamics and School of Psychology, University of Ottawa, Ontario K1N 6N5, Canada
| | - Sophie Zhang
- Center for Neural Dynamics and School of Psychology, University of Ottawa, Ontario K1N 6N5, Canada
| | - Nareg Berberian
- Center for Neural Dynamics and School of Psychology, University of Ottawa, Ontario K1N 6N5, Canada
| | - Jean-Philippe Thivierge
- Center for Neural Dynamics and School of Psychology, University of Ottawa, Ontario K1N 6N5, Canada
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Montangie L, Montani F. Effect of interacting second- and third-order stimulus-dependent correlations on population-coding asymmetries. Phys Rev E 2016; 94:042303. [PMID: 27841584 DOI: 10.1103/physreve.94.042303] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2016] [Indexed: 06/06/2023]
Abstract
Spike correlations among neurons are widely encountered in the brain. Although models accounting for pairwise interactions have proved able to capture some of the most important features of population activity at the level of the retina, the evidence shows that pairwise neuronal correlation analysis does not resolve cooperative population dynamics by itself. By means of a series expansion for short time scales of the mutual information conveyed by a population of neurons, the information transmission can be broken down into firing rate and correlational components. In a proposed extension of this framework, we investigate the information components considering both second- and higher-order correlations. We show that the existence of a mixed stimulus-dependent correlation term defines a new scenario for the interplay between pairwise and higher-than-pairwise interactions in noise and signal correlations that would lead either to redundancy or synergy in the information-theoretic sense.
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Affiliation(s)
- Lisandro Montangie
- Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), Universidad Nacional de La Plata, CONICET CCT-La Plata, Calle 59-789, La Plata 1900, Argentina
| | - Fernando Montani
- Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), Universidad Nacional de La Plata, CONICET CCT-La Plata, Calle 59-789, La Plata 1900, Argentina
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Wagatsuma N, von der Heydt R, Niebur E. Spike synchrony generated by modulatory common input through NMDA-type synapses. J Neurophysiol 2016; 116:1418-33. [PMID: 27486111 DOI: 10.1152/jn.01142.2015] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2015] [Accepted: 06/30/2016] [Indexed: 11/22/2022] Open
Abstract
Common excitatory input to neurons increases their firing rates and the strength of the spike correlation (synchrony) between them. Little is known, however, about the synchronizing effects of modulatory common input. Here, we show that modulatory common input with the slow synaptic kinetics of N-methyl-d-aspartate (NMDA) receptors enhances firing rates and also produces synchrony. Tight synchrony (correlations on the order of milliseconds) always increases with modulatory strength. Unexpectedly, the relationship between strength of modulation and strength of loose synchrony (tens of milliseconds) is not monotonic: The strongest loose synchrony is obtained for intermediate modulatory amplitudes. This finding explains recent neurophysiological results showing that in cortical areas V1 and V2, presumed modulatory top-down input due to contour grouping increases (loose and tight) synchrony but that additional modulatory input due to top-down attention does not change tight synchrony and actually decreases loose synchrony. These neurophysiological findings are understood from our model of integrate-and-fire neurons under the assumption that contour grouping as well as attention lead to additive modulatory common input through NMDA-type synapses. In contrast, circuits with common projections through model α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors did not exhibit the paradoxical decrease of synchrony with increased input. Our results suggest that NMDA receptors play a critical role in top-down response modulation in the visual cortex.
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Affiliation(s)
- Nobuhiko Wagatsuma
- School of Science and Engineering, Tokyo Denki University, Saitama, Japan; and Zanvyl Krieger Mind/Brain Institute, Johns Hopkins University, Baltimore, Maryland
| | | | - Ernst Niebur
- Zanvyl Krieger Mind/Brain Institute, Johns Hopkins University, Baltimore, Maryland
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Yim MY, Hanuschkin A, Wolfart J. Intrinsic rescaling of granule cells restores pattern separation ability of a dentate gyrus network model during epileptic hyperexcitability. Hippocampus 2014; 25:297-308. [DOI: 10.1002/hipo.22373] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2014] [Revised: 09/29/2014] [Accepted: 09/29/2014] [Indexed: 01/12/2023]
Affiliation(s)
- Man Yi Yim
- Department of Mathematics; University of Hong Kong; Hong Kong
| | - Alexander Hanuschkin
- Institute of Neuroinformatics, University of Zurich and ETH Zurich; Zurich Switzerland
| | - Jakob Wolfart
- Oscar Langendorff Institute of Physiology, University of Rostock; Rostock Germany
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