Models of neural computation: Difference between revisions

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'''Models of neural computation''' are attempts to elucidate, in an abstract and mathematical fashion, the core principles that underlie information processing in biological nervous systems, or functional components thereof. This article aims to provide an overview of the most definitive models of neuro-biological computation as well as the tools commonly used to construct and analyze them.

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===Robustness===

A model is robust if it continues to produce the same computational results under variations in inputs or operating parameters introduced by noise. For example, the direction of motion as computed by a robust [[motion perception|motion detector]] would not change under small changes of [[luminance]], [[contrast (vision)|contrast]] or velocity jitter. For simple mathematical models of neuron, for example the dependence of spike patterns on signal delay is much weaker than the dependence on changes in "weights" of interneuronal connections. <ref>{{cite journal |last1=Cejnar |first1=Pavel |last2=Vyšata |first2=Oldřich |last3=Vališ |first3=Martin |last4=Procházka |first4=Aleš |title=The Complex Behaviour of a Simple Neural Oscillator Model in the Human Cortex |journal=IEEE Transactions on Neural Systems and Rehabilitation Engineering |date=2019 |volume=27 |issue=3 |pages=337–347 |doi= 10.1109/TNSRE.2018.2883618 |pmid=30507514|s2cid=54527064 }}</ref>

===Gain control===

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A '''linear''' system is one whose response in a specified unit of measure, to a set of inputs considered at once, is the sum of its responses due to the inputs considered individually.

[[Linear algebra|Linear]] systems are easier to analyze mathematically and are a persuasive assumption in many models including the McCulloch and Pitts neuron, population coding models, and the simple neurons often used in [[Artificial neural network]]s. Linearity may occur in the basic elements of a neural circuit such as the response of a postsynaptic neuron, or as an emergent property of a combination of nonlinear subcircuits.<ref name="MolnarHsueh2009">{{cite journal|last1=Molnar|first1=Alyosha|last2=Hsueh|first2=Hain-Ann|last3=Roska|first3=Botond|last4=Werblin|first4=Frank S.|title=Crossover inhibition in the retina: circuitry that compensates for nonlinear rectifying synaptic transmission|journal=Journal of Computational Neuroscience|volume=27|issue=3|year=2009|pages=569–590|issn=0929-5313|doi=10.1007/s10827-009-0170-6 | pmid = 19636690|pmc=2766457}}</ref> Though linearity is often seen as incorrect, there has been recent work suggesting it may, in fact, be biophysically plausible in some cases.<ref>{{Cite journal|last1=Singh|first1=Chandan|last2=Levy|first2=William B.|date=2017-07-13|title=A consensus layer V pyramidal neuron can sustain interpulse-interval coding|journal=PLOS ONEOne|volume=12|issue=7|pages=e0180839|doi=10.1371/journal.pone.0180839|pmid=28704450|pmc=5509228|arxiv=1609.08213|bibcode=2017PLoSO..1280839S|issn=1932-6203}}</ref><ref>{{Cite journal|last1=Cash|first1=Sydney|last2=Yuste|first2=Rafael|date=1998-01-01|title=Input Summation by Cultured Pyramidal Neurons Is Linear and Position-Independent|journal=Journal of Neuroscience|language=en|volume=18|issue=1|pages=10–15|issn=0270-6474|pmid=9412481|doi=10.1523/JNEUROSCI.18-01-00010.1998|pmc=6793421|doi-access=free}}</ref>

==Examples==

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====Cross-correlation in sound localization: Jeffress model====

According to [[Lloyd A. Jeffress|Jeffress]],<ref>{{cite journal | last1 = Jeffress | first1 = L.A. | year = 1948 | title = A place theory of sound localization | url = | journal = Journal of Comparative and Physiological Psychology | volume = 41 | issue = 1| pages = 35–39 | doi=10.1037/h0061495 | pmid=18904764}}</ref> in order to compute the ___location of a sound source in space from [[interaural time difference]]s, an auditory system relies on [[Analog delay line|delay lines]]: the induced signal from an [[ipsilateral]] auditory receptor to a particular neuron is delayed for the same time as it takes for the original sound to go in space from that ear to the other. Each postsynaptic cell is differently delayed and thus specific for a particular inter-aural time difference. This theory is equivalent to the mathematical procedure of [[cross-correlation]].

Following Fischer and Anderson,<ref>{{cite journal | last1 = Fischer | first1 = Brian J. | last2 = Anderson | first2 = Charles H. | year = 2004 | title = A computational model of sound localization in the barn owl | url = | journal = Neurocomputing | volume = 58–60 | issue = | pages = 1007–1012 | doi=10.1016/j.neucom.2004.01.159}}</ref> the response of the postsynaptic neuron to the signals from the left and right ears is given by

<math>y_{R}\left(t\right) - y_{L}\left(t\right)</math>

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====Cross-correlation for motion detection: Hassenstein–Reichardt model====

A motion detector needs to satisfy three general requirements: pair-inputs, asymmetry and nonlinearity.<ref>Borst A, Egelhaaf M., 1989. Principles of visual motion detection. "Trends in Neurosciences" 12(8):297–306</ref> The cross-correlation operation implemented asymmetrically on the responses from a pair of photoreceptors satisfies these minimal criteria, and furthermore, predicts features which have been observed in the response of neurons of the lobula plate in bi-wing insects.<ref>{{cite journal | last1 = Joesch | first1 = M. |display-authors=etal | year = 2008 | title = Response properties of motion-sensitive visual interneurons in the lobula plate of Drosophila melanogaster | url = | journal = Curr. Biol. | volume = 18 | issue = 5| pages = 368–374 | doi=10.1016/j.cub.2008.02.022| pmid = 18328703 | s2cid = 18873331 }}</ref>

The master equation for response is

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===Anti-Hebbian adaptation: spike-timing dependent plasticity===

* {{cite journal | last1 = Tzounopoulos | first1 = T | last2 = Kim | first2 = Y | last3 = Oertel | first3 = D | last4 = Trussell | first4 = LO | year = 2004 | title = Cell-specific, spike timing-dependent plasticities in the dorsal cochlear nucleus | url = | journal = Nat Neurosci | volume = 7 | issue = 7| pages = 719–725 | doi=10.1038/nn1272| pmid = 15208632 | s2cid = 17774457 }}

* {{cite journal | last1 = Roberts | first1 = Patrick D. | last2 = Portfors | first2 = Christine V. | year = 2008 | title = Design principles of sensory processing in cerebellum-like structures| doi = 10.1007/s00422-008-0217-1 | pmid = 18491162 | journal = Biological Cybernetics | volume = 98 | issue = 6| pages = 491–507 | s2cid = 14393814 }}

===Models of [[sensory-motor coupling]] ===

====Neurophysiological metronomes: neural circuits for pattern generation====

Mutually [[inhibitory]] processes are a unifying motif of all [[central pattern generator]]s. This has been demonstrated in the stomatogastric (STG) nervous system of crayfish and lobsters.<ref>Michael P. Nusbaum and Mark P. Beenhakker, A small-systems approach to motor pattern generation, Nature 417, 343–350 (16 May 2002)</ref> Two and three-cell oscillating networks based on the STG have been constructed which are amenable to mathematical analysis, and which depend in a simple way on synaptic strengths and overall activity, presumably the knobs on these things.<ref>Cristina Soto-Treviño, Kurt A. Thoroughman and Eve Marder, L. F. Abbott, 2006. Activity-dependent modification of inhibitory synapses in models of rhythmic neural networks Nature Vol 4 No 3 2102–2121</ref> The mathematics involved is the theory of [[dynamical systems]].

====Feedback and control: models of flight control in the fly====

Flight control in the fly is believed to be mediated by inputs from the visual system and also the [[halteres]], a pair of knob-like organs which measure angular velocity. Integrated computer models of ''[[Drosophila]]'', short on neuronal circuitry but based on the general guidelines given by [[control theory]] and data from the tethered flights of flies, have been constructed to investigate the details of flight control.<ref>{{cite web|url=http://strawlab.org/2011/03/23/grand-unified-fly/|title=the Grand Unified Fly (GUF) model|publisher=}}</ref><ref>http://www.mendeley.com/download/public/2464051/3652638122/d3bd7957efd2c8a011afb0687dfb6943731cb6d0/dl.pdf{{Dead link|date=April 2020 |bot=InternetArchiveBot |fix-attempted=yes }}</ref>

====Cerebellum sensory motor control====

[[Tensor network theory]] is a theory of [[cerebellum|cerebellar]] function that provides a mathematical model of the [[transformation geometry|transformation]] of sensory [[space-time]] coordinates into motor coordinates and vice versa by cerebellar [[neuronal networks]]. The theory was developed by Andras Pellionisz and [[Rodolfo Llinas]] in the 1980s as a [[geometrization]] of brain function (especially of the [[central nervous system]]) using [[tensor]]s.<ref name="Neuroscience1980-Pellionisz">{{Cite journal| author =Pellionisz, A., Llinás, R. | year =1980 | title =Tensorial Approach Toto Thethe Geometry Ofof Brain Function: Cerebellar Coordination Via A Metric Tensor | journal = Neuroscience | volume =5 | issue = 7| pages = 1125––1136 | id = | url= https://www.academia.edu/download/31409354/pellionisz_1980_cerebellar_coordination_via_a_metric_tensor_fullpaper.pdf | doi = 10.1016/0306-4522(80)90191-8 | pmid=6967569| s2cid =17303132 }}</ref><ref name="Neuroscience1985-Pellionisz">{{Cite journal| author = Pellionisz, A., Llinás, R. | year =1985 | title= Tensor Network Theory Ofof Thethe Metaorganization Ofof Functional Geometries Inin Thethe Central Nervous System | journal = Neuroscience | volume =16 | issue =2 | pages = 245–273| doi = 10.1016/0306-4522(85)90001-6 | pmid = 4080158| s2cid =10747593 }}</ref>

==Software modelling approaches and tools==

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===NEURON===

The [[Neuron (software)|NEURON]] software, developed at Duke University, is a simulation environment for modeling individual neurons and networks of neurons.<ref>{{cite web|url=http://www.neuron.yale.edu/neuron/|title=NEURON - for empirically-based simulations of neurons and networks of neurons|publisher=}}</ref> The NEURON environment is a self-contained environment allowing interface through its [[Graphical user interface|GUI]] or via scripting with [[hoc (programming language)|hoc]] or [[Python (programming language)|python]]. The NEURON simulation engine is based on a Hodgkin–Huxley type model using a Borg–Graham formulation. Several examples of models written in NEURON are available from the online database ModelDB.<ref>McDougal RA, Morse TM, Carnevale T, Marenco L, Wang R, Migliore M, Miller PL, Shepherd GM, Hines ML.

Twenty years of ModelDB and beyond: building essential modeling tools for the future of neuroscience. J Comput Neurosci. 2017; 42(1):1–10.</ref>

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{{Neuroethology}}

{{animal cognition}}

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{{DEFAULTSORT:Models Of Neural Computation}}