Computational neuroscience

Computational neuroscience (also known as theoretical neuroscience or mathematical neuroscience)

is a branch of neuroscience which employs mathematical models, computer simulations, theoretical analysis
and abstractions of the brain to understand the principles that govern the development, structure, physiology
and cognitive abilities of the nervous system.[1][2][3][4]

Computational neuroscience employs computational simulations to validate and solve mathematical models,
and so can be seen as a sub-field of theoretical neuroscience; however, the two fields are often
synonymous.[5] The term mathematical neuroscience is also used sometimes, to stress the quantitative
nature of the field.[6]

Computational neuroscience focuses on the description of biologically plausible neurons (and neural
systems) and their physiology and dynamics, and it is therefore not directly concerned with biologically
unrealistic models used in connectionism, control theory, cybernetics, quantitative psychology, machine
learning, artificial neural networks, artificial intelligence and computational learning theory;[7][8] [9]
although mutual inspiration exists and sometimes there is no strict limit between fields,[10][11][12] with
model abstraction in computational neuroscience depending on research scope and the granularity at which
biological entities are analyzed.

Models in theoretical neuroscience are aimed at capturing the essential features of the biological system at
multiple spatial-temporal scales, from membrane currents, and chemical coupling via network oscillations,
columnar and topographic architecture, nuclei, all the way up to psychological faculties like memory,
learning and behavior. These computational models frame hypotheses that can be directly tested by
biological or psychological experiments.

History
The term 'computational neuroscience' was introduced by Eric L. Schwartz, who organized a conference,
held in 1985 in Carmel, California, at the request of the Systems Development Foundation to provide a
summary of the current status of a field which until that point was referred to by a variety of names, such as
neural modeling, brain theory and neural networks. The proceedings of this definitional meeting were
published in 1990 as the book Computational Neuroscience.[13] The first of the annual open international
meetings focused on Computational Neuroscience was organized by James M. Bower and John Miller in
San Francisco, California in 1989.[14] The first graduate educational program in computational
neuroscience was organized as the Computational and Neural Systems Ph.D. program at the California
Institute of Technology in 1985.

The early historical roots of the field can be traced to the work of people including Louis Lapicque,
Hodgkin & Huxley, Hubel and Wiesel, and David Marr. Lapicque introduced the integrate and fire model
of the neuron in a seminal article published in 1907,[15] a model still popular for artificial neural networks
studies because of its simplicity (see a recent review[16]).

About 40 years later, Hodgkin and Huxley developed the voltage clamp and created the first biophysical
model of the action potential. Hubel and Wiesel discovered that neurons in the primary visual cortex, the
first cortical area to process information coming from the retina, have oriented receptive fields and are
organized in columns.[17] David Marr's work focused on the interactions between neurons, suggesting
computational approaches to the study of how functional groups of neurons within the hippocampus and
neocortex interact, store, process, and transmit information. Computational modeling of biophysically
realistic neurons and dendrites began with the work of Wilfrid Rall, with the first multicompartmental
model using cable theory.

Major topics
Research in computational neuroscience can be roughly categorized into several lines of inquiry. Most
computational neuroscientists collaborate closely with experimentalists in analyzing novel data and
synthesizing new models of biological phenomena.

Single-neuron modeling

Even a single neuron has complex biophysical characteristics and can perform computations (e.g.[18]).
Hodgkin and Huxley's original model only employed two voltage-sensitive currents (Voltage sensitive ion
channels are glycoprotein molecules which extend through the lipid bilayer, allowing ions to traverse under
certain conditions through the axolemma), the fast-acting sodium and the inward-rectifying potassium.
Though successful in predicting the timing and qualitative features of the action potential, it nevertheless
failed to predict a number of important features such as adaptation and shunting. Scientists now believe that
there are a wide variety of voltage-sensitive currents, and the implications of the differing dynamics,
modulations, and sensitivity of these currents is an important topic of computational neuroscience.[19]

The computational functions of complex dendrites are also under intense investigation. There is a large
body of literature regarding how different currents interact with geometric properties of neurons.[20]

Some models are also tracking biochemical pathways at very small scales such as dendritic spines[21][22] or
synaptic clefts.[23]

There are many software packages, such as GENESIS and NEURON, that allow rapid and systematic in
silico modeling of realistic neurons. Blue Brain, a project founded by Henry Markram from the École
Polytechnique Fédérale de Lausanne, aims to construct a biophysically detailed simulation of a cortical
column on the Blue Gene supercomputer.

Modeling the richness of biophysical properties on the single-neuron scale can supply mechanisms that
serve as the building blocks for network dynamics.[24] However, detailed neuron descriptions are
computationally expensive and this computing cost can limit the pursuit of realistic network investigations,
where many neurons need to be simulated. As a result, researchers that study large neural circuits typically
represent each neuron and synapse with an artificially simple model, ignoring much of the biological detail.
Hence there is a drive to produce simplified neuron models that can retain significant biological fidelity at a
low computational overhead. Algorithms have been developed to produce faithful, faster running,
simplified surrogate neuron models from computationally expensive, detailed neuron models.[25]

Modeling Neuron-glia interactions

Glial cells participate significantly to the regulation of neuronal activity at a cellular but also at a network
level. Modeling this interaction allows to clarify the potassium cycle,[26][27] so important for maintaining
homeostatis and to prevent epileptic seizures. Modeling reveals the role of glial protrusions that can
penetrate in some cases the synaptic cleft to interfere with the synpatic transmission and thus control
synaptic communication.[28]

Development, axonal patterning, and guidance

Computational neuroscience aims to address a wide array of questions. How do axons and dendrites form
during development? How do axons know where to target and how to reach these targets? How do
neurons migrate to the proper position in the central and peripheral systems? How do synapses form? We
know from molecular biology that distinct parts of the nervous system release distinct chemical cues, from
growth factors to hormones that modulate and influence the growth and development of functional
connections between neurons.

Theoretical investigations into the formation and patterning of synaptic connection and morphology are still
nascent. One hypothesis that has recently garnered some attention is the minimal wiring hypothesis, which
postulates that the formation of axons and dendrites effectively minimizes resource allocation while
maintaining maximal information storage.[29]

Sensory processing

Early models on sensory processing understood within a theoretical framework are credited to Horace
Barlow. Somewhat similar to the minimal wiring hypothesis described in the preceding section, Barlow
understood the processing of the early sensory systems to be a form of efficient coding, where the neurons
encoded information which minimized the number of spikes. Experimental and computational work have
since supported this hypothesis in one form or another. For the example of visual processing, efficient
coding is manifested in the forms of efficient spatial coding, color coding, temporal/motion coding, stereo
coding, and combinations of them.[30]

Further along the visual pathway, even the efficiently coded visual information is too much for the capacity
of the information bottleneck, the visual attentional bottleneck.[31] A subsequent theory, V1 Saliency
Hypothesis (V1SH), has been developed on exogenous attentional selection of a fraction of visual input for
further processing, guided by a bottom-up saliency map in the primary visual cortex.[32]

Current research in sensory processing is divided among a biophysical modelling of different subsystems
and a more theoretical modelling of perception. Current models of perception have suggested that the brain
performs some form of Bayesian inference and integration of different sensory information in generating
our perception of the physical world.[33][34]

Motor control
Many models of the way the brain controls movement have been developed. This includes models of
processing in the brain such as the cerebellum's role for error correction, skill learning in motor cortex and
the basal ganglia, or the control of the vestibulo ocular reflex. This also includes many normative models,
such as those of the Bayesian or optimal control flavor which are built on the idea that the brain efficiently
solves its problems.

Memory and synaptic plasticity

Earlier models of memory are primarily based on the postulates of Hebbian learning. Biologically relevant
models such as Hopfield net have been developed to address the properties of associative (also known as
"content-addressable") style of memory that occur in biological systems. These attempts are primarily
focusing on the formation of medium- and long-term memory, localizing in the hippocampus. Models of
working memory, relying on theories of network oscillations and persistent activity, have been built to
capture some features of the prefrontal cortex in context-related memory.[35] Additional models look at the
close relationship between the basal ganglia and the prefrontal cortex and how that contributes to working
memory.[36]

One of the major problems in neurophysiological memory is how it is maintained and changed through
multiple time scales. Unstable synapses are easy to train but also prone to stochastic disruption. Stable
synapses forget less easily, but they are also harder to consolidate. One recent computational hypothesis
involves cascades of plasticity that allow synapses to function at multiple time scales.[37] Stereochemically
detailed models of the acetylcholine receptor-based synapse with the Monte Carlo method, working at the
time scale of microseconds, have been built.[38] It is likely that computational tools will contribute greatly to
our understanding of how synapses function and change in relation to external stimulus in the coming
decades.

Behaviors of networks

Biological neurons are connected to each other in a complex, recurrent fashion. These connections are,
unlike most artificial neural networks, sparse and usually specific. It is not known how information is
transmitted through such sparsely connected networks, although specific areas of the brain, such as the
visual cortex, are understood in some detail.[39] It is also unknown what the computational functions of
these specific connectivity patterns are, if any.

The interactions of neurons in a small network can be often reduced to simple models such as the Ising
model. The statistical mechanics of such simple systems are well-characterized theoretically. Some recent
evidence suggests that dynamics of arbitrary neuronal networks can be reduced to pairwise interactions.[40]
It is not known, however, whether such descriptive dynamics impart any important computational function.
With the emergence of two-photon microscopy and calcium imaging, we now have powerful experimental
methods with which to test the new theories regarding neuronal networks.

In some cases the complex interactions between inhibitory and excitatory neurons can be simplified using
mean-field theory, which gives rise to the population model of neural networks.[41] While many
neurotheorists prefer such models with reduced complexity, others argue that uncovering structural-
functional relations depends on including as much neuronal and network structure as possible. Models of
this type are typically built in large simulation platforms like GENESIS or NEURON. There have been
some attempts to provide unified methods that bridge and integrate these levels of complexity.[42]

Visual attention, identification, and categorization

Visual attention can be described as a set of mechanisms that limit some processing to a subset of incoming
stimuli.[43] Attentional mechanisms shape what we see and what we can act upon. They allow for
concurrent selection of some (preferably, relevant) information and inhibition of other information. In order
to have a more concrete specification of the mechanism underlying visual attention and the binding of
features, a number of computational models have been proposed aiming to explain psychophysical
findings. In general, all models postulate the existence of a saliency or priority map for registering the
potentially interesting areas of the retinal input, and a gating mechanism for reducing the amount of
incoming visual information, so that the limited computational resources of the brain can handle it.[44] An
example theory that is being extensively tested behaviorally and physiologically is the V1 Saliency
Hypothesis that a bottom-up saliency map is created in the primary visual cortex to guide attention
exogenously.[32] Computational neuroscience provides a mathematical framework for studying the
mechanisms involved in brain function and allows complete simulation and prediction of
neuropsychological syndromes.

Cognition, discrimination, and learning

Computational modeling of higher cognitive functions has only recently begun. Experimental data comes
primarily from single-unit recording in primates. The frontal lobe and parietal lobe function as integrators of
information from multiple sensory modalities. There are some tentative ideas regarding how simple
mutually inhibitory functional circuits in these areas may carry out biologically relevant computation.[45]

The brain seems to be able to discriminate and adapt particularly well in certain contexts. For instance,
human beings seem to have an enormous capacity for memorizing and recognizing faces. One of the key
goals of computational neuroscience is to dissect how biological systems carry out these complex
computations efficiently and potentially replicate these processes in building intelligent machines.

The brain's large-scale organizational principles are illuminated by many fields, including biology,
psychology, and clinical practice. Integrative neuroscience attempts to consolidate these observations
through unified descriptive models and databases of behavioral measures and recordings. These are the
bases for some quantitative modeling of large-scale brain activity.[46]

The Computational Representational Understanding of Mind (CRUM) is another attempt at modeling

human cognition through simulated processes like acquired rule-based systems in decision making and the
manipulation of visual representations in decision making.

Consciousness
One of the ultimate goals of psychology/neuroscience is to be able to explain the everyday experience of
conscious life. Francis Crick, Giulio Tononi and Christof Koch made some attempts to formulate consistent
frameworks for future work in neural correlates of consciousness (NCC), though much of the work in this
field remains speculative.[47] Specifically, Crick[48] cautioned the field of neuroscience to not approach
topics that are traditionally left to philosophy and religion.[49]

Computational clinical neuroscience

Computational clinical neuroscience is a field that brings together experts in neuroscience, neurology,
psychiatry, decision sciences and computational modeling to quantitatively define and investigate problems
in neurological and psychiatric diseases, and to train scientists and clinicians that wish to apply these
models to diagnosis and treatment.[50][51]

Predictive computational neuroscience

Predictive computational neuroscience is a recent field that combines signal processing, neuroscience,
clinical data and machine learning to predict the brain during coma [52] or anesthesia.[53] For example, it is
possible to anticipate deep brain states using the EEG signal. These states can be used to anticipate
hypnotic concentration to administrate to the patient.

Computational Psychiatry

Computational psychiatry is a new emerging field that brings together experts in machine learning,
neuroscience, neurology, psychiatry, psychology to provide an understanding of psychiatric
disorders.[54][55][56]

Technology

Neuromorphic computing

A neuromorphic computer/chip is any device that uses physical artificial neurons (made from silicon) to do
computations (See: neuromorphic computing, physical neural network). One of the advantages of using a
physical model computer such as this is that it takes the computational load of the processor (in the sense
that the structural and some of the functional elements don't have to be programmed since they are in
hardware). In recent times,[57] neuromorphic technology has been used to build supercomputers which are
used in international neuroscience collaborations. Examples include the Human Brain Project SpiNNaker
supercomputer and the BrainScaleS computer.[58]

See also
Action potential Differentiable programming
Biological neuron models Electrophysiology
Bayesian brain FitzHugh–Nagumo model
Brain simulation Galves–Löcherbach model
Computational anatomy Goldman equation
Connectomics Hodgkin–Huxley model
 Information theory Neuroplasticity
Mathematical model Neurophysiology
Nonlinear dynamics Noogenesis
Neural coding Systems neuroscience
Neural decoding Theoretical biology
Neural oscillation Theta model
Neuroinformatics

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See also

Software
BRIAN, a Python based simulator
Budapest Reference Connectome, web based 3D visualization tool to browse connections
in the human brain
Emergent, neural simulation software.
GENESIS, a general neural simulation system.
 NEST is a simulator for spiking neural network models that focuses on the dynamics, size
and structure of neural systems rather than on the exact morphology of individual neurons.

External links

Journals
Journal of Mathematical Neuroscience (https://www.springer.com/mathematics/journal/1340
8)
Journal of Computational Neuroscience (https://www.springer.com/10827)
Neural Computation (http://www.mitpressjournals.org/loi/neco)
Cognitive Neurodynamics
Frontiers in Computational Neuroscience (http://frontiersin.org/neuroscience/computationaln
euroscience/)
PLoS Computational Biology (http://www.ploscompbiol.org/home.action)
Frontiers in Neuroinformatics (http://www.frontiersin.org/Journal/specialty.aspx?s=752&nam
e=neuroinformatics&x=y)

Conferences
Computational and Systems Neuroscience (COSYNE) – a computational neuroscience
meeting with a systems neuroscience focus.
Annual Computational Neuroscience Meeting (CNS) (http://www.cnsorg.org) – a yearly
computational neuroscience meeting.
Computational Cognitive Neuroscience (https://ccneuro.org/) - a yearly computational
neuroscience meeting with a focus on cognitive phenomena.
Neural Information Processing Systems (NIPS) (http://www.nips.cc)– a leading annual
conference covering mostly machine learning.
Cognitive Computational Neuroscience (CCN) (https://ccneuro.org/) – a computational
neuroscience meeting focusing on computational models capable of cognitive tasks.
International Conference on Cognitive Neurodynamics (ICCN) (https://web.archive.org/web/
20070309063503/http://www.iccn2007.org/) – a yearly conference.
UK Mathematical Neurosciences Meeting (https://web.archive.org/web/20080705131550/htt
p://www.icms.org.uk/workshops/mathneuro)– a yearly conference, focused on mathematical
aspects.
Bernstein Conference on Computational Neuroscience (BCCN) (https://web.archive.org/we
b/20110429094455/http://www.nncn.de/Aktuelles-en/bernsteinsymposium/Symposium/vie
w?set_language=en)– a yearly computational neuroscience conference ].
AREADNE Conferences (http://www.areadne.org/index.html)– a biennial meeting that
includes theoretical and experimental results.

Websites
Encyclopedia of Computational Neuroscience (http://www.scholarpedia.org/article/Encyclop
edia_of_Computational_Neuroscience), part of Scholarpedia, an online expert curated
encyclopedia on computational neuroscience and dynamical systems
Retrieved from "https://en.wikipedia.org/w/index.php?title=Computational_neuroscience&oldid=1163457728"