Primer on the Biology of the Cerebral Cortex

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PDF version: Primer on the Biology of the Cerebral Cortex

Cortex cytoarchitecture

On the axial dimension, the cerebral cortex is partitioned into six layers of cells. Layer 1 of the cerebral cortex is the most superficial and layer 6 is the deepest relative to the surface of the brain. Layers 2 and 3 are often categorized together as layer 2/3. Laterally, the cerebral cortex is tiled by distinct regions called cortical columns which act as repeating units of similar function.

Layer 1 and layer 2/3 are called the supragranular layers and mostly perform intracortical computations. Layer 4 is called the granular layer and functions primarily to receive thalamic input. Layers 5 and 6 are called the infragranular layers and mainly send outputs to other parts of the brain.

Though the majority of cortical cells are excitatory pyramidal neurons, there are also many inhibitory interneurons which are crucial to cortical function. There are many morphologically distinct classes of inhibitory interneurons. Pyramidal cells also exhibit structural diversity, though their morphological differences are less often discussed in an explicit fashion.

Canonical cortical microcircuit 

The canonical cortical microcircuit is a model for some of the most frequently occurring patterns of cortical connectivity and function. Some neuroscientists hypothesize that most cortical circuits are variations of a canonical microcircuit. Though different authors have suggested somewhat different versions of the canonical cortical microcircuit model, there are some common patterns as follows.

According to the canonical cortical microcircuit model, strong thalamic inputs first arrive at layer 4 and stimulate both the layer’s inhibitory interneurons and its excitatory pyramidal neurons. Next, these layer 4 neurons transmit information to layer 2/3 pyramidal cells which in turn send excitatory projections to layers 5 and 6 (as well as to layer 1). Layers 5 and 6 send both excitatory and inhibitory signals to other parts of the brain (e.g. back to the thalamus, to the brainstem, etc.) Layers 5 and 6 also send both excitatory and inhibitory feedback to layer 4.


Cortical hierarchy and extrinsic connections

Links among neurons within a cortical column are referred to as intrinsic connections while links between neurons in different cortical columns are called extrinsic connections. Though the majority of cortical connections are intrinsic, the extrinsic connections often stimulate (via activation and inhibition) their targets more strongly.

There are three types of extrinsic connections; feedforward, feedback, and lateral connections. Feedforward connections are from supragranular pyramidal cells to layer 4, feedback connections are from infragranular pyramidal cells to any layer except layer 4 (usually the supragranular layers), and lateral connections are between cells in the same layer. By using this laminar system, a cortical hierarchy emerges with lower cortical areas such as V1 sending information to higher cortical areas such as the dorsal and ventral visual streams via feedforward connections.


Feedback connections are usually inhibitory and can be either modulatory or driving. Though only excitatory lateral connections are shown in the figure above, lateral connections vary in whether they are excitatory, inhibitory, modulatory, or driving. Modulatory connections produce weak metabotropic and ionotropic responses while driving connections produce strong ionotropic responses.

Extrinsic connections are mostly from excitatory glutamatergic neurons, yet feedback connections are usually inhibitory. As such, it is thought that feedback connections typically involve excitatory neurons stimulating layer 1 cells which subsequently send inhibitory projections to layer 2/3 pyramidal cells.

Feedforward connections are excitatory and driving. Feedforward connections might operate as either corticocortical links or as transthalamic links. Transthalamic refers to when a cortical projection goes to the thalamus and then the postsynaptic thalamic neuron sends an axon back to some other part of the cortex.

Reference: Bastos, A. M., Usrey, W. M., Adams, R. A., Mangun, G. R., Fries, P., & Friston, K. J. (2012). Canonical Microcircuits for Predictive Coding. Neuron, 76(4), 695–711.

Cover image: modified from Innovations Report article on Motta et al.’s paper

Publications by Logan Thrasher Collins

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First-Author Scientific Journal Articles

1. Design of a De Novo Aggregating Antimicrobial Peptide and a Bacterial Conjugation- Based Delivery System

2. The case for emulating insect brains using anatomical “wiring diagrams” equipped with biophysical models of neuronal activity

3. Synthetic Biology Approaches for Engineering Next-Generation Adenoviral Gene Therapies

4. Elucidation of SARS-Cov-2 Budding Mechanisms through Molecular Dynamics Simulations of M and E Protein Complexes

5. Synthetic Biology Design as a Paradigm Shift toward Manufacturing Affordable Adeno-Associated Virus Gene Therapies


1. The Sonata Machine (Andromeda Spaceways Magazine)

2. Neuraweb (Abyss & Apex Magazine)

3. Nueva Shikaga (Altered Reality Magazine)

4. Gorgeous Geometries (Altered Reality Magazine)

5. cyberjinn (Altered Reality Magazine)

6. Glimmerglimpse (Mithila Review)

7. Electrocologies (Mithila Review)

8. Foreversong (Silver Blade Magazine)

9. The Sonata Machine Reprint (Altered Reality Magazine)

Science Fiction

1. Relinquish / Metamorph (365tomorrows)

2. Queen of the Universe (Aphelion)

3. Honeybee and the Blot (Theme of Absence)

4. Events after the life of Edgar (The Centropic Oracle)

5. Mahabbah (After Dinner Conversation)

6. Oddballs (Across The Margin)

7. The Incandescence of Her Simulacrum (Zooscape)

8. Honeybee and the Blot Reprint (Metastellar)

9. Le Saga Electrik (All Worlds Wayfarer)


1. Deploying artificial genes to overcome antibiotic resistance (TEDxMileHigh)

2. Rational Romanticism (DaVinci Institute)

3. The case for insect brain emulation (Princeton Envision Conference)

4. Simulation of SARS-CoV-2 envelope assembly to help develop treatments for COVID-19 (IEEE InTech Forum) 

5. Logan Thrasher Collins talks to us about synthetic biology, aesthetics, and his research (Futurati Podcast)

6. Our Technologies Protect Your Health: an introduction to Conduit (A Mother’s Kiss: COVID-19 Fundraiser for Testing)


1. Structural Brain Mapping Using Antibody-Conjugated Gold Nanoparticles and X-ray Microscopy (undergraduate honors thesis; CU Scholar)

2. Towards Simulating the Human Brain (Dartmouth Undergraduate Journal of Science)

Links to most of these publications are also available on my main page

Notes on x-ray physics

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PDF version: Notes on x-ray physics – Logan Thrasher Collins

Thomson scattering and Compton scattering

  • Electrons are the main type of particle that can scatter x-rays. Elastic or Thomson scattering occurs when a non-relativistic electron is accelerated by the electrical component of an incoming electromagnetic field from an x-ray. The accelerated electron then reradiates light at the same frequency. Since the frequency of the input light and output light are the same, this is an elastic process.
  • The intensity of the re-emitted radiation at an observer’s location depends on the angle Χ between the incident light and the observer. Because of the sinusoidal wave character of light, the scattered intensity at the observer’s location is given by the proportionality equation below.


  • Light that encounters the electron is scattered if it is incident on the region defined by the electron’s classical radius. This region is called the Thomson scattering length r0. For a free electron, r0 = 2.82×10-5 Å.


  • Compton scattering occurs when an electron scatters a photon and the scattered photon has a lower energy than the incident photon (an inelastic process). For Compton scattering, a fraction of the incident photon’s energy is transferred to the electron.


  • The amount of energy lost via Compton scattering where the incident photon has energy E0 = hc/λ0 and the scattered photon has energy E1 = hc/λ1 is described by the following equation. Here, ψ represents the angle between the paths of the incident photon and the scattered photon.


Scattering from atoms

  • X-rays are scattered throughout the volumes of atomic electron clouds. For x-rays that scattered in the same direction as the incident x-rays, the strength of scattering is proportional to the atom’s Z-number. In the case of an ionic atom, this value is adjusted to equal the atom’s number of electrons. Note that this assumes free electron movement within the cloud.
  • By contrast, x-rays that are scattered at some angle 2θ relative to the incident x-rays exhibit lower scattering magnitudes. Each of the x-rays scattered at angle 2θ will possess different magnitudes and phases depending on where they were scattered from within the atomic cloud. As a result, the scattering amplitude for the x-rays at angle 2θ will be a vector sum of these waves with distinct magnitudes and phases.


  • A wavevector k is a vector with magnitude 2π/λ that points in the direction of a wave’s propagation. The difference between the wavevector of the incident wave k0 and the wavevector of the scattered wave k1 is equal to a scattering vector Q (that is, Q = k0k1). The magnitude of Q is given by the following equation.


  • The atomic scattering factor f describes the total scattering amplitude for an atom as a function of sin(θ)/λ. By assuming that the atom is spherically symmetric, f will depend only on the magnitude of Q and not on its orientation relative to the atom. Values for f can be found in the International Tables for Crystallography or computed using nine known coefficients a1,2,3,4, b1,2,3,4, and c (which can also be looked up) and the following expression. The coefficients vary depending on the atom and ionic state. The units of f are the scattering amplitude that would be produced by a single electron.


  • If the incident x-ray has an energy that is much less than that of an atom’s bound electrons, the response of the electrons will be damped due to their association with the atom. (This no longer assumes free electron movement within the cloud). As a result, f will be decreased by some value fa. The value fa increases when the incoming x-ray’s energy is close to the energy level of the electron and decreases when the incoming x-ray’s energy is far above the energy levels of the electrons.
  • When the incident x-ray’s energy is close to an electron’s energy level (called an absorption edge), the x-ray is partially absorbed. With this process of partial absorption, some of the radiation is still directly scattered and another part of the radiation is re-emitted after a delay. This re-emitted radiation interferes with the directly scattered radiation. To mathematically describe the effect of the re-emitted radiation’s phase shift and interference, f is adjusted by a second term fb (which is an imaginary value). Far from absorption edges, fb has a much weaker effect (it decays by E-2). The total atomic scattering factor is then given by the following complex-valued equation.


Refraction, reflection, and absorption

  • A material’s index of refraction can be expressed as a complex quantity nc = nRe + inIm. The real part represents the rate at which the wave propagates through the material and the imaginary part describes the degree of attenuation that the wave experiences as it passes through the material.
  • The reason that a material can possess a complex refractive index involves the complex plane wave equation. The wavenumber k = 2π/λ0 is the spatial frequency in wavelengths per unit distance and it is a constant within the complex plane wave equation (λ0 is the wave’s vacuum wavelength). The complex wavenumber kc = knc is the wavenumber multiplied by the complex refractive index. As such, the complex refractive index can be related to the complex wavenumber via kc = 2πnc0 where λ0 is the vacuum wavelength of the wave. After inserting 2π(nRe + inIm)/λ0 into the complex plane wave equation, a decaying exponential can be simplified out as a coefficient for the rest of the equation. The decaying exponential represents the attenuation of the wave in the material. Once this simplification is performed, the equation’s complex wavenumber is converted to a real-valued wavenumber.


  • For x-rays, a material’s complex refractive index for wavelength λ is related to the atomic scattering factors of atoms in the material using the following equation. Ni represents the number of atoms of type j per unit volume and fj(0) is the atomic scattering factor in the forward direction (angle of zero) for atoms of type j. Recall that r0 is the Thomson scattering length.


  • The refractive index is a function of the wavelength. For most optical situations, as the absorption maximum of a material is approached from lower frequencies, the refractive index increases. But when the radiation’s frequency is high enough that it passes the absorption maximum, the refractive index decreases to a value of less than one.
  • The refractive index is defined by n = c/v, where v is the wave’s phase velocity. Phase velocity is the rate at which a wave’s phase propagates (i.e. how rapidly one of the wave’s peaks moves through space). Rearranging the equation, v = c/n is obtained. When the refractive index is less than one, the phase velocity is greater than the speed of light. However, this does not violate relativity because the group velocity (not the phase velocity) carries the wave’s energy and information. For comparison, group velocity is the rate at which a change in amplitude of an oscillation propagates.
  • Anomalous dispersion occurs when the radiation’s frequency is high enough that the refractive index of a material is less than one. As a result, x-rays entering a material from vacuum are refracted away from the normal of the refracting surface. This is in contrast to the typical case where the radiation would be refracted toward the normal of the refracting surface. In addition, the refracted wave is phase shifted by π radians.
  • The complex refractive index is often expressed using the equation below. Here, δ is called the refractive index decrement and β is called the absorption index. Note that nRe = 1 – δ and nIm = β (as a comparison to the previously used notation). Recall that nIm = β describes the degree of a wave’s attenuation as it moves through a material.


  • The refractive index decrement can be approximately computed using the average density of electrons ρ, the Thomson scattering length r0, and the wavenumber k = 2π/λ0. Note that this approximation is better for x-rays that are far from an absorption edge.


  • With most materials, the resulting real part of the index of refraction is only slightly less than one when dealing with x-rays. For example, a typical electron density of one electron per cubic Angstrom yields a δ value of about 5×10-6.
  • Snell’s law applies to the index of refraction for x-rays and is given as follows.


  • Because the index of refraction for x-rays is slightly less than one, total external reflection can occur when x-rays are incident on a surface at angles less than the critical angle θcritical. This stands in contrast with the total internal reflection that commonly occurs with visible light.


  • The critical angle can be approximated with a high level of accuracy using the following equation (derived from the Taylor expansion of the cosine function). With typical values of δ on the order of 10-5, θcritical is often equal to just a few milliradians (or a few tenths of a degree). These small angles relative to the surface are called grazing angles.


  • Because grazing incident angles facilitate x-ray reflection, special curved mirrors can be used to focus x-rays. The curvature of these mirrors must be small enough that the steepest incident angle is less than θcritical. It should be noted that, even when undergoing total external reflection, x-rays do penetrate the reflecting material to a depth of a few nanometers via an evanescent wave.


  • The absorption index β is related to the value fb using the following equation where r0 is the Thomson scattering length. Recall that fb represents the effects of scattering from absorption and remission of x-rays with energies that are close to the absorption edges of a material.


  • Using the process explained earlier for computing the decaying exponential exp(-2πnImx/λ0) that represents the attenuation of a wave’s amplitude as it travels through a material, the decay of a wave’s intensity as it travels through a material can also be found. Recall that λ0 is the wavelength in a vacuum. Because intensity is proportional to the square of the amplitude, the equation below describes the exponential decay of a wave’s intensity in a material. (This decaying exponential function is multiplied by the equation of the wave). Here, μ is called the absorption coefficient and is defined as the reciprocal of the thickness of a material required to decrease a wave’s intensity by a factor of 1/e. The absorption coefficient is a rough indication of a material’s electron density and electron binding energy.


  • The correspondences between the atomic configurations associated with an x-ray absorption edge and the commonly used name for said absorption edge are given in the following table. The subscripts used with the configurations represent the total angular momenta.


X-ray fluorescence and Auger emission

  • Materials fluoresce after bombardment with x-rays or high-energy electrons. If electrons are used, the emitted light consists of Bremsstrahlung radiation (which comes from the deacceleration of the electrons) and fluorescence lines. The Bremsstrahlung radiation includes a broad spectrum of wavelengths and has low intensity while the fluorescence lines are sharp peaks and exhibit high intensity. If x-rays are used to bombard a material, there is no Bremsstrahlung radiation, but fluorescence lines occur.
  • Different materials exhibit different characteristic fluorescence lines. These x-ray fluorescence lines are caused by outer-shell electrons relaxing to fill the holes left after the ejection of photoelectrons. However, not all electronic transitions are allowed, only those which follow the selection rules for electric dipoles. These selection rules are given below. J is the total angular momentum and can be computed from the sum of the Azimuthal quantum number L (which determines the type of atomic orbital) and the spin quantum number S (which determines the direction of an electron’s spin).


  • The nomenclature for x-ray fluorescence lines is based on the shell to which an electron relaxes. If an excited electron relaxes to the 1s shell state, then the fluorescence line is part of the K series. For an excited electron that relaxes to the 2s or 2p state, the fluorescence line is part of the L series. The M series includes relaxations to 3s, 3p, and 3d. The N series includes relaxations to 5s, 5p, 5d, and 5f. As such, the Azimuthal quantum number determines if the fluorescence line falls into the K, L, M, or N series (there are some series beyond these as well which follow the same pattern). The transition within each series that exhibits the smallest energy difference is labeled with α (i.e. Kα), the transition with the next smallest energy difference is labeled with β, and so on. It should be noted that the fluorescence lines are further split by the effects of electron spin and angular momentum and so are labeled with suffixes of 1, 2, etc.
  • Auger emission is the process where a photoelectron is ejected, an outer shell electron relaxes to fill the hole, and the released energy causes ejection another electron instead of emitting a photon. The energies of emitted Auger electrons are independent of the energies of the incident photons.
  • The excess energy released by the relaxation of the outer shell electron is equal to |Ecore – Eouter|. In order for the last electron ejection to occur, the electron must have a binding energy that is less than the excess released energy from the relaxation. The kinetic energy of the ejected Auger electron is |Ecore – Eouter – Ebinding|. Note that Ebinding is the binding energy of the Auger electron in the ionized atom (which is different from the binding energy in the neutral form of the atom).
  • Auger emission and x-ray fluorescence are competitive with each other. Fluorescence is stronger for heavier atoms (higher Z-number) since they exhibit larger energy differences between adjacent shells as well as binding electrons more tightly. For the same reasons, Auger emission is stronger from atoms with lower Z-numbers.



Reference: Willmott, P. (2011). An Introduction to Synchrotron Radiation: Techniques and Applications. Wiley.

Cover image courtesy of: Asia Times






Global Highlights in Neuroengineering August 2005 to April 2019

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PDF version: Global Highlights in Neuroengineering August 2005 to April 2019 – Logan Thrasher Collins

Optogenetic stimulation using ChR2: August 2005

Reference: (Boyden, Zhang, Bamberg, Nagel, & Deisseroth, 2005)

  • Ed Boyden, Karl Deisseroth, and colleagues developed optogenetics, a revolutionary technique for stimulating neural activity.
  • Optogenetics involves engineering neurons to express light-gated ion channels. The first channel used for this purpose was ChR2 (a protein originally found in bacteria which responds to blue light). In this way, a neuron exposed to an appropriate wavelength of light will be stimulated.
  • Over time, optogenetics has gained a place as an essential experimental tool for neuroscientists across the world. It has been expanded upon and improved in numerous ways and has even allowed control of animal behavior via implanted fiber optics and other light sources. Optogenetics may eventually be used in the development of improved brain-computer interfaces.


Plans for Blue Brain Project announced

Reference: (Markram, 2006)

  • Henry Markram announced the European Blue Brain Project (which later gave rise to the Human Brain Project), a large-scale computational neuroscience initiative with the goal of simulating the brain in a supercomputer.
  • Plans for the early stages of the Blue Brain Project included reconstructing the morphologies of neuronal cell types from the rat neocortex, experimentally characterizing their electrophysiological parameters, building a virtual neocortical column with ~10,000 multicompartmental Hodgkin-Huxley-type neurons and over ten million synapses, and running simulations of the virtual neocortical column on the Blue Gene/L supercomputer.
  • These goals were met by the November of 2007 and the general properties of the simulations reflected the biological reality.
  • It should be noted that the virtual column’s connectivity was defined according the patterns of connectivity found in biological rats, but that this involved the numbers of inputs and outputs quantified for given cell types rather than exact wiring. Furthermore, the spatial distributions of boutons forming synaptic terminals upon target cells were also did not mirror biology exactly, but still reflected biological averages.

Cortical Column

Optogenetic silencing using halorhodopsin: March 2007

Reference: (Han & Boyden, 2007)

  • Ed Boyden continued developing optogenetic tools to manipulate neural activity. Along with Xue Han, he expressed a codon-optimized version of a bacterial halorhodopsin (along with the ChR2 protein) in neurons.
  • Upon exposure to yellow light, halorhodopsin pumps chloride ions into the cell, hyperpolarizing the membrane and inhibiting neural activity.
  • Using halorhodopsin and ChR2, neurons could be easily activated and inhibited using yellow and blue light respectively.

Halorhodopsin and ChR2 wavelengths

Brainbow: November 2007

Reference: (Livet et al., 2007)

  • Lichtman and colleagues used Cre/Lox recombination tools to create genes which express a randomized set of three or more differently-colored fluorescent proteins (XFPs) in a given neuron, labeling the neuron with a unique combination of colors. About ninety distinct colors were emitted across a population of genetically modified neurons.
  • The detailed structures within neural tissue equipped with the Brainbow system can be imaged much more easily since neurons can be distinguished via color contrast.
  • As a proof-of-concept, hundreds of synaptic contacts and axonal processes were reconstructed in a selected volume of the cerebellum. Several other neural structures were also imaged using Brainbow.
  • The fluorescent proteins expressed by the Brainbow system are usable in vivo.


Anatomically simplified simulation of 22 million neurons

Reference: (Djurfeldt et al., 2008)

  • As part of the European FACETs project, a simulation consisting of 22 million neurons and 11 billion synapses was carried out on the IBM Blue Gene/L supercomputer.
  • This simulation incorporated Hodgkin-Huxley-type models of three cell types including excitatory pyramidal cells, inhibitory basket cells, and inhibitory RNSP cells. Pyramidal cells were multicompartmental and consisted of six compartments.
  • The model organized its virtual cells into hypercolumns, each containing 100 minicolumns. These columns were intended to reflect the rough biological organization of cells found in layers II/III of the cortex. Neuronal connectivity came from a simple set of rules. This involved rules for each cell type making synapses on a specified set of other cell types (including some synapses between cells of the same type) and rules for projections within and between minicolumns.
  • Using this setup, the virtual neurons were able to store memories in the form of patterns of population activity. As with the situation in biological brains, stimulation of a subset of the population activity responsible for a certain memory caused the rest of that pattern of population activity to emerge.
  • The simulation also demonstrated several other emergent phenomena that occur in biological brains including sustained elevation of pyramidal cell membrane potential during periods of high population activity as well as an exponentially distributed inter-spike intervals during periods of high population activity.

22 million neuron simulation population activity

High temporal precision optogenetics: January 2010

Reference: (Gunaydin et al., 2010)

  • Karl Deisseroth, Peter Hegemann, and colleagues used protein engineering to improve the temporal resolution of optogenetic stimulation.
  • Glutamic acid at position 123 in ChR2 was mutated to threonine, producing a new ion channel protein (dubbed ChETA).
  • The ChETA protein allows for induction of spike trains with frequencies up to 200 Hz and greatly decreases the incidence of unintended spikes. Furthermore, ChETA eliminates plateau potentials (a phenomenon which interferes with precise control of neural activity).

Ultrafast optogenetics

Hardware for faster than real-time neuroscience simulations: May 2010

Reference: (Schemmel et al., 2010)

  • Scientists working under the European FACETs project developed a neuromorphic hardware system called BrainScaleS with the ability to simulate networks of adaptive exponential integrate-and-fire neurons 1,000 to 100,000 times faster than biological real-time.
  • Each neuromorphic wafer was able to simulate up to 180,000 neurons and 4•107 Furthermore, the design allowed for interconnection of multiple wafers in order to simulate larger neuronal populations. Each artificial neuron was able to receive up to 14,336 presynaptic inputs (a biologically realistic value).
  • To facilitate computational neuroscience applications using the neuromorphic wafers, a Python-based software interface called PyNN was created. In this way, the hardware could more easily be configured to simulate a desired neuronal system.

BrainscaleS wafer

Hippocampal prosthesis in rats: March 2012

Reference: (Berger et al., 2012)

  • Theodore Berger and his team developed an artificial replacement for neurons which transmit information from the CA3 region to the CA1 region of the hippocampus.
  • This cognitive prosthesis employs recording and stimulation electrodes along with a multi-input multi-output (MIMO) model to encode the information in CA3 and transfer it to CA1.
  • The hippocampal prosthesis was shown to restore and enhance memory in rats as evaluated by behavioral testing and brain imaging.

In vivo superresolution microscopy for neuroimaging: February 2012

Reference: (Berning, Willig, Steffens, Dibaj, & Hell, 2012)

  • Stefan Hell (2014 Nobel laureate in chemistry) developed stimulated emission depletion microscopy (STED), a type of superresolution fluorescence microscopy which allows imaging of synapses and dendritic spines.
  • STED microscopy uses a torus-shaped de-excitation laser that interferes with the excitation laser to deplete fluorescence except in a very small spot. In this way, the diffraction limit is surpassed since the resulting light illuminates extremely small regions of the sample.
  • Neurons in transgenic mice (equipped with glass-sealed holes in their skulls) were imaged using STED. Synapses and dendritic spines were observed up to fifteen nanometers below the surface of the brain tissue.

Superresolution microscopy in vivo

Eyewire as a crowdsourcing method for retina mapping: December 2012

Reference: (Marx, 2013)

  • The Eyewire project was created by Sebastian Seung’s research group. It is a crowdsourcing initiative for connectomic mapping within the retina towards uncovering neural circuits involved in visual processing.
  • Laboratories first collect data via serial electron microscopy as well as functional data from two-photon microscopy.
  • In the Eyewire game, images of tissue slices are provided to players who then help reconstruct neural morphologies and circuits by “coloring in” the parts of the images which correspond to cells and stacking many images on top of each other to generate 3D maps. Artificial intelligence tools help provide initial “best guesses” and guide the players, but the people ultimately perform the task of reconstruction.
  • By November 2013, around 82,000 participants had played the game. Its popularity continues to grow.


In vivo three-photon microscopy: January 2013

Reference: (Horton et al., 2013)

  • Multi-photon excitation uses pulsed lasers to excite fluorophores with two or more photons of light with long wavelengths. During the excitation, the photons undergo a nonlinear recombination process, yielding a single emitted photon with a much shorter wavelength. Because the excitation photons possess long wavelengths, they can penetrate tissue much more deeply than traditional microscopy allows.
  • Horton and colleagues developed a three-photon excitation method to facilitate even deeper tissue penetration than the commonly used two-photon microscopic techniques.
  • Since three photons were involved per excitation event, even longer excitation wavelengths (about 1,700 nm) were usable, allowing the construction of a 3-dimensional image stack that reached a depth of up to 1.4 mm within the living mouse brain.
  • Blood vessels and RFP-labeled neurons were imaged using this approach. Furthermore, the depth was sufficient to enable imaging of neurons within the mouse hippocampus.

3-photon microscopy

Whole-brain functional recording from larval zebrafish: March 2013

Reference: (Ahrens, Orger, Robson, Li, & Keller, 2013)

  • Laser-scanning light-sheet microscopy was used to volumetrically image the entire brains of larval zebrafish (an optically transparent organism).
  • The genetically encoded calcium sensor GCaMP5G facilitated functional recording at single-cell resolution from about 80% of the total neurons in the larval zebrafish brains. Computational methods were used to distinguish between individual neurons.
  • Populations of neurons that underwent correlated activity patterns were identified to show the technique’s utility for uncovering the dynamics of neural circuits. These populations included hindbrain neurons that were functionally linked to neural activity in the spinal cord and a population of neurons which showed coupled oscillations on the left and right halves.

Whole-brain recording from larval zebrafish

The BRAIN Initiative: April 2013

Reference: (“Fact Sheet: BRAIN Initiative,” 2013)

  • The BRAIN Initiative (Brain Research through Advancing Innovative Technologies) provided neuroscientists with $110 million in governmental funding and $122 million in funding from private sources such as the Howard Hughes Medical Institute and the Allen Institute for Brain Science.
  • The BRAIN Initiative focused on funding research which develops and utilizes new technologies for functional connectomics. It helped to accelerate research on tools for decoding the mechanisms of neural circuits in order to understand and treat mental illness, neurodegenerative diseases, and traumatic brain injury.
  • The BRAIN Initiative emphasized collaboration between neuroscientists and physicists. It also pushed forward nanotechnology-based methods to image neural tissue, record from neurons, and otherwise collect neurobiological data.

The CLARITY method for making brains translucent: May 2013

Reference: (Chung & Deisseroth, 2013)

  • Karl Deisseroth and colleagues developed a method called CLARITY to make samples of neural tissue optically translucent without damaging the fine cellular structures in the tissue. Using CLARITY, entire mouse brains have been turned transparent.
  • Mouse brains were infused with hydrogel monomers (acrylamide and bisacrylamide) as well as formaldehyde and some other compounds for facilitating crosslinking. Next, the hydrogel monomers were crosslinked by incubating the brains at 37°C. Lipids in the hydrogel-stabilized mouse brains were extracted using hydrophobic organic solvents and electrophoresis.
  • CLARITY allows antibody labeling, fluorescence microscopy, and other optically-dependent techniques to be used for imaging entire brains. In addition, it renders the tissue permeable to macromolecules, which broadens the types of experimental techniques that these samples can undergo (i.e. macromolecule-based stains, etc.)

CLARITY Imaging Technique

X-ray microscopy reconstructs Drosophila brain hemisphere: September 2013

Reference: (Mizutani, Saiga, Takeuchi, Uesugi, & Suzuki, 2013)

  • Mizutani and colleagues stained Drosophila brains with silver nitrate and tetrachloroaurate (a gold-containing compound), facilitating 3-dimensional imaging using X-ray microtomography at a voxel size of 220 × 328 × 314 nm.
  • To generate the X-rays, a synchrotron source was used. It should be noted that synchrotron sources require large facilities to operate.
  • Neuronal tracing was performed manually on the 3-dimensional X-ray images of the fly brain, a process which took about 1,700 person-hours. Some neuronal processes were too dense to be resolved, so they were “fused” into unified structures. Furthermore, some neuronal traces were fragmented and most of the cell bodies were not considered. This decreased the number of traces to one third of the estimated number of actual processes in the hemisphere.
  • Mizutani’s investigation represents an early effort at large-scale connectomics that sets the stage for further initiatives as neuronal tracing, sample preparation, and X-ray microtomography technologies continue to improve.

Traced Drosophila Brain Hemisphere

Telepathic rats engineered using hippocampal prosthesis: December 2013

Reference: (Deadwyler et al., 2013)

  • Berger’s hippocampal prosthesis was implanted in pairs of rats. When “donor” rats were trained to perform a task, they developed neural representations (memories) which were recorded by their hippocampal prostheses.
  • The donor rat memories were run through the MIMO model and transmitted to the stimulation electrodes of the hippocampal prostheses implanted in untrained “recipient” rats. After receiving the memories, the recipient rats showed significant improvements on the task that they had not been trained to perform.

Rat Telepathy

Integrated Information Theory 3.0: May 2014

Reference: (Oizumi, Albantakis, & Tononi, 2014)

  • Integrated information theory (IIT) was originally proposed by Giulio Tononi in 2004. IIT is a quantitative theory of consciousness which may help explain the hard problem of consciousness.
  • IIT begins by assuming the following phenomenological axioms; each experience is characterized by how it differs from other experiences, an experience cannot be reduced to interdependent parts, and the boundaries which distinguish individual experiences are describable as having defined “spatiotemporal grains.”
  • From these phenomenological axioms and the assumption of causality, IIT identifies maximally irreducible conceptual structures (MICS) associated with individual experiences. MICS represent particular patterns of qualia that form unified percepts.
  • IIT also outlines a mathematical measure of an experience’s quantity. This measure is called integrated information or ϕ.

Openworm: November 2014

Reference: (Szigeti et al., 2014)

  • The anatomical elegans connectome was originally mapped in 1976 by Albertson and Thomson. More data has since been collected on neurotransmitters, electrophysiology, cell morphology, and other characteristics.
  • Szigeti, Larson, and their colleagues made an online platform for crowdsourcing research on elegans computational neuroscience, with the goal of completing an entire “simulated worm.”
  • The group also released software called Geppetto, a program that allows users to manipulate both multicompartmental Hodgkin-Huxley models and highly efficient soft-body physics simulations (for modeling the worm’s electrophysiology and anatomy).

C. elegans Connectome

Multibeam SEM for connectomics: January 2015

Reference: (Eberle et al., 2015)

  • When mapping neuronal tissue with conventional scanning electron microscopy (SEM), the rate of data acquisition is severely limited by the amount of time it takes for the electron beam to image a single pixel on one slice of the sample. As such, imaging a 1 mm3 volume of tissue could take more than 25 years.
  • By constructing a SEM device that produces a hexagonal array of 61 electron beams (as opposed to just one beam), Eberle and colleagues were able to greatly improve the throughput of SEM imaging. It was estimated that imaging a 1 mm3 volume with this system would take just 6 months.
  • Multibeam SEM was designed for compatibility with both serial block-face techniques and automated serial sectioning methods.
  • Slices of brain tissue, a bone tissue section, and a silicon wafer with printed circuitry were imaged with the multibeam SEM system as proof-of-concept tests.

Expansion microscopy: January 2015

Reference: (F. Chen, Tillberg, & Boyden, 2015)

  • The Boyden group developed expansion microscopy, a method which enlarges neural tissue samples (including entire brains) with minimal structural distortions and so facilitates superior optical visualization of the scaled-up neural microanatomy. Furthermore, expansion microscopy greatly increases the optical translucency of treated samples.
  • Expansion microscopy operates by infusing a swellable polymer network into brain tissue samples along with several chemical treatments to facilitate polymerization and crosslinking and then triggering expansion via dialysis in water. With 4.5-fold enlargement, expansion microscopy only distorts the tissue by about 1% (computed using a comparison between control superresolution microscopy of easily-resolvable cellular features and the expanded version).
  • Before expansion, samples can express various fluorescent proteins to facilitate superresolution microscopy of the enlarged tissue once the process is complete. Furthermore, expanded tissue is highly amenable to fluorescent stains and antibody-based labels.

Expansion microscopy

Neural lace: June 2015

Reference: (Liu et al., 2015)

  • Charles Lieber’s group developed a syringe-injectable electronic mesh made of submicrometer-thick wiring for neural interfacing.
  • The meshes were constructed using novel soft electronics for biocompatibility. Upon injection, the neural lace expands to cover and record from centimeter-scale regions of tissue.
  • Neural lace may allow for “invasive” brain-computer interfaces to circumvent the need for surgical implantation. Lieber has continued to develop this technology towards clinical application.

Neural Lace

BigNeuron towards standardized neuronal morphology acquisition: July 2015

Reference: (Peng et al., 2015)

  • Because of the inconsistencies between neuronal reconstruction methods and lack of standardization found in neuronal morphology databases, BigNeuron was established as a community effort to improve the situation.
  • BigNeuron tests as many automated neuronal reconstruction algorithms as possible using large-scale microscopy datasets (from several types of light microscopy). It uses the Vaa3D neuronal reconstruction software as a central platform. Reconstruction algorithms are added to Vaa3D as plugins. These computational tests are performed on supercomputers.
  • BigNeuron aims to create a superior community-oriented neuronal morphology database, a set of greatly improved tools for neuronal reconstruction, a standardized protocol for future neuronal reconstructions, and a library of morphological feature definitions to facilitate classification.

The TrueNorth chip from DARPA and IBM: August 2015

Reference: (Akopyan et al., 2015)

  • The TrueNorth neuromorphic computing chip was constructed and validated by DARPA and IBM. TrueNorth uses circuit modules which mimic neurons. Inputs to these fundamental circuit modules must overcome a threshold in order to trigger “firing.”
  • The chip can emulate up to a million neurons with over 250 million synapses while requiring far less power than traditional computing devices.

Japan’s Brain/MINDS project: September 2015

Reference: (Okano, Miyawaki, & Kasai, 2015)

  • In 2014, the Brain/MINDS (Brain Mapping by Integrated Neurotechnologies for Disease Studies) project was initiated to further neuroscientific understanding of the brain. This project received nearly $30 million in funding for its first year alone.
  • Brain/MINDS focuses on studying the brain of the common marmoset (a non-human primate abundant in Japan), developing new technologies for brain mapping, and understanding the human brain with the goal of finding new treatments for brain diseases.

Human telepathy during a 20 questions game: September 2015

Reference: (Stocco et al., 2015)

  • Using an interactive question-and-answer setup, Stocco and colleagues demonstrated real-time telepathic communication between pairs of individuals via EEG and transcranial magnetic stimulation. Five pairs of participants played games of 20 questions and attempted to identify unknown objects.
  • EEG data were recorded from the respondent, computationally processed, and transmitted as transcranial magnetic stimulation signals into the mind (occipital lobe stimulation) of a respondent. The respondent’s answers were translated into higher-intensity transcranial magnetic stimulation pulses corresponding to “yes” answers or lower-intensity transcranial magnetic stimulation pulses corresponding to “no” answers.
  • When compared to control trials in which sham interfaces were used, the people using the brain-brain interfaces were significantly more successful at playing 20 questions games.

Twenty questions telepathy

Human Brain Project cortical mesocircuit simulation: October 2015

Reference: (Markram et al., 2015)

  • The Human Brain Project reconstructed a virtual version of a 0.29 mm3 region of rat cortical tissue including about 31,000 neurons and 37 million synapses.
  • The connectivity was defined according the patterns of connectivity found in biological rats, (though this involved the numbers of inputs and outputs quantified for given cell types rather than explicit wiring). In addition, the spatial distributions of boutons forming synaptic terminals upon target cells reflected biological data.
  • Detailed multicompartmental Hodgkin-Huxley-type models were used to take into account the effects of the morphologies of the neurons within the simulation.
  • The cortical mesocircuit was emulated using the Blue Gene/Q supercomputer and this emulation was sufficiently accurate to reproduce emergent neurological processes and yield insights on the mechanisms of their computations.

Cortical Mesocircuit

Recording from C. elegans neurons reveals motor operations: October 2015

Reference: (Kato et al., 2015)

  • Live elegans worms were immobilized in microfluidic devices and the neurons in their head ganglia as well as some of their motor systems were imaged and recorded from using the calcium indicator GCaMP. As the C. elegans connectome is well-characterized, Kato and colleagues were able to determine the identities of most of the cells that underwent imaging (with the help of computational segmentation techniques).
  • Principal component analysis was used to reduce the dimensionality of the neural activity datasets since over 100 neurons per worm were recorded from simultaneously.
  • Next, phase space analysis was utilized to visualize the patterns formed by the recording data. Motor behaviors including dorsal turns, ventral turns, forward movements, and backward movements were found to correspond to specific sequences of neural events as uncovered by examining the patterns found in the phase plots. Further analyses revealed various insights about these brain dynamics and their relationship to motor actions.

C. elegans brain dynamics

The China Brain Project: March 2016

Reference: (Poo et al., 2016)

  • The China Brain Project was launched to help understand the neural mechanisms of cognition, develop brain research technology platforms, develop preventative and diagnostic interventions for brain disorders, and to improve brain-inspired artificial intelligence technologies.
  • This project will take place from 2016 until 2030 with the goal of completing mesoscopic brain circuit maps.
  • China’s population of non-human primates and preexisting non-human primate research facilities give the China Brain Project an advantage. The project will focus on studying rhesus macaques.

Expansion FISH: July 2016

Reference: (F. Chen et al., 2016)

  • Boyden, Chen, Marblestone, Church, and colleagues combined fluorescent in situ hybridization (FISH) with expansion microscopy to image the spatial localization of RNA in neural tissue.
  • The group developed a chemical linker to covalently attach intracellular RNA to the infused polymer network used in expansion microscopy. This allowed for RNAs to maintain their relative spatial locations within each cell post-expansion.
  • After the tissue was enlarged, FISH was used to fluorescently label targeted RNA molecules. In this way, RNA localization was more effectively resolved.
  • As a proof-of-concept, expansion FISH was used to reveal the nanoscale distribution of long noncoding RNAs in nuclei as well as the locations of RNAs within dendritic spines.

Expansion FISH

Neural dust: August 2016

Reference: (Seo et al., 2016)

  • Michel Maharbiz’s group invented implantable, ~ 1 mm biosensors for wireless neural recording and tested them in rats.
  • This neural dust could be miniaturized to less than 0.5 mm or even to microscale dimensions using customized electronic components.
  • Neural dust motes consist of two recording electrodes, a transistor, and a piezoelectric crystal.
  • The neural dust received external power from ultrasound. Neural signals were recorded by measuring disruptions to the piezoelectric crystal’s reflection of the ultrasound waves. Signal processing mathematics allowed precise detection of activity.

Neural Dust

Bryan Johnson launches Kernel: August 2016

Reference: (Regalado, 2017)

  • Entrepreneur Bryan Johnson invested $100 million to start Kernel, a neurotechnology company.
  • Kernel plans to develop implants that allow for recording and stimulation of large numbers of neurons at once. The company’s initial goal is to develop treatments for mental illnesses and neurodegenerative diseases. Its long-term goal is to enhance human intelligence.
  • Kernel originally partnered with Theodore Berger and intended to utilize his hippocampal prosthesis. Unfortunately, Berger and Kernel parted ways after about six months because Berger’s vision was reportedly too long-range to support a financially viable company (at least for now).
  • Kernel was originally a company called Kendall Research Systems. This company was started by a former member of the Boyden lab. In total, four members of Kernel’s team are former Boyden lab members.

Somatosensory cortex stimulation for spinal cord injuries: October 2016

Reference: (Flesher et al., 2016)

  • Gaunt, Flesher, and colleagues found that microstimulation of the primary somatosensory cortex (S1) partially restored tactile sensations to a patient with a spinal cord injury.
  • Electrode arrays were implanted into the S1 regions of a patient with a spinal cord injury. The array performed intracortical microstimulation over a period of six months.
  • The patient reported locations and perceptual qualities of the sensations elicited by microstimulation. The patient did not experience pain or “pins and needles” from any of the stimulus trains. Overall, 93% of the stimulus trains were reported as “possibly natural.”
  • Results from this study might be used to engineer upper-limb neuroprostheses which provide somatosensory feedback.

Somatosensory Stimulation

Simulation of rat CA1 region: December 2016

Reference: (Bezaire, Raikov, Burk, Vyas, & Soltesz, 2016)

  • Detailed computational models of 338,740 neurons (including pyramidal cells and various types of interneurons) were equipped with connectivity patterns based on data from the biological CA1 region. External inputs were also estimated using biological data and incorporated into the simulation. It is important to note that these connectivity patterns described the typical convergence and divergence of neurites to and from particular cell types rather than explicitly representing the exact connections found in the biological rat.
  • Each neuron was simulated using a multicompartmental Hodgkin-Huxley-type model with its morphological structure based on biological data from the given cell type. Furthermore, different cell types received different numbers of presynaptic terminals at specified distances from the soma. In total, over five billion synapses were present within the CA1 model.
  • The simulation was implemented on several different supercomputers. Due to the model’s complexity, a four second simulation took about four hours to complete.
  • As with the biological CA1 region, the simulation gave rise to gamma oscillations and theta oscillations as well as other biologically consistent phenomena. In addition, parvalbumin-expressing interneurons and neurogliaform cells were identified as drivers of the theta oscillations, demonstrating the utility of detailed neuronal simulations for uncovering biological insights.

CA1 simulation

The $100 billion Softbank Vision Fund: May 2017

Reference: (Lomas, 2017)

  • Masayoshi Son, the CEO of Softbank (a Japanese telecommunications corporation), announced a plan to raise $100 billion in venture capital to invest in artificial intelligence. This plan involved partnering with multiple large companies in order to raise this enormous amount of capital.
  • By the end of 2017, the Vision Fund successfully reached its $100 billion goal. Masayoshi Son has since announced further plans to continue raising money with a new goal of over $800 billion.
  • Masayoshi Son’s reason for these massive investments is the technological singularity. He agrees with Kurzweil that the singularity will likely occur at around 2045 and he hopes to help bring the singularity to fruition. Though Son is aware of the risks posed by artificial superintelligence, he feels that superintelligent AI’s potential to tackle some of humanity’s greatest challenges (such as climate change and the threat of nuclear war) outweighs those risks.

UltraTracer enhances existing neuronal tracing software: March 2017

Reference: (Peng et al., 2017)

  • UltraTracer is an algorithm that can improve the efficiency of existing neuronal tracing software for handling large datasets while maintaining accuracy.
  • Datasets with hundreds of billions of voxels were utilized to test UltraTracer. Ten existing tracing algorithms were augmented.
  • For most of the existing algorithms, the performance improvements were around 3-6 times, though a few showed improvements of 10-30 times. Even when using computers with smaller memory, UltraTracer was consistently able to enhance conventional software.
  • UltraTracer was made opensource and is available as a plugin for the Vaa3D tracing software suite.

Elon Musk’s NeuraLink startup: March 2017

Reference: (Etherington, 2017)

  • Elon Musk (CEO of Tesla, SpaceX, and a number of other successful companies) initiated a neuroengineering venture called NeuraLink.
  • NeuraLink will begin by developing brain-computer interfaces (BCIs) for clinical applications, but the ultimate goal of the company is to enhance human cognitive abilities in order to keep up with artificial intelligence.
  • Though many of the details around NeuraLink’s research are not yet open to the public, it has been rumored that injectable electronics similar to Lieber’s neural lace might be involved.

Facebook announces effort to build brain-computer interfaces: April 2017

Reference: (Constine, 2017)

  • Facebook revealed research on constructing non-invasive brain-computer interfaces (BCIs) at a company-run conference in 2017. The initiative is run by Regina Dugan, Facebook’s head of R&D at division building 8.
  • Facebook’s researchers are working on a non-invasive BCI which may eventually enable users to type one hundred words per minute with their thoughts alone. This effort builds on past investigations which have been used to help paralyzed patients.
  • The building 8 group is also developing a wearable device for “skin hearing.” Using just a series of vibrating actuators which mimic the cochlea, test subjects have so far been able to recognize up to nine words. Facebook intends to vastly expand this device’s capabilities.

Whole-brain electron microscopy in larval zebrafish: May 2017

Reference: (Hildebrand et al., 2017)

  • Serial electron microscopy facilitated imaging of the entire brain of a larval zebrafish at 5.5 days post-fertilization.
  • Neuronal tracing software (a modified version of the CATMAID software) was used to reconstruct all the myelinated axons found in the larval zebrafish brain.
  • The reconstructed dataset included 2,589 myelinated axon segments along with some of the associated soma and dendrites. It should be noted that only 834 of the myelinated axons were successfully traced back to their cell bodies.

SSEM of larval zebrafish brain

Hardware for accelerated and biologically realistic simulations: May 2017

Reference: (Schemmel, Kriener, Müller, & Meier, 2017)

  • Scientists working within the Human Brain Project developed an extension of the BrainScaleS neuromorphic hardware system for emulating biologically realistic neurons at a speed 1,000 times faster than biological real-time.
  • The hardware’s design incorporates circuits blocks that act as compartments which represent segments of a dendritic tree. The organization and conductances of these compartments are configured using a system of switches. At a given time, each compartment can emulate either dendritic calcium spikes, dendritic NMDA spikes, or dendritic sodium spikes.
  • Any electronic neuron within the chip can receive up to 16,000 presynaptic inputs as configured by the user. In addition, the presynaptic neurons feeding into a postsynaptic neuron can be located either on the same chip or on a different chip. In this way, combining multiple chips allows simulation of larger-scale systems.
  • This neuromorphic system mimics biological plasticity using correlation sensors and a plasticity processing unit. The correlation sensors measure and locally store the exponentially weighted temporal difference between presynaptic and postsynaptic events within each electronic synapse. The plasticity processing unit reads these measurements along with the current weights and addresses of the synapses before implementing a software-defined algorithm for updating the synaptic weights and sometimes synaptic addresses. The algorithm can also be programmed to update the stored biophysical parameters of the circuit such as calcium spike threshold voltages, NMDA plateau durations, etc.

Human Brain Project analyzes brains using algebraic topology: June 2017

Reference: (Reimann et al., 2017)

  • Investigators at the Human Brain Project utilized algebraic topology to analyze the reconstructed ~ 31,000 neuron cortical microcircuit from their earlier work.
  • The analysis involved representing the cortical network as a digraph, finding directed cliques (complete directed subgraphs belonging to a digraph), and determining the net directionality of information flow (by computing the sum of the squares of the differences between in-degree and out-degree for all the neurons in a clique). In algebraic topology, directed cliques of n neurons are called directed simplices of dimension n-1.
  • Vast numbers of high-dimensional directed cliques were found in the cortical microcircuit (as compared to null models and other controls). Spike correlations between pairs of neurons within a clique were found to increase with the clique’s dimension and with the proximity of the neurons to the clique’s sink. Furthermore, topological metrics allowed insights into the flow of neural information among multiple cliques.
  • Experimental patch-clamp data supported the significance of the findings. In addition, similar patterns were found within the elegans connectome, suggesting that the results may generalize to nervous systems across species.

HBP algebraic topology

DARPA funds research to develop improved brain-computer interfaces: July 2017

Reference: (Hatmaker, 2017)

  • The U.S. government agency DARPA awarded $65 million in total funding to six research groups.
  • The recipients of this grant included five academic laboratories (headed by Arto Nurmikko, Ken Shepard, Jose-Alain Sahel and Serge Picaud, Vicent Pieribone, and Ehud Isacoff) and one small company called Paradromics Inc.
  • DARPA’s goal for this initiative is to develop a nickel-sized bidirectional brain-computer interface (BCI) which can record from and stimulate up to one million individual neurons at once.

Early testing of hippocampal prosthesis algorithm in humans: July 2017

Reference: (Song, She, Hampson, Deadwyler, & Berger, 2017)

  • Dong Song (who was working alongside Berger) tested the MIMO algorithm on human epilepsy patients using implanted recording and stimulation electrodes. The full hippocampal prosthesis was not implanted, but the electrodes acted similarly, though in a temporary capacity. Although only two patients were tested in this study, many trials were performed to compensate for the small sample size.
  • Hippocampal spike trains from individual cells in CA1 and CA3 were recorded from the patients during a delayed match-to-sample task. The patients were shown various images while neural activity data were recorded by the electrodes and processed by the MIMO model. The patients were then asked to recall which image they had been shown previously by picking it from a group of “distractor” images. Memories encoded by the MIMO model were used to stimulate hippocampal cells during the recall phase.
  • In comparison to controls in which the same two epilepsy patients were not assisted by the algorithm and stimulation, the experimental trials demonstrated a significant increase in successful pattern matching.

Brain imaging factory in China: August 2017

Reference: (Cyranoski, 2017)

  • Qingming Luo started the HUST-Suzhou Institute for Brainsmatics, a brain imaging “factory.” Each of the numerous machines in Luo’s facility performs automated processing and imaging of tissue samples. The devices make ultrathin slices of brain tissue using diamond blades, treat the samples with fluorescent stains or other contrast-enhancing chemicals, and image then using fluorescence microscopy.
  • The institute has already demonstrated its potential by mapping the morphology of a previously unknown neuron which “wraps around” the entire mouse brain.

China Brain Mapping Image

Automated patch-clamp robot for in vivo neural recording: August 2017

Reference: (Suk et al., 2017)

  • Ed Boyden and colleagues developed a robotic system to automate patch-clamp recordings from individual neurons. The robot was tested in vivo using mice and achieved a data collection yield similar to that of skilled human experimenters.
  • By continuously imaging neural tissue using two-photon microscopy, the robot can adapt to a target cell’s movement and shift the pipette to compensate. This adaptation is facilitated by a novel algorithm called an imagepatching algorithm. As the pipette approaches its target, the algorithm adjusts the pipette’s trajectory based on the real-time two-photon microscopy.
  • The robot can be used in vivo so long as the target cells express a fluorescent marker or otherwise fluoresce corresponding to their size and position.

Automated Patch Clamp System

Neuropixels probe: November 2017

Reference: (Jun et al., 2017)

  • Jun and colleagues created the Neuropixels probe to facilitate simultaneous recording from hundreds of individual neurons with high spatiotemporal resolution. Previous extracellular probes were only able to record from a few dozen individual neurons.
  • The Neuropixels recording shank is one centimeter long and includes 384 recording channels. Due to the small size of the accompanying apparatus (a 6×9 mm base and a data transmission cable), it enables high-throughput recording in freely moving animals. Because the shank is quite long, Neuropixels can record from multiple brain regions at once.
  • Voltage signals are processed directly on the base of the Neuropixels apparatus, allowing for noise-free data transmission along the cable for further analysis.


Genome editing in the mammalian brain: November 2017

Reference: (Nishiyama, Mikuni, & Yasuda, 2017)

  • Precise genome editing in the brain has historically been challenging because most neurons are postmitotic (non-dividing) and the postmitotic state prevents homology-directed repair (HDR) from occurring. HDR is a mechanism of DNA repair which allows for targeted insertions of DNA fragments with overhangs homologous to the region of interest (by contrast, non-homologous end-joining is highly unpredictable).
  • Nishiyama, Mikuni, and Yasuda developed a technique which allows genome editing in postmitotic mammalian neurons using adeno-associated viruses (AAVs) and CRISPR-Cas9.
  • The AAVs delivered ssDNA sequences encoding a single guide RNA (sgRNA) and an insert. Inserts encoding a hemagglutinin tag (HA) and inserts encoding EGFP were both tested. Cas9 was encoded endogenously by transgenic host cells and in transgenic host animals.
  • The technique achieved precise genome editing in vitro and in vivo with a low rate of off-target effects. Inserts did not cause deletion of nearby endogenous sequences for 98.1% of infected neurons.

Genome Editing Neurons

SpiNNaker neuromorphic supercomputer

Reference: (Brown, Chad, Kamarudin, Dugan, & Furber, 2018)

  • The SpiNNaker engine is a supercomputer designed to simulate spiking networks of neurons in real time. Its neuromorphic architecture facilitates optimal performance on these kinds of computational neuroscience tasks. SpiNNaker’s construction was funded by the Human Brain Project.
  • SpiNNaker consists of a 240×240 mesh of nodes. Each node contains 18 ARM9 cores. Although ARM9 is a type of processor found in conventional computers, the communication infrastructure is less traditional. Only fixed-size packets of information can be transmitted among the cores. These packets are small, designed to carry the equivalent of a neuronal spike spike. Using an entirely hardware-based routing infrastructure, the information packets facilitate rapid communication throughout the machine.
  • The system can be programmed to emulate any configuration of up to one billion neurons. It should be noted that this figure refers to point neuron models such as the leaky integrate-and-fire or Izhikevich models. However, it may also be possible to run multicompartmental models on SpiNNaker, though this would take more of its resources per neuron.


EEG-based facial image reconstruction: January 2018

Reference: (Nemrodov, Niemeier, Patel, & Nestor, 2018)

  • EEG data associated with viewing images of faces was collected and used to determine the neural correlates of facial processing. In this way, the images were computationally reconstructed in a fashion resembling “mind reading.”
  • It should be noted that the images reconstructed using data taken from multiple people were more accurate than the images reconstructed using single individuals. Nonetheless, the single individual data still yielded statistically significant accuracy.
  • In addition to reconstructing the images themselves, the process gave insights on the cognitive steps involved in perceiving faces.

EEG reconstructions of faces

Upconversion nanoparticles for optogenetic stimulation: February 2018

Reference: (S. Chen et al., 2018)

  • Upconversion nanoparticles absorb two or more low-energy photons and emit a higher energy photon. For instance, multiple near-infrared photons can be converted into a single visible spectrum photon.
  • Shuo Chen and colleagues injected upconversion nanoparticles into the brains of mice and used them to convert externally applied near-infrared (NIR) light into visible light within the brain tissue. In this way, optogenetic stimulation was performed without the need for surgical implantation of fiber optics or similarly invasive procedures.
  • The authors demonstrated stimulation via upconversion of NIR to blue light (to activate ChR2) and inhibition via upconversion of NIR to green light (to activate a rhodopsin called Arch).
  • As a proof-of-concept, this technology was used to alter the behavior of the mice by activating hippocampally-encoded fear memories.

Upconversion nanoparticles and NIR

Map of all neuronal cell bodies within mouse brain: March 2018

Reference: (Murakami et al., 2018)

  • Ueda, Murakami, and colleagues combined methods from expansion microscopy and CLARITY to develop a protocol called CUBIC-X which both expands and clears entire brains. Light-sheet fluorescence microscopy was used to image the treated brains and a novel algorithm was developed to detect individual nuclei.
  • Although expansion microscopy causes some increased tissue transparency on its own, CUBIC-X greatly improved this property in the enlarged tissues, facilitating more detailed whole-brain imaging.
  • Using CUBIC-X, the spatial locations of all the cell bodies (but not dendrites, axons, or synapses) within the mouse brain were mapped. This process was performed upon several adult mouse brains as well as several developing mouse brains to allow for comparative analysis.
  • The authors made the spatial atlas publicly available in order to facilitate global cooperation towards annotating connectivity among the neural cell bodies within the atlas.


Clinical testing of hippocampal prosthesis algorithm in humans: March 2018

Reference: (Hampson et al., 2018)

  • Further clinical tests of Berger’s hippocampal prosthesis were performed. Twenty-one patients took part in the experiments. Seventeen patients underwent CA3 recording so as to facilitate training and optimization of the MIMO model. Eight patients received CA1 stimulation so as to improve their memories.
  • Electrodes with the ability to record from single neurons (10-24 single-neuron recording sites) and via EEG (4-6 EEG recording sites) were implanted such that recording and stimulation could occur at CA3 and CA1 respectively.
  • Patients performed behavioral memory tasks. Both short-term and long-term memory showed an average improvement of 35% across the patients who underwent stimulation.

Precise optogenetic manipulation of fifty neurons: April 2018

Reference: (Mardinly et al., 2018)

  • Mardinly and colleagues engineered a novel excitatory optogenetic ion channel called ST-ChroME and a novel inhibitory optogenetic ion channel called IRES-ST-eGtACR1. The channels were localized to the somas of host neurons and generated stronger photocurrents over shorter timescales than previously existing opsins, allowing for powerful and precise optogenetic stimulation and inhibition.
  • 3D-SHOT is an optical technique in which light is tuned by a device called a spatial light modulator along with several other optical components. Using 3D-SHOT, light was precisely projected upon targeted neurons within a volume of 550×550×100 μm3.
  • By combining novel optogenetic ion channels and the 3D-SHOT technique, complex patterns of neural activity were created in vivo with high spatial and temporal precision.
  • Simultaneously, calcium imaging allowed measurement of the induced neural activity. More custom optoelectronic components helped avoid optical crosstalk of the fluorescent calcium markers with the photostimulating laser.

Optogenetic control of fifty neurons

Whole-brain Drosophila image data via serial electron microscopy: July 2018

Reference: (Zheng et al., 2018)

  • Zheng, Bock, and colleagues collected serial section electron microscopy data on the entire adult Drosophila brain, providing the data necessary to reconstruct a complete structural map of the fly’s brain at the resolution of individual synapses, dendritic spines, and axonal processes.
  • The data are in the form of 7050 transmission electron microscopy images (187500 x 87500 pixels and 16 GB per image), each representing a 40nm-thin slice of the fly’s brain. In total the dataset requires 106 TB of storage.
  • Although much of the data still needed to be processed to reconstruct a 3-dimensional map of the Drosophila brain, the authors did create 3-dimensional reconstructions of selected areas in the olfactory pathway of the fly. In doing so, they discovered a new cell type as well as several other previously unrealized insights about the organization of Drosophila‘s olfactory biology.

Drosophila connectome with SEM

RNA-seq within intact brain tissue: July 2018

Reference: (Wang et al., 2018)

  • Wang and colleagues developed a technique called STARmap for sequencing RNA within intact brain tissue, facilitating acquisition of three-dimensional spatial transcriptomic information.
  • Fixed tissue was infused with a hydrogel matrix. DNA amplicons were covalently linked to the matrix via amine-modified nucleotides. Along with reverse transcriptase, these amplicons facilitated amplification of local mRNAs via rolling circle replication. Each amplicon contained a gene-unique barcode sequence to facilitate identification of genes. In addition, the tissue’s transparency was enhanced by lipid removal and protease treatment.
  • To sequence the amplified mRNAs, two types of DNA probes were repeatedly washed through the tissue. Reading probes set the start position for decoding probes which were color-coded with fluorophores corresponding to the dinucleotides at their 3’ ends. With each cycle, the length of the reading probe was increased by one degenerate nucleotide, moving the reading start position ahead by one base. By observing the colors of the spots within the sample, each cycle facilitated identification of one nucleotide in all amplified mRNA molecules. After six or seven cycles of sequencing, the gene-unique barcode sequence associated with every mRNA could be identified. This sequencing process was called SEDAL.
  • STARmap was used to quantify the expression of 160 genes in a thin slice of mouse cortex. These data reproduced the spatial gene expression pattern from a known dataset, validating STARmap.
  • In thicker cortical volumes, the authors used STARmap to quantify spatial gene expression of 1020 genes across more than 30,000 cells. It was found that this number of genes represented an upper limit since trying to perform STARmap on a larger number of genes would result in too much overlap between the fluorescent spots.


Human telepathy using BrainNet: September 2018

Reference: (Jiang et al., 2018)

  • EEG recordings were taken from two individuals (termed senders) while they played a Tetris-like game. Next, the recordings were converted into transcranial magnetic stimulation signals that acted to provide a third individual (called a receiver) with the necessary information to make decisions in the game without seeing the screen. The occipital cortex was stimulated. Fifteen people (five groups of three) took part in the study.
  • To convey their information, the senders were told to focus upon either a higher or a lower intensity light corresponding to commands within the game (the two lights were placed on different sides of the computer screen). In the receiver’s mind, this translated to perceiving a flash of light. The receiver was able to distinguish the intensities and implement the correct command within the game.
  • Using only the telepathically provided stimulation, the receiver made the correct game-playing decisions 81% of the time.


Transcriptomic cell type classification across mouse neocortex: October 2018

Reference: (Tasic et al., 2018)

  • Single-cell RNA sequencing was used to characterize gene expression across 23,822 cells from the primary visual cortex and the anterior lateral motor cortex of mice.
  • Using dimensionality reduction and clustering methods, the resulting data were used to classify the neurons into 133 transcriptomic cell types.
  • Injections of adeno associated viruses (engineered to express fluorescent markers) facilitated retrograde tracing of neuronal projections within a subset of the sequenced cells. In this way, correspondences between projection patterns and transcriptomic identities were established.

Nanowire system as a memristive artificial synapse: December 2018

Reference: (Milano et al., 2018)

  • Milano and colleagues synthesized a memristive nanowire device consisting of a ZnO nanowire bridging between Ag and Pt electrodes on a SiO2 insulating substrate.
  • When a positive voltage is applied to the Ag electrode, Ag+ ions start migrating along the nanowire towards the Pt electrode. Ag deposition on the nanowire creates a conductive bridge that allows for current to flow across the device. Each time voltage is applied, more Ag is deposited on the bridge, increasing the conductance across the terminals. In this way, the system mimics synaptic potentiation.
  • Pulses with positive voltage across the terminals demonstrated the ability to increase the bridge’s conductance. Pulses with negative voltage were used to reset the nanowire bridge’s conductance back to the starting state.
  • If shorter pulses are applied, the bridge’s conductance spontaneously decays back to its original state in a similar way to how biological synapses lose their potentiation after a period of inactivity.
  • For a conductance increase to occur, a threshold amplitude of short pulses and a threshold number of consecutive short pulses were necessary. The amplitude and frequency of the pulses could be adjusted so that the kinetics of bridge formation and decay mimicked the kinetics of potentiation in biological synapses.

Nanowire memristor

Whole-brain Drosophila image data acquired via expansion LLSM: January 2019

Reference: (Gao et al., 2019)

  • Ed Boyden’s and Eric Betzig’s research groups combined lattice light-sheet microscopy with expansion microscopy to image the entire Drosophila brain as well as large volumes of mouse cortex at ~60×60×90 nm resolution. It should be noted that labeled subsets of structures were imaged rather than all structures within these volumes.
  • In the Drosophila brain (a 340×660×90 μm volume), all ~110 dopaminergic neuronal membranes were immunostained with one color while all ~40 million presynaptic boutons were immunostained with a different color. Of these boutons, ~530,000 were associated with dopaminergic neurons. Eight of the dopaminergic cells underwent segmentation via manual tracing.
  • Mouse somatosensory cortex (a ~100×150×150 μm subvolume) was imaged for the purpose of analyzing fluorescently labeled subcellular organelles within layer V pyramidal cells. 2893 mitochondria and 222 lysosomes were identified within five pyramidal cell bodies, five pyramidal cell apical dendrite initial portions, and three descending axon segments. These organelles were segmented and their morphological parameters were quantified.
  • More mouse somatosensory cortex (a ~320×280×60 μm subvolume) was imaged with the purpose of examining cortical myelin sheaths. Myelin basic protein was immunostained in YFP-expressing pyramidal cells and the average structural properties of the myelin sheaths were quantified.
  • Since the lattice light-sheet microscope had a limited 160 μm field of view, hundreds to thousands of tiles within the volumes were imaged and then computationally stitched together using customized software.


Pipeline for mesoscale mapping of the marmoset brain: February 2019

Reference: (Lin et al., 2019)

  • Lin and colleagues established a histological pipeline for mapping mesoscale connectivity in the marmoset brain as part of Japan’s Brain/MINDS project. “Mesoscale” refers to connectivity between anatomical regions rather than individual neurons.
  • MRI was performed upon living marmosets to determine proper locations for the injection of fluorescent neural tracers. Each marmoset brain was then sectioned into ~1700 slices with 20 μm thickness. In addition to the injected fluorescent tracers, the slices received a set of chemical stains to enhance visualization of neural features. The slices were then imaged.
  • Using the images of the slices, three-dimensional reconstructions of marmoset brains were created. The MRI data helped to correct distortions in these reconstructions and to register the reconstructions into a standard three-dimensional atlas of the marmoset brain.
  • The fluorescent tracer injections facilitated the construction of connectivity maps between distinct anatomical regions (i.e. V1 to V5, etc.) Projection strength between target and source regions was quantified using the number of voxels containing the fluorescent tracer labels.
  • Using their experimental and computational pipeline, the authors predict that a mesoscale connectivity matrix for the entire marmoset brain could be finished by 2024 or earlier depending on the degree of collaboration with multiple groups.

Neural probes that resemble neurons: February 2019

Reference: (Yang et al., 2019)

  • Charles Lieber’s group developed neural probes with the approximate size and shape of neurons (called NeuE probes). The NeuE probes consisted of soma-like platinum recording electrodes and neurite-like filaments made from a polymer insulator. At the core of the polymer, gold interconnect wiring carried current. The filaments were woven into a mesh.
  • The electrodes exhibited similar dimensions compared with neuronal soma and the filaments had similar dimensions compared to dendrites and axons. In addition, the filaments demonstrated similar levels of flexibility relative to axons.
  • The NeuE probes were highly biocompatible since they possessed similar size, shape, and flexibility compared to biological neurons. Microglia and astrocytes did not surround the probes, indicating a lack of immune response. Furthermore, neurons were not depleted around the probes. These results contrast with other neural implants that induce harmful immune reactions.
  • NeuE probes with 16 electrodes were implanted in the hippocampal and cortical regions of living mouse brains. These probes demonstrated stable single-unit recording over a period of 90 days.
  • After performing the recordings, the mice were killed and the brain tissue with the NeuE probes was imaged three-dimensionally using two-photon confocal microscopy. Mathematical analysis of the recording data helped identifiy which neurons were recorded by which electrodes.

NeuE probe

Injectable nanoparticles give mice infrared vision: April 2019

Reference: (Ma et al., 2019)

  • Sub-retinal injections of upconversion nanoparticles gave mice the ability to perceive complex shapes on the near-infrared spectrum.
  • The upconversion nanoparticles were linked to a protein that binds carbohydrates on the cell surface of photoreceptors. Since upconversion nanoparticles absorb longer wavelengths and then emit shorter wavelengths (i.e. near-infrared wavelengths are transformed to visible wavelengths), this allowed the mice to perceive infrared light patterns as if they were visible light.
  • Treated mice retained their ability to see visible light alongside their new ability to see infrared light. The nanoparticle treatment also did not cause any adverse effects in the mice beyond some minor side effects (cataracts and corneal opacity) that happen with any sub-retinal injection. These minor side effects disappeared completely after two weeks. Furthermore, the mice still could distinguish complex near-infrared shapes ten weeks after injection of the nanoparticles, demonstrating the treatment’s long-term stability.

NIR vision using upconversion nanoparticles

Reconstruction from whole-brain Drosophila image data

Reference: (Li et al., 2019)

  • The whole-brain Drosophila electron microscopy data acquired by Zheng et al. underwent an automated image segmentation process to reconstruct all of the neurons in the fly’s brain. An algorithmic pipeline that involved flood-filling networks was used.
  • It should be noted that the reconstruction is an “over-segmentation.” That is, each neuron is split into separate segments with an average length of 54 μm. However, improvements to the flood-filling algorithm may ameliorate this issue in the future. Furthermore, the separate segments can be manually joined at a rate ten times faster than full manual tracing of the neurons.

Whole-brain Drosophila ssTEM dataset segmentation

Perovskite nickelates directly interface with neurons: April 2019

Reference: (Zhang et al., 2019)

  • A perovskite nickelate lattice with covalently linked horseradish peroxidase enzymes facilitated measurement of dopamine release from synapses within a mouse brain slice.
  • When the dopaminergic neurons in the slice were stimulated, dopamine release triggered a hydrogen transfer process onto the perovskite nickelate lattice. This caused an increase in the lattice’s resistivity corresponding to the increase in dopamine concentration.
  • Even in the complex media of an artificial cerebrospinal fluid, the device specifically detected dopamine. Furthermore, the device’s sensitivity was high enough that dopamine could be detected at concentrations as low as 5•10-17
  • In separate experiments, a glucose oxidase enzyme was covalently linked to the perovskite nickelate lattice. When this device was exposed to glucose, hydrogen was transferred onto the lattice, causing a resistivity increase corresponding to the glucose concentration. The device only reacted with glucose and did not respond to mannose or galactose solutions. In addition, the device exhibited sufficient sensitivity to detect glucose at concentrations as low as 5•10-16

Perovskite nickelate device

Decoding sentences from brain activity: April 2019

Reference: (Anumanchipalli, Chartier, & Chang, 2019)

  • Anumanchipalli and colleagues constructed a system for translating neural activity into sentences.
  • Electrocorticography (ECoG) was used to record the brain activity of several participating subjects while they spoke sentences aloud.
  • A machine learning tool was used on audio recording data to create a model for inferring the facial movements that take place during speech. Another form of machine learning was used to predict inferred facial movements from brain activity. In addition, acoustic features were extracted from audio recordings of speech.
  • By using the training data, the researchers developed a machine learning algorithm for mapping ECoG signals to inferred facial movements and inferred facial movements to sound.
  • The algorithm allowed for generation of synthesized speech from brain activity. Listeners could often transcribe the synthesized sentences perfectly. However, some errors did occur. Nonetheless, the algorithm performed well enough that it could be very helpful to patients with disorders which prevent them from speaking.



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Notes on nanoparticle physics

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PDF version: Notes on nanoparticle physics

Nanoparticle surfaces

  • Because of their small size, populations of nanoparticles possess very large surface areas.
  • The surface area to volume ratio R for a single spherical nanoparticle with diameter d, surface area a = πd2, and volume v = πd3/6 is given below. Note that, as the value of the diameter decreases, the surface area to volume ratio increases.


  • The surface area per mole of spherical nanoparticles can be expressed using the following equation. M represents the molecular weight of one nanoparticle, A is the surface area per mole of nanoparticles, ρ describes the density of the nanoparticles in the solution, and n is Avogadro’s number.


  • Due to their high surface areas, populations of nanoparticles tend to aggregate via Van der Waals forces and sometimes other attractive forces.
  • The surface layer, a layer that represents the region of transition between the material of the nanoparticle and the outside world, makes up a significant portion of the nanoparticle’s volume. Depending on the specific property under investigation, this layer’s thickness can usually be regarded as between 0.5 nm and 1.0 nm.
  • To compute the volume of a surface layer with thickness δ, use the first formula below. The ratio of the surface layer’s volume to the total volume is given by the second equation below.


  • Surface energy is the energy required to form new surfaces via the process of breaking an object into two or more pieces.
  • For populations of nanoparticles, this means that the Fig.1surface energy describes the energy driving each patch of nanoparticle surface to aggregate with other patches of nanoparticle surface. The surface energy for a nanoparticle with surface area a is given by the following equation where γ is the energy required to separate a single unit area of surface between two coagulated nanoparticles.


  • Nanoparticles can coagulate and cause a rapid increase in temperature due to their large surface area and the exothermic reaction of surface energy release. The change in temperature (in Kelvin) from this flash can be computed using the following equation where M is the molecular weight of one nanoparticle, ρ is the density of the nanoparticles, and Cp represents the heat capacity of the system.


Diffusion within nanoparticles

  • According to solutions of the diffusion equation, the mean square diffusion distance of a population is proportional to the diameter of the diffusing objects. Here, the diffusion coefficient D is multiplied by a factor of six because a three-dimensional system is assumed. This value is four in the two-dimensional case and is two in the one-dimensional case.


  • For diffusion of particles within a solid (i.e. a nanoparticle), the diffusion coefficient can be modeled using the following temperature-dependent equation. T is the temperature in Kelvin, Ea is the activation energy for diffusion, D0 is a proportionality constant, and k represents Boltzmann’s constant.


  • Because of their small size and the physics described above, diffusion inside of a nanoparticle occurs very rapidly. If the nanoparticle’s diameter is assumed as the length of the diffusion path, then halving the diameter leads to a four-fold decrease in the time needed for diffusion.
  • Since diffusion occurs so rapidly within a nanoparticle, homogenization takes milliseconds. In general, any thermally activated reaction inside a nanoparticle will happen almost instantaneously. As such, nonequilibrium states usually are not stable in nanoparticles (unlike with many conventional materials).

Thermal energy and state fluctuations

  • Every nanoparticle possesses a thermal energy that is proportional to temperature. Furthermore, every nanoparticle favors a state of minimum energy. The energy difference between the lowest energy state and a higher energy state often depends on the nanoparticle’s mass. Since nanoparticles have very small masses, their thermal energy is sometimes larger than the energy difference between the states. As a result, the nanoparticle can fluctuate among the states.
  • Thermal energy of an isolated particle is given by uthermal = kT where T is the temperature in Kelvin and k represents Boltzmann’s constant. If the following inequality is true, then the nanoparticle’s state fluctuates.


  • To provide a concrete example, consider the thermal energy necessary to lift a nanoparticle of density ρ and volume V from elevation x1 (its minimum energy state) to elevation x2 (its higher energy state). If the inequality below is satisfied true, then the nanoparticle jumps between elevation zero and elevation x due to its thermal energy.



Reference: Vollath, D. (2013). Nanoparticles – Nanocomposites – Nanomaterials: An Introduction for Beginners. Wiley.