Wrap-Up

A student asked the following question, which raises the most fundamental idea we've studied in the course, that of a Hebb synapse:

"I was going over the material and I am confused about one thing: High frequency AP's cause significant amount of glutamate release, binding to AMPA --> significant Na+ entry --> NMDAR release of Mg2+ --> --> --> LTP ... but further studies find "silent synapses" deficient in AMPA receptors do not respond to pre-synaptic activity (release of glutamate), and LTP is necessary for appearance of AMPARs. If entry of sodium via AMPARs cause LTP by causing changes in NMDAR, allowing Ca2+ entry, how can LTP occur in silent synapses? Are all synapses initially silent? or is absence of AMPA a property of only a specific subset of neurons? Does this have anything to do with backpropagating spikes?"

I answered as follows:

"Yes it does have to do with backAPs. The key point is that ltp is triggered not by local depolarisation (at the synapse itself, eg caused by locally released glu acting on  ampaRs) but by the occurrence of a spike (starting at the beginning of the postsynaptic axon, the initial segment) which backpropagates into the dendrites and thus reaches all the synapses.

This answers your dilemma: at a silent synapse (most synapses start silent) the release of glu does not cause significant local depolarization, but nevertheless the neuron might fire a spike (as a result of near-simultaneous glu release at other, non-silent, synapses). When that spike backprops and reaches the silent synapse in question, it will trigger unblocking of the NMDARs at that synapse, and Ca entry, which can trigger strengthening (by adding AMPARs).

The whole point here that the decision to strengthen a particular synapse (or not) should depend not just on what is happening at that synapse (i.e. the arrival of a presynaptic spike) but the collective decision of the whole postsynaptic neuron (does it fire a spike too?).

Similarly at a particular nonsilent synapse: this synapse will depolarise (because it already has some ampaRs) if the input axon fires, but we don't want that synapse to locally depolarise enough to unblock the nmdars because then it would strengthen regardless of what the whole neuron is doing - we only want the synapse to strengthen if the postsynaptic neuron fires (mostly as a result of the other active synapses, but in small part because of the synapse in question). So we can adjust each synapse individually based on what the relevant pre- and postsynaptic axon are doing: if they both fire (the pre slightly before the post)  then strengthen it! This mechanism implements the Hebb rule, fire together wire together.

We can capture the behavior of a neuron with 2 simple equations: dw/dt = xy and y = f(x.w). In the first equation w refers to the strength of a particular synapse (it should have a subscript i since we are referring to the ith synapse) and y is the firing rate of the neuron. The second, "dot-product", equation says y depends on how well the current input pattern (vector x) matches the current strength pattern of the whole set of synapses (the vector w). The 2 equations together mean that gradually over time the relative strength of all the synapses will come to reflect regularities (correlations) in the entire set of input pattens the neuron sees over its lifetime (which is essentially the lifetime of the animal). Since detecting regularities is what we mean by "understanding", this implies  the brain (just a collection of neurons!) can "understand" - i.e. have a mind (a not uninteresting conclusion).

Of course the devil is in the details. The whole thing would be undermined if (a) the local depolarisation due to ampaRs were big enough to unblock the nmdaRs or (b) the Ca signal at one synapse could influence, even to a tiny degree, what happens at other synapses. Both these point are controversial.

In the case where all the synapses are initially silent (eg in the early fetus), it would appear that there's no way to get the ball rolling: no ampars means no firing! However, it turns out that very early on GABA acts as an excitatory transmitter (chloride pumps have not yet matured and Ecl is positive to threshold)! Probably initially random firing leads to some random unsilencing, and only later do the synapses get further adjusted in an experience-dependent way.

If you can answer the question and my answer, the course will have been a success, no matter what your final grade.

 

Visual Cortex; the vanishing cow

Here's a nice overview of visual cortex, with a few cool experiments you can try on yourself:http://www.tutis.ca/Senses/L2VisualCortex/L2V1.pdf
When testing your blind spot, I suggest moving the test screen back and forth a bit while fixating the X target: you will see that at one particular distance the center of the blind spot becomes invisible - or, better, gets "filled in" with the rest of the pattern. It's at this distance that the central patch falls exactly on the blind spot (use 1 eye only, and don't cheat: you must fixate the X.) Here's another example: fixate the + and find the distance from the screen where the cow vanishes. Why and how does the cow vanish?
from http://www.psy.ritsumei.ac.jp/~akitaoka/moten01.jpg

The brain dilemma: Electrical and Chemical Spread

Synapses have 2 main functions. First, they transmit information (about input firing and synapse strength) to the axon initial segment where spikes are initiated and sent to other neurons. Second they can change their strength, primarily in response to input/output co-activity. These 2 processes interact so that the output that inputs cause becomes more useful (e.g. to survival and reproduction). The first is largely a fast, rather global, electrical process (individual synaptic currents spread down dendrites and combine to trigger spikes) and the second is largely a slower sharply localized chemical process confined to individual synapses. The first process is the "computation" and the second the "programming" (which has to be mostly self-programming).

However, these global and local changes are to some degree contradictory. To see this we can consider a simple model of the spread of electrical and chemical signals within neurons, cable theory. We have studied in class electrical cable theory, which looks at the combined effect of membrane capacitance and resistance, and cytoplasmic resistance, on electrical spread. As long as a synapse is reasonably close to the cell body (1 space constant or less,  lamda V ~ 1mm) it can influence firing, albeit with a delay.

But one can also write a cable equation for chemical spread. Here we replace capacitance by the ability of intracellular calcium-binding molecules to "buffer" rapid calcium changes. Membrane resistance corresponds to calcium pumps (e.g. in the spine neck), which extrude or degrade calcium and other chemicals. Cytoplasmic resistance corresponds to intracellular diffusion, typically at ~ 1 um^2/msec.

The black lines below represent a cable - either the dendrites or the spine neck. The colored lines represent voltage or chemical signals. In the dendrites one wants good voltage spread, so the neuron can "integrate" its synaptic inputs (the basic computation). Between spines one wants no spread (so changes in synapses do not affect each other).

Putting in reasonable numbers for these parameters one can write  lamdaC ~ 1um for the chemical space constant. However, the distance from synapses to cell bodies is ~ 1 mm and between spine heads ~ 1 um. So it looks as though the brain cannot work well, since 1mm/1mm ~ 1um/1um ~ 1.

Of course one can try to squeeze synapses closer to the IS, but this just decreases the distance between them, worsening chemical isolation, on which learning (or self-programming) hinges.

The only real way this can work is to decrease the number of inputs, which of course greatly lowers computational power.

One can fiddle at the margins with this dilemma, but I suspect that it means that most animals have to rely on instinct, i.e, the computational power of Darwinian evolution. Since humans have language we can "program" each other (but still most programs have to be discovered by individuals). From this perspective, language (and limitless symbols generally) rather than big brains would be the key to human success.

Are synaptic strengths set by co-activity?

Although there is good evidence that Hebbian (co-activity-dependent) synapses do exist, and in some cases the machinery is understood (NMDARs, back-APs etc), and there is also evidence that strength changes underlie learning, only very recently has evidence been obtained that synaptic strength is set by the history of co-activity at that synapse (http://biorxiv.org/content/biorxiv/early/2015/03/11/016329.full.pdf)

The authors used detailed 3D reconstruction from serial EM, and studied pairs of synapses in the hippocampus that were either made by an axon on the same dendrite or on either different dendrites or by different axons (where it's unlikely the axons or dendrites belonged to the same neuron). The idea is that in the former case the 2 synapses would have identical histories of co-activity, and in the latter case, different histories. The above figure shows (A) one example, in which an axon makes 2 synapses on a dendrite (arrows point to the 2 post-synaptic densities, in red) (B) many pairs of examples (C) the relation between the 2 spine head volumes (top) or  PSD areas (next) for the pairs. Spine head volumes or PSD areas should be good measures of synapses strength, and they are tightly correlated for the 2 members of each pair, though they vary over a large range. This suggests that co-activity history determines synapse strength. When the 2 synapses are made by different axons or on different dendrites, the strengths do not correlate well:

A related 3D reconstruction study in the neocortex shows that if an axon makes one synapse on a dendrite, it tends to make others (again consistent with shared co-activity history), though in this case these synapses do not seem to have similar size.

The authors (Kasthuri et al., 2015, Cell 162, 648–661) conclude: " Thus axon-dendrite adjacency, while of course necessary for synapses to form, is insufficient to explain why some axons establish multiple synapses on

some dendrites and not others. This is an explicit refutation of

Peters’ rule. Rather this result argues that there are different

probabilities for synapses between particular dendrites and

particular excitatory axons." Of course a shared history of co-activity and Hebbian plasticity could account for these probabilities.
"Peters' Rule refers to the hypothesis that synapses are made solely on the basis of physical axon and dendrite proximity, without regard to their past history of co-activity. Connections in the brain would then be determined solely by the chance close encounters of axons and dendrites. These in turn would reflect the general geometry of axodendritic overlap, which might reflect genetic specification of axonal arborization dendritic branching patterns. Several recent papers show that this idea is not generally valid, but do not directly suggest a role for co-activity and Hebbian learning. However, there may be situations in which connections do follow Peters' rule. One example would be the bipolar-starburst amacrine synapses I discussed in a recent post.

I favor the extreme opposite view - that connection probabilities and strengths are determined by co-activity and thus indirectly by input correlations - especially by subtle higher-order correlations. This would probably require extraordinary degrees of synapse isolation and independence, and could endow neurons with powerful computational abilities, perhaps transcending what is achievable with current silicon technology. However strong experimental evidence on this point is currently lacking. 

what does the retina do? - and how? The EyeWire Video Game

EyeWire is an online video-game that is fun to play and useful to neuroscience!

The retina is perhaps the most accessible part of the brain, and in some ways the simplest (though it's still amazingly complicated) - see the comparison below of the retina and the neocortex:

The retina has at least 4 jobs.

1. It converts the current pattern of light intensity and color falling on the retina (in particular, on the outer segments of the photoreceptors) into an electrical pattern (in particular, the potentials inside the photoreceptors, which act as 100 million "image pixels"). 

2. This electrical pattern is then compressed 100-fold  into a pattern of spikes on the axons of the ganglion cells and sent to the rest of the brain (especially the visual thalamus and superior colliculus) for interpretation.

3. Some specialized ganglion cells can already "interpret" aspects of the visual image. For example, some ganglion cells respond to directed motion at particular locations. 

1 is accomplished by the phototransduction machinery. Light causes a structural change in the (one of four) photopigments expressed by the photoreceptor, which activates an enzyme that breaks down cGMP. This in turn closes some of the CNG-channels that normally allow a background influx of sodium ions into the photoreceptor, thus hyperpolarizing the photoreceptor, reducing ongoing glutamate release.

2. Compression is achieved by the center-surround receptive field organization. In a nutshell, since neighboring points in retinal images tend to show similar light intensities, it's usually more informative (more "surprising")  to send to the brain information about differences in local intensities. Thus an "on"  ganglion cell could be caused to fire by light hitting a "central" photoreceptor that provides (via a bipolar) depolarizing input, especially when the illumination of immediately neighboring photoreceptors decreases. These neighbors provide input to GABAergic "horizontal cells", which reduce release from the central photoreceptor, as well as inhibiting the corresponding bipolar. Vice-versa for "off" ganglion cells. In statistics terms this corresponds to a "local" version of PCA called ZCA, as discussed in class. The comparison with neighbors implies sensitivity to pairwise statistics, also a feature of PCA. However, straight PCA is not practical in the retina, because it involves global (and long-distance) connections, which would enormously thicken the retina. Because the pairwise image correlations (mostly caused by optical imperfections of the eye itself) are usually highly local, the local wiring needed for ZCA is much more practical, and equally efficient. Because of inevitable off-axis chromatic aberrations in the lens, local green/blue or red/green center-surround comparisons may also do good compression.  

Note that the goal of PCA is to find directions in multidimensional pixel space along which image projections vary maximally. 

In the foveola, which aligns with the optical axis of the eye, image blur is minimal, and here each ganglion cell has input from just 1 cone, so there is no image compression: the brain receives the full, detailed,  RAW image. Of course it has to interpret it - which is why the visual cortex is so complex (see top image). Note that though the fovea is only a small part of the retina, a large part of the visual cortex is devoted to its analysis - this "magnification factor" is at least 100 fold. 

3. The mechanism of the direction selectivity of ganglion cells has been recently worked out (e.g http://www.nature.com.proxy.library.stonybrook.edu/nature/journal/v471/n7337/full/nature09818.html) These ganglion cells come in on and off types, reflecting the sign of the bipolar to which they are connected, and the inner plexiform sublayer where their axons/dendrites meet . But in addition they respond selectively when the light or dark spot to which they are tuned moves in a particular direction. This directionality arises from additional inhibitory input from GABAergic  "starburst amacrine cells",  which inhibits firing when the spot moves in one particular direction, but not the other. Amacrine cells do not have axons. This type is aptly named, because their dendrites spread out in all directions in ether the on or off sublayer, making synapses on ganglion cell dendrites in that layer. The starburst dendrites also get input from bipolars. Each spreading SBA dendrite branches out in a sector, and within that sector it gets excitatory input from overlying bipolars. However these BP-SBA epsps arrive at different times because of cable properties. In particular, if a spot of light moves away from the SBA cell body,  it first depolarises the proximal SB dendrite, then the distal. The distally and proximally generated epsps will thus peak at the same time in the distal dendrite; dendrodendritic SBA-GC synapses in the distal dendrites will thus be strongly activated. Notice that this arrangement makes each separate dendrite respond to centrifugal motion in a particular direction (eg north, south east or west). Now it turns out that a northward GC receives inhibitory synapses from a northwards-tuned SBA dendrite, and so forth, and therefore inherits its directional tuning. Note that individual SBA cells are NOT tuned to individual directions, though its dendrites are. Here we have an example of local dendritic computation, a principle which some neuroscientists are vainly trying to extend to excitatory neurons with axons (e.g. pyramidal cells - see Hebbery Notes.). 

The SBA is in black, and the synapses it makes on 4 (N,S,E,W; different colors) directional GCs is shown as colored balls. One of these synapses is shown in detail. All the other neuron processes are shown in gray. Seung and Denk Nature

514,394(16 October 2014) doi:10.1038/nature13877

Toyota Invests $1 Billion in Machine Learning; Will we become slaves to clever machines?

"Machine Learning" is a very hot new field that is taking over from the older field of Artificial Intelligence, and is central to increasingly ubiquitous technologies such as Siri, Watson and self-driving cars. It also has increasingly strong links to neuroscience, and draws on applied math, statistics, physics and computer science. It's sometimes referred to as the "New AI".
ML is essentially the science of learning by machines (especially computers). Since the central assumption underlying neuroscience is that the brain is a machine, and since neural plasticity and learning are fundamental to brain function, especially in mammals, the 2 sciences are natural allies.
In today's New York Times a front page article (http://www.nytimes.com/2015/11/06/technology/toyota-silicon-valley-artificial-intelligence-research-center.html?emc=eta1) reveals that Toyota is investing $1B in ML in Silicon Valley, already the epicenter of ML. The same page features a banner ad by IBM touting Watson and the "Cognitive Era".

Why has ML moved to the fore? First, it's increasingly realized that learning is the key to intelligence. Indeed, one could almost define intelligence as the ability to learn how to solve problems - any problem, but especially new problems. Second, there's an increasing focus on using rigorous, quantitative approaches, often based on statistics. In particular so-called "Bayesian statistics" - a systematic approach to improving one's hypotheses as new information becomes available. Third, rapid (though somewhat decelerating) advances in computing power allow the heavy number crunching required by ML techniques. Fourth, some of the most powerful ML approaches are partly inspired by neuroscience, so advances in both fields are synergistic.

In the course we already touched on one of the simplest and oldest examples of ML when we considered motor learning in the cerebellum. We saw that parallel fibers make synapses on Purkinje neurons, and these can automatically change their strength based on 2 coincident factors, the parallel fiber firing (signalled by glutamate release) and an error signal (conveyed by climbing fiber firing). We formulated this as "weight decrease at synapse number i is proportional to PF number i firing rate times CF firing rate" - sometimes known as the "delta rule".
Clearly once the movement error goes to zero under this rule the PF strengths will stop changing, suggesting that a Purkinje cell might learn to fire in the way needed for accurate movements (by inhibiting deep cerebellar neurons that influence movement details). However we did not actually prove that this delta rule always improves things (which requires the implicit assumption that there ARE PF synapse strengths that allow perfect movements.)

Clearly this delta rule has a "Hebbian" flavor (see my last post) - synapse strength change depends on both input and output firing. Related rules underlie much of the most sophisticated new ML techniques.

Will ML succeed, and if so would machines take over our jobs, condemning almost all of us to abject poverty? If ML is to succeed it requires that our machines (e.g. computers) can do the required number crunching, and this tends to become prohibitively expensive as the numbers increase. So far Moore's Law has allowed  hardware to keep up with software, but this is now slowing, and researchers are exploring "neuromorphic" (brainlike) strategies. But it's not yet clear that implementing Hebbian synapses at extremely high density is straightforward either for the brain or for machines (see my last post).

 This is really not just a scientific question, but also one about politics and morality: should the owners of these technologies become the new economic aristocrats that the USA was founded to eliminate? In the meantime it's an exciting period in neuroscience and AI.

The Hebbian excitatory synapse

This diagram shows several key features a typical Hebbian  synapse. The transmitter glutamate is released from vesicles (orange) when a presynaptic spike arrives. This stimulates both AMPA-type receptors (green) and NMDA-type receptors (blue). The NMDARs generate very little current, because when they open they are immediately blocked by extracellular magnesium ions. The AMPARs generate an inward sodium current which depolarizes the spine head, and less strongly and with a slight delay, the cell body and the axon initial segment. If a lot of other synapses fire at roughly the same time, these small somatic depolarizations can add up and trigger a spike, which travels down the axon to the neuron's output synapses made on other neurons. But this spike also travels back along the dendrites, and reaches the synapse shown here (and the others that help trigger the spike). This pops out the Mg from the open NMDARs, which allows calcium to enter (shown as a red cloud; a few calcium ions are already around at rest). This calcium signal can then trigger, via CaMkinase, strengthening of the synapse by addition of more AMPARs (either from perisynaptic membrane and/or an intracellular source).

IMPORTANT POINTS                                                                                       

(1) the briefly open AMPARs do not permit Ca entry (Q/R switch) 

(2) the unplugged open NMDARs do ; this Ca signal triggers LTP (or perhaps LTD) 

(3) the occurrence of a back-propagating spike reflects the cooperative action of the firing of many individually weak synapses, each resembling that shown here, but varying in "strength" (= numbers of AMPARs). 

 (4) some synapses lack AMPARs - they are "silent". However, they can be unsilenced in exactly the same way as shown here.

 (5) If a backpropagating spike should arrive prematurely, before a presynaptic spike releases glutamate, or not at all, there is a much smaller calcium signal in the spine head (and therefore no LTP) but the early bAP can cause e.g. endocannabinoid release, which combined with subsequent stimulation of another type of presynaptic NMDARs (not shown), can cause, in the future, less transmitter release, weakening the synapse ("LTD"). 

(6) the calcium signal (and other second messengers underlying ltp/ltd) does not significantly spread to neighboring synapses, despite their extremely close packing (~ 1 um apart or less) and their rapid diffusion (~ 1 um^2/msec). Of course the devil is in that "significantly". My own research focuses on this rather neglected but crucial issue - more anon.