# Ocular dominance column

Post-publication activity

Curator: Ana Calabrese

Figure 1: Ocular dominance columns in macaque monkey and cat. The upper panel shows the pattern over nearly the complete visual hemifield in a macaque monkey. The outer boundaries of the pattern correspond to the vertical midline of the visual field; F indicates the fovea; OD the optic disc and MS the monocular segment. The lower panel shows the distribution of radioactivity (bright regions) in a photomontage of sections of flattened cat striate cortex following injection of radioactive label into one eye. With permission from Swindale 1996.

Information from the two eyes is combined at the level of primary visual cortex (V1). Binocular neurons in V1 (i.e., neurons receiving input from the two eyes) typically show stronger response to stimulation coming from one or the other eye. As in other areas of neocortex, neurons that share similar visual preferences are typically grouped into columns. Evidence for this columnar organization has been found in multiple cortical areas. In the primary visual cortex, for example, cells with the same eye preference are grouped into ocular dominance columns. The concept of ocular dominance was introduced by the groundbreaking work of Wiesel and Hubel in cats in the 1960’s (Hubel and Wiesel 1969). They observed that in any micro-electrode penetration presumably perpendicular to the surface of the cortex most or all of the observed cells prefer one eye. To measure the influence of each of the two eyes in the responses of these neurons, they divided the cells studied into seven groups that range from exclusively contralateral eye dominance, to exclusively ipsilateral eye dominance. This way of dividing the cells is known as Hubel-Wiesel 7-point scale. Each group has one number asigned (from 1 to 7), where 4 means that the cell responds equally to the two eyes, 1 means exclusively contralateral and 7 exclusively ipsilateral dominance.

The characteristic periodicity and morphology of ocular dominance columns varies across different species. Moreover, recent evidence shows that the expression of ocular dominance columns can be highly variable among members of the same species, or even in different portions of the visual cortex in the same individual (Horton et al., 2005). For example, in the macaque monkey ( Figure 1, upper panel) the columns constitute branching stripes with an average width that ranges from 400 to approximately 700 μm (Horton et al., 1996; LeVay et al., 1985). In the cat ( Figure 1, lower panel) the pattern is less regular than in the macaque, and the column spacing range from approximately 800 to 1400 μm in area 17 (Rathjen et al., 2002). In humans, ocular dominance column widths range from 730 μm to 1 mm (Adams et al., 2007). [maybe a good idea to make the description consistent - either column widths, or the center-to-center spacing]

It is important to note that not all species have ocular dominance columns. Rodents do not seem to have ocular dominance columns or any other columnar organization in V1 (Gordon et al., 1996; Flogel et al. 2007; Van Hooser et a., 2005). In a series of studies, Adams and Horton (2003, 2006) showed that many squirrel monkeys do not have ocular dominance columns.

It is also important to note that the term 'ocular dominance' is sometimes used to refer to behavioral preference of one eye over the other. In this article, we refer to 'ocular dominance' in the context of the circuitry in primary visual cortex underlying the responses of cortical cells to inputs from one or the other eye. [Is there any evidence that the two are related in any way? If not, it might be a good idea to stress even further the independence of the two concepts in order not to confuse neophytes]

## Development of ocular dominance columns

Figure 2: Schematic of the visual system after development of ocular dominance patches. Retinal ganglion cells from the two eyes project to separate laminae of the LGN (represented by A and A1). Neurons from these two layers in turn project to separate patches or stripes within layer 4 of V1. Binocular regions are pictured at the borders between patches. With permission from Miller et al. 1989.
Figure 3: Timeline of development of the visual system in cats (upper panel) and ferrets (lower panel). Major events are plotted against embryonic (E) and postnatal (P) age.

In the adult visual system, alternate layers of the lateral geniculate nucleus (LGN) receive axons from either the left or the right eye. The cellular events involved in eye-specific retinogeniculate refinements are [or 'are currently being'] intensely studied. After an initial overlap phase (in which the retinal ganglion cell axons from the two eyes overlap extensively within the LGN), the inputs from the two eyes segregate to form eye-specific layers. This segregation process requires anatomical remodeling of axonal arbors that involve the formation of synapses and axon terminals in the same-eye territory and the elimination of synapses and axon terminals in opposite-eye territory (Huberman, 2007).

LGN projects to primary visual cortex (V1), the first cortical stage where binocular responses are observed (see Figure 2). Like eye-specific retinogeniculate projections, ocular dominance columns do not require visual experience to form (Horton et al., 1996). However, whether ocular dominance columns emerge through activity-dependent axonal refinement, or through directed in-growth mediated by axon guidance cues (or both mechanisms) has been intensely debated. Early studies showed that overlapping thalamocortical projections innervate the cortex early in development, with subsequent refinement in response to visual experience during a critical period. Two paradigmatic examples of experimental manipulation that researchers have been using to study the effects of visually driven activity on ocular dominance development are dark rearing (DR) and monocular deprivation (MD). It has been observed that depriving kittens of visual stimulation by rearing in darkness leads to reduced or abnormal segregation of ocular dominance columns (Hubel and Wiesel 1962; Wiesel and Hubel 1963; Swindale 1981, 1988; Mower et al. 1985). This does not seem to be true for monkeys where it has been found that a normal pattern of ocular dominance stripes developed in a macaque monkey reared in darkness after birth (LeVay et al. 1980; Horton et al. 1996). Monocular deprivation during this same early postnatal period results in a pronounced decrease in the area occupied by geniculocortical arbors representing the deprived eye and a corresponding increase in the area occupied by arbors representing the nondeprived eye (Hubel et al. 1977; Shatz and Stryker 1978; LeVay et al. 1980).

Most of these studies, which used monocular injections of transneuronal tracers to label retino-LGN-V1 axonal projections, observed continuous label in V1 (indicating lack of ocular dominance columns) of young animals, and alternating label in V1 (indicating the presence of ocular dominance columns) of older animals (LeVay et al. 1978). These observations led the authors to conclude that ocular dominance columns emerge from an initially overlapping and imprecise state.

The tendency for transneuronal tracers to spillover in the LGN of young animals caused other researchers (Crowley and Katz, 1999, 2000) to call such results into question and challenge the idea that ocular dominance columns segregate from initially overlapping projections. Crowley and Katz observed that projections from LGN to V1 were patchy from a much earlier stage in thalamortical development than it had been seen in the classical autoradiography studies. Form their observations they proposed that the two eyes’ inputs grow directly into segregated patches and that the locations of the two eyes’ patches are genetically specified.

Recently, optical imaging studies have shown that ocular dominance columns are present earlier in development in V1 of cats than can be detected by transneuronal tracing from the eye (Crair et al. 1998, 2001). Crair et al. observed that early in development, the contralateral eye dominates and projects inputs everywhere, while the ipsilateral eye projects to periodic islands. They found that the two eyes’ projections roughly develop into the mature pattern of ocular dominance columns only if there is visual experience. That is, without visual experience, the ocular dominance segregation remains in its initial, immature state.

There have been several experiments evaluating the role of activity in ocular dominance development. The fact that fully formed ocular dominance columns are present in primates at birth suggests that patterned spontaneous activity, and not visual experience, contributes to the initial establishment of ocular dominance columns. Even before the onset of visual experience, spatio-temporal patterns of neuronal activity within different levels of the developing visual pathway, from the retina to the visual cortex, are highly organized. Before eye-opening, characteristic waves of action potentials propagate across the retina, thereby coordinating the activity among neighboring ganglion cells (Wong et al. 1993, Shatz 1997). Recently, Huberman et al. carried out experiments in which they pharmacologically blocked spontaneous retinal activity before ocular dominance columns form in ferrets. The result of this early activity blockade is that ocular dominance columns do not segregate normally (Huberman et al. 2006). Furthermore, spontaneous activity, within and between different eye-specific layers of the LGN also has a highly specific correlational structure (Weliky and Katz, 1999). Correlational activity is highest between cells with the same eye-specific layer, and weaker between different eye-specific layers. In a series of studies, Weliky and co-workers showed that at the level of V1, synchronous bursts of activity occur early in development in ferrets, well before what had been regarded as the time ocular dominance develops (Chiu and Weliky 2001, 2002).

To sum up, despite considerable debate in recent years, a growing body of experimental data supports the notion that both patterned spontaneous retinal activity and axon guidance cues together contribute to the formation of ocular dominance columns. Once the initial circuit is formed, studies demonstrate a critical period of time during which ocular dominance columns can be modified in response to visual experience. This vision-dependent critical period does not always start at the onset of eye opening. In cats, rodents and ferrets, ocular dominance plasticity begins after 5-10 days of vision (see Figure 3), while the visual cortex of macaque monkeys is most vulnerable to deprivation during the first weeks of life (Horton et al. 1996).

### Functionality of ocular dominance columns

Half a century after the discovery of ocular dominance columns, their functionality remains an enigma. The fact that stripes can develop in situations in which they would not normally be present (e.g. in the marmoset, the owl, and the three-eyed frog) suggests they might be a consequence of the developmental process without any functional role (Constantine-Paton 1983). One candidate function for ocular dominance columns has been stereopsis. However, it has been reported that squirrel monkeys, which lack ocular dominance stripes [this has to be qualified by Horton's finding of highly variable OD columns in squirrel monkeys - some have them, some don't], have a stereoacuity comparable to that of human observers (Livingstone et al. 1995). Furthermore, several observations indicate that species with no clear ocular dominance columns still display excellent visual capabilities. Another candidate function for ocular dominance columns (and for columns in general) is the minimization of connection lengths and processing time, which could be evolutionary crucial. [the relationship between OD and disparity selectivity, or lack of it, could be discussed further]

## Molecular basis of plasticity in the visual cortex

Although visual cortical plasticity has been widely studied since its initial discovery by Hubel and Wiesel more than 40 years ago, the underlying molecular mechanisms that control the developmental plasticity of visual cortical connections are still unclear. Here we describe some of the mechanisms that might be involved in these processes (For a more detailed discussion see Reviews by Berardi et al. (2003); Hensch (2005)): [Nigel Daw's Scholarpedia article on Critical Periods also covers some of this material]

• NMDA receptors. The first modifications induced by experience in visual cortical circuits are likely to be changes in synaptic efficacy. Ever since the discovery of NMDA receptors (NMDARs), these synaptic receptors have been associated with experience-dependent plasticity. The involvement of NMDARs in developmental visual cortical plasticity has been initially suggested by the observations that the blockade of NMDARs in cortical cells, eliminates the effects of monocular deprivation (Kleinschmidt et al. 1987 and Bear et al. 1990). Their characteristic of being both transmitter- and voltage- dependent, and their coupling via Ca2+ influx to plasticity-related intracellular signaling, has led to the notion that they might be a neural implementation of Hebbian synapses.
• Neurotrophins. Several observations have suggested that the formation of ocular dominance columns might involve competition between axons or axon branches for target-derived neurotrophic factors. Neurotrophins or neurotrophic factors are substances (proteins) found in the blood stream which are capable of signaling particular cells to survive, differentiate, or grow. Neurotrophin production and release depend on electrical activity and, in particular, depend on visual activity (McAllister et al. 1995). In turn, neurotrophins can modulate electrical activity and synaptic transmission at both presynaptic and postsynaptic levels (Poo 2001). They exhibit both fast actions (by increasing transmitter release (Jovanovic et al. 2000) or by directly depolarizing neurons (Kafitz et al. 1999), and slow actions, (by modulating gene expression). It has been observed that continuous infusion of the neurotrophin NT-4/5 or the neurotrophin BDNF in the cat visual cortex during the critical period, prevents the formation of ocular dominance columns (Cabelli et. al. 1995). As expected when axons compete for neurotrophic factor, removal of neurotrophic factor by application of neurotrophic factor antagonists prevents the formation of ocular dominance columns by eliminating inputs from both eyes (Cabelli et al. 1997). In monocular deprivation experiments in cat, excess neurotrophic factor mitigates the relative increase in the size of the ocular dominance stripes associated with the open eye (Carmignoto et al. 1993, Hata et al. 1996), possibly by overwhelming the competitive disadvantage of the closed eye.
• Intracortical inhibition. Recently, it has become clear that inhibition has an important role in shaping the pattern of electrical activity. Indeed, Hensch et al. have shown that inhibitory interactions are necessary for the manifestation of experience dependent plasticity. In transgenic mice lacking the 65-kDa isoform of the GABA-synthesizing enzyme GAD (GAD65), experience-dependent plasticity in response to monocular deprivation is deficient (Hensch et al. 1998). Development of inhibition seems also to be a determinant of the critical period: an accelerated development of GABA-mediated inhibition results in an early opening and closure of the critical period.

## Theoretical studies of ocular dominance column development

Several models in which competition plays an important role have been proposed to explain the development of columnar organization in the visual system, especially ocular dominance (For a detailed review of models see Van Ooyen 2001, 2005; Swindale 1996). Most of the models of visual cortical development proposed so far are based on a common set of postulates. These are: (i) Hebb synapses; (ii) Correlated or spatially patterned activity in the afferents to cortical neurons; (iii) Fixed connections between cortical neurons which are locally excitatory and inhibitory at slightly grater distances; (iv) Normalization of synapse strength.

Normalization typically ensures that the sum of the synaptic weights converging on each postsynaptic neuron remains constant, or that the sum of the weights of each input cell remains the same, or some combination of the two. These constraints can be enforced by multiplying or subtracting appropriate values from the weights.

To see how competition between input connections can be enforced, consider n inputs, with synaptic strengths $$w_i(t) (i = 1,...,n)\ ,$$ impinging on a given postsynaptic cell at time t. Simple Hebbian rules for the change $$\Delta w_i(t)$$ in synaptic weight in the time interval $$\Delta t$$ state that the synaptic strength should grow in proportion to the product of th post synaptic activity level $$y(t)$$ and the activity level $$x_i(t)$$ of the ith input. Thus $\tag{1} \Delta w_i(t) \propto y(t)x_i(t)\Delta t.$

If two inputs (e.g. two eyes) innervate a common target and if the activity level in both inputs is sufficient to achieve potentiation, then the rule causes both pathways to be strongly potentiated. Experimental evidence shows that when the synaptic strength of one input grows, the strength of the other one decreases. One mechanism to achieve this competition mathematically is to keep $$\sum^n_i w_i(t)$$ constant (synaptic normalization). The synaptic strengths can be forced to satisfy this normalization constraint either by multiplying each synaptic strength with a certain amount (multiplicative normalization; Willshaw and Von der Malsburg 1976) or by subtracting from each synaptic strength a certain amount (subtractive normalization; Miller et al. 1989). The final outcome of development may differ depending on whether multiplicative or subtractive normalization is used (for a full discussion of the effect of different kinds of weight normalization see Miller et al. 1994 and Goodhill et al. 1994).

### Miller et al., 1989

Figure 4: Afferents from the left-eye (white) and right-eye (black) layers of the LGN innervate layer 4 of the visual cortex. $$\alpha$$ and $$\alpha '$$ label position in the LGN, and $$x$$ and $$x'$$ label the retinotopically corresponding points in the cortex; $$\gamma$$ labels an additional position in the cortex. The afferent correlation functions are functions of separation across the LGN. The arbor function A measures anatomical connectivity (number of synapses) from a geniculate point to a cortical point, as a function of the retinotopic distance between them. The cortical interaction function I depends on distance across cortex. The left-eye and right-eye synaptic strengths, $$S^R$$ and $$S^L\ ,$$ from a geniculate location to a cortical location, depend upon both locations. With permission from Miller et al. 1989.

Miller et al. (1989) formulated a model describing how spatially correlated neuronal activity in the two layers of the LGN might lead, in the presence of Hebbian synaptic modification rules, to the segregation of inputs in the cortex into periodically alternating ocular dominance stripes. A pre-existing spatial topography was assumed to exist between the input layers and the cortex. Inputs from location $$\alpha$$ in the LGN were assumed to make contact with cortical neurons centered on a location $$x$$ in the cortex, and spread over a surrounding region, described by a fixed arborization function $$A(x - \alpha)\ .$$ The arborization function was usually 1 over a small square region and zero elsewhere, although in subsequent analyses (Miller and Stryker 1990; Miller 1990a) this restriction was relaxed. The statistical structure of the input patterns was described by four radially symmetric functions, $$C^{LL}\ ,$$ $$C^{RR}\ ,$$ $$C^{LR}$$ and $$C^{RL}$$ specifying how the correlation in neural firing rates varies with lateral separation in the LGN (a scheme of the model is shown in Figure 4). The strength of the connection from the two eyes, from a position $$\alpha$$ in the LGN, to a position x in the cortex at time t was given by two functions, $$S^L(\alpha,x,t)$$ and $$S^R(\alpha,x,t)\ .$$ Lateral interactions in the cortex were described by a function $$I(x)\ .$$ The contribution of a synapse $$S(x',\alpha')$$ to the correlation value associated with a second synapse $$S(x,\alpha)$$ was assumed to be proportional to the product of the correlation value associated with the separation between the cells of origin in the LGN, i.e. $$C(\alpha-\alpha')\ ,$$ the strength of the synapse itself i.e. $$S(x',\alpha')\ ,$$ and the value of the lateral interaction function for separation of the synapses in the cortex, i.e. $$I(x-x')\ .$$ This led to the following equation for the change of synaptic strength with time:

$\frac{\textrm{d} S^L}{\textrm{d} t}(x, \alpha, t) = \lambda A(x-\alpha)\sum_{x',\alpha'}I(x-x')[C^{LL}(\alpha - \alpha')S^L(x',\alpha',t) + C^{LR}(\alpha - \alpha')S^R(x',\alpha',t)] - \gamma S^L(x, \alpha, t) - \epsilon A(x- \alpha)$

Figure 5: Typical development of ocular dominance patches. Ocular dominance of cortex at timesteps T = 0, 10, 20, 30, 40, 80. Each pixel represents a single cortical cell. The colors represent ocular dominance of each cell. Red indicates complete dominance by the right eye, green indicates complete dominance by the left eye, and blue represents equality of the two eyes. With permission from Miller et al. 1989.

with a corresponding equation for $$S^R$$ obtained by interchanging L and R. A multistep normalization procedure was also used, in which the sum of the synaptic weights at each cortical location was kept constant. This was done by subtracting from the weights, rather than dividing them. This difference is important because it has been shown that, if multiplicative normalization is used instead, segregation will not occur in the presence of positive correlations between the two eyes (Miller et al. 1989; Miller 1990a, b; Miller and Mackay 1994; Goodhill and Barrow 1994).

Miller et al. examined the behavior of this system by mathematical analysis and computer simulation. Under certain assumptions of the correlation functions and the cortical interaction function, a striped periodic pattern of ocular dominance developed on the cortical surface (see Figure 5).

The simulations and analysis (Miler et al 1989; Miller and Stryker 1990; Miller 1990a) allowed to study the effect of different arbor widths, different correlation functions and different cortical interaction functions. When the cortical interaction function contained both short-range excitatory and long-range inhibitory components, the spacing of the ocular dominance stripes was determined by the shape of the cortical interaction function, I(x). When I(x) was purely excitatory, the width of the individual ocular dominance stripes was about equal to the arbor size. The input correlations mainly affected the receptive field sizes and the monocularity of the cortex: a narrower within-eye correlation function resulted in a less monocular cortex (i.e. more binocular cells at the borders of the stripes) and smaller receptive field sizes.

The parameters specified in Miller’s model are in principle measurable quantities. Weliky et al. (1999) studied early LGN correlations and showed that indeed within-eye correlations were stronger than between-eye correlations as predicted by the model. In relation to whether input correlations might affect column width, Rathjen et al. (2002) showed that strabismus did not affect column width. Hensch and Stryker (2004) showed that alterations in the intracortical interactions could indeed alter column width.

## Modified hebbian learning rules

A biophysically more plausible approach for achieving competition is to modify Eq. (1) such that both increases in synaptic strength (long term potentiation, or LTP) and decreases in synaptic strength (long term depression, or LTD) can take place. This can be accomplished by assuming that $$y(t)$$ and $$x_i(t)$$ must be above some thresholds $$\theta_y$$ and $$\theta_{xi}\ ,$$ respectively, to achieve LTP and otherwise yield LTD (Miller et al. 1996); i.e., $\Delta W_i(t) \propto [x_i(t) - \theta_x][y(t) - \theta_y] \Delta t$

If both $$y(t)$$ and $$x_i(t)$$ are below their thresholds (note that in this case the rule would imply that LTP occurs), $$\Delta W_i$$ is set to 0, which corresponds to no change in synaptic strength (for a full discussion see Miller et al. 1989). A stable mechanism for ensuring that when some synaptic strengths increase, others must correspondingly decrease is to make one of the thresholds variable. If $$\theta_{xi}$$ increases sufficiently as $$y(t)$$ or $$w_i(t)$$ (or both) increase, conservation of synaptic strength can be achieved (Miller 1996). Similarly, if $$\theta_y$$ increases faster than linearly with the average postsynaptic activity, then the synaptic strengths will adjust to keep the postsynaptic activity near a set point value (Bienenstock et al. 1982).

### Harris et al., 1997

Figure 6: The model by Harris et al. (1997). Each cortical cell i receives input from both the left(L) and the right(R) eye. The connection from each eye has a fixed total amount of material available, so that —for the right eye, for example— the current connection strength $$w^r_i$$ plus the free store of raw material $$f^r_i$$ remains constant. The rate at which raw material is reversibly transformed into connection strength is affected by the amount $$n^r_i$$ of neurotrophin taken up by the connection. Each cortical cell has a fixed total amount of neurotrophin available, so that the amounts taken up by the right and left eye connections($$n^r_i$$,$$n^l_i$$)plus the amount of free neurotrophin left at cortical cell $$i$$ remains constant. From Van Ooyen 2001.

There exists a rich literature on the molecular changes that accompany ocular dominance development. A pioneering approach for incorporating some of these events into a quantitative model was provided by Harris et al 1997. This model of ocular dominance columns development incorporates a combination of Hebbian synaptic modification with activity-driven competition for neurotrophic factors (NTs).

In the model, each cortical cell has a fixed pool of neurotrophin to distribute over its input connections$N_i^f +(n_i^r + n_i^l) = N_i$ (where $$N_i$$ is the total amount of NT available at cortical cell $$i\ ,$$ $$(n_i^r + n_i^l)$$ equals the sum of the amounts currently taken up by the right and the left inputs, and $$N_i^f$$ is the amount of free NT left at cell $$i$$).

In the model it is also considered that there is a reversible interchange between connection strength and free store of raw material, formulated in terms of mass action kinetics: $\tag{2} f^r_i = (1 - w^r_i) \rightleftharpoons ^{K^+(n^r_i,v_i,a^r)}_{K^-(v_i)} w^r_i$

where $$w^r_i$$ is the current amount of connection strength of the input from the right aye. The rate constants are functions depending on the firing rates of the inputs, the firing rate of the cortical cell, and the current amount of synaptic trophic factor. The trophic factor uptake dynamics obey a simple kinetic equation as well: $\tag{3} N^f_i = N_i-(n^r_i + n^l_i) \rightleftharpoons^{w^r_i}_{\beta_2} n^r_i$

From which can be seen that the higher the connection strength, the faster the uptake of NT (see Figure 6). Finally, it is considered that connection strength increases due to Hebbian LTP at a rate that depends on the amount of neurotrophin taken up (together with the previous assumption this creates a positive feedback loop). Connection strength decreases due to heterosynaptic LTD.

The model shows that ocular dominance columns develop normally –even with positive inter-eye correlations- when available NT is below a critical amount and that column development is prevented when excess neurotrophin is added. Harris et al. (2000) showed that their model can also account for the experimental results that column formation is prevented by removal of NT (Cabelli et al. 1997) and that the shift to the open eye in monocular deprivation experiments is mitigated by excess neurotrophin (Carmignoto et al. 1993; Hata et al. 1996).

Elliott and Shadbolt proposed a model of the development of the visual system that explicitly describes anatomical plasticity and incorporates the role of electrical activity, both in the release and in the uptake of neurotrophin.

The variable in the model is the number $$s^n_i$$ of synapses that axon $$i$$ has on the target at time step $$n\ .$$ The target releases neurotrophin, in amount $$r^n\ .$$ The uptake $$u^n_i$$ of neurotrophin by axon $$i$$ increases with its number of synapses and its level of activity: $\tag{4} u^n_i = Q^nr^ns^n_ig(a^n_i)\rho^n_i$

where $$Q^n$$ is constant of proportionality, $$g$$ is some function of the axon's activity, and $$\rho_i$$ is the affinity of each synapse for the neurotrophin and is interpreted as the number of neurotrophin receptors. Uptake of neurotrophin increases the number of synapses: $\tag{5} s_i^{n+1} - s_i^n = \epsilon (u^n_i - s^n_i)$

where $$\epsilon$$ is a constant determining the growth rate. From this equation, for an axon to sustain its synapses it needs to take up neurotrophin; if $$u^n_i = 0\ ,$$ the number of synapses decreases. Equations (4) and (5) incorporate a positive feedback: neurotrophin increases the number of synapses, and more synapses mean a higher uptake of neurotrophin.

This model permits the formation of ocular dominance columns, even in the presence of positive inter-eye correlations. Elliott and Shadbolt (1999) found that a high level of NT released in an activity-independent manner prevents the formation of ocular dominance columns. In a further study (Elliott and Shadbolt 1999), they used their competition model to show that spontaneous retinal activity can drive the segregation of afferents into eye-specific laminae (LGN) and columns (cortex), as well as the refinement of topographic and receptive fields in the retinogeniculocortical pathway.

## Spike-Timing dependent plasticity

Yet another mechanism that can balance synaptic strengths is based on spike-timing dependent plasticity (STDP; reviewed in Bi and Poo 2001). Presynaptic action potentials that precede postsynaptic spikes strengthen a synapse, whereas presynaptic action potentials that follow postsynaptic spikes weaken it. Subject to a limit on the strengths of individual synapses, STDP keeps the total synaptic input to the neuron roughly constant, independently of the presynaptic firing rates (Song et al. 2000).

## Two models for inhibitory control of cortical plasticity

### Hensch, 2005

Figure 7: Two models for inhibitory control of sensory plasticity. (a) Somatic inhibition by fast-spiking parvalbumin-positive (PV+) cells (green) expressing the potassium channel Kv3.1 is mediated by the GABA A ($$\gamma$$-aminobutyric acid type A) $$\alpha 1$$-subunit, whereas axonal inhibition is mediated by the GABA A $$\alpha 2$$-subunit. Somatic inhibition is ideally situated for suppression, or 'editing' of unwanted spikes, preventing them from back-propagating through the cell body into the dendritic tree (red arrow). This is an 'instructive' model, as individual action potentials can produce long-term potentiation (LTP) or depression (LTD) based on precise spike-timing dependent windows at individual synapses of coincident pre- and postsynaptic activity123,124. Notably, failure to regulate excess spiking at the axon initial segment can still be differentiated by fast-spiking inhibition at the cell body. (b) Gap junctional coupling endows networks of parvalbumin-positive (PV+) interneurons with the ability to detect synchronous input. Even a slight jitter in input timing (for example, between eyes) dampens network activity through reciprocal GABA- mediated contacts (enriched with GABA A-receptor $$\alpha 1$$-subunits). Only synchronous open-eye input will produce maximal, activity-dependent release or uptake of 'permissive' factors for neurite growth (for example, tissue-type plasminogen activator and brain-derived neurotrophic factor). Competition is determined extracellularly. With permission from Hensch, 2005.

Based on the identification of a particular GABA circuit that drives the onset of the critical period and the subsequent anatomical changes, Hensch proposes two different scenarios centered on the parvalbumin-positive basket cell (PV+).Figure 7a (Hensch 2005) shows a schematic of the first model. In this model, powerful somatic inhibition by fast-spiking PV+ cells edits one-by-one the action potentials that can pass into the dendritic arbor by back-propagation through the cell body. The idea is that individual action potentials can produce long-term potentiation (LTP) or depression (LTD) based on precise spike-timing dependent windows at individual synapses of coincident pre- and postsynaptic activity.

The second model is based on newfound knowledge of PV+ cell biology. Basket cells can be coupled electrically into groups of 40 or 50 cells, forming a network with the ability to detect synchrony (see Figure 7b, Hensch 2005). Whereas simultaneous inputs (for example, from the same eye) rapidly co-excite cells through gap junctions, a small input jitter (for example between opposite eyes) is sufficient to dampen the coupling by reciprocal GABA synapses. As a result, these are maximally active on a columnar scale, time locked to release growth or plasticity factors when strong synchronous activity arrives in the neocortex.

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Internal references

• Eugene M. Izhikevich (2006) Bursting. Scholarpedia, 1(3):1300.
• Rodolfo Llinas (2008) Neuron. Scholarpedia, 3(8):1490.
• Jose-Manuel Alonso and Yao Chen (2009) Receptive field. Scholarpedia, 4(1):5393.
• John Dowling (2007) Retina. Scholarpedia, 2(12):3487.
• Philip Holmes and Eric T. Shea-Brown (2006) Stability. Scholarpedia, 1(10):1838.
• Arkady Pikovsky and Michael Rosenblum (2007) Synchronization. Scholarpedia, 2(12):1459.