In order to control behavior, the brain relies on the ability of its neuronal networks to process information arising from external and internal sources. How single neurons decode combinations of sensory features and transform them into a spiking output is still unknown, and represents a subject of intense study. The complexity of the single neuronal coding problem can be illustrated by the paradoxical finding that neurons exhibiting narrowly tuned receptive fields often appear to be driven by synaptic inputs that themselves are broadly tuned (Chadderton et al., 2014). One hypothesis is that nonlinear dendritic transformations are critical for such neuronal computations. Decades of experimental and modeling studies on dendrites have led to the consensus that active properties of dendrites are primarily responsible for nonlinear integration, in particular supralinear operations (Mel, 1994; Spruston and Kath, 2004; Johnston and Narayanan, 2008). Nonetheless other findings indicate that sublinear integration of synaptic inputs is possible in multiple neuron types, and results from either active (Cash and Yuste, 1998; Hu et al., 2010) or passive dendritic properties (Abrahamsson et al., 2012; Vervaeke et al., 2012).

What is the evidence that nonlinear dendritic properties contribute to neuronal computations? Numerical simulations suggest that supralinear dendritic operations are essential for translation-invariant orientation tuning (Mel et al., 1998) and binocular disparity tuning (Archie and Mel, 2000), while sublinear dendritic operations contribute to coincidence detection of auditory stimuli (Agmon-Snir et al., 1998). Recently, state-of-the-art in vivo recordings have shown that dendritic supralinearities are associated with various other neuronal computations: formation of hippocampal place fields (Lee et al., 2012), detection of multi-modal sensory stimuli (Xu et al., 2012), angular tuning of barrel cortex pyramidal neurons (Lavzin et al., 2012), and enhancement of orientation tuning (Smith et al., 2013). Sublinear operations have also been shown to underlie orientation selectivity of binocular neurons in visual cortex in vivo (Longordo et al., 2013).

Nevertheless, a direct link between the dendritic transformations and the associated neuronal computations is still lacking. Analytical methods implementing mathematical approximations of measured dendritic operations can be used to make estimates of the possible number and type of neuronal computations. For example, binary neuron models were used to quantify what was previously shown with biophysical models (Mel, 1994), namely that nonlinear dendrites support a larger number of neuronal computations (Poirazi and Mel, 2001; Cazé et al., 2013). Such simplifications can provide analytical insight and make testable predictions as to which computations are made possible by dendritic operations. Moreover, analytical methods show under which conditions the expanded computational capacities are generic, i.e., not tied to the specific example parameters of the biophysical model.

Here we review the biophysical determinants of different classes of dendritic operations (linear, sublinear and supralinear), how they are measured experimentally, and finally, using a recently published Boolean-based analysis of equivalent dendritic trees (Cazé et al., 2012, 2013, 2014), we review how these operations combine with other cellular properties to determine neuronal computations.

Neurons integrate synaptic inputs arriving primarily on dendritic trees carrying information from presynaptic neurons, by transforming them into synaptic potentials using a variety of cell-specific synaptic and cellular mechanisms. During synaptic transmission, the activation of neurotransmitter-gated conductances results in either a transient depolarization or hyperpolarization of the postsynaptic membrane potential. When the net depolarization resulting from synaptic integration of multiple synaptic inputs is greater than the spike threshold potential, the neuron generates an action potential (AP), or spike. Synaptic integration is a critical determinant of neuronal computations, the process by which a postsynaptic neuron transforms presynaptic information (coded in input activation patterns) into an output signal (encoded in a firing pattern) (Häusser and Mel, 2003; London and Häusser, 2005; Silver, 2010; Larkum, 2013; Chadderton et al., 2014). This review will focus primarily on the integration of excitatory post-synaptic potentials (EPSPs) mediated by ionotropic glutamate receptors.

Dendritic integration can be quantified by comparing the observed depolarization resulting from the simultaneous activation of the same synaptic inputs (Figure 1B), also called a compound EPSP, and the arithmetic sum of individual EPSPs (expected membrane depolarization) (Figure 1C). The dendritic subthreshold input-output (sI/O) relationship is easily described by plotting observed vs. expected depolarizations for different numbers of co-activated synapses (Figure 1). Mathematical functions can be used to describe the operation performed. The sI/O relationships fall into three categories of dendritic operations: (1) linear, where the observed depolarization equals the expected depolarization; (2) supralinear, where the observed depolarization exceeds the expected depolarization (above the linear line; Figure 1D, left); and (3) sublinear, where the observed depolarization is less than the expected depolarization (below the linear line; Figure 1D, right). Much of the experimental evidence of nonlinear integration suggests dendrites perform supralinear operations, resulting from the contribution of active dendritic conductances (Mel, 1994; Johnston and Narayanan, 2008; Spruston, 2008). Recent studies suggest that sublinear operations could be mediated solely by passive properties (Abrahamsson et al., 2012; Vervaeke et al., 2012), while other studies have shown that activation of potassium channels can produce sublinear summation (Cash and Yuste, 1999; Hu et al., 2010). The detailed biophysical mechanisms determining specific dendritic operations are discussed in depth below.

The type of dendritic operation strongly contributes to the nature of the resultant neuronal computation. For example, co-activation of synapses within a single electrical compartment that exhibits supralinear integration will produce dendritic voltage signals that are larger than expected due to amplification by activation of voltage-sensitive channels. This large depolarization is thereby more likely to drive the neuron to spike threshold. The resulting sI/O will reflect a neuronal computation that is cluster sensitive (Figures 1E,F, left, θ₁). For a neuron with sublinear dendrites, clustered synaptic activity will be less efficient at triggering a spike than if the same inputs were distributed in different compartments, thus promoting computations that are scatter sensitive (Figures 1E,F, right, θ₁; Cazé et al., 2013). Such neuronal computations enable the discrimination of patterns of synaptic activation with different levels of spatial and temporal correlations, which could not be otherwise performed by linear dendrites (Mel, 1992). Nevertheless, it should be noted that the dendritic operation is insufficient to define the computation, synaptic placement and spike threshold also influence the final neuronal computation. In Figures 1D–F we show that lowering the spike threshold (θ₂) would restrict the access to only the linear regime of the subthreshold dendritic operation. Finally, ongoing synaptic activity can occur in the presence of AP firing, and thus constitutes supra-threshold synaptic integration (Silver, 2010), which we will not address in this review.

How do researchers study the biophysical properties of dendrites and their influence on excitatory synaptic integration? Classical electrophysiology methods such as sharp electrode- or patch-clamp-based recordings of somatic membrane potential provided insight into the intrinsic passive electrical properties of neurons by measuring the input resistance and the membrane time constant (τ = R_m*C_m) (Spruston and Johnston, 1992). When combined with multi-compartmental dendritic models, with either simplified morphologies (equivalent cylinder approximation) or full anatomical reconstructions (Clements and Redman, 1989; Major et al., 1994), the passive electrotonic properties of dendrites can be estimated from model parameters that predict the membrane potential decay from somatic current injections (Rall et al., 1992). These constrained models are then used to examine dendritic transformations of EPSPs as they propagate to the soma.

Unfortunately, single electrode recordings at the soma do not provide sufficient information about dendritic properties to constrain complex morphological models. With the advent of dendritic patch recordings (Stuart et al., 1993), at least for large diameter dendrites (≥1 µm), cable model predictions could be directly verified. This powerful recording method allows estimations of the critical parameters influencing dendritic filtering, such as internal resistivity (R_i; Stuart et al., 1993; Stuart and Spruston, 1998; Roth and Häusser, 2001; Nevian et al., 2007; Schmidt-Hieber et al., 2007; Hu et al., 2010), R_m and voltage-gated channel properties and density along the somato-dendritic axis (Magee and Johnston, 1995; Stuart and Spruston, 1998; Hu et al., 2010). Dendritic recordings also enabled the measurement of local EPSPs and EPSCs, which allowed the authors to conclude that dendritic filtering can be compensated by a distance-dependent increase in synaptic conductance in certain neuron types (Magee and Cook, 2000).

More recently, fluorescence imaging techniques have greatly increased the toolkit for studying dendritic integration, particularly in those dendrites with narrow diameters (<1 µm). Ca²⁺ indicators are one of the most popular class of fluorescence probes, which are used to indirectly study dendritic nonlinearities resulting from activation of voltage-dependent ion channels, provided at least one type of Ca²⁺ conductance was activated (Markram et al., 1995; Schiller et al., 1995, 1997, 2000). Ca²⁺ indicators have also been used to monitor synaptic activity because of the prevalence of NMDAR activation in single spines and Ca²⁺-permeable AMPARs at synapses in interneurons (Soler-Llavina and Sabatini, 2006). In vivo two-photon Ca²⁺ imaging experiments provided the first insights into the spatial and temporal distribution of sensory-evoked synaptic signaling within dendrites (Varga et al., 2011; Lavzin et al., 2012; Smith et al., 2013; Jia et al., 2014; Palmer et al., 2014). The contribution of in vivo Ca²⁺ imaging studies to understanding dendritic function has been recently reviewed by Grienberger et al (Grienberger et al., 2015). However, a limitation of using Ca²⁺ imaging to study synaptic integration is that it does not report the true dendritic voltage, a parameter critically influencing dendritic operations. Also, the slow nature of the whole-cell averaged [Ca²⁺] and the use of high affinity Ca²⁺ indicators limits the temporal resolution of this method (Farinella et al., 2014; Fernández-Alfonso et al., 2014). Voltage-sensitive dyes are, in principle, an ideal alternative for direct measurement of dendritic integration. Whereas voltage-sensitive dye recordings have provided unprecedented optical reports of the spatial and temporal distribution of APs in axons (Foust et al., 2010; Popovic et al., 2011) and dendrites (Acker and Antic, 2009; Casale and McCormick, 2011), their use to monitor EPSPs in dendrites has been less successful due to poor signal-to-noise ratio, typically requiring hundreds of trials of averaging (Palmer and Stuart, 2009). However, inhibitory post-synaptic potentials (IPSPs) have been detected (Canepari et al., 2008) and a recent study reports good signal-to-noise ratios sufficient to detect spine EPSPs (Popovic et al., 2014). The advances in genetically-encoded voltage indicators are also rapidly maturing (Hochbaum et al., 2014; St-Pierre et al., 2014; Zou et al., 2014), and could eventually provide a powerful tool for studying dendritic integration in vivo.

Another widely-used in vitro technique to characterize the integration properties of dendrites is to directly activate postsynaptic receptors using photolysis of caged-neurotransmitter (i.e., caged-glutamate) within the diffraction-limited focal volume of the microscope (Gasparini and Magee, 2006; Losonczy and Magee, 2006). Using galvanometer-driven mirrors, the type regularly used in scanning confocal microscopy, the focal illumination volume can be rapidly moved (within 0.1–1 ms) and positioned at multiple locations. The uncaging light pulse is then rapidly gated at each location to focally release glutamate. This allows for the near simultaneous activation of many postsynaptic sites. The somatic depolarization is then recorded using standard whole-cell patch-clamp methods. The observed response to uncaging at multiple synaptic locations (typically within 1 ms) is compared to the arithmetic sum of the uncaging-evoked responses at individual sites. The resulting plot is identical to the sI/O plots described in Figures 1, 3, provided that the uncaging responses are similar to synaptic activation. Using light, rather than presynaptic vesicular release, to activate neurotransmitter receptors provides a more flexible strategy to systematically vary the number, pattern, and timing of synapse activation. Electrical stimulation does not permit a precise identification of the synapses being activated, nor precise control of the number of synapses activated. Holographic illumination provides an alternative strategy for true simultaneous glutamate uncaging at multiple sites within the dendrites and is more amenable to multibranch activation (Lutz et al., 2008; Yang et al., 2014, 2011). The only potential drawback of uncaging is the difficulty in some preparations to accurately reproduce very fast synaptic conductances due to the large volume of diffraction-limited focal spots relative to the point source nature of neurotransmitter release from synaptic vesicles (DiGregorio et al., 2007), as well as a tendency to partially block GABARs (Fino et al., 2009). Nevertheless, neurotransmitter uncaging is an essential tool for quantifying the biophysical properties underlying dendritic operations.

Because experimental evidence of a direct link between the dendritic operations and the associated neuronal computations is still lacking, a parallel strategy is to use analytical models to make testable predictions (Poirazi and Mel, 2001; Legenstein and Maass, 2011; Cazé et al., 2013). These methods take advantage of mathematical approximations of measured dendritic operations to make estimates of the possible number and type of neuronal computations. Biophysical models, in contrast, although explicit, do not easily provide insight into the classes of possible computations because of the large parameter space. There is no doubt that such models have provided deep insights into neuronal computations that involve nonlinear dendritic operations. They have been used to show that neurons with supralinear dendrites are cluster-sensitive (Mel, 1993) and neurons with sublinear dendrites are scatter-sensitive (Koch et al., 1983; Cazé et al., 2013). Yet it was not clear whether either type of nonlinearity provides similar computational advantages. To examine the difference between supralinear and sublinear operations of binary neuron models Cazé et al. (2013) used a Boolean-based analysis. Here we review how this Boolean framework can be used to argue that either supralinear or sublinear summation is sufficient to endow neurons with a new class of computations.

Within this analytical framework, neurons are modeled as having binary inputs (x_i), which can be weighted and integrated, resulting in binary outputs (y). In this context the input-output relation is described by a unique truth table, corresponding to a Boolean function. In Figure 4A, the truth table describes three simple Boolean functions: OR, AND and XOR. This well-known mathematical framework (Wegener, 1987; Crama and Hammer, 2011), which deals with binary classifications of binary words, allows us to analytically determine what type of classifications are possible with nonlinear dendrites and which are otherwise impossible.

The simplest binary neuron model is called the threshold linear unit, also known as the point neuron model as described first by McCulloch and Pitts (Figure 4B; McCulloch and Pitts, 1943). Synapses are assigned a binary value of 0 or 1, for inactive or active states, which is then multiplied by a positive synaptic weight for excitatory synapses. The sum of the active weighted inputs is then compared to a somatic spike threshold Θ. If this weighted sum is greater than the threshold, the output is assigned a value of 1, and otherwise zero. If one considers a neuron with linearly summing excitatory inputs, adjustment of the threshold allows it to either perform a Boolean AND or OR (Figure 4B). However, it is not possible to find a threshold value and positive synaptic weight that allows the computation of the XOR, the function corresponding to a binary neuron that would fire only when one synapse is active, but not otherwise. This illustrates well the fact that the threshold linear unit can only perform functions that are linearly separable, i.e., there is a set of weights and a spike threshold that categorizes the inputs into two distinct groups, which differ by their output values (Figure 4A). The XOR does not meet this criterion and is therefore a part of the class of functions that are linearly non-separable. To solve this problem we must either invoke a non-monotone function to combine synaptic values (Zador et al., 1992) or consider synaptic inhibition by using negative weights (Mel, 1994; Cazé et al., 2014). Because the former has not been described experimentally, and the latter requires specific wiring within the network, we will focus here on linearly non-separable functions that can be implemented with only excitatory synapses and monotone dendritic operations. These functions are known as positive Boolean functions (Cazé et al., 2013).

Linearly–separable functions represent only a small fraction of all the possible computations (Cazé et al., 2013). However, a neuron with nonlinear dendritic compartments can implement the set of linearly non-separable functions, which encompasses a much larger fraction of all computations (Cazé et al., 2013). Thus both supralinear and sublinear compartments unlock the access to all the possible computations (Mel and Koch, 1990; Mel, 1991). This formal result is true for an infinite number of dendritic compartments (Poirazi and Mel, 2001). This is clearly impossible in practice. So what can a neuron compute with a finite number of dendritic compartments?

To address this question we can construct a two-layer binary model with nonlinear dendritic compartments. We first approximated the dendritic sI/O with functions each having a characteristic dendritic threshold θ, which represents the threshold of the dendritic nonlinearity, and h, which represents the maximal value of the dendritic nonlinearity. To approximate supralinear compartments we used a Heaviside function, and for sublinear functions we used a piecewise linear saturating function (Figure 4C). The output of the dendritic compartments is then linearly summed and compared with spike threshold (Figure 4D). If we vary synaptic weights, the thresholds, and the nonlinear dendritic operations, we can use Boolean analysis to examine the different functions this model can implement. A functionally salient neuronal computation that requires dendritic nonlinearities is the association (or binding) of two features of an object (for example, their shape and color). This is known as the feature binding problem (FBP). If we suppose that that different features of objects are encoded by different groups of pre synaptic neurons impinging on the same post synaptic neuron, then it is obvious that by allowing the features of an object to target the same supralinear dendrite, the coincidence of those features can be easily detected when co-active (i.e., “red” + “apple shape”; Figure 4E). It can also be shown that a sublinear operation can bind features if the inputs that encode object features are distributed onto different dendritic subunits (and the spiking threshold increased). From these simple binary models it is again clear that supralinear operations favor cluster sensitivity and sublinear operations favor scatter sensitivity. However, a keen eye may notice that the sublinear model will also produce a spike if the apple shape and banana shape are both activated. This therefore constitutes a partial FBP. Below we will describe a neuron model with equivalent dendrites that can implement the complete FBP.

Because neurons are known to have both linear and nonlinear compartments, we considered how more realistic dendritic trees could be represented using our simple binary model, by creating a neuron model with equivalent dendrites (Figures 5A,B). All linear regions of the dendritic tree (typically, the perisomatic compartment or the large diameter primary dendrites) were collapsed to a single equivalent “linear” compartment (black regions of schematic neuron and left branch of the model neuron). The nonlinear dendritic compartments receiving more than one synaptic input were represented as a second equivalent dendritic branch. This then generalizes to an equivalent dendritic branch for each nonlinear electrical compartment (Figure 4D). The presence of a linear compartment is important, since inputs contacting two separate nonlinear dendrites will sum linearly (Figure 5A). Also, even inputs contacting the same nonlinear dendrite, provided they are not in the same electrical compartment, will sum linearly.

Legenstein et al. demonstrated that a model neuron with supralinear dendritic integration is capable of learning and computing the FBP (Legenstein and Maass, 2011). This function detects any correct combination of features for an object, but not incorrect combinations. In the Boolean framework this would be the truth table corresponding to (“red” + “apple shape”) or (“yellow” + “banana shape”). In Figure 4 we showed that two supralinear dendrites are sufficient to solve the FBP for two objects made of two features each. In Figure 5, a neuron displaying at least one supralinear compartment and a linear compartment can also solve the FBP for four inputs. In this case, inputs encoding the features of one object are assigned to the supralinear compartment, and the features corresponding to the other object are assigned to the linear compartment (Figure 5C). Because the features of the object must “cluster” on the same compartment we refer to this model as using a local strategy of computation. Interestingly, it is also possible to implement the same computation using a global strategy, meaning that the features corresponding to one object need to be “scattered” onto both the nonlinear and the linear compartment (Figure 5D), provided that appropriate changes in the synaptic weights and threshold values are also implemented. As shown by Cazé et al. (2013), a model with a linear and sublinear compartment requires the global strategy to perform the FBP (Figure 5E). The synaptic weights and threshold will also be different than in the case of a model neuron with a supralinear compartment. The fact that the FBP can be implemented using a global strategy contrasts with the notion that recognition of an object required the clustering of the inputs carrying its features onto a same dendritic branch (Legenstein and Maass, 2011), and the assumption that two-layer integration models require independent branch-specific operations (Behabadi and Mel, 2014). Using a biophysical model with a model stellate cell morphology, Cazé et al. showed the predictions are robust, since only passive thin dendrites were necessary to convey a scatter sensitivity of output firing, even in the presence of synaptic noise (Cazé et al., 2013).

How might simplified Boolean models be modified for more features and/or more objects? For objects represented by more than two features, clustered strategies would simply require more synaptic inputs, such that the number of the number of inputs per subunit (dendritic compartment) equals the number features. A change in threshold would also be required. The requirements for neuronal computations using sublinear dendrites, however, depend on the type of computation and are less straightforward to determine explicitly. The necessary number of nonlinear subunits also varies given the implementation strategy, the number of objects, the type of nonlinear subunits and the number of features. To solve the FBP with more objects using supralinear operations, each object will require at least one subunit (Cazé et al., 2012). For computations with sublinear operations, Cazé et al. showed that using binary weights, the FBP requires a maximum of 2ⁿ subunits (Cazé et al., 2012). Considering non-binary weights then reduces the number of subunits needed, but this number is still higher than the number of necessary supralinear subunits (n_subunits = n_objects).

In summary, neurons with sublinear dendrites are capable of solving linearly non-separable functions, but require using a distributed strategy of synaptic placement (Figure 5E). These neurons will be scatter sensitive. On the other hand, neurons with supralinear dendrites can also access the same class of computations either by using this strategy (Figure 5C) or by clustering functionally relevant inputs onto the same compartment (Figure 5C). Hence they can be either scatter or cluster sensitive. Thus, the final neuronal computations depend not only on the type of dendritic operation and the dendritic and axosomatic thresholds, but also the global mapping of input features throughout the dendritic tree.

To understand how a neuron integrates its synaptic inputs we need precise knowledge of the morphology, ion channel distribution along the tree, strength and time course of synaptic conductances carrying particular information features, the output spike threshold, and the spatio-temporal pattern of activation of the synapses carrying these features. Although we can determine most of these parameters, as we reviewed above, the most challenging experiments are those designed to estimate the spatio-temporal distribution of all synapses carrying relevant sensory features (i.e., a functional connectivity map). Strategies using injection of viral-based retrograde tracers (Marshel et al., 2010) are powerful for the identification of connected presynaptic cells, but these methods lack information about features conveyed by the inputs. Using in vivo Ca²⁺ imaging, researchers have begun the herculean task of estimating how sensory features are mapped onto dendritic trees by examining how single synapses and dendrites respond to behavioral stimuli. It is not clear whether such feature mapping can be performed on the entire dendritic tree, but initial results provide hints as to whether there may be general mapping rules. Some studies argue that features are clustered in single dendrites within the somato-sensory cortex (Takahashi et al., 2012), consistent with a local computation strategy, while other studies have shown that neighboring synapses onto layer 2/3 pyramidal neurons of the visual and auditory cortex respond maximally for activation of inputs carrying different sensory features (Jia et al., 2010; Chen et al., 2011), consistent with a global strategy. In light of the conclusions described here, both computation strategies are capable of performing linearly non-separable functions.

Why might neurons use different dendritic operations and wiring strategies? It is conceivable that differences in timing of sensory development or optimal local circuit wiring may constrain wiring strategies for particular neurons. Thus to perform the same computation, different wiring and dendritic strategies are needed. Global wiring strategies are more amenable to “random wiring,” in contrast to the specific connectivity required for engaging local strategies. We speculate that different dendritic operations may be implemented by neurons given certain biological constraints, such as limitations in the number and location of synapses carrying a particular feature, or spike threshold. For example when both principal neurons and interneurons receive a common set of input features along relatively fixed axonal projections, but are required to perform different computations, they may engage different dendritic operations. In the cerebellum interneurons have been shown to exhibit sublinear dendritic operations (Abrahamsson et al., 2012; Vervaeke et al., 2012) on their parallel fiber inputs, while Purkinje cells are thought to receive the same or similar features from the same set of input fibers, yet display supralinear dendritic operations (Rancz and Häusser, 2006). One could speculate that the different nonlinearities and synaptic placement strategies of Purkinje neurons and interneurons may enable them to implement complementary computations, which ultimately could result in a microcircuit that is highly selective for specific input patterns.

What are the wiring rules? Three possible wiring strategies are (1) predetermined connectivity (genetically encoded); (2) random connectivity; and (3) activity-dependent pruning and stabilization of connections. Although the exact contribution of each mechanism is yet to be determined, synaptic plasticity has been shown to modify and ultimately determine the functional connectivity. For example computational modeling showed that a local wiring strategy, in which synapses carrying features of objects are clustered, can be learned using simple plasticity rules (Legenstein and Maass, 2011). Experimental evidence supports this theoretical work, suggesting that activity-dependent, branch-specific plasticity strengthens clustered synaptic inputs and their compartmentalization (Makara et al., 2009; Makino and Malinow, 2011; Takahashi et al., 2012). On the other hand, synaptic plasticity could also reinforce global computational strategies. In cerebellar stellate cells, high-frequency firing of clustered inputs has been described to induce profound presynaptic short- and long-term synaptic depression (Beierlein and Regehr, 2006; Soler-Llavina and Sabatini, 2006). Such plasticity mechanisms would reinforce the neuron’s scatter sensitivity, and thus tend to optimize the output firing for specific spatially and temporally sparse synaptic activity patterns (Abrahamsson et al., 2012; Cazé et al., 2013).

Synchronized neuronal activity is known to cause oscillations of the dendritic voltage, which would inevitably reinforce electrical interactions between dendrites and thus alter the effective number of isolated dendritic subunits that contribute to the neuronal computation. For example, Remme et al. (2009) showed theoretically that input-dependent synchronization of intrinsic dendritic voltage oscillations can facilitate global voltage propagation, even throughout highly distributed dendritic trees. It will be important to examine how local and global dendritic integration strategies might be influenced by brain oscillations, thus ultimately altering neuronal and even circuit computations.

Since many types of interneurons are known to contact specific locations within the dendritic tree, inhibition will undoubtedly influence integration properties and information processing by neuronal circuits (as reviewed by Palmer et al., 2012). Nevertheless, the experimental challenge is to determine not only the timing and location of inhibition within the dendrite, in order to determine their alteration of dendritic operations, but also whether particular features are conveyed similarly or differently by excitatory and inhibitory inputs. Although complex, the problem is critical to understanding brain function as the balance of excitation and inhibition is well known to be tightly regulated, with alterations being implicated in disease (Yizhar et al., 2011). Using the Boolean analysis of equivalent dendrites, one can deduce that negative weight associated with inhibition is capable of performing the Boolean NOT function. Such a function would enable a simple implementation of XOR computations, further expanding the number of computable linearly non-separable functions.

In this review we described categories of biophysical and cellular mechanisms that influence dendritic operations: passive and active membrane properties of the dendritic tree, the time course and amplitude of synaptic activation, the output spike threshold, and finally the location and pattern of the activation of synaptic inputs. We discussed how each of these parameters shapes and tunes the sI/O. We briefly discussed techniques for the characterization of dendritic operations, including electrode-based methods to stimulate and/or record from dendrites, optical techniques to image dendritic activity or uncage neurotransmitter, and biophysical modeling. In order to understand how the major classes of dendritic operations (linear, sublinear and supralinear) link to neuronal computations, we reviewed the use of binary models associated with Boolean analysis. This analysis provides insight into the types of computable neuronal functions, such as the object feature binding problem. We also reviewed how such functions can be implemented with either supralinear or sublinear dendrites depending on the spatial mapping of those features within the dendritic tree. Because the synaptic activity pattern ultimately determines the neuronal computations, we propose that the elemental computational unit is the neuron rather than the dendrite (Cazé et al., 2014). Although there are cases (local strategies) where dendritic operations can dictate the neuronal computation, dendritic operations must be studied and understood in the context of the knowledge of the wiring of specific features onto the dendritic tree.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.