We first examined how plasticity induced by dendritic plateau potentials changes the intracellular membrane potential (V_m) dynamics in neurons already exhibiting location-specific firing (i.e. place cells). Intracellular voltage recordings from CA1 pyramidal neurons were established in head-fixed mice trained to run for a water reward on a circular treadmill decorated with visual and tactile cues to distinguish spatial positions (~185 cm in length). Brief step currents (700 pA, 300 ms) were injected through the intracellular electrode for a small number (Nakazawa et al., 2004; O’Keefe and Conway, 1978; Mehta et al., 1997; Lever et al., 2002; Dupret et al., 2010; Zaremba et al., 2017; Turi et al., 2019; Ziv et al., 2013) of consecutive laps to evoke plateau potentials at a second location that was between 0 and 150 cm from the initial place field (labeled ‘Induction 2’ in Figure 1A and B; n = 26 plasticity inductions in 24 neurons). In 8/24 neurons a ‘natural’ pre-existing place field was expressed from the start of recording, while in 16/24 the initial place field was first experimentally induced by the same procedure (labeled ‘Induction 1’ in Figure 1A and B). In 2/24 neurons the induction procedure was repeated a third time with plateaus evoked at a different location, resulting in a total of 26 plasticity inductions in cells with pre-existing place fields (see Figure 1—figure supplement 1E and Materials and methods).

In most cases the evoked dendritic plateaus shifted the location of the neuron’s pre-existing place field toward the position of the second induction site (Figure 1A and B). Place field firing is known to be driven by a slow, ramping depolarization of V_m from sub- to supra-threshold levels (Bittner et al., 2015; Harvey et al., 2009). Isolation of these low-pass filtered V_m ramps (Figure 1—figure supplement 2A-H; Materials and methods) revealed that plateau potentials likewise shifted the neuron’s V_m ramp toward the position of the plateau, such that the new V_m ramp peaked near the plateau position in most neurons (average distance = 19.5 ± 4.7 cm; n = 26; Figure 1C–E and Figure 1—figure supplement 2; example cells shown in Figure 1C are indicated with matching colored arrows in Figure 1D). We also observed similar shifts in place field position to be induced by spontaneous, naturally occurring plateau potentials in a separate set of recordings (n = 5; Figure 1—figure supplement 2I-M).

The spatial profile of plateau-induced V_m changes (ΔV_m) (Figure 2A) was obtained by subtracting the average V_m ramp for trials occurring before plateau initiation (Figure 1C; before) from the average V_m ramp for trials occurring after (Figure 1C; after). These data indicate that plateaus induced both positive and negative changes to V_m ramp amplitude (Figure 2A and B). In general, the increases in V_m depolarization peaked near the position of the plateau, while the negative changes peaked near the initial place field (Figure 2A and B, and Figure 2—figure supplement 1A and B). Although these changes varied considerably in magnitude across cells, the peak change in the positive direction was greater than the peak change in the negative direction (mean positive change± SEM vs. mean negative change± SEM: 6.73 ± 0.73 mV vs. 3.89 ± 0.32 mV, n = 26 inductions; p = 0.0001, paired two-way Student’s t-test; Figure 2—figure supplement 1A). Aligning each ΔV_m trace to the position of the plateau (Figure 2A and B) demonstrates that the increases in V_m depolarization observed near the plateau position decay with distance, eventually becoming hyperpolarizing decreases in V_m. At even greater distances from a plateau, ΔV_m decays back to zero (Figure 2B). To summarize the data presented thus far, dendritic plateau potentials change the location of place field firing by depolarizing V_m around the plateau position and hyperpolarizing V_m at positions within a pre-existing place field.

Previously we showed that location-specific increases in V_m depolarization induced by plateau potentials are the result of synapse-specific increases in the strength of spatially tuned excitatory inputs (Bittner et al., 2017). The above results suggest that, in addition to this synaptic potentiation, BTSP is also capable of inducing synaptic depression to cause location-specific decreases in V_m depolarization. In analyzing the spatial extent of the V_m changes induced by plateaus, we observed a strong linear relationship between the width of the resulting ΔV_m and the running speed of the animal during plateau induction laps (Figure 2C and D), which had a slope on the order of seconds. This suggested that the run trajectory of the animal (Figure 2C) affected the spatial extent of the plasticity (Figure 2A and B) by determining which positions were traversed within a fixed seconds-long temporal window for plasticity, as we previously reported (Bittner et al., 2017). Therefore, we next analyzed the temporal relationship between plateau potentials and location-specific potentiation and depression. To do this, we used the running trajectory of the mice during plateau induction trials (Figure 2C) as a time base for ΔV_m (Figure 2E; see also Figure 1—figure supplement 1, Figure 1—figure supplement 2A-H and Materials and methods). This analysis showed that the positive and negative changes to V_m induced in place cells occurred over a timescale of multiple seconds (Figure 2F), with the positive changes appearing to be asymmetric with respect to the onset time of the plateaus (ratio of potentiation duration before/after plateau onset: 2.2; black circles and crossmarks in Figure 2F mark the time points when ΔV_m crosses zero). This asymmetry was similar to that observed for the positive V_m changes induced by BTSP in silent cells (Bittner et al., 2017). The negative changes (i.e. the hyperpolarizations indicative of synaptic depression) occurred within a time window between ±2 and ±6 s from the plateau in many neurons that expressed pre-existing place fields (Figure 2E and F). Notably, this hyperpolarization was greatly reduced, or even absent, in a set of place cells where the time delay between plateau onset and the initial place field V_m ramp was greater than 4–5 s (red traces in Figures 1C, 2A and E; see also Figure 2—figure supplement 1C-F), further indicating the time delimited aspect of the depression component. These data reinforce the idea that BTSP is a bidirectional form of synaptic plasticity with a seconds-long timescale that enables dendritic plateau potentials to shift the locations of hippocampal place fields by inducing both synaptic potentiation and depression.

We next sought to understand why dendritic plateaus induce both V_m depolarization and V_m hyperpolarization in cells expressing pre-existing place fields (Figures 1 and 2), but induce only V_m depolarization in spatially untuned silent cells (Figure 3—figure supplement 1; Bittner et al., 2017). Figure 3A shows that the initial temporal profile of V_m in place cells with pre-existing place fields was highly variable across neurons, as plateaus were experimentally induced at different temporal intervals from the existing place field in different neurons. In contrast, the change in V_m (ΔV_m) induced by plateaus showed a more consistent shape in time that appeared to depend on the initial level of V_m depolarization at each time point prior to plasticity (Figure 3B). Large positive changes occurred at time points with relatively hyperpolarized initial V_m, while time points with more depolarized initial V_m were associated with less positive and more negative ΔV_m. These changes resulted in final V_m profiles that were highly similar across neurons, regardless of the initial V_m (Figure 3C). These results indicate that BTSP induces variable changes in synaptic strength that reshape the selectivity of neurons toward a common target shape – a place field centered near the location of evoked plateau potentials that decays toward baseline over many seconds in each direction.

In Figure 3D-F, we examined this further by comparing data from initially hyperpolarized silent cells (black; n = 29 inductions, see Figure 3—figure supplement 1 and Materials and methods) to data from place cells (dark red; n = 26 inductions). Place cells were on average more depolarized before plasticity than silent cells (Figure 3D), and more depression occurred in place cells compared to silent cells (Figure 3E). However, each place cell had both spatial positions where it was depolarized within its place field, and positions where it was hyperpolarized out-of-field. To determine if spatial positions that were initially depolarized were associated with larger depression, we grouped V_m ramp data from all place cells, considering only spatial bins where each cell was more depolarized than a threshold of –56 mV (light red traces labeled ‘PCs (within-field)’ in Figure 3D-F). Indeed, more depression and less potentiation was induced in place cells at those spatial positions that were initially most depolarized (Figure 3E). However, the final V_m ramps after plasticity were less sensitive to the initial state of depolarization across spatial bins of place cells (Figure 3F). This analysis further supported the findings that, while changes in V_m induced by plateaus were highly dependent on initial V_m, these changes drove the resulting final V_m ramp toward a common target shape (Figure 3F). Indeed, when all spatial bins from all place cells were analyzed, ΔV_m showed a strong inverse correlation with initial V_m (m = –0.91; Figure 3G). In contrast, final V_m showed a very weak positive correlation with initial V_m (m = 0.04; Figure 3H), which reflects that some spatial bins show no change in V_m during plasticity, either because they were traversed outside the temporal window for plasticity or because the V_m at those positions had already reached a final V_m target value.

That BTSP induces variable changes in V_m that reshape the V_m ramp toward a particular target shape is further evident from a heatmap depicting the relationships of ΔV_m to both initial V_m ramp depolarization and time from plateau onset (Figure 3I, positive ΔV_m in red, and negative ΔV_m in blue; see Materials and methods). The white regions of this plot trace out a temporal profile of V_m that corresponds to the final target place field shapes shown in Figure 3C and F. All initial deviations from this equilibrium V_m profile resulted in either positive or negative changes to approach this target place field shape (see dashed arrows). It should also be noted that the depression of V_m in place cells appeared to be weaker than the potentiation, leaving some residual depolarization at positions distant from the peak (Figure 3F). The functional significance of this is unclear, but may suggest that BTSP induces synaptic depression at a slower rate than potentiation (Cone and Shouval, 2021). To summarize, BTSP induces precise changes in synaptic strength that modify pre-existing place fields with any initial shape such that they approach a target shape that peaks near the location where dendritic plateaus were evoked.

Altogether these data revealed that, in general, the magnitude and direction of ΔV_m depended on the time from the plateau potential, and correlated inversely with the initial V_m ramp amplitude prior to plasticity induction. Does this anti-correlation reflect a causal relationship between postsynaptic depolarization and changes in synaptic weight induced by BTSP? This possibility would require that small depolarizations induce synaptic potentiation and large depolarizations induce synaptic depression, which is actually opposite to what has been observed in CA1 pyramidal cells with a variety of other plasticity protocols (Shouval et al., 2010; Yang et al., 1999; Graupner and Brunel, 2012; Clopath et al., 2010; Clopath and Gerstner, 2010; Jedlicka et al., 2015). Furthermore, the increased V_m depolarization within a cell’s place field also reflects the activation of strongly weighted synaptic inputs, which have been potentiated by prior plasticity (Bittner et al., 2015; Bittner et al., 2017; Figure 3J). Thus, a causal dependency on either V_m or synaptic weight could explain the data so far.

To discriminate between these two possibilities, we next devised a set of voltage perturbation experiments. We reasoned that, if increased depolarization and spiking within a cell’s place field causes synaptic depression, then artificially increasing V_m and inducing spiking in otherwise silent cells would cause plateau potentials to induce negative ΔV_m. Likewise, artificially decreasing V_m and preventing spiking in place cells would prevent plateau potentials from inducing negative ΔV_m (Figure 3K). On the contrary, if the direction of plasticity depended instead on the initial strengths of synapses prior to plasticity, these voltage manipulations would have no effect on the balance between positive and negative ΔV_m (Figure 3K). It is important to note that these somatic voltage manipulations are not expected to strictly control or even completely overwhelm V_m at the synaptic sites relevant to plasticity induction (Magee and Johnston, 1997; Koester and Sakmann, 1998; Froemke et al., 2005) due to attenuation of current and voltage along the dendritic cable (Magee, 1998; Golding et al., 2005), and compartmentalization of synaptic voltage in dendritic spines (Harnett et al., 2012). However, by either increasing or decreasing the generation of somatic action potentials, this manipulation will unequivocally alter the number of action potentials that back-propagate into dendrites, which will in turn influence the activation of voltage-gated channels in dendrites and spines (e.g. Na⁺ channels, Ca²⁺ channels, and NMDA-Rs) (Magee and Johnston, 1997; Takahashi and Magee, 2009). Expected changes to the mean V_m in active dendritic spines were supported by simulations of a biophysically and morphologically detailed CA1 place cell model expressing voltage-gated ion channels and receiving rhythmic excitation and inhibition to mimic the in vivo recording conditions (Figure 4—figure supplement 1; Grienberger et al., 2017). Moreover, manipulation of somatic V_m and spike timing is widely used to successfully influence plasticity induction in vitro and in vivo (Malinow and Miller, 1986; Jacob et al., 2007; Schulz et al., 2010).

According to the above scheme, we first recorded from spatially untuned silent cells, and injected current (~100 pA) through the intracellular pipette to depolarize the neurons’ V_m by ~10 mV and to increase spiking during plasticity induction trials (Figure 4A; baseline trials mean AP rate: 0.26 ± 0.25 Hz; first induction trial mean AP rate: 4.8 ± 1.4 Hz, n = 8; blue trace in Figure 4B). In all neurons tested, we observed plateau potentials to induce large positive ΔV_m at spatial positions surrounding the plateau location, and no negative ΔV_m at any spatial positions (Figure 4A; blue trace in Figure 4C). This result is inconsistent with a causal dependence on initial V_m (Figure 3K), which predicted a ΔV_m profile similar to that of control place cells at their most depolarized positions within their pre-existing place fields (red traces, ‘control PCs (within-field)’ in Figure 4B and C repeated from Figure 3D and E for comparison).

Next, we performed the inverse manipulation by recording from place cells and injecting current (~–150 pA) to hyperpolarize the neurons’ V_m by ~–15 mV and prevent spiking at spatial locations surrounding their pre-existing place fields while plasticity was induced at a second location (Figure 4D; baseline trials in-field mean AP rate 10.66 ± 0.93 Hz; first induction trial in-field mean AP rate 0.06 ± 0.06 Hz, n = 5; green trace in Figure 4E). This manipulation did not prevent negative ΔV_m at positions within the original place field (Figure 4D; green trace in Figure 4F), again incompatible with synaptic depression requiring elevated postsynaptic depolarization and spiking (Figure 3K). In fact, full amplitude synaptic depression was observed at locations within the original place field despite the somatic V_m being more hyperpolarized than either the silent cell (black traces in Figure 4E and F) or control place cell groups (red traces, ‘control PCs’ in Figure 4E and F).

These data clearly show that the direction of plasticity induced by dendritic plateau potentials is not determined by the activation state of the postsynaptic neuron. Instead, the results of these voltage perturbation experiments support the alternative hypothesis that it is the initial strength of each synapse that controls whether an input will be potentiated or depressed by BTSP (Figure 3K). However, the magnitude of potentiation and depression was slightly affected by the voltage perturbations (e.g. potentiation was slightly but significantly increased in silent cells during artificial depolarization compared to control, Figure 4C). This is consistent with the previously reported finding that BTSP induction requires activation of voltage-dependent ion channels, including NMDA-type glutamate receptors (NMDA-Rs) and voltage-gated calcium channels (Bittner et al., 2017), which would have predicted BTSP to depend on postsynaptic depolarization. To examine this further, we performed an additional set of experiments in which silent cells were strongly hyperpolarized by somatic current injection (~–50 mV for ~3 s just before plateau initiation) during plasticity induction (Figure 4—figure supplement 2). This manipulation decreased synaptic potentiation (Figure 4—figure supplement 2), consistent with a requirement for activation of voltage-dependent NMDA-Rs. That such a large, non-physiological level of global V_m hyperpolarization was required to alter BTSP reinforces the finding that, operationally, the dependence is not on voltage signals associated with neuronal activation state (sustained somatodendritic V_m and action potentials), but rather on those associated with synaptic input (transient local spine depolarization) (Beaulieu-Laroche and Harnett, 2018). Finally, these experiments do not support a role for synaptic depolarization in determining the direction of changes in synaptic strengths.

The above voltage perturbation experiments suggested that the form of synaptic plasticity underlying BTSP does not depend on the activation state of the postsynaptic neuron (Figure 4). This contrasts with Hebbian plasticity rules that typically depend on either the firing rate or depolarization of the postsynaptic cell to determine the amplitude and direction of changes in synaptic weight. Another difference is that BTSP appears to be inherently stable, converting synaptic potentiation into depression when input strengths exceed a particular range, whereas most models of Hebbian learning require additional homeostatic mechanisms to counteract synaptic potentiation in highly active neurons (Oja, 1982; Bienenstock et al., 1982; Abbott and Nelson, 2000; Zenke et al., 2013; Turrigiano and Nelson, 2004). To better understand the synaptic learning rule underlying BTSP and its functional consequences, we next sought a mathematical description of BTSP to account for the following features of the in vivo recording data:

As mentioned previously, ‘three-factor’ plasticity models propose a mechanism for the strengths of activated synapses to be modified after a time delay – a biochemical intermediate signal downstream of synaptic activation marks each recently activated synapse as ‘eligible’ to undergo a plastic change in synaptic weight. This ‘ET’ decays over a longer timescale than synaptic activation, and while it does not induce plasticity by itself, it enables plasticity to be induced upon the arrival of an additional modulatory biochemical signal. While ‘three-factor’ models consider synaptic ETs to be generated by a coincidence of presynaptic spikes (factor 1) and postsynaptic spikes or sustained depolarization (factor 2), the results of the above voltage perturbation experiments suggest that if BTSP involves the generation of synaptic ETs, these signals depend only on a single factor – local synaptic activation. In the context of BTSP, the modulatory or ‘instructive signal’ (IS) could be instantiated by a dendritic plateau potential. To model this, we assumed that the large magnitude dendritic depolarization associated with a plateau potential (~60 mV) effectively propagates to all synapses (Xu et al., 2012), activating an IS at each synapse and allowing a spatially and temporally local interaction between ET and IS to drive plasticity independently at each individual synapse (Figure 5A). To account for plasticity that occurs at inputs activated up to multiple seconds after a plateau, this IS would have to decay slowly enough to overlap in time with ETs generated after the end of the plateau (Figure 5A).

Accordingly, we modeled changes in synaptic weights as a function of the time-varying amplitudes of these two biochemical intermediate signals, ET and IS. For simplicity, we first considered how BTSP would change the weight W of a single synapse activated by a single presynaptic spike with precise timing relative to the onset of a plateau potential (Figure 5A). We modeled the synaptic ET as a signal that increases upon synaptic activation at time ts and decays exponentially with time course τET (see Figure 5A and Materials and methods). The IS was modeled as a signal that increases during a plateau potential with onset at time tp and duration d and decays exponentially with time course τIS (see Figure 5A and Materials and methods).

Next, we modeled bidirectional changes in synaptic weight dWdt as a function of the temporal overlap or product of these two signals, ET*IS. To account for the observation that BTSP favors synaptic potentiation at weak synapses and synaptic depression at strong synapses, we expressed dWdt in terms of two separate plasticity processes q+ and q− with opposite dependencies on the current synaptic weight W:(1)dWdt=(Wmax−W)∗k+∗q+(ET∗IS)−W∗k−∗q−(ET∗IS)

where W is saturable up to a maximum weight of Wmax , and k⁺ and k⁻ are learning rate constants that control the magnitudes of synaptic potentiation and depression per plateau potential. This formula can be obtained from a two-state model of finite synaptic resources (see Materials and methods). When the current synaptic weight W is near Wmax , the potentiation rate becomes zero, and when W is near zero, the depression rate becomes zero. To calculate the net change in synaptic weight ∆W after plasticity induction, dWdt was integrated in time for the duration of plasticity induction laps.

Experimental evidence suggests that synaptic potentiation and depression processes involve biochemical interactions between enzymes (e.g. phosphokinases-like CaMKII and phosphatases-like calcineurin) and synaptic protein substrates (e.g. AMPA-type glutamate receptors) (Herring and Nicoll, 2016; Mansuy, 2003). Such concentration-limited reactions are typically saturable and nonlinear (Graupner and Brunel, 2012). Accordingly, we defined the plasticity processes q+ and q− as saturable (sigmoidal) functions of the signal overlap ET*IS (see Materials and methods). If the depression process q− has a lower threshold for activation than the potentiation process q+ (Graupner and Brunel, 2007; Inglebert et al., 2020), the resulting change in synaptic weight dWdt is positive and increases monotonically when initial weights are low, but is negative and non-monotonic when initial weights are high (Figure 5B). At intermediate weights, dWdt transitions from negative (depression) to positive (potentiation) for values of signal overlap ET*IS that are beyond a threshold (Figure 5B). Thus, the largest negative changes in synaptic weight occur when inputs are initially large in weight and signal overlap ET*IS is intermediate in amplitude. This is consistent with the in vivo data, which showed that negative changes in place field ramp V_m were largest at intermediate delays from a plateau (Figure 3B and I).

We tested this weight-dependent model of bidirectional BTSP by varying both the timing of a single presynaptic spike relative to a plateau (Figure 5A) and the initial weight of the activated synapse (Figure 5B). Model parameters were calibrated (see Materials and methods) such that synapses with an initial weight less than a baseline weight of 1 undergo only potentiation, while synapses with higher weight undergo either potentiation or depression, depending on the timing of their activation relative to the plateau (Figure 5C). This produced a profile of changes in synaptic weight similar to the profile of changes in intracellular V_m measured in vivo (Figure 3I). This model also recapitulated the finding that the positive and negative changes in weight induced by BTSP appear to drive synaptic inputs toward a stable target weight, after which additional plateaus do not induce any further changes in strength (indicated in white, compare Figures 3I and 5C).

We next exploited the mathematical formulation of the model to analyze these equilibrium conditions in more detail. We defined Weq as the stable equilibrium value of W where potentiation and depression processes are exactly balanced, and the change in weight ∆W is zero over the course of a trial from times t0 to t1 :(2)ΔW=0=(Wmax−Weq)∗k+∗∫t0t1q+(ET∗IS)dt−Weq∗k−∗∫t0t1q−(ET∗IS)dt

If we abbreviate the integrated potentiation and depression terms as:(3)ΔQ+=∫t0t1q+(ET∗IS)dt(4)ΔQ−=∫t0t1q−(ET∗IS)dt

then Weq can be expressed as:(5)Weq=Wmax∗K+∗ΔQ+K+∗ΔQ++k−∗ΔQ−

Note that the quantities ΔQ+ and ΔQ− , and therefore the value of Weq , will vary with the activation time of the input (ts), and the onset time (tp) and duration (d) of a plateau. For a plateau with fixed onset time and duration, this produces a distribution of target equilibrium weights that varies only with the timing of synaptic activation relative to plateau onset (dashed line in Figure 5C), and matches the asymmetric shape of place fields induced by BTSP. In contrast, an alternative version of the model in which the potentiation and depression processes were defined to be linear instead of sigmoidal, predicted a single value for Weq regardless of the timing of synaptic activation (Figure 5D), thus failing to account for the data. Finally, we verified that the model requires long timescales for ET and IS by testing the model with shorter values (100 ms) for the decay time constants τET and τIS (Figure 5E). This was unable to explain changes in synaptic weight at inputs activated at seconds-long time delays to a plateau.

Having demonstrated that this weight-dependent model of plasticity at single synapses captures the essential features of BTSP, we next tested if the model can account quantitatively for the in vivo place field translocation data (Figures 1—3). For this purpose, we assumed that the V_m ramp depolarization measured in a CA1 pyramidal cell during locomotion on the circular treadmill reflects a weighted sum of presynaptic inputs that are themselves place cells with firing rates that vary with spatial position (see Figure 3J and Materials and methods). As a population, the place fields of these inputs uniformly tiled the track, and the firing rate of an individual input depended on the recorded run trajectory of the animal (Figure 6A, first and second rows). In this case, presynaptic activity patterns were modeled as continuous firing rates rather than discrete spike times. For each cell in the experimental dataset (n = 26 inductions from 24 neurons, Figures 1—3), the initial weight Wi of each presynaptic input i was inferred from the recorded initial V_m, and the changes in weight ∆Wi during plasticity induction laps containing evoked plateau potentials were computed as above (Equation 1; see Materials and methods). The relevant signals modeled for an example lap from a representative cell from the dataset are shown in Figure 6A. Note that, at inputs activated before the onset time of the plateau, changes in synaptic weight (bottom row) do not begin until after plateau onset when the instructive signal IS and the signal overlap ET*IS are nonzero. The parameters of the model were optimized to predict the final synaptic weights (Figure 6B) and reproduce the final V_m ramp (Figure 6C) after multiple plasticity induction laps (Figure 6—figure supplement 1, Materials and methods). Across all cells, these predictions quantitatively matched the corresponding experimental data (Figure 6D). Finally, the sensitivity of changes in V_m to initial V_m and time to plateau predicted by the model recapitulated that measured from the in vivo intracellular recordings (Figure 6E and Figure 6—figure supplement 2).

The above modeling results help to clarify the differences between BTSP and previously characterized forms of associative synaptic plasticity based on input-output correlations over short timescales (Gerstner et al., 2018; He et al., 2015; Brzosko et al., 2015; Brzosko et al., 2017). First, the model supports the hypothesis that a dependence on initial synaptic weight is the actual source of the observed inverse relationship between initial V_m and plasticity-induced changes in V_m (Figure 3). Second, the scaling of both potentiation and depression by synaptic weight produces a balanced form of plasticity that rapidly stabilizes during repeated inductions (Figure 1, and Figure 6—figure supplement 1A and B; Shouval et al., 2010; Jedlicka et al., 2015; Bienenstock et al., 1982; Abraham, 2008; Cooper and Bear, 2012). Third, the time course of BTSP is determined by temporal overlap between slow eligibility signals associated with synaptic activity and slow IS associated with plateau potentials. This selects a subpopulation of synaptic inputs activated with appropriate timing to undergo a change in synaptic strength (Figure 6—figure supplement 3). Finally, IS are internal signals activated by dendritic plateau potentials, rather than by spiking output, arguing that BTSP is not simply a variant of Hebbian plasticity that depends on input-output correlations over a longer timescale.

The above observations imply that BTSP could enable spatial representations to be shaped non-autonomously by delayed behavioral outcomes, if dendritic inputs carrying information about those outcomes are able to evoke plateau potentials (Muller et al., 2019). To evaluate the feasibility and implications of this theory, we next considered the conditions that are required for dendritic plateau potentials to be generated in the context of the hippocampal neural circuit. Previous work has shown that (1) plateau potentials are positively regulated by excitatory inputs from entorhinal cortex (Bittner et al., 2015; Takahashi and Magee, 2009; Milstein et al., 2015), (2) they are negatively regulated by dendrite-targeting inhibition (Grienberger et al., 2017; Milstein et al., 2015; Lovett-Barron et al., 2012; Royer et al., 2012; Palmer et al., 2012), (3) they occur more frequently in novel environments (Cohen et al., 2017) and precede the emergence of new place fields (Sheffield et al., 2017), and (4) introduction of a fixed reward site induces large shifts in the place field locations of many place cells in a population, as assayed by calcium imaging (Turi et al., 2019). In order to explore the consequences of these regulatory mechanisms on memory storage by BTSP at the network level, we next constructed a network model of the CA1 microcircuit that incorporates these critical elements to regulate plateau initiation (Figure 7A) and implements the above-described weight-dependent model of BTSP (Figures 5 and 6) at each input to the network.

In a population of 500 firing rate model CA1 pyramidal neurons, plateaus were positively regulated by a long-range feedback input from entorhinal cortex and negatively regulated by local feedback inhibition (Figure 7A and B; Stefanelli et al., 2016). Generation of plateau potentials within the population of CA1 neurons in the model was stochastic, which would result from fluctuations in inputs from entorhinal cortex that occasionally cross a threshold for the generation of a plateau potential in different cells at different times. The presence of reward delivered at a fixed goal location was implemented as an increase in input from entorhinal cortex (Boccara et al., 2019; Butler et al., 2019), although an equivalent increase in plateau generation could result instead from neuromodulatory input that directly increased dendritic excitability or reduced dendritic inhibition (Sjöström et al., 2008; Pi et al., 2013; Tyan et al., 2014; Guerguiev et al., 2017).

During goal-directed navigation, hippocampal neurons have been shown to preferentially acquire new place fields near behaviorally relevant locations, and to translocate existing place fields toward those locations (Dupret et al., 2010; Zaremba et al., 2017; Turi et al., 2019; Hollup et al., 2001; Gauthier and Tank, 2018; Lee et al., 2020). We modeled this situation by simulating a virtual animal running on a circular treadmill for three separate phases of exploration (Figure 7C). At each time step (10 ms), instantaneous plateau probabilities were computed for each cell (Figure 7B), determining which neurons would initiate a dendritic plateau and undergo plasticity. During the first few laps of simulated exploration, CA1 pyramidal neurons rapidly acquired place fields that, as a population, uniformly tiled the track (Figure 7C and D). As neurons increased their activity over time, feedback inhibition increased proportionally and prevented further plasticity (Figure 7A–C). During the next phase a goal was presented at a fixed location, resulting in both acquisition of new place fields nearby the goal location in a population of initially silent neurons, and translocation of place fields toward the goal location in a separate population of cells with pre-existing fields (Figure 7E, left; Figure 7—figure supplement 1). Overall, this resulted in an increased proportion of place cells with fields near the goal position (Figure 7E, right), recapitulating experimentally observed modifications in CA1 network activity during goal-directed behavior (Zaremba et al., 2017). The asymmetric time course of BTSP caused the population representation of the goal in the model to peak before the goal location itself, producing a predictive memory representation of the path leading to the goal (Mehta et al., 1997; Stachenfeld et al., 2017). Simulated place cell activity remained stable in a final phase of exploration without reward (Figure 7C and Figure 7—figure supplement 1). These network modeling results demonstrate that plasticity regulated by local network activity and long-range feedback, rather than by pairwise correlations, can enable populations of place cells to rapidly adapt their spatial representations to changes in the environment without any compromise in selectivity.

All experimental methods were approved by the Janelia or Baylor College of Medicine Institutional Animal Care and Use Committees (Protocols 12–84 and 15–126). All experimental procedures in this study, including animal surgeries, behavioral training, treadmill and rig configuration, and intracellular recordings, were performed identically to a previous detailed report (Bittner et al., 2017) in an overlapping set of experiments, and are briefly summarized here.

In vivo experiments were performed in 6- to 12-week-old mice of either sex. Craniotomies above the dorsal hippocampus for simultaneous whole-cell patch clamp and local field potential (LFP) recordings, as well as affixation of head bar implants were performed under deep anesthesia. Following a week of recovery, animals were prepared for behavioral training with water restriction, handling by the experimenter, and addition of running wheels to their home cages. Mice were trained to run on the cue-enriched linear treadmill for a dilute sucrose reward delivered through a licking port once per lap (~187 cm). A MATLAB GUI interfaced with a custom microprocessor-controlled system for position-dependent reward delivery and intracellular current injection. Animal-run velocity was measured by an encoder attached to one of the wheel axles.

Plasticity was induced in vivo by injecting current (700 pA, 300 ms) intracellularly into recorded CA1 neurons to evoke dendritic plateau potentials at the same position on the circular treadmill for multiple consecutive laps. In most cases, plateaus were evoked on five consecutive laps (Figure 1—figure supplement 1E, left). However, during some experiments, large changes in the spatial V_m ramp depolarization could be observed to develop after as few as one plateau (consistent with the observation that plasticity could be induced by a single spontaneously-occurring plateau), and so fewer induction laps were used. In other experiments, plateaus were induced on more than five consecutive laps if place field expression remained weak after the first five trials (Figure 1—figure supplement 1E, left). The source of this variability across cells/animals is not yet clear, and requires future investigation. Overall, this procedure induced changes in spatial V_m ramp depolarization in 100% of cells in which it was attempted by three investigators. In some cells, the initial place field was first induced by this procedure, and then the procedure was repeated a second or third time in the same cell with plateaus induced at different locations. In those cases, there was no systematic difference in the number of plateaus required to induce the first place field compared to subsequent fields (Figure 1—figure supplement 1E, right).

Since the time window for plasticity induction by BTSP extends for seconds around each plateau, and plateaus were typically evoked on multiple consecutive laps, the changes in synaptic weights induced by BTSP depended on the run behavior of the animals across all induction laps. We showed in Figure 3D that the spatial width of place fields induced by BTSP varied with the average velocity of animals across all plasticity induction laps. Another factor that contributed to the spatial width of induced fields is the proximity of the evoked plateaus to the reward site, as animals tended to stop running briefly to lick near the fixed reward site. Variability across laps in either the run velocity or the duration of pauses could pose a challenge in trying to relate spatial changes in V_m ramp depolarization to the time delay to the plateau (see below). Figure 1—figure supplement 1 shows the full run trajectories of animals during all plasticity induction laps for the five representative example cells shown in Figure 1. While some variability across induction laps was observed, each animal tended to run consistently at similar velocities across laps.

To establish whole-cell recordings from CA1 pyramidal neurons, an extracellular LFP electrode was lowered into the dorsal hippocampus using a micromanipulator until prominent theta-modulated spiking and increased ripple amplitude was detected. Then a glass intracellular recording pipette was lowered to the same depth while applying positive pressure. The intracellular solution contained (in mM): 134 K-gluconate, 6 KCl, 10 HEPES, 4 NaCl, 0.3 MgGTP, 4 MgATP, 14 Tris-phosphocreatine, and in some recordings, 0.2% biocytin. Current-clamp recordings of intracellular membrane potential (V_m) were amplified and digitized at 20 kHz, without correction for liquid junction potential. The silent-cell population of neurons (n = 29) contained recordings from 17 neurons that have been previously reported (Bittner et al., 2017).

In a subset of experiments (Figure 4 and Figure 4—figure supplement 2), in addition to position-dependent step current to evoke plateau potentials, additional current was injected either to depolarize neurons beyond spike threshold or to hyperpolarize neurons below spike threshold, during plasticity induction laps. While these perturbations to V_m at the soma are expected to attenuate along the path to distal dendrites (Golding et al., 2005), the pairing of back-propagating action potentials with synaptic inputs has been shown to significantly amplify dendritic depolarization (Jarsky et al., 2005; Stuart and Häusser, 2001; Migliore et al., 1999; Schiller and Schiller, 2001). Simulations of a biophysically detailed CA1 place cell model with realistic morphology and distributions of dendritic ion channels (Grienberger et al., 2017) suggest that somatic depolarization of a silent CA1 cell increases distal dendritic depolarization, and that somatic hyperpolarization of a place cell substantially reduces distal dendritic depolarization at the peak of its place field (Figure 4—figure supplement 1).

To analyze subthreshold V_m ramps, action potentials were first removed from raw V_m traces and linearly interpolated, then the resulting traces were low-pass filtered (<3 Hz). For each of 100 equally sized spatial bins (~1.85 cm), V_m ramp amplitudes were computed by averaging across 10 laps of running on the treadmill both before and after plasticity induction. The spatially binned ramp traces were then smoothed with a Savitzky-Golay filter with wrap-around. Ramp amplitude was quantified as the difference between the peak and the baseline (average of the 10% most hyperpolarized bins). For cells with a second place field induced, the same baseline V_m value determined from the period before the second induction was also used to quantify ramp amplitude after the second induction. Plateau duration was estimated as the duration of intracellular step current injections, or as the full width at half maximum V_m in the case of spontaneous naturally occurring plateaus.

V_m ramp half-width (Figure 2D and Figure 6—figure supplement 1C) was calculated from the ΔV_m traces as the time (s) or distance (cm) between the plateau and the final return of ΔV_m to zero (or at least to 25% of min; see Figure 2—figure supplement 1G). In most cases this only occurred on one side of the plateau, during either the running period before or after the plateau. In 5/26 inductions, the mouse ran so quickly that the ΔV_m did not have time to reach 25% of min on either side of the plateau (Figure 2—figure supplement 1G), resulting in an underestimation of the ramp half-width. The average velocity was calculated as the mean velocity of the mouse from the plateau to the end of the plasticity (Figure 2—figure supplement 1).

In order to relate spatial changes in V_m ramp depolarization to the time delay to a plateau (e.g. Figures 2E, F—4B, C, E, F–6E), we assigned to each spatial position the shortest time delay to plateau that occurred across multiple induction laps (Figure 1—figure supplement 1). This is a conservative estimate, as the shortest delay between presynaptic activity and postsynaptic plateau will generate the largest overlap between ET and IS, and will result in the largest changes in synaptic weight. While this method is imperfect and did discard variability in running behavior across laps, it enabled direct comparison of the time course of BTSP across neurons. We also note that, to generate the modeling results shown in Figure 6, the full run trajectory of each animal during all induction laps, including pauses, was provided as input to the model (see details below). This resulted in good quantitative agreement between experimentally recorded and modeled spatial V_m ramps (Figure 6D). Since not all possible pairs of initial ramp amplitude and time delay relative to plateau onset were sampled in the experimental dataset, expected changes in ramp amplitude (e.g. Figure 3I) were predicted from the sampled experimental or model data points by a two-dimensional Gaussian process regression and interpolation procedure using a rational quadratic covariance function, implemented in the open-source Python package sklearn (Abraham et al., 2014; Rasmussen and Williams, 2006).

To statistically compare ΔV_m vs. time plots among groups each individual induction trace was binned in time (average of values in 80, 100 ms, bins from –4 to +4 s). The number of points in each bin for each group is as follows: silent cells (−4, + 4 s): n = 19, 19, 19, 0, 20, 20, 21, 21, 25, 26, 26, 27, 27, 27, 27, 27, 28, 28, 28, 28, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 27, 25, 25, 25, 24, 21, 20, 19, 17, 16, 14, 14, 10, 9, 9, 8, 8, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6. Silent + depolarization (−4, + 4 s): n = 2, 2, 4, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 6, 6, 6, 6, 5, 5, 5, 5, 3, 3. Depolarized PCs (–4 to +4 s): n = 6, 6, 6, 6, 6, 5, 5, 5, 4, 4, 5, 6, 6, 6, 7, 7, 6, 6, 6, 7, 7, 8, 7, 7, 7, 7, 6, 6, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 7, 8, 8, 8, 9, 10, 14, 14, 15, 15, 15, 15, 15, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 13, 12, 12, 10, 9, 9. All PCs (–1 to +4 s): n = 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 25, 24, 24. PCs + hyperpolarization (–1 to +4 s): n = 5, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8. Silent+ large hyperpolarization (–4 to +4): n = 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2.

Statistical details of experiments can be found in the figure legends. Unless otherwise specified, measured values and ranges reflect mean ± SEM. Significance was defined as p < 0.05. Sample sizes were not determined by statistical methods, but efforts were made to collect as many samples as was technically feasible. No data or subjects were excluded from any analysis.