Understanding how active dendrites are exploited for behaviorally relevant computations is a fundamental challenge in neuroscience. Grid cells in medial entorhinal cortex are an attractive model system for addressing this question, as the computation they perform is clear: they convert synaptic inputs into spatially modulated, periodic firing. Whether active dendrites contribute to the generation of the dual temporal and rate codes characteristic of grid cell output is unknown. We show that dendrites of medial entorhinal cortex neurons are highly excitable and exhibit a supralinear input–output function in vitro, while in vivo recordings reveal membrane potential signatures consistent with recruitment of active dendritic conductances. By incorporating these nonlinear dynamics into grid cell models, we show that they can sharpen the precision of the temporal code and enhance the robustness of the rate code, thereby supporting a stable, accurate representation of space under varying environmental conditions. Our results suggest that active dendrites may therefore constitute a key cellular mechanism for ensuring reliable spatial navigation.
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Magee, J.C. Dendritic integration of excitatory synaptic input. Nat. Rev. Neurosci. 1, 181–190 (2000).
Major, G., Larkum, M.E. & Schiller, J. Active properties of neocortical pyramidal neuron dendrites. Annu. Rev. Neurosci. 36, 1–24 (2013).
London, M. & Häusser, M. Dendritic computation. Annu. Rev. Neurosci. 28, 503–532 (2005).
Mel, B.W. Information processing in dendritic trees. Neural Comput. 6, 1031–1085 (1994).
Lavzin, M., Rapoport, S., Polsky, A., Garion, L. & Schiller, J. Nonlinear dendritic processing determines angular tuning of barrel cortex neurons in vivo. Nature 490, 397–401 (2012).
Smith, S.L., Smith, I.T., Branco, T. & Häusser, M. Dendritic spikes enhance stimulus selectivity in cortical neurons in vivo. Nature 503, 115–120 (2013).
Xu, N.L. et al. Nonlinear dendritic integration of sensory and motor input during an active sensing task. Nature 492, 247–251 (2012).
Takahashi, N., Oertner, T.G., Hegemann, P. & Larkum, M.E. Active cortical dendrites modulate perception. Science 354, 1587–1590 (2016).
Sheffield, M.E. & Dombeck, D.A. Calcium transient prevalence across the dendritic arbour predicts place field properties. Nature 517, 200–204 (2015).
Lee, D., Lin, B.J. & Lee, A.K. Hippocampal place fields emerge upon single-cell manipulation of excitability during behavior. Science 337, 849–853 (2012).
Bittner, K.C. et al. Conjunctive input processing drives feature selectivity in hippocampal CA1 neurons. Nat. Neurosci. 18, 1133–1142 (2015).
Hafting, T., Fyhn, M., Molden, S., Moser, M.B. & Moser, E.I. Microstructure of a spatial map in the entorhinal cortex. Nature 436, 801–806 (2005).
Burak, Y. & Fiete, I.R. Accurate path integration in continuous attractor network models of grid cells. PLoS Comput. Biol. 5, e1000291 (2009).
Burgess, N., Barry, C. & O'Keefe, J. An oscillatory interference model of grid cell firing. Hippocampus 17, 801–812 (2007).
Fuhs, M.C. & Touretzky, D.S. A spin glass model of path integration in rat medial entorhinal cortex. J. Neurosci. 26, 4266–4276 (2006).
Kropff, E. & Treves, A. The emergence of grid cells: intelligent design or just adaptation? Hippocampus 18, 1256–1269 (2008).
Domnisoru, C., Kinkhabwala, A.A. & Tank, D.W. Membrane potential dynamics of grid cells. Nature 495, 199–204 (2013).
Schmidt-Hieber, C. & Häusser, M. Cellular mechanisms of spatial navigation in the medial entorhinal cortex. Nat. Neurosci. 16, 325–331 (2013).
Schmidt-Hieber, C. & Häusser, M. How to build a grid cell. Phil. Trans. R. Soc. Lond. B 369, 20120520 (2013).
Boccara, C.N. et al. Grid cells in pre- and parasubiculum. Nat. Neurosci. 13, 987–994 (2010).
Sargolini, F. et al. Conjunctive representation of position, direction, and velocity in entorhinal cortex. Science 312, 758–762 (2006).
Gatome, C.W., Slomianka, L., Lipp, H.P. & Amrein, I. Number estimates of neuronal phenotypes in layer II of the medial entorhinal cortex of rat and mouse. Neuroscience 170, 156–165 (2010).
Zhang, S.J. et al. Optogenetic dissection of entorhinal-hippocampal functional connectivity. Science 340, 1232627 (2013).
Sun, C. et al. Distinct speed dependence of entorhinal island and ocean cells, including respective grid cells. Proc. Natl. Acad. Sci. USA 112, 9466–9471 (2015).
Garden, D.L., Dodson, P.D., O'Donnell, C., White, M.D. & Nolan, M.F. Tuning of synaptic integration in the medial entorhinal cortex to the organization of grid cell firing fields. Neuron 60, 875–889 (2008).
Giocomo, L.M., Zilli, E.A., Fransén, E. & Hasselmo, M.E. Temporal frequency of subthreshold oscillations scales with entorhinal grid cell field spacing. Science 315, 1719–1722 (2007).
Tang, Q. et al. Pyramidal and stellate cell specificity of grid and border representations in layer 2 of medial entorhinal cortex. Neuron 84, 1191–1197 (2014).
Golding, N.L., Staff, N.P. & Spruston, N. Dendritic spikes as a mechanism for cooperative long-term potentiation. Nature 418, 326–331 (2002).
Losonczy, A. & Magee, J.C. Integrative properties of radial oblique dendrites in hippocampal CA1 pyramidal neurons. Neuron 50, 291–307 (2006).
Schiller, J., Major, G., Koester, H.J. & Schiller, Y. NMDA spikes in basal dendrites of cortical pyramidal neurons. Nature 404, 285–289 (2000).
Takahashi, H. & Magee, J.C. Pathway interactions and synaptic plasticity in the dendritic tuft regions of CA1 pyramidal neurons. Neuron 62, 102–111 (2009).
Kamondi, A., Acsády, L. & Buzsáki, G. Dendritic spikes are enhanced by cooperative network activity in the intact hippocampus. J. Neurosci. 18, 3919–3928 (1998).
Larkum, M.E. & Zhu, J.J. Signaling of layer 1 and whisker-evoked Ca2+ and Na+ action potentials in distal and terminal dendrites of rat neocortical pyramidal neurons in vitro and in vivo. J. Neurosci. 22, 6991–7005 (2002).
Pastoll, H., Solanka, L., van Rossum, M.C. & Nolan, M.F. Feedback inhibition enables θ-nested γ oscillations and grid firing fields. Neuron 77, 141–154 (2013).
Hafting, T., Fyhn, M., Bonnevie, T., Moser, M.B. & Moser, E.I. Hippocampus-independent phase precession in entorhinal grid cells. Nature 453, 1248–1252 (2008).
Fernandez, F.R., Malerba, P. & White, J.A. Non-linear membrane properties in entorhinal cortical stellate cells reduce modulation of input-output responses by voltage fluctuations. PLoS Comput. Biol. 11, e1004188 (2015).
Stringer, S.M., Trappenberg, T.P., Rolls, E.T. & de Araujo, I.E. Self-organizing continuous attractor networks and path integration: one-dimensional models of head direction cells. Network 13, 217–242 (2002).
Mongillo, G., Barak, O. & Tsodyks, M. Synaptic theory of working memory. Science 319, 1543–1546 (2008).
Papoutsi, A., Sidiropoulou, K. & Poirazi, P. Dendritic nonlinearities reduce network size requirements and mediate ON and OFF states of persistent activity in a PFC microcircuit model. PLoS Comput. Biol. 10, e1003764 (2014).
Wang, X.J. Synaptic basis of cortical persistent activity: the importance of NMDA receptors to working memory. J. Neurosci. 19, 9587–9603 (1999).
Barry, C., Ginzberg, L.L., O'Keefe, J. & Burgess, N. Grid cell firing patterns signal environmental novelty by expansion. Proc. Natl. Acad. Sci. USA 109, 17687–17692 (2012).
Kamondi, A., Acsády, L., Wang, X.J. & Buzsáki, G. Theta oscillations in somata and dendrites of hippocampal pyramidal cells in vivo: activity-dependent phase-precession of action potentials. Hippocampus 8, 244–261 (1998).
Losonczy, A., Zemelman, B.V., Vaziri, A. & Magee, J.C. Network mechanisms of theta related neuronal activity in hippocampal CA1 pyramidal neurons. Nat. Neurosci. 13, 967–972 (2010).
Magee, J.C. Dendritic mechanisms of phase precession in hippocampal CA1 pyramidal neurons. J. Neurophysiol. 86, 528–532 (2001).
Samsonovich, A. & McNaughton, B.L. Path integration and cognitive mapping in a continuous attractor neural network model. J. Neurosci. 17, 5900–5920 (1997).
Zhang, K. Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: a theory. J. Neurosci. 16, 2112–2126 (1996).
Goldberg, J.A., Rokni, U. & Sompolinsky, H. Patterns of ongoing activity and the functional architecture of the primary visual cortex. Neuron 42, 489–500 (2004).
Branco, T. & Häusser, M. Synaptic integration gradients in single cortical pyramidal cell dendrites. Neuron 69, 885–892 (2011).
Behabadi, B.F. & Mel, B.W. Mechanisms underlying subunit independence in pyramidal neuron dendrites. Proc. Natl. Acad. Sci. USA 111, 498–503 (2014).
Häusser, M., Major, G. & Stuart, G.J. Differential shunting of EPSPs by action potentials. Science 291, 138–141 (2001).
Kitamura, T. et al. Island cells control temporal association memory. Science 343, 896–901 (2014).
Ray, S. et al. Grid-layout and theta-modulation of layer 2 pyramidal neurons in medial entorhinal cortex. Science 343, 891–896 (2014).
Alonso, A. & Llinás, R.R. Subthreshold Na+-dependent theta-like rhythmicity in stellate cells of entorhinal cortex layer II. Nature 342, 175–177 (1989).
Dickson, C.T. et al. Properties and role of I(h) in the pacing of subthreshold oscillations in entorhinal cortex layer II neurons. J. Neurophysiol. 83, 2562–2579 (2000).
Erchova, I., Kreck, G., Heinemann, U. & Herz, A.V.M. Dynamics of rat entorhinal cortex layer II and III cells: characteristics of membrane potential resonance at rest predict oscillation properties near threshold. J. Physiol. (Lond.) 560, 89–110 (2004).
Pastoll, H., Ramsden, H.L. & Nolan, M.F. Intrinsic electrophysiological properties of entorhinal cortex stellate cells and their contribution to grid cell firing fields. Front. Neural Circuits 6, 17 (2012).
Guzman, S.J., Schlögl, A. & Schmidt-Hieber, C. Stimfit: quantifying electrophysiological data with Python. Front. Neuroinform. 8, 16 (2014).
Saville, D.J. Multiple comparison procedures: the practical solution. Am. Stat. 44, 174–180 (1990).
Carnevale, N.T. & Hines, M.L. The NEURON Book (Cambridge University Press, 2006).
Fransén, E., Alonso, A.A., Dickson, C.T., Magistretti, J. & Hasselmo, M.E. Ionic mechanisms in the generation of subthreshold oscillations and action potential clustering in entorhinal layer II stellate neurons. Hippocampus 14, 368–384 (2004).
Katz, Y. et al. Synapse distribution suggests a two-stage model of dendritic integration in CA1 pyramidal neurons. Neuron 63, 171–177 (2009).
Bahl, A., Stemmler, M.B., Herz, A.V.M. & Roth, A. Automated optimization of a reduced layer 5 pyramidal cell model based on experimental data. J. Neurosci. Methods 210, 22–34 (2012).
Deb, K. Multi-objective Optimization Using Evolutionary Algorithms (Wiley, 2001).
Schmidt-Hieber, C. & Bischofberger, J. Fast sodium channel gating supports localized and efficient axonal action potential initiation. J. Neurosci. 30, 10233–10242 (2010).
Burgess, N. Grid cells and theta as oscillatory interference: theory and predictions. Hippocampus 18, 1157–1174 (2008).
Yoon, K. et al. Specific evidence of low-dimensional continuous attractor dynamics in grid cells. Nat. Neurosci. 16, 1077–1084 (2013).
Destexhe, A., Rudolph, M., Fellous, J.M. & Sejnowski, T.J. Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons. Neuroscience 107, 13–24 (2001).
Gillespie, D.T. Exact numerical simulation of the Ornstein-Uhlenbeck process and its integral. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54, 2084–2091 (1996).
We are grateful to P. Latham, A. Packer and S. Turaga for discussions and comments on the manuscript, and to S. Chun for assistance with histology. This work was supported by grants from the Wellcome Trust (M.H.), ERC (StG 678790 NEWRON to C.S.-H. and AdG 695709 DendriteCircuits to M.H.) and Gatsby Charitable Foundation (M.H.).
The authors declare no competing financial interests.
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Schmidt-Hieber, C., Toleikyte, G., Aitchison, L. et al. Active dendritic integration as a mechanism for robust and precise grid cell firing. Nat Neurosci 20, 1114–1121 (2017). https://doi.org/10.1038/nn.4582
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