Abstract
The biophysical properties of neurons are the foundation for computation in the brain. Neuronal size is a key determinant of single neuron input–output features and varies substantially across species^{1,2,3}. However, it is unknown whether different species adapt neuronal properties to conserve how single neurons process information^{4,5,6,7}. Here we characterize layer 5 cortical pyramidal neurons across 10 mammalian species to identify the allometric relationships that govern how neuronal biophysics change with cell size. In 9 of the 10 species, we observe conserved rules that control the conductance of voltagegated potassium and HCN channels. Species with larger neurons, and therefore a decreased surfacetovolume ratio, exhibit higher membrane ionic conductances. This relationship produces a conserved conductance per unit brain volume. These sizedependent rules result in large but predictable changes in somatic and dendritic integrative properties. Human neurons do not follow these allometric relationships, exhibiting much lower voltagegated potassium and HCN conductances. Together, our results in layer 5 neurons identify conserved evolutionary principles for neuronal biophysics in mammals as well as notable features of the human cortex.
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Acknowledgements
We thank M. Tadross, S. HerculanoHouzel, M. T. Do, A. Chang, C. Yaeger, V. Francioni and A. Landau for comments on the manuscript; M. Brecht for the gift of Etruscan shrews; J. Haupt for veterinary assistance with procedures; Z. Fu, G. Feng, R. Desimone, M. Jazayeri, E. Miller, M. DeMedonsa, M. Livingstone, M. Greenberg, G. Boulting, A. Chang, C. Walsh and E. DeGennaro for their help with tissue acquisition; J. Fox and the division of comparative medicine (DCM) at MIT for expert care and supervision of animals; B. Coughlin for help with the epileptic rats; and A. O’Donnell, A. Paulk and Y. Chou for assistance in acquiring human tissue. L.B.L. was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) (PGSD25170682018) and a Friends of the McGovern Institute fellowship. E.H.S.T. was supported by the National Institute of General Medical Sciences (T32GM007753) and the Paul & Daisy Soros Fellowship. M.T.H. was supported by the Dana Foundation David Mahoney Neuroimaging Grant Program, the NIH (RO1NS106031) and the Harvard–MIT Joint Research Grants Program in Basic Neuroscience. M.T.H. is a KlingensteinSimons Fellow, a Vallee Foundation Scholar and a McKnight Scholar.
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L.B.L. designed experiments, collected human brain samples, extracted animal brains, prepared slices, performed electrophysiological recordings, analysed data, prepared the figures and wrote the manuscript. N.J.B. performed and analysed electrophysiological recordings, prepared fixed tissues for histology, performed histological stainings and created illustrations for the figures. M.H. performed and analysed electrophysiological recordings. E.H.S.T. performed biophysical modelling. J.S. performed animal surgeries. Z.M.W. and G.R.C. performed the surgeries that resulted in the human tissue. M.P.F. oversaw the removal and parcellation of that tissue as well as overall IRB aspects and regulatory aspects of the project with regard to human participants. S.S.C. helped in designing methods for acquiring human tissue and ensured that the tissue was collected. M.T.H supervised all aspects of the project.
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Extended data figures and tables
Extended Data Fig. 1 Histological identification of cortical layers. Related to Fig. 1.
a, Nisslstained brain slices from the 10 species with labelled cortical layers. Box plots on the right of individual slices denote the median and 25–75th percentiles of somatic depth for electrophysiological recordings (Etruscan shrew n = 39, mouse n = 162, gerbil n = 105, rat n = 215, ferret n = 31, guinea pig n = 118, rabbit n = 87, marmoset n = 41, macaque n = 34, human n = 208). b, The shrew slice from a, expanded to show detail (n = 39).
Extended Data Fig. 2 Somatic impedance profiles and voltage sag. Related to Fig. 1.
ad, Somatic impedance profiles (Etruscan shrew n = 29, mouse n = 71, gerbil n = 39, rat n = 64, ferret n = 28, guinea pig n = 35, rabbit n = 37, marmoset n = 30, macaque n = 25, human n = 100). Pooled data represent mean ± SEM for ab. Box plots denote the median and 25–75th percentiles for cd. a, Impedance profile in response to sinewaves of 50100 pA injected at the indicated frequencies for 2 s. b, Phase offset between the voltage response and the injected current. c, Maximal impedance (p < 10^{−49} KruskalWallis; χ^{2} = 259 & 9 df). d, Resonance frequency (p < 10^{−13} KruskalWallis; χ^{2} = 81 & 9 df). Data points displayed as a beeswarm plot to show overlapping integers. e, Somatic voltage sag (p < 10^{−57} KruskalWallis, χ^{2} = 298 & 9 df; Etruscan shrew n = 39, mouse n = 85, gerbil n = 58, rat n = 117, ferret n = 31, guinea pig n = 47, rabbit n = 40, marmoset n = 41, macaque n = 34, human n = 126). Box plots denote the median and 25–75th percentiles.
Extended Data Fig. 3 Somatic firing properties. Related to Fig. 1.
Somatic firing properties (Etruscan shrew n = 22, mouse n = 59, gerbil n = 46, rat n = 93, ferret n = 23, guinea pig n = 30, rabbit n = 33, marmoset n = 34, macaque n = 29, human n = 104). a, Firing rates as a function of injected current. The lines and shaded error bars represent population medians and 95% confidence intervals. bg, Box plots denote the median and 25–75th percentiles. b, Rheobase (p < 10^{−47} KruskalWallis, χ^{2} = 250 & 9 df). Data points displayed as a beeswarm plot to show overlapping integers. c, Slope of firing ratecurrent relationship (p < 10^{−59} KruskalWallis, χ^{2} = 304 & 9 df). d, Maximal firing rate (p < 10^{−26} KruskalWallis, χ^{2} = 146 & 9 df). e, Maximal current eliciting action potentials before entering depolarization block (p < 10^{−54} KruskalWallis, χ^{2} = 283 & 9 df). f, Representative action potential waveforms. g, Width of first action potential at rheobase (p < 10^{−13} KruskalWallis, χ^{2} = 86 & 9 df). hj, Correlation between action potential width (at rheobase) and other parameters for macaque L5 neurons of different somatic sizes (not restricted to large L5 with thick dendrites). h, Correlation with soma diameter (R^{2} = 0.145, p = 0.006, linear regression, F = 8.3 & 49 df, n = 51). i, Correlation with soma input resistance (R^{2} = 0.596, p < 10^{−13}, linear regression, F = 94.5 & 64 df, n = 66). j, Correlation with soma voltage sag (n = 66; R^{2} = 0.079, p = 0.02, linear regression, F = 5.5 & 64 df, n = 66). km, Rat somatic firing properties of L5b neurons in TEA (n = 93) versus M1 (n = 39). Orange lines represent median L5 macaque data from Extended Data Fig. 3d, g. k, Firing rates as a function of injected current. The lines and shaded error bars represent population medians and 95% confidence intervals. l, Maximal firing rate (p < 10^{−8}, twosided Wilcoxon rank sum, Z = 5.93). m, Width of first action potential at rheobase (p < 10^{−3}, twosided Wilcoxon rank sum, Z = 3.34).
Extended Data Fig. 4 Somatic bursting properties. Related to Fig. 1.
Somatic bursting properties (Etruscan shrew n = 22, mouse n = 59, gerbil n = = 46, rat n = 93, ferret n = 23, guinea pig n = 30, rabbit n = 33, marmoset n = 34, macaque n = 29, human n = 104). a, Minimum instantaneous interspike interval (ISI) on a log scale as a function of injected current above rheobase. The lines and shaded error bars represent population medians and 95% confidence intervals. b, Percentage of neurons exhibiting bursts with different frequency thresholds at rheobase. c, Same as b but at double the rheobase. de, Box plots denote the median and 25–75th percentiles. d, Maximal action potential amplitude reduction (p < 10^{−18} KruskalWallis, χ^{2} = 107 & 9 df). e, Maximal action potential dV/dt reduction (p < 10^{−15} KruskalWallis, χ^{2} = 95 & 9 df).
Extended Data Fig. 5 Dendritic impedance profiles. Related to Fig. 2.
Dendritic impedance profiles (mouse n = 26, gerbil n = 19, rat n = 59, guinea pig n = 37, rabbit n = 23, human n = 25). Pooled data represent mean ± SEM for ab. Box plots denote the median and 25–75th percentiles for de. a, Impedance profile in response to sinewaves of 50100 pA injected at the indicated frequencies for 2 s. b, Phase offset between the voltage response and the injected current. c, Mean data from b. d, Maximal impedance (p < 10^{−10} KruskalWallis, χ^{2} = 59 & 5 df). e, Resonance frequency (p < 10^{−6} KruskalWallis, χ^{2} = 39 & 5 df). Data points displayed as a beeswarm plot to show overlapping integers.
Extended Data Fig. 6 Additional dendritic properties. Related to Fig. 2.
Voltage sag (mouse n = 76, gerbil n = 47, rat n = 108, guinea pig n = 71, rabbit n = 47, human n = 72), resting membrane potential (mouse n = 76, gerbil n = 47, rat n = 108, guinea pig n = 71, rabbit n = 47, human n = 72), and spike properties (mouse n = 51, gerbil n = 40, rat n = 65, guinea pig n = 45, rabbit n = 35, human n = 49) as a function of distance from the soma. Triangles are somatic medians. Lines are an exponential fit to the data or double exponential fit for spike dV/dt. Spike width and area are on a log scale.
Extended Data Fig. 7 Proximal dendritic properties and additional distal dendritic properties. Related to Fig. 2.
a, Twophoton zstack montage image of mouse neuron with a proximal patchclamp electrode 63 μm from soma. b, Proximal dendritic voltage in response to subthreshold (top) or threshold (bottom) step current injections. cd, Subthreshold properties of proximal dendrites (mouse n = 31, gerbil n = 23, rat n = 19, guinea pig n = 28, rabbit n = 21, human n = 27). Box plots denote the median and 25–75th percentiles. c, Proximal input resistance (p < 10^{−18} KruskalWallis, χ^{2} = 98 & 5 df). d, Proximal voltage sag (p < 10^{−8} KruskalWallis, χ^{2} = 47 & 5 df). ei, Suprathreshold properties of proximal dendrites (mouse n = 19, gerbil n = 20, rat n = 9, guinea pig n = 18, rabbit n = 12, human n = 15). Box plots denote the median and 25–75th percentiles. e, Proximal rheobase (p < 10^{−9} KruskalWallis, χ^{2} = 51 & 5 df). Data points displayed as a beeswarm plot to show overlapping integers. f, Proximal spike threshold (p < 10^{−4} KruskalWallis, χ^{2} = 31 & 5 df). g, Proximal spike area on a log scale (p < 10^{−6} KruskalWallis, χ^{2} = 36 & 5 df). h, Proximal spike width on a log scale (p < 10^{−5} KruskalWallis, χ^{2} = 36 & 5 df). i, Proximal maximum spike dV/dt (p < 10^{−5} KruskalWallis, χ^{2} = 35 & 5 df). jm, Additional suprathreshold properties of distal dendrites (mouse n = 18, gerbil n = 19, rat n = 47, guinea pig n = 25, rabbit n = 20, human n = 25). Box plots denote the median and 25–75th percentiles. j, Distal rheobase (p < 10^{−4} KruskalWallis, χ^{2} = 28 & 5 df). Data points displayed as a beeswarm plot to show overlapping integers. k, Distal spike threshold (p < 10^{−11} KruskalWallis, χ^{2} = 61 & 5 df). l, Distal spike area on a log scale (p < 10^{−10} KruskalWallis, χ^{2} = 58 & 5 df). m, Maximum distal spike dV/dt (p < 10^{−13} KruskalWallis, χ^{2} = 74 & 5 df). no, Somatic outsideout currents in sclerosis (n = 44), tumour (n = 30) and others (n = 12). Box plots denote the median and 25–75th percentiles. n, Somatic K_{v} peak currents (p = 0.39 KruskalWallis, χ^{2} = 1.90 & 2 df). o, Somatic K_{v} plateau currents (p = 0.35 KruskalWallis, χ^{2} = 2.09 & 2 df). p, Example EEG recording of epileptic seizure in rat kainic acid model. qr, Somatic outsideout currents in control (n = 80) and epileptic (n = 68) rats. Box plots denote the median and 25–75th percentiles. q, Somatic K_{v} peak currents (p = 0.65, twosided Wilcoxon rank sum, Z = 0.45). r, Somatic K_{v} plateau currents (p = 0.525, twosided Wilcoxon rank sum, Z = 0.64).
Extended Data Fig. 8 Additional conductance measurements. Related to Fig. 3.
a, Dendritic outsideout patches were pulled from proximal dendrites after obtaining wholecell recordings. Top, HCN currents with the associated voltageclamp protocol on the left. Bottom, K_{v} currents with the associated voltageclamp protocol on the left. bg, Box plots denote the median and 25–75th percentiles. b, Proximal K_{v} peak currents (p = 0.010 KruskalWallis, χ^{2} = 15 & 5 df; mouse n = 32, gerbil n = 38, rat n = 38, guinea pig n = 37, rabbit n = 35, human n = 44). c, Proximal HCN steadystate currents (p=0.07 KruskalWallis, χ^{2} = 10 & 5 df; mouse n = 29, gerbil n = 30, rat n = 38, guinea pig n = 30, rabbit n = 31, human n = 42). d, Somatic K_{v} peak currents (p < 10^{19} KruskalWallis, χ^{2} = 115 & 9 df; Etruscan shrew n = 59, mouse n = 56, gerbil n = 80, rat n = 80, ferret n = 80, guinea pig n = 70, rabbit n = 53, marmoset n = 63, macaque n = 87, human n = 86). e, Somatic K_{v} plateau currents (p < 10^{19} KruskalWallis, χ^{2} = 115 & 9 df; Etruscan shrew n = 59, mouse n = 56, gerbil n = 80, rat n = 80, ferret n = 80, guinea pig n = 70, rabbit n = 53, marmoset n = 63, macaque n = 87, human n = 86). f, Proximal K_{v} plateau currents (p < 10^{4} KruskalWallis, χ^{2} = 29 & 5 df; mouse n = 32, gerbil n = 38, rat n = 38, guinea pig n = 26, rabbit n = 35, human n = 44). g, Distal K_{v} plateau currents (p =0.00001 KruskalWallis, χ^{2} = 30 & 5 df; mouse n = 35, gerbil. n = 46, rat n = 59, guinea pig n = 58, rabbit n = 39, human n = 43). hk, Conductance as a function of neuron size. The lines and shaded error bars represent the fit and 95% confidence interval of an allometric relationship constructed excluding humans. h, Total K_{v} plateau conductance on a loglog scale (exponent 1.24 ± 0.09, R^{2} = 0.983, p < 10^{3}, linear regression on loglog scale, F = 176 & 3 df, n = 5 for mouse, gerbil, rat, guinea pig, and rabbit). i, Somatic K_{v} plateau conductance on a loglog scale (exponent 1.98 ± 0.15, R^{2} = 0.962, p < 10^{5}, linear regression on loglog scale, F = 175 & 7 df, n = 9 for shrew, mouse, gerbil, rat, ferret, guinea pig, rabbit, marmoset, and macaque). j, Normalized average of HCN, K_{v} peak and K_{v} plateau conductance (exponent 1.43 ± 0.15, R^{2} = 0.966, p = 0.003, linear regression on loglog scale, F = 85.7 & 3 df, n = 5 for mouse, gerbil, rat, guinea pig, and rabbit). k, Normalized average of somatic K_{v} peak and K_{v} plateau conductance (exponent 1.82 ± 0.12, R^{2} = 0.968, p < 10^{5}, linear regression on loglog scale, F = 212 & 7 df, n = 9 for shrew, mouse, gerbil, rat, ferret, guinea pig, rabbit, marmoset and macaque). l, Relationship between somatic (normalized average of somatic K_{v} peak and K_{v} plateau conductance) and dendritic (normalized average of HCN, K_{v} peak and K_{v} plateau conductance) conductance (R^{2} = 0.891, p = 0.005, linear regression, F = 32.7 & 4 df, n = 6 for mouse, gerbil, rat, guinea pig, rabbit, and human). m, Soma volume as a function of neuronal density (Extended Data Table 1) on a loglog scale (exponent 0.74 ± 0.10, R^{2} = 0.897, p < 10^{3}, linear regression, F = 52.3 & 6 df, n = 8 for shrew, mouse, rat, ferret, guinea pig, rabbit, marmoset, and macaque). The line and shaded error bars represent the fit and 95% confidence interval of an allometric relationship constructed excluding humans. nt, Allometric relationship on a loglog scale. The lines and shaded error bars represent the fit and 95% confidence interval of the relationship constructed excluding humans. no, Somatic K_{v} plateau conductance densities in volumes as in Fig. 4c. n, Membrane conductance density (exponent 0.98 ± 0.15, R^{2} = 0.860, p < 10^{3}, linear regression, F = 43.0 & 7 df, n = 9 for shrew, mouse, gerbil, rat, ferret, guinea pig, rabbit, marmoset, and macaque). o, Volume K_{v} peak conductance density where the volume is filled with somas (exponent 0.53 ±0.15, R^{2} = 0.651, p = 0.009, linear regression, F = 13.1 & 7 df, n = 9 for shrew, mouse, gerbil, rat, ferret, guinea pig, rabbit, marmoset, and macaque). pq, Somatic K_{v} plateau conductance densities in volumes as in Fig. 4g. Gerbils were not included because the necessary information was not available in the literature (Extended Data Table 1). p, Cortex conductance density with accurate neuronal densities (exponent 0.27 ± 0.34, R^{2} = 0.092, p = 0.47, linear regression, F = 0.61 & 6 df, n = 8 for shrew, mouse, rat, ferret, guinea pig, rabbit, marmoset, and macaque). q, Total cortex conductance (exponent 1.09 ± 0.06, R^{2} = 0.985, p < 10^{5}, linear regression, F = 393 & 6 df, n = 8 for shrew, mouse, rat, ferret, guinea pig, rabbit, marmoset and macaque). rt, Same analysis as in Fig. 4f, but including dendrites in the volume and conductance calculation. r, Volume K_{v} peak conductance density where the volume is filled with somas and dendrites (exponent 0.05 ±0.10, R^{2} = 0.083, p = 0.64, linear regression, F = 0.272 & 3 df, n = 5 for mouse, gerbil, rat, guinea pig, and rabbit). s, Volume K_{v} plateau conductance density where the volume is filled with somas and dendrites (exponent 0.02 ±0.13, R^{2} = 0.006, p = 0.90, linear regression, F = 0.02 & 3 df, n = 5 for mouse, gerbil, rat, guinea pig, and rabbit). t, Volume HCN conductance density where the volume is filled with somas and dendrites (exponent 0.5 ±0.29, R^{2} = 0.500, p = 0.18, linear regression, F = 2.99 & 3 df, n = 5 for mouse, gerbil, rat, guinea pig, and rabbit).
Extended Data Fig. 9 Outsideout patch size estimation. Related to Fig. 3.
a, Rat dual nucleated patch recordings to test the efficacy of voltageclamp under nucleated patch configuration. b, Voltageclamp command action potential waveform (black) and independently observed waveform (grey) without compensation (left) or with series resistance and wholecell capacitance predicted and compensated >90% and lag <10 µs (right). c, Percentage of command waveform amplitude observed with the independent electrode (n = 4; p = 0.0045, twosided paired t test, t = 4.41 & 6 df). Pooled data represent mean ± SEM. d, Rat nucleated patch recording with series resistance and wholecell capacitance predicted and compensated >90% and lag <10 µs. e, K_{v} currents from the recording in d. f, Rat K_{v} peak current density computed using the K_{v} currents and patch surface area (n = 22). Pooled data represent mean ± SEM. g, Rat K_{v} peak currents in somatic outsideout patch (n = 80). Box plots denote the median and 25–75th percentiles. h, Outsideout patch surface area computed using the mean K_{v} peak current density in f and the median K_{v} peak current in g. ij, Recapitulation of outsideout patch recordings in a compartmental model of rat L5 neuron. i, Model dendritic outsideout patches as spheres of 50 µm^{2}. HCN (top) and K_{v} (bottom) currents (right) with associated voltageclamp protocol (left). j, Model K_{v} currents in somatic outsideout patches. k, Morphology used in the model taken from (https://senselab.med.yale.edu/ModelDB/ShowModel?model=124043#tabs3). l, Distal dendritic (520 µm from soma) and somatic voltage in response to subthreshold step current injections in the model. m, Somatic and dendritic input resistance as a function of distance from the soma. Fit to experimental rat data in blue taken from Fig. 2d versus model data in black. n, Somatic and dendritic voltage sag as a function of distance from the soma. Fit to experimental rat data in blue taken from Extended Data Fig. 6 versus model data in black.
Extended Data Fig. 10 Only human neurons are consistent outliers in electrophysiological features. Related to Fig. 4.
a, Explained variance of allometric relationship with (xaxis) versus without (yaxis) individual species for the same electrophysiological properties as in Fig. 4b. b, Calculation of outlier index. Positive outlier indices reflect cases in which a given species is an outlier and does not follow a conserved pattern observed in the other species. c, Percentage of features with substantial positive outlier indices (threshold at 0.2 or 0.4) for the different species.
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BeaulieuLaroche, L., Brown, N.J., Hansen, M. et al. Allometric rules for mammalian cortical layer 5 neuron biophysics. Nature 600, 274–278 (2021). https://doi.org/10.1038/s41586021040723
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DOI: https://doi.org/10.1038/s41586021040723
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