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Allometric rules for mammalian cortical layer 5 neuron biophysics

Nature volume 600, pages 274–278 (2021)Cite this article

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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 species1,2,3. However, it is unknown whether different species adapt neuronal properties to conserve how single neurons process information4,5,6,7. 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 voltage-gated potassium and HCN channels. Species with larger neurons, and therefore a decreased surface-to-volume ratio, exhibit higher membrane ionic conductances. This relationship produces a conserved conductance per unit brain volume. These size-dependent rules result in large but predictable changes in somatic and dendritic integrative properties. Human neurons do not follow these allometric relationships, exhibiting much lower voltage-gated 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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Fig. 1: Highly variable neuron size and input–output properties across species.
Fig. 2: Dendritic input–output properties are not conserved across species.
Fig. 3: Ionic conductance increases with size except in human neurons.
Fig. 4: Humans are an exception to the allometric relationship that normalizes ionic conductance per brain volume.

Data availability

All data generated and supporting the findings of this study are presented in the paper. Additional information will be made available upon reasonable request.

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Acknowledgements

We thank M. Tadross, S. Herculano-Houzel, 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. De-Medonsa, 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) (PGSD2-517068-2018) 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 Klingenstein-Simons Fellow, a Vallee Foundation Scholar and a McKnight Scholar.

Author information

Authors and Affiliations

  1. McGovern Institute for Brain Research, Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA

    Lou Beaulieu-Laroche, Norma J. Brown, Marissa Hansen, Enrique H. S. Toloza & Mark T. Harnett

  2. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Enrique H. S. Toloza

  3. Harvard Medical School, Boston, MA, USA

    Enrique H. S. Toloza

  4. Picower Institute for Learning and Memory, Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA

    Jitendra Sharma

  5. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital and Harvard Medical School, Boston, MA, USA

    Jitendra Sharma

  6. Department of Neurosurgery, Massachusetts General Hospital, Boston, MA, USA

    Ziv M. Williams

  7. C.S. Kubik Laboratory for Neuropathology, Massachusetts General Hospital, Boston, MA, USA

    Matthew P. Frosch

  8. Department of Neurosurgery, Brigham and Women’s Hospital, Boston, MA, USA

    Garth Rees Cosgrove

  9. Department of Neurology, Harvard Medical School and Massachusetts General Hospital, Boston, MA, USA

    Sydney S. Cash

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  1. Lou Beaulieu-Laroche
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Contributions

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.

Corresponding author

Correspondence to Mark T. Harnett.

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Extended data figures and tables

Extended Data Fig. 1 Histological identification of cortical layers. Related to Fig. 1.

a, Nissl-stained 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.

a-d, 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 a-b. Box plots denote the median and 25–75th percentiles for c-d. a, Impedance profile in response to sinewaves of 50-100 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 Kruskal-Wallis; χ2 = 259 & 9 df). d, Resonance frequency (p < 10−13 Kruskal-Wallis; χ2 = 81 & 9 df). Data points displayed as a beeswarm plot to show overlapping integers. e, Somatic voltage sag (p < 10−57 Kruskal-Wallis, χ2 = 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. b-g, Box plots denote the median and 25–75th percentiles. b, Rheobase (p < 10−47 Kruskal-Wallis, χ2 = 250 & 9 df). Data points displayed as a beeswarm plot to show overlapping integers. c, Slope of firing rate-current relationship (p < 10−59 Kruskal-Wallis, χ2 = 304 & 9 df). d, Maximal firing rate (p < 10−26 Kruskal-Wallis, χ2 = 146 & 9 df). e, Maximal current eliciting action potentials before entering depolarization block (p < 10−54 Kruskal-Wallis, χ2 = 283 & 9 df). f, Representative action potential waveforms. g, Width of first action potential at rheobase (p < 10−13 Kruskal-Wallis, χ2 = 86 & 9 df). h-j, 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 (R2 = 0.145, p = 0.006, linear regression, F = 8.3 & 49 df, n = 51). i, Correlation with soma input resistance (R2 = 0.596, p < 10−13, linear regression, F = 94.5 & 64 df, n = 66). j, Correlation with soma voltage sag (n = 66; R2 = 0.079, p = 0.02, linear regression, F = 5.5 & 64 df, n = 66). k-m, 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, two-sided Wilcoxon rank sum, Z = -5.93). m, Width of first action potential at rheobase (p < 10−3, two-sided 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. d-e, Box plots denote the median and 25–75th percentiles. d, Maximal action potential amplitude reduction (p < 10−18 Kruskal-Wallis, χ2 = 107 & 9 df). e, Maximal action potential dV/dt reduction (p < 10−15 Kruskal-Wallis, χ2 = 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 a-b. Box plots denote the median and 25–75th percentiles for d-e. a, Impedance profile in response to sinewaves of 50-100 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 Kruskal-Wallis, χ2 = 59 & 5 df). e, Resonance frequency (p < 10−6 Kruskal-Wallis, χ2 = 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, Two-photon z-stack montage image of mouse neuron with a proximal patch-clamp electrode 63 μm from soma. b, Proximal dendritic voltage in response to subthreshold (top) or threshold (bottom) step current injections. c-d, 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 Kruskal-Wallis, χ2 = 98 & 5 df). d, Proximal voltage sag (p < 10−8 Kruskal-Wallis, χ2 = 47 & 5 df). e-i, 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 Kruskal-Wallis, χ2 = 51 & 5 df). Data points displayed as a beeswarm plot to show overlapping integers. f, Proximal spike threshold (p < 10−4 Kruskal-Wallis, χ2 = 31 & 5 df). g, Proximal spike area on a log scale (p < 10−6 Kruskal-Wallis, χ2 = 36 & 5 df). h, Proximal spike width on a log scale (p < 10−5 Kruskal-Wallis, χ2 = 36 & 5 df). i, Proximal maximum spike dV/dt (p < 10−5 Kruskal-Wallis, χ2 = 35 & 5 df). j-m, 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 Kruskal-Wallis, χ2 = 28 & 5 df). Data points displayed as a beeswarm plot to show overlapping integers. k, Distal spike threshold (p < 10−11 Kruskal-Wallis, χ2 = 61 & 5 df). l, Distal spike area on a log scale (p < 10−10 Kruskal-Wallis, χ2 = 58 & 5 df). m, Maximum distal spike dV/dt (p < 10−13 Kruskal-Wallis, χ2 = 74 & 5 df). n-o, Somatic outside-out currents in sclerosis (n = 44), tumour (n = 30) and others (n = 12). Box plots denote the median and 25–75th percentiles. n, Somatic Kv peak currents (p = 0.39 Kruskal-Wallis, χ2 = 1.90 & 2 df). o, Somatic Kv plateau currents (p = 0.35 Kruskal-Wallis, χ2 = 2.09 & 2 df). p, Example EEG recording of epileptic seizure in rat kainic acid model. q-r, Somatic outside-out currents in control (n = 80) and epileptic (n = 68) rats. Box plots denote the median and 25–75th percentiles. q, Somatic Kv peak currents (p = 0.65, two-sided Wilcoxon rank sum, Z = 0.45). r, Somatic Kv plateau currents (p = 0.525, two-sided Wilcoxon rank sum, Z = 0.64).

Extended Data Fig. 8 Additional conductance measurements. Related to Fig. 3.

a, Dendritic outside-out patches were pulled from proximal dendrites after obtaining whole-cell recordings. Top, HCN currents with the associated voltage-clamp protocol on the left. Bottom, Kv currents with the associated voltage-clamp protocol on the left. b-g, Box plots denote the median and 25–75th percentiles. b, Proximal Kv peak currents (p = 0.010 Kruskal-Wallis, χ2 = 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 steady-state currents (p=0.07 Kruskal-Wallis, χ2 = 10 & 5 df; mouse n = 29, gerbil n = 30, rat n = 38, guinea pig n = 30, rabbit n = 31, human n = 42). d, Somatic Kv peak currents (p < 10-19 Kruskal-Wallis, χ2 = 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 Kv plateau currents (p < 10-19 Kruskal-Wallis, χ2 = 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 Kv plateau currents (p < 10-4 Kruskal-Wallis, χ2 = 29 & 5 df; mouse n = 32, gerbil n = 38, rat n = 38, guinea pig n = 26, rabbit n = 35, human n = 44). g, Distal Kv plateau currents (p =0.00001 Kruskal-Wallis, χ2 = 30 & 5 df; mouse n = 35, gerbil. n = 46, rat n = 59, guinea pig n = 58, rabbit n = 39, human n = 43). h-k, 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 Kv plateau conductance on a log-log scale (exponent 1.24 ± 0.09, R2 = 0.983, p < 10-3, linear regression on log-log scale, F = 176 & 3 df, n = 5 for mouse, gerbil, rat, guinea pig, and rabbit). i, Somatic Kv plateau conductance on a log-log scale (exponent 1.98 ± 0.15, R2 = 0.962, p < 10-5, linear regression on log-log scale, F = 175 & 7 df, n = 9 for shrew, mouse, gerbil, rat, ferret, guinea pig, rabbit, marmoset, and macaque). j, Normalized average of HCN, Kv peak and Kv plateau conductance (exponent 1.43 ± 0.15, R2 = 0.966, p = 0.003, linear regression on log-log scale, F = 85.7 & 3 df, n = 5 for mouse, gerbil, rat, guinea pig, and rabbit). k, Normalized average of somatic Kv peak and Kv plateau conductance (exponent 1.82 ± 0.12, R2 = 0.968, p < 10-5, linear regression on log-log 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 Kv peak and Kv plateau conductance) and dendritic (normalized average of HCN, Kv peak and Kv plateau conductance) conductance (R2 = 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 log-log scale (exponent -0.74 ± 0.10, R2 = 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. n-t, Allometric relationship on a log-log scale. The lines and shaded error bars represent the fit and 95% confidence interval of the relationship constructed excluding humans. n-o, Somatic Kv plateau conductance densities in volumes as in Fig. 4c. n, Membrane conductance density (exponent 0.98 ± 0.15, R2 = 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 Kv peak conductance density where the volume is filled with somas (exponent 0.53 ±0.15, R2 = 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). p-q, Somatic Kv 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, R2 = 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, R2 = 0.985, p < 10-5, linear regression, F = 393 & 6 df, n = 8 for shrew, mouse, rat, ferret, guinea pig, rabbit, marmoset and macaque). r-t, Same analysis as in Fig. 4f, but including dendrites in the volume and conductance calculation. r, Volume Kv peak conductance density where the volume is filled with somas and dendrites (exponent 0.05 ±0.10, R2 = 0.083, p = 0.64, linear regression, F = 0.272 & 3 df, n = 5 for mouse, gerbil, rat, guinea pig, and rabbit). s, Volume Kv plateau conductance density where the volume is filled with somas and dendrites (exponent 0.02 ±0.13, R2 = 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, R2 = 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 Outside-out patch size estimation. Related to Fig. 3.

a, Rat dual nucleated patch recordings to test the efficacy of voltage-clamp under nucleated patch configuration. b, Voltage-clamp command action potential waveform (black) and independently observed waveform (grey) without compensation (left) or with series resistance and whole-cell 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, two-sided paired t test, t = 4.41 & 6 df). Pooled data represent mean ± SEM. d, Rat nucleated patch recording with series resistance and whole-cell capacitance predicted and compensated >90% and lag <10 µs. e, Kv currents from the recording in d. f, Rat Kv peak current density computed using the Kv currents and patch surface area (n = 22). Pooled data represent mean ± SEM. g, Rat Kv peak currents in somatic outside-out patch (n = 80). Box plots denote the median and 25–75th percentiles. h, Outside-out patch surface area computed using the mean Kv peak current density in f and the median Kv peak current in g. i-j, Recapitulation of outside-out patch recordings in a compartmental model of rat L5 neuron. i, Model dendritic outside-out patches as spheres of 50 µm2. HCN (top) and Kv (bottom) currents (right) with associated voltage-clamp protocol (left). j, Model Kv currents in somatic outside-out patches. k, Morphology used in the model taken from (https://senselab.med.yale.edu/ModelDB/ShowModel?model=124043#tabs-3). 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 (x-axis) versus without (y-axis) 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.

Extended Data Table 1 Species information
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Extended Data Table 2 Breakdown of dataset of 2,257 recordings from temporal cortex
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Extended Data Table 3 Information on patients with epilepsy (related to Methods)
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Beaulieu-Laroche, 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/s41586-021-04072-3

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