Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Therapeutic deep brain stimulation reduces cortical phase-amplitude coupling in Parkinson's disease

Nature Neuroscience volume 18, pages 779–786 (2015)Cite this article

Subjects

Abstract

Deep brain stimulation (DBS) is increasingly applied for the treatment of brain disorders, but its mechanism of action remains unknown. Here we evaluate the effect of basal ganglia DBS on cortical function using invasive cortical recordings in Parkinson's disease (PD) patients undergoing DBS implantation surgery. In the primary motor cortex of PD patients, neuronal population spiking is excessively synchronized to the phase of network oscillations. This manifests in brain surface recordings as exaggerated coupling between the phase of the beta rhythm and the amplitude of broadband activity. We show that acute therapeutic DBS reversibly reduces phase-amplitude interactions over a similar time course as that of the reduction in parkinsonian motor signs. We propose that DBS of the basal ganglia improves cortical function by alleviating excessive beta phase locking of motor cortex neurons.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it

$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Electrodes localization, task, and timeline of recordings.
Figure 2: Example M1 recordings and their spectral characteristics, before filtering the stimulation artifact, in a single patient.
Figure 3: Acute therapeutic STN stimulation reduces PAC in the resting state.
Figure 4: DBS does not affect resting state power spectral density.
Figure 5: Examples of M1 LFP and PAC during the arm movement task in one patient.
Figure 6: Both DBS and movement reduce PAC during the arm movement task.
Figure 7: Movement-related cortical changes before, during and after DBS.

References

  1. Benabid, A.L., Chabardes, S., Mitrofanis, J. & Pollak, P. Deep brain stimulation of the subthalamic nucleus for the treatment of Parkinson's disease. Lancet Neurol. 8, 67–81 (2009).

    Article  PubMed  Google Scholar 

  2. Wingeier, B. et al. Intra-operative STN DBS attenuates the prominent beta rhythm in the STN in Parkinson's disease. Exp. Neurol. 197, 244–251 (2006).

    Article  PubMed  Google Scholar 

  3. Kühn, A.A. et al. High-frequency stimulation of the subthalamic nucleus suppresses oscillatory beta activity in patients with Parkinson's disease in parallel with improvement in motor performance. J. Neurosci. 28, 6165–6173 (2008).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  4. Ray, N.J. et al. Local field potential beta activity in the subthalamic nucleus of patients with Parkinson's disease is associated with improvements in bradykinesia after dopamine and deep brain stimulation. Exp. Neurol. 213, 108–113 (2008).

    Article  CAS  PubMed  Google Scholar 

  5. Bronte-Stewart, H. et al. The STN beta-band profile in Parkinson's disease is stationary and shows prolonged attenuation after deep brain stimulation. Exp. Neurol. 215, 20–28 (2009).

    Article  CAS  PubMed  Google Scholar 

  6. Rossi, L. et al. Subthalamic local field potential oscillations during ongoing deep brain stimulation in Parkinson's disease. Brain Res. Bull. 76, 512–521 (2008).

    Article  CAS  PubMed  Google Scholar 

  7. Eusebio, A. et al. Deep brain stimulation can suppress pathological synchronisation in parkinsonian patients. J. Neurol. Neurosurg. Psychiatry 82, 569–573 (2011).

    Article  CAS  PubMed  Google Scholar 

  8. Whitmer, D. et al. High frequency deep brain stimulation attenuates subthalamic and cortical rhythms in Parkinson's disease. Front. Hum. Neurosci. 6, 155 (2012).

    Article  PubMed  PubMed Central  Google Scholar 

  9. Stoffers, D. et al. Slowing of oscillatory brain activity is a stable characteristic of Parkinson's disease without dementia. Brain 130, 1847–1860 (2007).

    Article  CAS  PubMed  Google Scholar 

  10. Melgari, J.M. et al. Alpha and beta EEG power reflects L-DOPA acute administration in parkinsonian patients. Front. Aging Neurosci. 6, 302 (2014).

    Article  PubMed  PubMed Central  Google Scholar 

  11. Litvak, V. et al. Resting oscillatory cortico-subthalamic connectivity in patients with Parkinson's disease. Brain 134, 359–374 (2011).

    Article  PubMed  Google Scholar 

  12. Hirschmann, J. et al. Distinct oscillatory STN-cortical loops revealed by simultaneous MEG and local field potential recordings in patients with Parkinson's disease. Neuroimage 55, 1159–1168 (2011).

    Article  CAS  PubMed  Google Scholar 

  13. de Hemptinne, C. et al. Exaggerated phase-amplitude coupling in the primary motor cortex in Parkinson disease. Proc. Natl. Acad. Sci. USA 110, 4780–4785 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  14. Manning, J.R., Jacobs, J., Fried, I. & Kahana, M.J. Broadband shifts in local field potential power spectra are correlated with single-neuron spiking in humans. J. Neurosci. 29, 13613–13620 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  15. Suffczynski, P., Crone, N.E. & Franaszczuk, P.J. Afferent inputs to cortical fast-spiking interneurons organize pyramidal cell network oscillations at high-gamma frequencies (60–200 Hz). J. Neurophysiol. 112, 3001–3011 (2014).

    Article  PubMed  PubMed Central  Google Scholar 

  16. Canolty, R.T. & Knight, R.T. The functional role of cross-frequency coupling. Trends Cogn. Sci. 14, 506–515 (2010).

    Article  PubMed  PubMed Central  Google Scholar 

  17. Jacobs, J., Kahana, M.J., Ekstrom, A.D. & Fried, I. Brain oscillations control timing of single-neuron activity in humans. J. Neurosci. 27, 3839–3844 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  18. Axmacher, N. et al. Cross-frequency coupling supports multi-item working memory in the human hippocampus. Proc. Natl. Acad. Sci. USA 107, 3228–3233 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  19. Canolty, R.T. et al. High gamma power is phase-locked to theta oscillations in human neocortex. Science 313, 1626–1628 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  20. Cohen, M.X., Elger, C.E. & Fell, J. Oscillatory activity and phase-amplitude coupling in the human medial frontal cortex during decision making. J. Cogn. Neurosci. 21, 390–402 (2009).

    Article  PubMed  Google Scholar 

  21. Voytek, B. et al. Shifts in gamma phase-amplitude coupling frequency from theta to alpha over posterior cortex during visual tasks. Front. Hum. Neurosci. 4, 191 (2010).

    Article  PubMed  PubMed Central  Google Scholar 

  22. Yanagisawa, T. et al. Regulation of motor representation by phase-amplitude coupling in the sensorimotor cortex. J. Neurosci. 32, 15467–15475 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  23. Miller, K.J. et al. Human motor cortical activity is selectively phase-entrained on underlying rhythms. PLoS Comput. Biol. 8, e1002655 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  24. Purzner, J. et al. Involvement of the basal ganglia and cerebellar motor pathways in the preparation of self-initiated and externally triggered movements in humans. J. Neurosci. 27, 6029–6036 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  25. Kühn, A.A. et al. Event-related beta desynchronization in human subthalamic nucleus correlates with motor performance. Brain 127, 735–746 (2004).

    Article  PubMed  Google Scholar 

  26. Williams, D. et al. The relationship between oscillatory activity and motor reaction time in the parkinsonian subthalamic nucleus. Eur. J. Neurosci. 21, 249–258 (2005).

    Article  PubMed  Google Scholar 

  27. Temel, Y. et al. Differential effects of subthalamic nucleus stimulation in advanced Parkinson disease on reaction time performance. Exp. Brain Res. 169, 389–399 (2006).

    Article  PubMed  Google Scholar 

  28. López-Azcárate, J. et al. Coupling between beta and high-frequency activity in the human subthalamic nucleus may be a pathophysiological mechanism in Parkinson's disease. J. Neurosci. 30, 6667–6677 (2010).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  29. Özkurt, T.E. et al. High frequency oscillations in the subthalamic nucleus: a neurophysiological marker of the motor state in Parkinson's disease. Exp. Neurol. 229, 324–331 (2011).

    Article  PubMed  Google Scholar 

  30. Eusebio, A. et al. Effects of low-frequency stimulation of the subthalamic nucleus on movement in Parkinson's disease. Exp. Neurol. 209, 125–130 (2008).

    Article  PubMed  PubMed Central  Google Scholar 

  31. Crone, N.E. et al. Functional mapping of human sensorimotor cortex with electrocorticographic spectral analysis. I. Alpha and beta event-related desynchronization. Brain 121, 2271–2299 (1998).

    Article  PubMed  Google Scholar 

  32. Crone, N.E., Miglioretti, D.L., Gordon, B. & Lesser, R.P. Functional mapping of human sensorimotor cortex with electrocorticographic spectral analysis. II. Event-related synchronization in the gamma band. Brain 121, 2301–2315 (1998).

    Article  PubMed  Google Scholar 

  33. Lakatos, P., Karmos, G., Mehta, A.D., Ulbert, I. & Schroeder, C.E. Entrainment of neuronal oscillations as a mechanism of attentional selection. Science 320, 110–113 (2008).

    Article  CAS  PubMed  Google Scholar 

  34. Tort, A.B. et al. Dynamic cross-frequency couplings of local field potential oscillations in rat striatum and hippocampus during performance of a T-maze task. Proc. Natl. Acad. Sci. USA 105, 20517–20522 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  35. Tort, A.B., Komorowski, R.W., Manns, J.R., Kopell, N.J. & Eichenbaum, H. Theta-gamma coupling increases during the learning of item-context associations. Proc. Natl. Acad. Sci. USA 106, 20942–20947 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  36. Moran, A., Bergman, H., Israel, Z. & Bar-Gad, I. Subthalamic nucleus functional organization revealed by parkinsonian neuronal oscillations and synchrony. Brain 131, 3395–3409 (2008).

    Article  CAS  PubMed  Google Scholar 

  37. Pogosyan, A. et al. Parkinsonian impairment correlates with spatially extensive subthalamic oscillatory synchronization. Neuroscience 171, 245–257 (2010).

    Article  CAS  PubMed  Google Scholar 

  38. Crowell, A.L. et al. Oscillations in sensorimotor cortex in movement disorders: an electrocorticography study. Brain 135, 615–630 (2012).

    Article  PubMed  PubMed Central  Google Scholar 

  39. Gradinaru, V., Mogri, M., Thompson, K.R., Henderson, J.M. & Deisseroth, K. Optical deconstruction of parkinsonian neural circuitry. Science 324, 354–359 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  40. Hashimoto, T., Elder, C.M., Okun, M.S., Patrick, S.K. & Vitek, J.L. Stimulation of the subthalamic nucleus changes the firing pattern of pallidal neurons. J. Neurosci. 23, 1916–1923 (2003).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  41. Vitek, J.L., Zhang, J., Hashimoto, T., Russo, G.S. & Baker, K.B. External pallidal stimulation improves parkinsonian motor signs and modulates neuronal activity throughout the basal ganglia thalamic network. Exp. Neurol. 233, 581–586 (2012).

    Article  PubMed  Google Scholar 

  42. Dejean, C., Hyland, B. & Arbuthnott, G. Cortical effects of subthalamic stimulation correlate with behavioral recovery from dopamine antagonist induced akinesia. Cereb. Cortex 19, 1055–1063 (2009).

    Article  PubMed  Google Scholar 

  43. Kuriakose, R. et al. The nature and time course of cortical activation following subthalamic stimulation in Parkinson's disease. Cereb. Cortex 20, 1926–1936 (2010).

    Article  PubMed  Google Scholar 

  44. Li, Q. et al. Therapeutic deep brain stimulation in parkinsonian rats directly influences motor cortex. Neuron 76, 1030–1041 (2012).

    Article  CAS  PubMed  Google Scholar 

  45. Voytek, B. & Gazzaley, A. Stimulating the aging brain. Ann. Neurol. 73, 1–3 (2013).

    Article  PubMed  Google Scholar 

  46. Follett, K.A. et al. Pallidal versus subthalamic deep-brain stimulation for Parkinson's disease. N. Engl. J. Med. 362, 2077–2091 (2010).

    Article  CAS  PubMed  Google Scholar 

  47. Little, S. et al. Adaptive deep brain stimulation in advanced Parkinson disease. Ann. Neurol. 74, 449–457 (2013).

    Article  PubMed  PubMed Central  Google Scholar 

  48. Rosin, B. et al. Closed-loop deep brain stimulation is superior in ameliorating parkinsonism. Neuron 72, 370–384 (2011).

    Article  CAS  PubMed  Google Scholar 

  49. Koop, M.M., Andrzejewski, A., Hill, B.C., Heit, G. & Bronte-Stewart, H.M. Improvement in a quantitative measure of bradykinesia after microelectrode recording in patients with Parkinson's disease during deep brain stimulation surgery. Mov. Disord. 21, 673–678 (2006).

    Article  PubMed  Google Scholar 

  50. Yousry, T.A. et al. Localization of the motor hand area to a knob on the precentral gyrus. A new landmark. Brain 120, 141–157 (1997).

    Article  PubMed  Google Scholar 

  51. Starr, P.A. et al. Implantation of deep brain stimulators into the subthalamic nucleus: technical approach and magnetic resonance imaging-verified lead locations. J. Neurosurg. 97, 370–387 (2002).

    Article  PubMed  Google Scholar 

  52. Shahlaie, K., Larson, P.S. & Starr, P.A. Intra-operative CT for DBS surgery: technique and accuracy assessment. Neurosurgery 68, 114–124 (2011).

    PubMed  Google Scholar 

  53. Mann, J.M. et al. Brain penetration effects of microelectrodes and DBS leads in STN or GPi. J. Neurol. Neurosurg. Psychiatry 80, 794–797 (2009).

    Article  CAS  PubMed  Google Scholar 

  54. Tort, A.B. et al. Dynamic cross-frequency couplings of local field potential oscillations in rat striatum and hippocampus during performance of a T-maze task. Proc. Natl. Acad. Sci. USA 105, 20517–20522 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  55. Osipova, D., Hermes, D. & Jensen, O. Gamma power is phase-locked to posterior alpha activity. PLoS ONE 3, e3990 (2008).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  56. Penny, W.D., Duzel, E., Miller, K.J. & Ojemann, J.G. Testing for nested oscillation. J. Neurosci. Methods 174, 50–61 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

Download references

Acknowledgements

Thanks to our patients who participated in this study, to R. Steiner for programming the iPad task, to A. Kreitzer for critical review of the manuscript, to S. Miocinovic for symptom assessment, and to N. Ziman and S. Qasim for helping to collect data. This study was supported by a grant from the Michael J. Fox foundation and by US National Institutes of Health grant R01 NS069779.

Author information

Authors and Affiliations

  1. Department of Neurological Surgery, University of California, San Francisco, San Francisco, California, USA.,

    Coralie de Hemptinne, Nicole C Swann, Elena S Ryapolova-Webb & Philip A Starr

  2. Department of Neurology, University of California, San Francisco, San Francisco, California, USA.,

    Jill L Ostrem, Marta San Luciano & Nicholas B Galifianakis

  3. Graduate Program in Neuroscience, University of California, San Francisco, San Francisco, California, USA

    Philip A Starr

Authors
  1. Coralie de Hemptinne
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nicole C Swann
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jill L Ostrem
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Elena S Ryapolova-Webb
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Marta San Luciano
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Nicholas B Galifianakis
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Philip A Starr
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Conceived and designed the experiments: C.d.H., P.A.S. Performed the experiments: C.d.H., N.C.S., E.S.R.-W., P.A.S. Analyzed the data: C.d.H. Obtained consent from patients: C.d.H., N.C.S., E.S.R.-W. Recruited patients and characterized patients symptoms: J.L.O., M.S.L., N.B.G. Wrote the paper: C.d.H., P.A.S. Performed surgical procedures and supervised the project: P.A.S.

Corresponding author

Correspondence to Coralie de Hemptinne.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Integrated supplementary information

Supplementary Figure 1 Physiologic characteristic of STN and cortex at rest.

a. STN and M1 are coherent in the β band. Left panel shows a typical example of STN and M1 coherence. Peak coherence and its frequency were determined for each patient (18 patients, STN LFP was not recorded or noisy in 5 patients). The distribution of these frequencies of peak coherence is shown on the right panel. Coherence was computed using mscohere matlab function with a 512 window and 50% overlap. b. Reduction of STN β power during DBS (red curves) compared to baseline without stimulation (blue curves). STN LFPs were recorded before and during DBS using contact 0 and 2 surrounding the contact used for stimulation, in five patients (table S6). Each panel shows the STN LFPs recorded in each patient. Monopolar DBS was delivered using contact 1 as the active and a grounding pad as the reference contact. For these recordings, signals were sampled at 3000, amplified 7000 fold and an online low pass filter (100Hz) was applied to avoid saturation of the STN LFP by stimulation artifact. For each patient, log PSD was averaged in the beta band (13-30Hz). The mean log β observed during DBS is plotted versus that observed before DBS. Each dot represents one patient. c. Strong PAC, and a reduction in PAC induced by DBS, is found in the primary motor cortex but not in the primary sensory cortex. PAC was computed using an ECoG contact pair covering the motor cortex and another contact pair covering the sensory cortex (S1) in 20 patients (3 patients did not have sensory cortex coverage), using the same method as the one used in the main manuscript (Tort 2008). Boxplot of the mean PAC averaged across β (13-30Hz) and broadband activity (50-200Hz) before and during DBS is shown for M1 (left panel) and S1 (right panel).

Source data

Supplementary Figure 2 DBS effects are insensitive to the presence of stimulation artifact and to the method used to compute PAC.

a. Typical example of log power spectral density computed on M1 ECoG potential, filtered at the stimulation artifact and noise harmonic (red curve) and without any filter (blue curve). b. Example of PAC computed with unfiltered and filtered data is shown on the left and right panels, respectively. Same patient as in a. c. Boxplot showing the significant reduction of mean β PAC during STN DBS when PAC is computed using unfiltered ECoG potentials. Note the similarity of these results and these presented in figure 3 C suggesting that stimulation artifact does not affect the results. d. Five PAC characteristics were evaluated using filtered and unfiltered data and represented in a scatterplot. From left to right, mean β PAC is the modulation index averaged across β (13-30Hz) and the all broad band power (50-200Hz), PAC mean 70-110 is the modulation index averaged across β and frequencies unaffected by any artifact (70-110), max PAC is the maximum coupling, max frequency for phase and amplitude are the frequency at which the maximum coupling occurs. Each dot represents a patient. A highly significant correlation was observed (red line is the regression) for each PAC variable suggesting that stimulation artifact does not alter PAC.e. Broadband activity is not modulated during DBS even in the presence of stimulation artifact. Log PSDs were computed from unfiltered ECoG potentials, averaged across the all broadband activity (50-200Hz) and compared between stimulation conditions. DBS did not significantly modulate this variable similar to what was observed with filtered data (Fig 4). f. Mean β PAC was reduced during DBS using two alternative methods of analyzing phase-amplitude interactions, the phase-locking value (PVL, left panel, see penny et al. 2008 for methods ) and coherence-cross-frequency coupling (CFC, right pane, see Osipova et al. 2008 for methods). Same convention as in fig 3d

Source data

Supplementary Figure 3 Time course of beta PAC and log PSD at the DBS transitions

Time course of β PAC and log PSD at the transitions at which DBS is turned OFF (a,c,d) or ON (b) studied in four patients. Periods of stimulation are indicated by a red bar above PAC plot. PAC was computed over a 3s sliding window of 100ms using Tort method (as in the manuscript), with the β phase estimated in small steps (13-30Hz with step of 2 Hz) but extracting the amplitude signal between 50-110 Hz in order to compute PAC over time. Signal was filtered between 50 and 110 Hz to avoid the stimulation artifact. PAC decreased or increased gradually once DBS was turned ON and OFF, respectively. These transitions take 2-4s suggesting that the reduction of PAC during DBS is not due to the stimulation artifact. (In this figure, in some of the examples, a correlation between β power and β PAC can be observed).

Supplementary Figure 4 M1 PAC correlates with symptoms as assessed by a blinded neurologist in a randomized stimulation paradigm.

a. ECoG potentials were recorded while DBS was turned OFF or ON using therapeutic and sub-optimal stimulation settings in a single subject. PAC was evaluated during the 30s without movement in each condition sub-optimal stimulation using low voltage (1-2+, 0.5V, 160Hz, upper left panel), therapeutic stimulation (1-2+, 4V, 160Hz, upper right panel), no stimulation (lower left panel), sub-optimal stimulation using low frequency (1-2+, 4V, 70Hz, lower right panel). For each condition the patient was instructed to stay quiet with eyes open for 30s then a neurologist blinded to stimulation settings was asked to assessed rigidity, tremor (rest and postural) and bradykinesia (finger tapping and hand opening and closing). b. Corresponding PSD on which the artifact of stimulation and β power can be observed. c. shows the correlation between symptoms severity (rigidity score + tremor score + bradykinesia) and mean β PAC. This result, using a within-subjects design and a blinded movement disorders neurologist, suggest that DBS reduced PAC in a manner that correlate with symptoms.

Source data

Supplementary Figure 5 Inconsistent effect of DBS on beta power

DBS does not significantly reduce β power even when this frequency band was subdivided into β power in low (12-20 Hz, left panel) and high β (20-30Hz, right panel). Mean log PSD during DBS is plotted versus that observed before DBS for low and high β power in the left and right panels, respectively. Each dot represents a patient. Diagonal is shown in dashed line.

Source data

Supplementary Figure 6 DBS reduces PAC significantly irrespective of the direction of change in spectral power.

a. Patients were divided into those with an increase in β power (10 patients, left top panel), and those with a decrease (13 patients, right top panel) and the effect of DBS on phase-amplitude coupling was then evaluated for these 2 groups. A significant decrease of PAC in both groups of patients was observed. b. Patients were also divided into those with an increase in broadband power (12 patients, left lower panel) and those with a decrease in that frequency band (11 patients, right lower panel). Both groups of patients show a significant reduction of PAC during stimulation. These results suggest that DBS-induced reductions in PAC are not related solely to alterations in cortical β or broadband activity, although both, PAC and β power, are correlated..Same convention as in fig 3d

Source data

Supplementary information

Supplementary Text and Figures

Supplementary Figures 1–6 and Supplementary Tables 1–6 (PDF 861 kb)

Supplementary Methods Checklist (PDF 360 kb)

Source data

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

de Hemptinne, C., Swann, N., Ostrem, J. et al. Therapeutic deep brain stimulation reduces cortical phase-amplitude coupling in Parkinson's disease. Nat Neurosci 18, 779–786 (2015). https://doi.org/10.1038/nn.3997

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nn.3997

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing