Neural firing rate homeostasis via inhibitory synaptic plasticity

Xue Xiao-Dan; Wang Mei-Li; Shao Yu-Zhu; Wang Jun-Song

doi:10.7498/aps.68.20182234

Abstract

Neural firing rate homeostasis, as an important feature of neural electrical activity, means that the firing rate in brain is maintained in a relatively stable state, and fluctuates around a constant value. Extensive experimental studies have revealed that the firing rate homeostasis is ubiquitous in brain, and provides a base for neural information processing and maintaining normal neurological functions, so that the research on neural firing rate homeostasis is a central problem in the field of neuroscience. Cortical neural network is a highly complex dynamic system with a large number of input disturbance signals and parameter perturbations due to dynamic connection. However, it remains to be further investigated how firing rate homeostasis is established in cortical neural network, furthermore, maintains robustness to these disturbances and perturbations. The feedback neural circuit with recurrent excitatory and inhibitory connection is a typical connective pattern in cortical cortex, and inhibitory synaptic plasticity plays a crucial role in achieving neural firing rate homeostasis. Here, by constructing a feedback neural network with inhibitory spike timing-dependent plasticity (STDP), we conduct a computational research to elucidate the mechanism of neural firing rate homeostasis. The results indicate that the neuronal firing rate can track the target firing rate accurately under the regulation of inhibitory synaptic plasticity, thus achieve firing rate homeostasis. In the face of external disturbances and parameter perturbations, the neuron firing rate deviates transiently from the target firing rate value, and converges to the target firing rate value at a steady state, which demonstrates that the firing rate homeostasis established by the inhibitory synaptic plasticity can maintain strong robustness. Furthermore, the analytical research qualitatively explains the firing rate homeostasis mechanism underlined by inhibitory synaptic plasticity. Finally, the simulations further demonstrate that the learning rate value and the firing rate set point value also exert a quantitative influence on the firing rate homeostasis. Overall, these findings not only gain an insight into the firing rate homeostasis mechanism underlined by inhibitory synaptic plasticity, but also inspire testable hypotheses for future experimental studies.

Keywords:

Authors and contacts

1.
School of Biomedical Engineering and Technology, Tianjin Medical University, Tianjin 300070, China
2.
Cangzhou People's Hospital, Cangzhou 061000, China

Corresponding author: Wang Jun-Song, wjsong2004@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61473208, 61876132), and Tianjin Research Program of Application Foundation and Advanced Technology (Grant No. 15JCYBJC47700).

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References

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Cited By

图 1 反馈神经回路模型结构

Figure 1. Structure of the feedback neural network.

DownLoad: Full-Size Img PowerPoint

图 2 抑制性突触可塑性(STDP)调节规则示意图

Figure 2. The regulation rule of inhibitory synaptic plasticity (STDP).

DownLoad: Full-Size Img PowerPoint

图 3 目标放电率为5 Hz时的神经元放电率自稳态分析图　(a)神经元膜电位; (b)神经元平均放电率曲线; (c)抑制性突触权重变化曲线

Figure 3. Firing rate homeostasis with the target firing rate equal to 5 Hz: (a) Neural membrane potential; (b) the average firing rate; (c) the strength of inhibitory synapse.

DownLoad: Full-Size Img PowerPoint

图 4 目标放电率为10 Hz时的神经元放电率自稳态分析图　(a)神经元膜电位; (b)神经元平均放电率曲线; (c)抑制性突触权重变化曲线

Figure 4. Firing rate homeostasis with the target firing rate equal to 10 Hz: (a) Neuronal membrane potential; (b) the average firing rate; (c) the strength of inhibitory synapse.

DownLoad: Full-Size Img PowerPoint

图 5 目标放电率为20 Hz时的神经元放电率自稳态分析图　(a)神经元膜电位; (b)神经元平均放电率曲线; (c)抑制性突触权重变化曲线

Figure 5. Firing rate homeostasis with the target firing rate equal to 20 Hz: (a) Neuronal membrane potential; (b) the average firing rate; (c) the strength of inhibitory synapse.

DownLoad: Full-Size Img PowerPoint

图 6 目标放电率为50 Hz时的神经元放电率自稳态分析图　(a)神经元膜电位; (b)神经元平均放电率曲线; (c)抑制性突触权重变化曲线

Figure 6. Firing rate homeostasis with the target firing rate equal to 50 Hz: (a) Neuronal membrane potential; (b) the average firing rate; (c) the strength of inhibitory synapse.

DownLoad: Full-Size Img PowerPoint

图 7 神经元实际放电率跟踪目标放电率的总体情况

Figure 7. The simulation firing rate and target firing rate.

DownLoad: Full-Size Img PowerPoint

图 8 噪声干扰下的神经元放电率鲁棒性　(a)噪声干扰信号; (b)神经元膜电位; (c)神经元平均放电率曲线; (d)抑制性突触权重变化曲线

Figure 8. The robustness of neural firing rate homeostasis under noise disturbances: (a) The noise signal; (b) neuronal membrane potential; (c) the average firing rate; (d) the strength of inhibitory synapse.

DownLoad: Full-Size Img PowerPoint

图 9 参数摄动下的放电率自稳态鲁棒性　(a)参数摄动信号; (b)神经元膜电位; (c)神经元平均放电率曲线; (d)抑制性突触权重变化曲线

Figure 9. The robustness of neural firing rate homeostasis under parameter perturbation: (a) The parameter perturbation signal; (b) neuronal membrane potential; (c) the average firing rate; (d) the strength of inhibitory synapse.

DownLoad: Full-Size Img PowerPoint

图 10 参数干扰时有无抑制性突触可塑性两种情况下的神经元平均放电率自稳态特性　(a)参数摄动信号; (b)神经元膜电位; (c)神经元平均放电率曲线; (d)抑制性突触权重变化曲线

Figure 10. The firing rate characteristics with and without inhibitory synaptic plasticity under parameter perturbation: (a) The parameter perturbation signal; (b) neural membrane potential; (c) the average firing rate; (d) the strength of inhibitory synapse.

DownLoad: Full-Size Img PowerPoint

图 11 学习率对放电率自稳态的影响　(a)参数摄动信号; (b)不同学习率时的神经元平均放电率曲线

Figure 11. The effect of learning rate on neural firing rate homeostasis: (a) The parameter perturbation signal; (b) the firing rate with different learning rates.

DownLoad: Full-Size Img PowerPoint

图 12 神经元实际放电率极限值

Figure 12. The limitation value of neural firing rate.

DownLoad: Full-Size Img PowerPoint

图 13 目标放电率的确定^[43]

Figure 13. Establishing a set point for the neuronal firing rate^[43].

DownLoad: Full-Size Img PowerPoint

表 1 神经网络结构相关参数取值

Table 1. Parameters values of the neural feedback model structure.

参数描述取值

N_E 兴奋性神经元规模 800
N_I 抑制性神经元规模 200
P_EE E-E的连接概率 0.2
P_EI E-I的连接概率 0.4
P_IE I-E的连接概率 0.4
P_II I-I的连接概率 0.4

DownLoad: CSV

表 2 神经元模型各参数取值

Table 2. Parameters values of LIF neuron model.

参数取值单位

${\tau _{\rm{m}}}$ 20 ms
${V^{{\rm{rest}}}}$ –60 mV
${V_{{\rm{th}}}}$ –50 mV
${V^{\rm{E}}}$ 0 mV
${V^{\rm{I}}}$ –70 mV
${g^{{\rm{leak}}}}$ 10 nS

DownLoad: CSV

表 3 突触模型参数取值

Table 3. Parameters values of synapse model.

参数取值单位

${\tau _{\rm{E}}}$ 5 ms
${\tau _{\rm{I}}}$ 10 ms
${\bar g^{\rm{E}}}$ 140 pS
${\bar g^{\rm{I}}}\normalsize$ 350 pS

DownLoad: CSV

表 4 抑制性突触可塑性的参数取值

Table 4. Parameters values of inhibitory synaptic plasticity.

参数描述取值

${W_{ij}}^{}$ 抑制性突触权重 0
${\tau _{{\rm{STDP}}}}$ 可塑性时间常数 20
$\eta $ 学习率 0.005
$\alpha $ 抑制因子 0.12
${\rho _0}\normalsize$ 目标放电率

DownLoad: CSV

[1]	Gläser C, Joublin F 2011 IEEE T. Auton. Ment. De. 3 285 Google Scholar
[2]	Hengen K B, Lambo M E, Hooser S D, van Katz D B, Turrigiano G G 2013 Neuron 80 335 Google Scholar
[3]	Corner M A, Ramakers G J A 1992 Dev. Brain Res. 65 57 Google Scholar
[4]	Ramakers G J A, Corner M A, Habets A M M C 1990 Exp. Brain Res. 79 157 Google Scholar
[5]	Ramakers G J A, Galen H V, Feenstra M G P, Corner M A, Boer G J 1994 Int. J. Dev. Neurosci. 12 611 Google Scholar
[6]	Pol A N V D, Obrietan K, Belousov A 1996 Neuroscience 74 653 Google Scholar
[7]	Turrigiano G G, Leslie K R, Desai N S, Rutherford L C, Nelson S B 1998 Nature 391 892 Google Scholar
[8]	Rutherford L C, Nelson S B, Turrigiano G G 1998 Neuron 21 521 Google Scholar
[9]	Burrone J, O'Byrne M, Murthy V N 2002 Nature 420 414 Google Scholar
[10]	Turrigiano G G, Nelson S B 2004 Nat. Rev. Neurosci. 5 97 Google Scholar
[11]	Turrigiano G 2012 CSH Perspect. Biol. 4 a005736 Google Scholar
[12]	Cannon J, Miller P 2016 J. Neurophysiol. 116 2004 Google Scholar
[13]	Cannon J, Miller P 2017 J. Math. Neurosc. 7 1 Google Scholar
[14]	Miller P, Cannon J 2018 Biol. Cybern. 113 47
[15]	McClelland J L, McNaughton B L, O'Reilly R C 1995 Psychol. Rev. 102 419 Google Scholar
[16]	Frankland P W, O'Brien C, Ohno M, Kirkwood A, Silva A J 2001 Nature 411 309 Google Scholar
[17]	Carcea I, Froemke R C 2013 Prog. Brain. Res. 207 65 Google Scholar
[18]	Martin S J, Grimwood P D, Morris R G M 2000 Annu. Rev. Neurosci. 23 649 Google Scholar
[19]	Sanderson J L, Dell'Acqua M L 2011 Neuroscientist 17 321 Google Scholar
[20]	Yong L, Kauer J A 2010 Synapse 51 1 Google Scholar
[21]	Haas J S, Thomas N, Abarbanel H D I 2006 J. Neurophysiol. 96 3305 Google Scholar
[22]	D'Amour J A, Froemke R C 2015 Neuron 86 514 Google Scholar
[23]	Hartmann K, Bruehl C, Golovko T, Draguhn A 2008 Plos One 3 e2979 Google Scholar
[24]	Tohru K, Kazumasa Y, Yumiko Y, Crair M C, Yukio K 2008 Neuron 57 905 Google Scholar
[25]	Stephen G, James R W 2001 Cereb. Cortex 11 37 Google Scholar
[26]	Luz Y, Shamir M 2012 Plos. Comput. Biol. 8 e1002334 Google Scholar
[27]	Hennequin G, Agnes E J, Vogels T P 2017 Annu. Revi. Neurosci. 40 557 Google Scholar
[28]	Park H J, Friston K 2013 Science 342 1238411 Google Scholar
[29]	Isaacson J S, Massimo S 2011 Neuronv 72 231 Google Scholar
[30]	Maass W, Joshi P, Sontag E D 2007 Plos Comput. Biol. 3 e165 Google Scholar
[31]	Jansen B H, Rit V G 1995 Biol. Cybern. 73 357 Google Scholar
[32]	Chacron M J, André L, Leonard M 2005 Phys. Rev. E 72 051917 Google Scholar
[33]	Froemke R C, Jones B J 2011 Neurosci. Biobehav. R. 35 2105 Google Scholar
[34]	王俊松, 徐瑶 2014 物理学报 63 068701 Google Scholar Wang J S, Xu Y 2014 Acta Phys. Sin. 63 068701 Google Scholar
[35]	王美丽, 王俊松 2015 物理学报 64 108701 Google Scholar Wang M L, Wang J S 2015 Acta Phys. Sin. 64 108701 Google Scholar
[36]	Vogels T P, Abbott L F 2009 Nat. Neurosci. 12 483 Google Scholar
[37]	Stepp N, Plenz D, Srinivasa N 2015 Plos Comput. Biol. 11 e1004043 Google Scholar
[38]	Vogels T P, Sprekeler H, Zenke F, Clopath C, Gerstner W 2011 Science 334 1569 Google Scholar
[39]	Maass W 2014 P. IEEE 102 860 Google Scholar
[40]	Mcdonnell M D, Ward L M 2011 Nat. Rev. Neurosci. 12 183 Google Scholar
[41]	Garrett D D, Mcintosh A R, Grady C L 2011 Nat. Rev. Neurosci. 12 612 Google Scholar
[42]	Mcdonnell M D, Ward L M 2011 Nat. Rev. Neurosci. 12 415 Google Scholar
[43]	Turrigiano G G 2008 Cell 135 422 Google Scholar
[44]	Marder E, Tang L S 2010 Neuron 66 161 Google Scholar
[45]	Sharon B, Dickman D K, Davis G W 2010 Neuron 66 220 Google Scholar

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Vol. 68, Issue 7 - 2019-04-05

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