人体生理学 (5).pdf

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1、1Scientific RepoRts|(2019)9:9078|https:/doi.org/10.1038/s41598-019-45011- logic behind neural control of breathing patternAlona Ben-tal 1,Yunjiao Wang2&Maria C.A.Leite3the respiratory rhythm generator is spectacular in its ability to support a wide range of activities and adapt to changing environme

2、ntal conditions,yet its operating mechanisms remain elusive.We show how selective control of inspiration and expiration times can be achieved in a new representation of the neural system(called a Boolean network).the new framework enables us to predict the behavior of neural networks based on proper

3、ties of neurons,not their values.Hence,it reveals the logic behind the neural mechanisms that control the breathing pattern.our network mimics many features seen in the respiratory network such as the transition from a 3-phase to 2-phase to 1-phase rhythm,providing novel insights and new testable pr

4、edictions.The mechanism for generating and controlling the breathing pattern by the respiratory neural circuit has been debated for some time16.In 1991,an area of the brainstem,the pre Btzinger Complex(preBtC),was found essential for breathing7.An isolated single PreBtC neuron could generate tonic s

5、piking(a non-interrupted sequence of action potentials),bursting(a repeating pattern that consists of a sequence of action potentials fol-lowed by a time interval with no action potentials)or silence(no action potentials)8.These signals are transmit-ted,through other populations of neurons,to spinal

6、 motor neurons that activate the respiratory muscle4,6.The respiratory muscle contracts when it receives a sequence of action potentials from the motor neurons and relaxes when no action potentials arrive9.Hence,the occurrence of tonic spiking,bursting and silence can be associated with breath holdi

7、ng,breathing and no breathing(apnoea)respectively10.Tonic spiking,bursting and silence also appear in a population of coupled preBtC neurons when it is isolated in vitro11,12.Breathing can be performed with different combinations of frequency and amplitude to meet the body metabolic needs.However,th

8、e abili-ties to hold the breath and not to breathe are also important for supporting other activities such as diving,vocal communications and eating.Hence,we also expect to find tonic spiking,bursting and silence in a population of coupled preBtC neurons when it is embedded in the brainstem.The occu

9、rrence of bursting in the preBtC when this population interacts with other populations of neurons in the brainstem has been studied experimentally6,13.It was found that the preBtC population is activated during inspiration for about a third of the respiratory cycle,while two other distinct populatio

10、ns of neurons(called post-I and aug-E)are active consecutively during the remaining expiratory time of the cycle13.This was called a 3-phase pattern.A change in the conditions of the brainstem such as decreased carbon dioxide,transforms the 3-phase into a 2-phase pattern of inspiration and expiratio

11、n where only one population of expiratory neurons(aug-E)remains active6.In extreme conditions of hypoxia(lack of oxygen),and despite being embedded in the brainstem where it could potentially interact with other populations of neurons,only the preBtC population remains active,generating a 1-phase pa

12、ttern,similar to the pattern generated by the isolated preBtC population6,14.When the preBtC population activates the res-piratory muscle,the 3-phase pattern leads to a normal breathing pattern while the 1-phase pattern leads to gasp-ing-a breathing pattern with an abrupt inspiration.These findings

13、illustrate the state-dependency and incredible plasticity of the respiratory neural network which are essential for survival.However,the existence of multiple mechanisms for generating breathing also makes understanding how the neural system works more difficult and may explain why it remains elusiv

14、e.Many of the experimental studies of the respiratory neural network were accompanied by theoretical studies using mathematical and computational models8,11,1519.These models rely on differential equations with parame-ters that cannot always be measured directly and need to be estimated.Additionally

15、,none of the existing models provide a clear understanding of how selective control of inspiration and expiration times can be achieved.In order to translate the models from the animal on which the experiments where based to humans,the models need to be re-scaled.This is because respiratory rates di

16、ffer significantly across species.However,our impaired 1School of natural and computational Sciences,Massey University,Auckland,new Zealand.2Department of Mathematics,texas Southern University,Houston,tX,USA.3Mathematics and Statistics Unit,University of South Florida St Petersburg,St Petersburg,FL,

17、USA.Alona Ben-Tal and Yunjiao Wang contributed equally.Correspondence and requests for materials should be addressed to A.B.-T.(email:a.ben-talmassey.ac.nz)Received:10 January 2019Accepted:29 May 2019Published:xx xx xxxxopeN2Scientific RepoRts|(2019)9:9078|https:/doi.org/10.1038/s41598-019-45011- of

18、 neural control of breathing and our inability to measure or estimate parameters in human mod-els,make the translation from animals to humans difficult.The aim of this study is to unravel the logic behind the operation of the respiratory neural network and to provide a general mathematical framework

19、 for the study of neural control of breathing in all mammalian species.We do this by using Boolean networks in which the nodes could have only two values:“1”or“0”2024.Our approach stems from the observation that the amplitude of action potentials is not functionally important-control signals stimula

20、ting the neural system(called tonic drive)convey information by changing the rate(frequency)of the action potentials,not their amplitude.We represent an action potential by“1”and the time that passes between action potentials by a sequence of“0”s.This allows us to generate signals that consist of sp

21、iking at various frequencies as well as other types of signals or patterns such as bursting,a critical characteristic of the respiratory rhythm generator.The control signals that stimulate the neural system,arrive from other brainstem regions and are regulated by chemoreceptors(which sense blood par

22、tial pressures of O2 and CO2)and mechanoreceptors(which sense lung inflation)6,25.Variations in the spik-ing frequency of control signals result in adjustments to the breathing pattern and ensure that blood gas partial pressures are maintained at the same levels.The Boolean network we present in thi

23、s paper enables us to explore a key question for understanding control of breathing:how are the activation and quiescent times in a bursting signal changed selectively by varying the rate of tonic spikes in a control input signal?Such control of timing is crucial for supporting a wide range of activ

24、ities involving breathing with diverse and dynamic combinations of inspiration and expiration times.ResultsNotation and framework setup.Figure1,panels A and B,show two examples of Boolean networks that can produce bursting in response to a tonic spiking input.The node C1 denotes a control signal inp

25、ut and the node X1 signifies a neural output.The nodes I1 and SSS,k12 represent internal processes of the neuron X1.Connections between nodes could be excitatory()or inhibitory().The states of all the nodes are updated simultaneously every step based on the current states of all the other nodes.This

26、 is done according to the follow-ing Rules(adapted with some modifications from Albert et al.21,26,see the Discussion for the neurophysiological interpretation):(a)A node will be“1”in the next step if N activators are“1”in the current step and all the inhibitors are“0”;We call the number N a thresho

27、ld and it can change from node to node;(b)A node will be“0”in the next step if there are less than N activators which are“1”in the current step;(c)A node will be“0”in the next step if at least one of the inhibitors is“1”in the current step,regardless of the state of the activators.As the steps progr

28、ess forward,we get a sequence of states for each node,called a trajectory.These trajectories could have certain characteristics:(I)The trajectory (000)(0)is silent.(II)The trajectory (111)(1)is tonic spiking with period 1.(III)The trajectory?(100100)100p is tonic spiking with period p.Where the over

29、-line denotes a repeated pattern.The trajectory of node C1(the control input signal)is always tonic spiking with period p,where p is a control parameter.The trajectory of the output X1 could,in principle,be silent or tonic spiking and could also exhibit bursting or mixed mode oscillations.For exampl

30、e,the trajectories(111000),(10101000)or(11101010010000)exhibit bursting and the trajectories(1010100100)or(11101010)exhibit mixed mode oscillations(a formal defi-nition of bursting and mixed mode oscillations is given in the Methods).There is one potential problem in the scheme we just presented her

31、e.If C1=0 in the current step,how do we know if it will be“1”or“0”in the next step?We show in Methods,Lemma 1,that this problem can be solved by keeping track of the states in another Boolean network,enabling us to know the value of C1 at every step.We further show in Lemma 1,that by increasing the

32、number of connections in the network we can reduce the fre-quency of the spikes.This can be interpreted as changes in the internal properties of a neuron due to variations in a biophysical parameter.Characteristic response of minimal bursting networks.The Boolean networks we constructed in Fig.1,pan

33、els A and B,represent some other properties of neurons.Specifically,the nodes SSS,k12 represent“memory”the build-up of voltage potential in the neuron when it receives action potentials from external sources.The parameter k is the size of the memory.In network A(Fig.1),the memory is preserved even a

34、fter an action potential is generated in X1(i.e.the state of X1 is“1”).However,an action potential will erase some of the memory in network B(Fig.1)in the time step following X1 becoming“1”.The parameter m gives the size of the memory that remains.The node I1 represents self excitation a property th

35、at has been shown to exist in certain neurons,including the preBtC8.We show in panels C and D(Fig.1)that each of the networks A and B has its own characteristic response when the period of the input signal increases(the tonic spiking frequency decreases).In both networks,X1 exhibits spiking(1)for a

36、low period of C1(high spiking frequency)and silence(0)when the period of C1 is high(the spiking frequency is low).For mid-range values of C1,both networks exhibit bursting with increasing breathing(bursting)period as the period of C1 increases.However,in network A,an increase in the breathing period

37、 is always accompanied by a reduction in inspiration time(number of consecutive“1”s),3Scientific RepoRts|(2019)9:9078|https:/doi.org/10.1038/s41598-019-45011- in network B,the inspiration time is constant.This characteristic response depends on neural properties such as the existence of memory,exist

38、ence of a threshold and self excitation regardless of the actual values of these properties(provided the values are feasible).The actual values will affect the number of consecutive“1”s within a burst and the points where transitions from tonic spiking to bursting to silence occur but will not chang

39、e the characteristic response qualitatively(see Methods for a proof of our general result).Constructing a larger bursting network.While all the Boolean networks we found exhibit bursting(see the Supplementary Material and Methods),none allow for independent control of inspiration time and expiration

40、 time through variations in the period of C1.However,we can achieve independent control of the bursting pattern by connecting one type-A network(Fig.1,Panel A)with two type-B networks(Fig.1,Panel B).The structure of the larger network is shown in Fig.2.The output of each sub-network is denoted by X1

41、,X3 or X4 and the control input to each sub-network is denoted by C1,C3 or C4.For simplicity,we only show the first node to which the control input connects(Si1,where i is the sub-network number,this is equivalent to S1 in Fig.1).This structure can be related to a schematic representation of the res

42、piratory neural network hypothesized by Smith et al.6.The cen-tral pattern generator in Smith et al.6 consists of four core populations of neurons:“pre-I”(a population of neu-rons within the PreBtC region,active during inspiration),“early-I”(a population of neurons within the PreBtC region,active du

43、ring inspiration),“post-I”(a population of neurons within the BtC region,active in the first phase of expiration,under normal conditions)and“aug-E”(a population of neurons within the BtC region,active in the later phase of expiration,under normal conditions).The three populations,early-I,post-I and

44、aug-E,mutually inhibit each other.Post-I and aug-E also inhibit pre-I,while pre-I excites early-I.In our large network,the sub-network X1 could represent pre-I,X3 could represent aug-E and X4 could represent post-I.Sub-network X2,which is missing from our diagram,could represent early-I.Unlike Smith

45、 et al.6,we found that this sub-network is not essential for generating and controlling the bursting signal.Another difference between our Figure 1.Examples of Boolean networks and their characteristic response to an input signal C1.An action potential(spike)is represented by“1”and the time that pas

46、ses between action potentials is signified by a sequence of zeros.Panel(A)shows a network where the memory(represented by SSS,k12)is preserved after an action potential has been generated in X1.Panel(B)shows a network with self excitation(depicted by I1)where some of the memory is erased after a spi

47、ke has been generated(the nodes SSS,m12 convey the memory that remains).Panel(C)shows the response of Network A and Panel(D)shows the response of Network B to changes in the period of C1.In both networks when the period of C1,p,is low(the spiking frequency is high),X1 exhibits tonic spiking with per

48、iod 1(i.e.=X1111).When=pk/+N1 in Network A,=+pm2 in Network B,bursting appears(for example,=X111000011100001).When pk/N(1)in Network A,pk in Network B,X1 exhibits silence(i.e.=X0001).The number of consecutive“1”within a burst is reduced in Network A as the period of C1 increases but stays constant i

49、n Network B(the only exceptions are when=+pm1 and=pk1 where we get different kinds of bursting,see Theorem 5).This characteristic response does not depend on the actual values of k(memory size),m(size of memory that was not erased)and N(threshold of X1 in Network A).4Scientific RepoRts|(2019)9:9078|

50、https:/doi.org/10.1038/s41598-019-45011- and the network hypothesized in Smith et al.6 is that X3 is not affected by the other populations(see also the Section Mechanism of pattern generation).The control signals C1,C3 and C4 could represent,respectively,tonic drives from other brainstem regions suc