hyperpolarization - activated and cyclic nucleotide - gated ( hcn ) channels , first identified in 1976 in the heart by noma and irisawa   and characterized by brown and difrancesco   and weiss and his colleague , are cation channels that open when the membrane potential is hyperpolarized . the general structure of hcn channels resembles that of the voltage - gated k channels . hcn channels consist of four subunits that have six transmembrane segments , the canonical gyg sequence in the pore forming region , and the positively charged s4 segment [ 4 , 5 ] . but the k permeability of hcn channels is not so selective as typical k channels and is permeable to na . thus a typical current reversal potential of hcn channels is around 30  mv . for voltage - dependent gating , inward movement of s4 segment in response to hyperpolarization is reported [ 79 ] , but molecular aspects of channel opening are still unknown . for example , hcn channels require extracellular cl and extracellular k to open . cyclic - amp-(camp- ) binding site locates near the c terminus , and camp affects the voltage dependence of activation in some hcn channel isoforms . phosphatidylinositol 4,5-bisphosphate ( pip2 ) is also known as a modulator of hcn channels ; it shifts the voltage dependence through a different mechanism from that of camp [ 11 , 12 ] . these multifaceted features endow hcn channels to work in many functions described below . in this paper , we try to understand the physiological significance of these functions by using simple numerical simulations . previous literatures reported that hcn channels are expressed in heart , brain , taste buds , and pancreatic cells . this paper focuses on the electrophysiological function of hcn channels in the central nervous system . in the brain , hcn1 isoform is expressed strongly in cerebral cortex , hippocampus , and superior colliculus , and hcn2 is expressed ubiquitously in the brain . expression of hcn3 and hcn4 is found in localized regions in the brain . in the neuron expression in axon terminals is reported at the calyx of held   and the globus pallidus neurons . previous reports showed that expression of hcn channels on the cell surface is uneven in some neurons . hcn channels are expressed more strongly in distal dendrites than in somas in thalamic reticular neurons , whereas they distribute nearly evenly in thalamocortical relay neurons . for example , hcn1 is expressed strongly in dendrites in layer 5 pyramidal neurons of matured rats , whereas hcn2 is mainly expressed in the soma . expression and kinetics of hcn channels are affected by unusual neuronal activity like epilepsy and environmental stimuli . recent studies showed that channel current and surface expression of hcn channels decrease in one hour after pilocarpine - induced status epilepticus , but decreases in total channel protein and mrna occur in the subsequent week . involvement of activation of calcineurin and inactivation of p38 mitogen - activated protein kinase ( p38 mapk ) in the hyperpolarizing shift of voltage - dependence is reported . on the other hand , some reports showed that sensory inputs are necessary to increase or keep the expression level of hcn channels . deprivation of whiskers decreases the expression of dendritic hcn channels in the rat somatosensory cortex . reported increased hcn2 in ca3 and decreased hcn1 and hcn2 in ca1 in the same epilepsy model . based on the multifaceted features , hcn channels are involved in many kinds of functions that range from cellular to behavior levels ( working memory task , initiation of neuropathic pain ) . in this paper , we focus on neuron - level functions , which include regulation of resting membrane potential , normalization of synaptic inputs , selective filtering for coincident inputs , modulation of intrinsic cellular frequency characteristics , and regulation of membrane resistance . we summarize these functions and show typical examples of stimulations obtained by using neuron simulator ( figure 1(a ) ) . conditions for the simulation are summarized at the end of the text . because a typical current reversal potential of hcn channels is about 30  mv that is higher than the normal threshold for the generation of action potential , hcn channel currents depolarize and control the membrane potential near the resting membrane potential . when hcn channel conductance is removed , a simulated neuron shows a hyperpolarized membrane potential ( figure 1(b ) ) . although hcn channel conductance decreases the epsp amplitude ( see below and figure 2(a ) ) , this inhibitory effect is masked by depolarization of the membrane potential ( figure 1(c ) ) . in addition , the effect of inhibitory synaptic inputs is suppressed by hcn channels , because hyperpolarizing conductance of inhibitory synaptic input opens hcn channels to evoke depolarizing conductance .   when voltage dependence of hcn channels is shifted to the depolarizing direction by camp or pip2 , hcn channels can be active at around the resting membrane potential and can work as an excitatory factor . furthermore , in an interesting case , dendritic hcn channels are necessary to generate dendritic spikes at a short and fixed latency following optic fiber stimulation in the rat superior colliculus . as hcn channels activate more , the amplitude and kinetics of postsynaptic potentials become smaller and shorter ( figures 2(a ) , 2(b ) , 2(c ) , and 2(d ) ) . current density of hcn channels increases along with the distance from the soma in hippocampal   and neocortical pyramidal neurons . such dendritic hcn channels scale the epsp amplitude measured at the soma and suppress the location dependency of synaptic inputs in hippocampal   and neocortical pyramidal neurons . we use two models with the gradient and even hcn channel distributions ( figure 3(a ) ) , and computer simulation can reproduce a similar effect ( figure 3(b ) ) . interestingly note that , despite of different hcn channel distributions , both models show similar current amplitudes and overlapping voltage dependence of hcn channels in this condition ( figures 3(c ) and 3(d ) ) . activated hcn channels are involved in the detection of coincidental synaptic inputs . because hcn channel conductance shortens the rise time and decay time of the epsps through the decrease in membrane resistance ( figure 2 ) , summation of repetitive epsps that occur at a low frequency is suppressed . this suppression filters out low - frequency inputs , and thus improves the selectivity for synchronous synaptic inputs   ( figure 4(a ) ) . active conductance of ion channels enables neurons to produce intrinsic membrane potential oscillation and resonance . such rhythmic activity can filter inputs at certain frequencies , and can influence the precision of spike timing [ 39 , 40 ] . our simulation successfully shows that hcn channel conductance suppresses intrinsic activities particularly around 10  hz ( figures 4(b ) and 4(c ) ) . because hcn channels can work as both excitatory and inhibitory factors , it is difficult to predict which is the major role of hcn channels in controlling neural activity without conducting actual experiments . for example , k channels and cav3 ( t - type ) ca channels can indirectly affect the activation of hcn channels through modulation of membrane potential and resistance , and vice versa [ 43 , 44 ] . especially , delayed - rectifier m - type k channels ( km ) , also called kv7 or kcnq channels , have a large impact on the role of the hcn channels , because km channels open slowly at relatively polarized potentials from about 60  mv and do not inactivate . ( 2009 ) showed that km channels determine whether hcn channels function as an excitatory or an inhibitory factor , on the basis of recordings from hippocampal pyramidal neurons and computational simulation of model neurons . we further advanced the simulation study and examined the role of km channel conductance on the threshold potential for spike generation by using a model neuron with conductances for hcn , km , delayed rectifier k , na , and ca channels . our simulation reproduces a similar effect of km channels on the hcn channel function ( figures 5(a ) and 5(b ) ) . for a weak synaptic input , the membrane potential at the peak epsps ( vpeak ) is more depolarized with hcn channel conductance than without hcn channel conductance ( figure 5(b ) ) . but as the synaptic input becomes stronger , the relation between vpeak with and without hcn channel conductance reverses . the crossing point of the relationship shifts in a km conductance - dependent manner ( figure 5(b ) ) . because our model contains na conductances , we can also analyze the effect of hcn channel conductance on the threshold potential to generate action potential in various km conductance conditions . our simulation suggests that when km conductance is very small , hcn channel conductance reduces the minimum intensity of synaptic input to generate action potential . but when km conductance becomes large , hcn channel conductance increases the minimum intensity of synaptic input to generate action potential ( figure 5(c ) ) . the relationships between required intensity of synaptic input and km conductance with and without hcn channel conductance crosses ( figure 5(d ) ) . conversely , when t - type ca channel conductance was altered to shift the action potential threshold , the relation of the threshold does not reverse in our simulation condition ( figures 5(e ) and 5(f ) ) . a previous study showed that presynaptic hcn1 channels regulate cav3.2 channel activity and neurotransmission at specific cortical synapses . in order to uncover how hcn channels contribute to the neural activity , it will be necessary to compare the effects of k channels and ca channels by actual experiments . to elucidate the role of hcn channels in the neuron , modulators of hcn channels are indispensable . a number of modulators are reported for hcn channels ( summarized by lewis et al . ) . previous studies showed that camp , pip2 , and ethanol shift the voltage dependence to the depolarizing direction and accelerate the gating kinetics [ 48 , 49 ] . in contrast , trip8b shifts the voltage dependence to the hyperpolarizing direction and slows the kinetics . these modulators can shift the voltage dependence by as large as 10  mv in either direction . we examined the effect of such shifts of voltage dependence on neural activity as well as effects of km and t - type channel conductance . briefly , hyperpolarizing and depolarizing shifts of the voltage dependence , respectively , result in decrease and increase in channel conductance ( figures 5(g ) and 5(h ) ) . importance of modulated voltage dependence of hcn channels in the nervous system has already reported . for example , hcn channels are inhibited via suppression of camp by the activation of 2a - adrenoceptors that are colocalized with hcn channels in dendritic spines in the prefrontal cortex . this inhibition results in improved working memory in monkey and rat . increased neural activity caused by enhanced hcn channel activity with camp previous reports showed the involvement of hcn channels in brain disorders , including absence seizures , febrile seizures , and parkinson 's disease . reduced hcn channel activity following the establishment of status epilepticus is reported in many epilepsy models [ 2326 ] . decreased hcn channel activity is also reported in the external segment of the globus pallidus in rodent models of parkinson 's disease . it is not known well , however , whether such reductions precede or follow the onset of the diseases . genetic mutations of hcn channels are found in human epilepsy ( [ 51 , 52 ] , and references therein ) . null mice show absence epilepsy , and hcn1 null mice are more susceptible to kainic acid - induced seizures . these reports imply , at least , dysfunction of hcn channel can promote the onset of seizures . because hcn channels can work both excitatory and inhibitory , and these effects can be altered by pharmacological modulation , hcn channels are one of the promising pharmacological targets in treating diseases of the brain . further studies about complex relations between hcn channels and other ion channels and about mechanisms underlying modulation of voltage dependence will provide us a concrete step for clinical usage of hcn channel modulation . for computer simulation , a simplified neuron model is used , because the complicated dendritic structure can be compactified according to the rall 's rule   ( figure 1(a ) ) . membrane capacitance ( 1.4  f / cm ) and axial resistance ( 150 cm ) are even throughout the neuronal structure . the model neuron contains conductances for two kinds of na channels , delayed rectifier k channel , muscarinic k ( km ) channel , and hcn channel . in addition , nonspecific leak conductance is set in all models ( conductance , 40  s / cm ; reversal potential , 70  mv ) . conductance for the t - type ca channel is included in some of the simulations , where addition is explicitly stated . most conductances , except for delayed rectifier k and km channels , are taken from a model of the rat subthalamic nucleus . in order to change the voltage dependence , synaptic input is always applied to the soma using the exp2syn function of the neuron simulator ( tau1 , 1.5  ms ; tau2 , 4  ms ) . reversal potentials of excitatory and inhibitory inputs are 0 and 85  mv , respectively .
hyperpolarization - activated and cyclic nucleotide - gated ( hcn ) channels were first reported in heart cells and are recently known to be involved in a variety of neural functions in healthy and diseased brains . 
 hcn channels generate inward currents when the membrane potential is hyperpolarized . 
 voltage dependence of hcn channels is regulated by intracellular signaling cascades , which contain cyclic amp , pip2 , and trip8b . 
 in addition , voltage - gated potassium channels have a strong influence on hcn channel activity . 
 because of these funny features , hcn channel currents , previously called funny currents , can have a wide range of functions that are determined by a delicate balance of modulatory factors . 
 these multifaceted features also make it difficult to predict and elucidate the functional role of hcn channels in actual neurons . in this paper 
 , we focus on the impacts of hcn channels on neural activity . the functions of hcn channels reported previously will be summarized , and their mechanisms will be explained by using numerical simulation of simplified model neurons .