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Nonassociative learning is a basic neuroadaptive behavior exhibited across animal phyla and sensory modalities but its role in brain intelligence is unclear. Current literature on habituation and sensitization, the classic "dual process" of nonassociative learning, gives highly incongruous accounts between varying experimental paradigms. Here we propose a general theory of nonassociative learning featuring four base modes: habituation/primary sensitization in primary stimulus-response pathways, and desensitization/secondary sensitization in secondary stimulus- response pathways. Primary and secondary modes of nonassociative learning are distinguished by corresponding activity-dependent recall, or nonassociative gating, of neurotransmission memory. From the perspective of brain computation, nonassociative learning is a form of integral-differential calculus whereas nonassociative gating is a form of Boolean logic operator – both dynamically transforming the stimulus-response relationship. From the perspective of sensory integration, nonassociative gating provides temporal filtering whereas nonassociative learning affords low-pass, high-pass or band-pass/band-stop frequency filtering – effectively creating an intelligent sensory firewall that screens all stimuli for attention and resultant internal model adaptation and reaction. This unified framework ties together many salient characteristics of nonassociative learning and nonassociative gating and suggests a common kernel that correlates with a wide variety of sensorimotor integration behaviors such as central resetting and self-organization of sensory inputs, fail-safe sensorimotor compensation, integral-differential and gated modulation of sensorimotor feedbacks, alarm reaction, novelty detection and selective attention, as well as a variety of mental and neurological disorders such as sensorimotor instability, attention deficit hyperactivity, sensory defensiveness, autism, nonassociative fear and anxiety, schizophrenia, addiction and craving, pain sensitization and phantom sensations, etc. associative learning and nonassociative gating that dem- 1. Background Brain calculus – or integral-differential neural dynamics – onstrate brain calculus and Boolean logic computations. is an emerging paradigm in computational neuroscience The resultant neural network theory proves to illuminate [1,2]. In behavioral neuroscience, the dynamics of senso- a variety of behavioral and brain functions and disorders. rimotor integration are often ascribed to learning and memory. We hereby propose a general framework of non- Page 1 of 21 (page number not for citation purposes) Behavioral and Brain Functions 2006, 2:29 http://www.behavioralandbrainfunctions.com/content/2/1/29 This article is written with a broad readership in mind. the same stimulus (e.g., startle response to repetitive loud Beginning with a thorough review of the oft-conflicting noise). literature on habituation and sensitization, the so-called "dual process" of nonassociative learning, Section 2 devel- Certain conjectures of the dual-process theory have subse- ops a unified framework of primary and secondary sensitiza- quently been verified in a variety of invertebrate and tion in analogy to pain sensitization. In Section 3, we mammalian brain systems [17-30]. Circumstantial evi- introduce the notion of response desensitization  and dence for dual-process learning could also be inferred, show that this novel nonassociative learning mechanism albeit unwittingly, from other animal models of nonasso- provides a common kernel which may explain a variety of ciative learning reported in the literature (reviewed in sensory remapping phenomena. Section 4 presents a ). novel behavioral paradigm called nonassociative gating which affords activity-dependent temporal filtering or 2.1.2. Properties of response habituation Boolean logic-gating of the stimulus-response relation- Typically, habituation may be induced by a stimulus that ship. These emergent concepts cumulate in a general the- is presented continuously or intermittently with a variable oretical framework elaborated in Section 5, which interstimulus interval (ISI). The dual-process theory expounds the computational roles of nonassociative defined habituation by the following stimulus-response learning as gated neural integrator and differentiator criteria [9,10,32]: 1) exponential development with (low-pass and high-pass filter) in neural pathways. Sec- repeated stimulus applications, causing exponential tion 6 discusses the functional roles of the various modes decrease of response to the stimulus; 2) spontaneous of nonassociative learning in brain intelligence as the recovery with a short-term memory upon cessation of building blocks of a "sensory firewall" for Cartesian mind- stimulus; 3) successive potentiation or accumulation with body internal model adaptation. Section 7 concludes the repeated training sessions; 4) dependence on stimulus fre- discourse. quency with rate and magnitude of habituation being directly related to frequency of stimulus bouts (and inversely related to ISI); 5) dependence on stimulus inten- 2. Dual-process theory revisited Although a universally agreed model of nonassociative sity with rate and magnitude of habituation being learning is presently lacking (for reviews see [4-8]), a use- inversely related to stimulus intensity; 6) dependence on ful starting point is the classic dual-process theory of stimulus quantity with spontaneous recovery of habitua- response habituation and sensitization [9-11]. In the fol- tion becoming much slower after an excessive number of lowing, we present a unified framework that extends and stimulus bouts; 7) cross-modal generalization or transfer reconciles the dual-process theory and other models of of habituation to other stimuli that share common habit- nonassociative learning. uating elements with the primary stimulus; 8) dishabitu- ation or trumping of habituation by a novel stimulus; and 2.1. Habituation and sensitization: the 'dual-process 9) habituation of dishabituation upon repeated applica- theory' tions of the dishabituating stimulus. 2.1.1. Dual-process theory According to this classic theory, an animal's behavioral These postulated properties of habituation have been response to a repetitive stimulus may wane or wax borne out for the most part in many animal models from through two complementary learning processes called nematodes  to mammals – down to the level of a habituation and sensitization. At the system level these proc- monosynaptic junction in the hippocampus . It is esses are thought to correspond, respectively, to short- generally assumed that response habituation is mediated term depression (STD) of neurotransmission in a primary primarily by homosynaptic depression in the stimulus- stimulus-response pathway and short-term potentiation response pathway  although other mechanisms such (STP) or facilitation of neurotransmission in a secondary, as increased inhibition (see [5,35]) or decreased neuronal collateral pathway or "state system" that presumably excitability  are also possible. determines the animal's general level of excitation, 2.2. A unified framework for response sensitization arousal or motivation to respond. Here, "short-term" plas- ticity (potentiation or depression) refers to the short-term Although the above characterizations of habituation modifiability and short-term memory commonly seen in appear to prevail across animal phyla and sensory modal- nonassociative learning although long-term memory (> ities, those of response sensitization are less clear. The lack 24 hr) is also possible [12-16]. In some model systems of a consistent taxonomy for sensitization has made it dif- habituation is induced by an innocuous stimulus (such as ficult to decipher and relate the vast amounts of pertinent gentle touch) and sensitization is induced by noxious (and oft-conflicting) data from diverse animal models, stimulus (forceful touch or electrical shock). In other sys- sparking considerable confusion and controversy in the tems habituation and sensitization could be induced by literature. Here we review two conventional characteriza- Page 2 of 21 (page number not for citation purposes) Behavioral and Brain Functions 2006, 2:29 http://www.behavioralandbrainfunctions.com/content/2/1/29 tions, intrinsic and extrinsic sensitization, which have occa- untrained tail sensory neuron . Apart from the simi- sioned renewed interests (reviewed in ). We then larity of the sensitizing and test stimuli, however, such propose a unified framework that reconciles the discrep- "intrinsic sensitization" is mechanistically analogous to ancies between these characterizations of sensitization "extrinsic sensitization" in Aplysia gill withdrawal reflex and the dual-process theory. . These seeming anomalies call for a revamping of the taxonomy for sensitization. 2.2.1. Ambiguities of intrinsic and extrinsic sensitization According to the dual-process theory, sensitization may 2.2.2. Primary and secondary sensitization be induced by repeated applications of a primary, or The above intrinsic-extrinsic classification of sensitization intrinsic, stimulus. Such "intrinsic sensitization" has been is based solely on the induction process. As pointed out by implicated in the increment phase of the rat acoustic star- Prescott , it is important to distinguish the induction tle response  and the monosynaptic ventral root reflex and expression phases of sensitization. Here we propose a of the frog spinal cord . It may also account for certain unified framework that rectifies the ambiguities of intrin- forms of sensitization such as the reported incremental sic and extrinsic sensitization. sensitization of defensive striking in larval Manduca Sexta , iterative enhancement of the sea slug Tritonia swim In keeping with the dual-process theory we refer to the response [40,41], warm-up phase in the local bending stimulus that induces learning as the primary stimulus and reflex of the medicinal leech Hirudo medicinalis , the the corresponding stimulus-response pathway the primary "windup" or central sensitization of mammalian pain pathway. Further, any collateral pathway that is indirectly pathways [43-46] and the progressive intensification of influenced (e.g., through heterosynaptic or presynaptic the evoked irritant sensation upon repeated applications modulation) by the primary pathway is termed secondary of the pungent chemical capsaicin to the tongue . pathway and the corresponding driving stimulus a second- ary stimulus. Under this nomenclature, we define primary More commonly, sensitization is characterized as an and secondary sensitization as sensitization expressed in the increase in the response to a primary stimulus after prim- primary or secondary pathway, respectively, regardless of ing by an extrinsic, often strong and noxious stimulus. any extrinsic influences on the corresponding induction This form of sensitization has been variously referred to as process (Fig. 1A). "conventional" or "nociceptive" sensitization  or "extrinsic" sensitization [10,27,37,42,48,49]. Its underly- This emphasis on expression instead of induction of sen- ing mechanisms (as demonstrated in the Aplysia gill with- sitization circumvents the ambiguities in previous studies. drawal reflex) may include short-term presynaptic or On one hand, primary sensitization is analogous to heterosynaptic facilitation of convergent pathways intrinsic sensitization in that both are induced and [50,51] or long-term cellular changes [52,53]. expressed directly in the primary pathway. On the other hand primary sensitization does not exclude possible Although such an intrinsic-extrinsic classification of sensi- extrinsic influences as does intrinsic sensitization. Simi- tization is useful, their distinction is not always clear-cut. larly, secondary sensitization is analogous to extrinsic sen- Thus, a stimulus could sometimes induce both forms of sitization in that both are expressed for a stimulus sensitization simultaneously rather than one or the other different than the sensitizing stimulus, but secondary sen- exclusively. In the snail Helix aspersa tentacle withdrawal sitization is distinguished from primary sensitization by reflex, for instance, mixed intrinsic-extrinsic sensitization its indirect expression. Thus, secondary sensitization satis- may be induced by a strong intrinsic stimulus when com- factorily accounts for extrinsic sensitization and reconciles bined with inputs from the CNS [27,49]. the seeming discrepancy with the above-mentioned anomalies [48,54,55]. Another anomaly to the above classification scheme is exemplified by the whole-body shortening reflex of the 2.2.3. Sensitization of pain: hyperalgesia and allodynia medicinal leech Hirudo medicinalis [48,54], in which a The above definitions of primary and secondary sensitiza- stimulus at one site of the leech body wall may sensitize tion of sensory inputs may also shed light on the problem the response to the same stimulus at a proximal but dis- of peripheral or central sensitization of pain pathways fol- tinct body wall site. This phenomenon is analogous to lowing physical insults. Peripheral sensitization is medi- extrinsic sensitization even though it involves only ated by noxious input-dependent release of inflammatory "intrinsic" stimuli and does not generalize to other loci or neuromodulators which (by activating protein kinases) other sensory modalities. Similarly, in the "intrinsic sensi- increase the transduction sensitivity and excitability of the tization" of Aplysia tail withdrawal reflex, activity of one nociceptor terminal. "Classical" central sensitization is tail sensory neuron during habituation training may het- mediated by activity-dependent increases in excitability or erosynaptically facilitate the response to a proximal but expansion in receptive fields of nociceptive relay neurons Page 3 of 21 (page number not for citation purposes) Behavioral and Brain Functions 2006, 2:29 http://www.behavioralandbrainfunctions.com/content/2/1/29 Secondary Input Secondary Primary Input Primary C Secondary Input (Allodynia) Gating Primary Input Of Primary (Hyperalgesia) Pathway P C Secondary Input Secondary Primary Primar pai Figure 1 n sey and secondary sensitization nsitization and input-gating effect and their correspondence to hyperalgesia and allodynia forms of Primary and secondary sensitization and input-gating effect and their correspondence to hyperalgesia and allodynia forms of pain sensitization. A. Schematic illustration of habituation (H) and secondary sensitization (S) mediated by homosynaptic STD (filled inner triangle, blue) in primary pathway and heterosynaptic STP (open inner triangle, red) in secondary pathway. Open triangles denote non-adaptive excitatory synapses. Primary sensitization could occur independently of habituation through homosynaptic STP (open inner triangle, red) in primary pathway. Other primary-secondary pathway configurations of nonasso- ciative learning are also possible . B. Input-gating effect: upon cessation of primary input, all memory components in pri- mary pathway are gated off abruptly and become latent. C. Schematic illustration of hyperalgesia and allodynia respectively as primary and secondary sensitization at peripheral (P) or central (C) sites. The pain sensation and sensitization are relieved once the stimulus ceases – a behavior that epitomizes the input-gating effect. at the superficial (lamina I) or deep (lamina V) dorsal responsiveness to noxious stimuli) although their mecha- horn of the spinal cord  or higher-order central sites. nisms and loci in the pain pathway may vary. In the Inflammatory modulators increase the excitability of present framework, such nonassociative and input- these relay neurons by activating protein kinases, blocking dependent hypersensitivity mechanisms of hyperalgesia specific glycine receptor subtype  or upregulating spe- are in perfect agreement with the notion of primary sensi- cific sodium channels . In recent years, other forms of tization as defined in Section 2.2.2. central sensitization have been found which involve activ- ity-dependent increases in synaptic efficacy of these relay In contrast to hyperalgesia, which pertains to the same neurons, with varying onset latencies and memory dura- nociceptive input perpetuating the pain sensation, allody- tions reflecting distinct transcription-dependent or -inde- nia is hypersensitivity to normally innocuous inputs pendent cellular events [59,60]. These modern forms of (such as gentle touch) secondary to a nociceptive input. A central sensitization have been likened to synaptic plastic- prevailing explanation of tactile allodynia is that low- ity-related learning and memory [59-63]. Both peripheral threshold mechanosensitive Aβ afferents with weak syn- sensitization and the classical or modern forms of central aptic connection at nociceptive relay neurons may be pre- sensitization contribute to hyperalgesia (increased synaptically or heterosynaptically sensitized by the Page 4 of 21 (page number not for citation purposes) Behavioral and Brain Functions 2006, 2:29 http://www.behavioralandbrainfunctions.com/content/2/1/29 primary nociceptive input, thus facilitating this normally aptic facilitation. Thus, primary and secondary sensitiza- silent tactile pathway (Fig. 1C) [59,64]. A similar explana- tion effectively account for all experimental data that tion may also apply to spontaneous pain if the sensitized formed the cornerstone of the dual-process theory. convergent pathway has tonic activity. Such nonassocia- tive and activity-dependent sensitization of convergent Another experimental paradigm that motivated the dual- pathway mediating allodynia lends further support for process theory was the rat acoustic startle response our definition of secondary sensitization as a generic [10,66]. As with the cat hindlimb flexion reflex, primary mode of nonassociative learning in neural pathways (Sect. and secondary sensitization are evident in this reflex in 2.2.2). the form of complex response sensitization-habituation to a repetitive primary (auditory) stimulus and a subse- In some instances, pain sensations (especially milder quent, spontaneously-decaying sensitization triggered by types of pain) may habituate upon repeated presentation a secondary (visual) stimulus. Thus, the present defini- of the stimuli . The pain habituation, hyperalgesia tions of habituation and primary/secondary sensitization and allodynia effects of pain sensation are analogous to provide a unified theoretical framework that reconciles the habituation, primary sensitization and secondary sen- the dual-process theory and varying definitions of sensiti- sitization forms of nonassociative learning. zation. 2.3. Dual-process theory reconciled 2.3.2. Secondary sensitization as "generalization of sensitization" 2.3.1. Relations to intrinsic and extrinsic sensitization The notion of secondary sensitization also rectifies Our definitions of primary and secondary sensitization another archaic conjecture of the dual-process theory, clarify the ambiguities of the dual-process theory. The namely, the so-called "generalization of sensitization" original theory pertaining to an acute spinal cat prepara- where sensitization to one input may supposedly spread tion was predicated on a sensitization-habituation com- to other inputs [9,10]. This conjecture is in actuality an plex observed in the cat's hindlimb flexion reflex response oxymoron as the generalization of intrinsic sensitization to a repetitive electrical stimulus. The sensitization was simply amounts to extrinsic sensitization, both being attributed to certain interneurons presumably located in instances of secondary sensitization. an extrinsic "state" system that was directly activated by the primary stimulus [10,11]. As such, the sensitization 2.3.3. Dishabituation as primary or secondary sensitization process on which the theory was based is neither intrinsic According to the dual-process theory, the so-called "disha- nor extrinsic sensitization. bituation" effect was neither a disruption of habituation nor an independent process in itself, but rather, an By contrast, the sensitization-habituation complex of the instance of sensitization superimposed on habituation – cat hindlimb flexion reflex fits well with the notion of pri- such that the dual process of habituation and sensitiza- mary sensitization and habituation. Rather than mediated tion would adequately account for all incrementing and by an extrinsic state system as originally proposed, sensi- decrementing behavioral responses. Although this view tization induced by a repetitive primary stimulus could be was later challenged by studies of Aplysia gill- and siphon- expressed in the primary pathway(s) as with habituation, withdrawals, which revealed certain subtle differences thus evidencing primary sensitization. Indeed, as demon- between dishabituation and sensitization at the behavio- strated in the frog spinal reflex, primary sensitization and ral and cellular levels [67,68], such discrepancies were habituation could occur even across the same synaptic subsequently found to be attributable to an interaction junction . between habituation and inhibition in some modulatory pathways [69,70]. Thus, dishabituation may represent a Another instance of sensitization in the cat hindlimb flex- form of sensitization that is gated by habituation (see ion reflex was observed when a strong stimulus was deliv- Sect. 4.3.2). ered at skin sites near the primary stimulus that induced the dual-process response sensitization-habituation. The Most previous studies of dishabituation used a secondary resulting response sensitization differed from dishabitua- stimulus to reverse habituation. In a recent model of tail- tion in that it decayed spontaneously regardless of the elicited siphon withdrawal in Aplysia [69,71], however, continuance/discontinuance of the primary stimulus dishabituation is expressed in reflex pathways both ipsi- . However, this form of sensitization is clearly distin- lateral or contralateral to the primary stimulus even guishable from the first, which was elicited by the primary though habituation and sensitization are expressed only stimulus itself. Rather, it resembles secondary sensitiza- in the pathway ipsilateral to the primary stimulus. This tion as defined in Section 2.2.2 (but with the primary and finding is consistent with the notion of primary and sec- secondary pathways reversed) in that it was induced by a ondary sensitization, in that dishabituation could be separate stimulus, perhaps via heterosynaptic or presyn- expressed in both primary and secondary pathways rather Page 5 of 21 (page number not for citation purposes) Behavioral and Brain Functions 2006, 2:29 http://www.behavioralandbrainfunctions.com/content/2/1/29 than confined to the primary pathway as suggested by the dual-process theory. Thus, the present framework brings into harmony a body of confounding observations relating to intrinsic, extrinsic and anomalous sensitization, generalization of sensitiza- tion and dishabituation, which are otherwise incongru- ous with the dual-process theory. 3. Desensitization: a novel form of nonassociative learning The above framework of habituation and primary/sec- ondary sensitization is complementary to a new mode of nonassociative learning called response desensitization. In the following, we review the experimental evidence of response desensitization and show how this novel con- cept may yield new insights to some sensory remapping behaviors such as phantom sensation and drug addiction. 3.1. Desensitization as nonassociative learning 3.1.1. Desensitization as secondary habituation A corollary to the above definitions of primary and sec- ondary sensitization is the notion of primary and secondary habituation. For simplicity, we abbreviate primary and sec- Response desensitization and pha Figure 2 ntom sensation ondary habituation as habituation and desensitization, Response desensitization and phantom sensation. A. Sche- respectively (Fig. 2A). matic illustration of desensitization (D) in relation to habitua- tion (H) and primary sensitization (S). The secondary 3.1.2. Desensitization of descending pathways pathway is desensitized by heterosynaptic STD (filled inner Instances of response desensitization have often gone triangle, blue) secondary to the primary stimulus, leaving it unnoticed because it is easily mistaken for "habituation". dormant (broken line). B. Phantom sensation: following deaf- An example is the crayfish tail-flip escape response to ferentation, the primary stimulus ceases and the secondary repetitive primary afferent activations, which exhibited pathway is re-sensitized, producing a phantom sensation. tonic GABAergic inhibition via a descending pathway to the motor circuitry . Desensitization as a new mode of nonassociative learning was first formalized in studies of . Generalization of habituation between sensory modal- the rat Hering-Breuer reflex, which evidenced a decre- ities is best illustrated by the Aplysia siphon and gill with- menting response adaptation secondary to habituation drawal reflex, in which habituation training at one upon sustained application of a primary (vagal) stimulus sensory site (gill) may transfer to an untrained site and a short-term memory of the adaptation upon termi- (siphon) through heterosynaptic modulation (e.g., heter- nation of the primary stimulus . The secondary adapta- osynaptic depression or inhibition ) via the periph- tion component was selectively abolished by pontine eral nervous system  or some perceptron-like parallel lesion or pharmacological blockade of NMDA receptor- processing . Generalization of habituation between gated channels, suggesting STD of tonic excitation (or STP sensory sites is seen in the escape swim of the marine mol- of tonic inhibition) of some descending ponto-medullary lusk Tritonia diomedea  and the shortening reflex of the pathway [73,74]. The habituation-desensitization para- medicinal leech Hirudo medicinalis [48,54], where digm exemplified by these animal models is in contrast to response habituation elicited at one body site may trans- the purported habituation-sensitization dual process that fer to an untrained site. has permeated previous studies of nonassociative learn- ing. The putative generalization/transfer of habituation is con- verse to the secondary sensitization in similar animal 3.1.3. Desensitization as generalization/transfer of habituation models (albeit with differing stimulus intensity or type). Indeed, response desensitization has long lurked under In particular, the heterosynaptic inhibition in Aplysia is the dual-process theory as the putative "generalization of mechanistically opposite to the heterosynaptic facilitation habituation"  or "transfer of habituation" [76,77] (see that is thought to contribute to the extrinsic sensitization Sect. 2.1.2), sometimes also called "extrinsic habituation" of its gill- and siphon-withdrawal reflex . Therefore, Page 6 of 21 (page number not for citation purposes) Behavioral and Brain Functions 2006, 2:29 http://www.behavioralandbrainfunctions.com/content/2/1/29 generalization/transfer of habituation is operationally nisms that underlie NMDA receptor-dependent homosy- and mechanistically analogous to secondary sensitization naptic LTD in the rat visual cortex have been linked to the but with differing response polarity and activation thresh- characteristic visual impairment resulting from hours of old. As such, it represents a distinct form of nonassociative monocular deprivation during early postnatal life [97,98]. learning in its own right. These observations lend further These recent findings point to a possible role for synaptic support for response desensitization as a bona fide mode plasticity such as LTD/LTP in the masking/unmasking of of nonassociative learning rather than an extension of somatosensory pathways before and after deafferentation. habituation. In keeping with the notion of unmasking of preexisting 3.2. Desensitization and referred pain sensations pathways, we propose a two-tier nonassociative learning 3.2.1. Somatosensory remapping model of somatosensory organization, with the primary The present notion of response desensitization as a new and referred sensations being mediated by a primary path- mode of nonassociative learning may shed light on the way and a latent surrogate pathway, respectively (Fig. 2B). enigmatic "referred phantom sensation" (such as phan- The primary and surrogate (secondary) pathways are func- tom pain) experienced by some amputees [46,81,82]. tionally equivalent to the primary and secondary path- Recent findings have linked such phantom sensations to ways of nonassociative learning (Fig. 1A). In contrast to remapping at cortical  and thalamic or sub-thalamic the inhibition/disinhibition hypothesis of unmasking, levels  such that the deprived primary pathway is the present theory postulates that the surrogate pathway referred to a separate pathway with distinct receptive field may be normally desensitized and, hence, rendered ineffec- and an expanded central representation that invades the tive by the primary pathway. Deafferentation abolishes original primary representation. A possible mechanism of ("gates off", see Sect. 4.1) the primary pathway and its such remapping is collateral sprouting (a rather slow proc- sensory dominance, allowing the intact surrogate path- ess); another prevailing hypothesis is that such referred way to strengthen over time through synaptic plasticity pathway may be preexisting but latent, and are unmasked processes such as LTP. The resultant sensitization effect after deafferentation [85,86] presumably by disinhibition unmasks the surrogate pathway, giving a phantom sensa- [86-89]. tion. In particular, if the primary pathway is part of a pain pathway then the referred phantom sensation may give However, disinhibition is a fast neurotransmission proc- rise to phantom pain if the surrogate pathway or its ess that may take effect rapidly. Although rapid somato- referred central representation in the pain pathway is sensory reorganization post-deafferentation (within hypersensitized. minutes) has been reported [90,91], amputated subjects generally do not experience phantom sensations until The above model suggests a new perspective to the neural much later. As pointed out by Chen, Cohen and Hallet reorganization that reportedly underlies phantom sensa- , the mechanisms of nervous system reorganization tions. In those patients, recordings in the thalamic region following injury may differ depending on the timeframe. that normally respond to the missing limb revealed new The timeframe of phantom sensations (reportedly in receptive fields on its stump; microstimulation of this hours or days) [93,94] does not appear to match those of remapped thalamic region evoked phantom sensations of sprouting (in weeks or months) or disinhibition (in sec- the missing limb, including phantom pain . These onds and minutes), suggesting that other mechanisms of findings suggest that the thalamic representation of the remapping might be involved. amputated limb was remapped to a surrogate pathway from the stump of the missing limb, presumably via learn- 3.2.2. Two-tier learning model of phantom sensation ing. This two-tier learning model of somatosensory rema- As an alternative hypothesis, we suggest that phantom pping based on the general theory of nonassociative sensation might result from unmasking of latent somato- learning provides a coherent explanation of referred sensory pathways through learning and memory instead phantom sensation and phantom pain and related exper- of (or in addition to) disinhibition, perhaps by means of imental observations in relation to a general class of syn- synaptic plasticity such as long-term potentiation (LTP) aptic plasticity and nonassociative learning processes (which has been implicated in the reshaping of cortical widely reported across animal phyla from invertebrates to motor maps ). In support of this hypothesis, recent humans. evidence indicates that somatosensory reorganization 3.2.3. Capsaicin sensitization and "desensitization" associated with perceptual learning in human subjects may occur within a timeframe of hours of training and The response desensitization as defined above is distinct may be controlled by similar basic mechanisms that from the desensitization of nociception associated with underlie NMDA receptor-dependent synaptic plasticity certain irritants such as capsaicin, the pungent chemical in such as LTP . Furthermore, similar molecular mecha- red chili pepper. In human subjects, the burning/pricking Page 7 of 21 (page number not for citation purposes) Behavioral and Brain Functions 2006, 2:29 http://www.behavioralandbrainfunctions.com/content/2/1/29 sensation elicited by oral capsaicin typically intensifies mechanism has remained unclear [110,111]. Current with its repeated applications at an ISI of ~1 min, a hyper- models of craving (for overviews, see [112,113]) ascribe algesic effect that is akin to response sensitization. How- this psychophysical drive to certain cognitive or neuroad- ever, following a hiatus of several minutes reapplication aptive processes such as behavioral sensitization – a phe- of capsaicin elicits a much weaker sensation. This latent nomenon characterized by enhanced psychomotor and refractory process has been called "desensitization" by motivational effects of an addictive drug along with some authors [47,99] in analogy to desensitization of increased midbrain dopamine neurons reactivity upon nociceptive vanilloid receptors, which are generally repeated drug applications [114,115]. Recent evidence thought to mediate the pungency of capsaicin . suggests a possible link between behavioral sensitization and LTD of AMPA receptor-mediated synaptic transmis- The waxing and waning of the pungency following sion in the nucleus accumbens . Although behavio- repeated capsaicin application is reminiscent of the sensi- ral sensitization is not tantamount to craving, it is often tization-habituation dual process of nonassociative learn- thought to induce compensatory homeostatic or incen- ing [10,37]. As such, the refractory response to capsaicin tive-motivational adaptations which, in turn, could incu- following sensitization training should be a classic case of bate craving or "pathological wanting" that may be habituation in the primary nociceptive pathway instead of rekindled by stress or drug cues during prolonged absti- "desensitization". The successive increase and decrease of nence [117-121]. capsaicin pungency on varying timescales indicates that 3.3.2. Desensitization model of craving the habituation component develops more slowly but lasts longer than sensitization. If so, a weaker sensitization In contrast to previous sensitization models of craving effect should unmask the progressive development of during relapse, we propose a desensitization model of habituation during behavioral training. Indeed, repetitive craving during the onset of addiction, as follows (Fig. 3). oral application of other irritants such as nicotine, men- Central to our model is the notion that craving of any kind thol, zingerone or mustard oil elicits sensations that may represent an innate (rather than acquired) instinct, decline successively across trials [101-104], evidencing not fundamentally different than basic instincts such as response habituation with weak or no sensitization. thirst, hunger, sex, and yearning for love or happiness, etc. However, unlike ordinary psychophysical drives that are It has been suggested that capsaicin sensitization may be critical for animal survival or procreation and are mediated by an increase in excitability of peripheral noci- expressed at birth or during puberty, craving for substance ceptors or central relay neurons, or spatial recruitment of of abuse is functionally deleterious (hence "pathologi- vanilloid receptors in nociceptor endings . These cal") and hence its expression is likely to be repressed hypothesized cellular mechanisms are consistent with pri- through evolution. In a naïve (or "innocent") state, path- mary sensitization (as defined in Sect. 2.2.2). On the other ological craving may be inhibited intrinsically by certain hand, capsaicin sensitization has been shown to promote tonic central inputs that promote self-restraint (or self- hypersensitivity to and aftersensations of other pain stim- reward) – presumably via some midbrain dopaminergic uli applied to the affected site . This secondary or glutamatergic pathways – hence keeping craving and hyperalgesic effect is indicative of secondary sensitization addiction in check. Exposure to an addictive drug may dis- or central sensitization involving secondary nociceptive or rupt this equilibrium state and arouse addiction in multi- allodynic pathways, perhaps via wide dynamic range neu- ple possible ways. Firstly, it activates (i.e., "gates on", see rons in spinal dorsal horn . Sect. 4.1) a normally-latent primary sensory pathway that serves to relieve craving and evoke gratification in addi- 3.3. Desensitization and drug addiction tion to the central (secondary) craving-inhibiting path- It is well-known that repeated drug administrations may ways, thus producing an immediate euphoric effect. result in drug tolerance and/or sensitization , which Secondly, activity in the primary pathway may in turn are attributable to the dual process of response habitua- desensitize the secondary craving-inhibiting pathways, tion and sensitization [107-109]. The notion of response thus debilitating the brain's natural defensive against desensitization presently proposed adds a new dimension addiction. This critical step may correspond to the "loss of to the understanding of the behavioral mechanisms of inhibitory control in decision making" against addiction drug tolerance and, indeed, of drug craving and addiction suggested by some investigators . Thirdly, desensiti- itself. zation in the secondary pathways (together with possible habituation in the primary pathway) may cause increas- 3.3.1. Sensitization models of craving ing tolerance to the drug, hence drawing higher-and- Craving plays an important role in the pathogenesis of higher dosages in order to relieve craving or regain eupho- many addictive disorders (such as alcohol, nicotine, nar- ria, further deepening the addiction. Finally, abrupt absti- cotic or other psychostimulant drug dependencies) but its nence in a desensitized state may unleash the craving and Page 8 of 21 (page number not for citation purposes) Behavioral and Brain Functions 2006, 2:29 http://www.behavioralandbrainfunctions.com/content/2/1/29 precipitate any accompanying withdrawal symptoms, A. Naïve State Secondary which may subside over time as the reward system gradu- Input Rehabilitation ally re-sensitizes. No No Addiction Craving The above model predictions depict the early drug- Initial B. Euphoric State Addictive induced degeneration of the brain's reward system from a Stimulus Secondary Input naïve state to a desensitized state and the subsequent recovery during abstinence. However, once exposed to an Primary Euphoria No Addiction addictive stimulus the brain may not be totally "innocent" Input anymore in that the reward system may begin to give way Repeated C. Addiction State Addictive to other, non-reward related hysteretic mechanisms which Stimulus Secondary Tertiary Input Input may ensue even after recovery. For example, repeated drug exposures may mobilize other neuroadaptive processes, Primary Craving Addictive Behavior Input such as behavioral sensitization, which promote relapses Initial (see above). Also, a craving-driven addiction could later Withdrawal D. “Cold Turkey” State Of Addictive turn into a completely craving-free habit or even compul- Secondary Stimulus Input sion [122-124], perhaps via the dynamic modulation of some cortical-basal ganglia circuits . These tertiary Craving Addictive Behavior hysteretic processes could perpetuate the drug-seeking Continued Withdrawal behavior independent of dopamine-mediated reward E. Abstinence State Of Addictive Secondary Stimulus [126,127], with or without provoking craving [128,129]. Input On the basis of these observations, we suggest that desen- No sitization of secondary craving-inhibiting pathways and Incubation Craving Continued sensitization of tertiary hysteretic pathways may underlie Withdrawal F. Relapse Of Addictive the acquisition and maintenance of addiction behavior, Secondary Tertiary Stimulus Input Input respectively, such that their sequential inductions upon the first encounter with an addictive drug create a water- Craving Addictive Behavior shed effect that irreversibly usurps the brain's built-in self- restraint mechanism to stave off addiction (Fig. 3). Graphical depiction of a theore recovery Figure 3 tical model of addiction and 3.3.3. Context-dependent habituation and desensitization Graphical depiction of a theoretical model of addiction and In contrast to habituation and primary sensitization (the recovery. (A) In the naïve state, an intrinsic secondary input quintessential dual process of nonassociative learning), suppresses craving via an inhibitory pathway. (B) Upon initial desensitization and secondary sensitization could also exposure to an addictive stimulus, the craving center is fur- involve associative training by primary and secondary ther inhibited by the primary pathway resulting in a feeling of stimuli. Some classic models of nonassociative learning euphoria. (C) With continued exposure to the addictive such as Aplysia siphon and gill-withdrawal reflex are stimulus, the secondary pathway is desensitized by the pri- mary pathway (with possible habituation in the primary path- known to demonstrate classical conditioning, which way not shown), resulting in craving and the onset of shares similar cellular and molecular mechanisms with addictive behavior. The latter can lead to more craving via a nonassociative learning [130-132]. A variant of conven- positive feedback vicious cycle as well as mobilization of a tional habituation called context-dependent habituation tertiary process that can independently perpetuate the addic- has been shown in some animal models such as the nem- tive behavior. (D) Sudden withdrawal of the addictive stimu- atode C. elegans  and the crab Chasmagnathus , lus precipitates a state of "cold turkey" characterized by where the retention of habituation after training is also enhanced craving due to the loss of the primary input, con- influenced by certain environmental cues. The depend- tinued desensitization of the secondary pathway and contin- ence on environmental cues indicates that the primary ued positive feedback from the addictive behavior. (E) stimulus-response pathway is not merely habituated by Sustained abstinence will allow resensitization of the second- the primary input but likely also desensitized by certain ary pathway and temporary relief of craving. The addictive behavior subsides, but the tertiary process is still lurking and context-dependent sensory inputs in an associative man- intensifying. Complete rehabilitation to the naïve state (A) ner. calls for extirpation of the tertiary process. (F) Otherwise, reactivation of the tertiary pathway by contextual cues, Such context-dependent learning effect has important memory or stress could once again desensitize the secondary implications in certain addictive disorders, where envi- pathway, triggering a relapse. ronmental cues are known to promote drug-dependent behavioral sensitization and relapses [121,135]. Hence, Page 9 of 21 (page number not for citation purposes) Behavioral and Brain Functions 2006, 2:29 http://www.behavioralandbrainfunctions.com/content/2/1/29 environmental cues may serve as a conditioned stimulus mum ISI condition for training is tacit in studies of non- to certain tertiary pathways which, when activated, may associative learning reported in the literature. independently desensitize the secondary craving-inhibit- ing pathways during abstinence (Fig. 3) in a manner anal- 4.1.3. Primary and secondary memory ogous to the conditioned drug response in associative The activity-dependent and pathway-specific properties of learning [136,137]. Further studies are needed to eluci- input gating make it a useful behavioral marker for mem- date the possible role of associative learning in the induc- ory in the primary pathway vs. those via the secondary tion of secondary sensitization and desensitization in pathway, hereinafter referred to as primary and secondary these experimental models. memory, respectively. This marker readily distinguishes nonassociative learning modes mediated by the primary 4. Temporal filtering by nonassociative gating and secondary pathways. Thus, habituation and desensiti- The notion of primary and secondary sensitization intro- zation are readily distinguished by the absence/presence duced in Section 2 underscores a novel behavioral para- of a STD memory trace in the resultant behavioral digm we call nonassociative gating. Several forms of response, whereas primary and secondary sensitization nonassociative gating have been identified that provide are distinguished by corresponding absence or presence of computational capabilities complementary to nonassoci- a STP memory trace. These criteria have been successfully ative learning. applied to the experimental classifications of primary and secondary memory in the rat respiratory chemoreflex and 4.1. Input gating mechanoreflex [2,3,74,138-140]. 4.1.1. Input gating and memory recall An important property of neurotransmission memory is 4.2. Output gating that it is discernible only during recall, i.e., when the path- 4.2.1. Output gating and refractory period way is activated by a stimulus eliciting combined reflex Memory recall requires not only an enabling input but, and memory responses. Once the activation ceases, the also, an observable output. In some sensory modalities corresponding memory becomes latent and unobserva- such as olfaction and vision, the output of nonassociative ble. We call this an input gating effect, namely an on-off learning is registered continuously as a sensory percept in switching of neurotransmission memory by the stimulus the brain without fail and thus the memory trace is gated itself (Fig. 1B). Thus, a primary stimulus that induces only by the input. In other sensory modalities, however, learning and memory in the primary pathway may simul- the behavioral output may be registered as discrete motor taneously recall the memory by "gating" it on. Conversely, response (or other effector response) with a definite memory in the primary pathway is automatically gated off refractory period. If so, the memory trace may be gated off once the primary stimulus disappears and thus any resid- during the refractory of the output as well. We call this an ual response must reflect persisting activity in the second- output gating effect in contradistinction to input gating. ary pathway [2,138]. 4.2.2. Minimum interstimulus interval For instance, deafferentation effectively gates off the pri- The notion of output gating has important implications in mary pathway (Sect. 3.2.2). Another example is the phe- determining the minimum ISI for nonassociative learning nomenon of pain sensitization (Fig. 1C). In hyperalgesia, experiments. For example, in the classic Aplysia gill-with- increased pain sensation due to peripheral or central sen- drawal reflex a strong tactile stimulus to the siphon may sitization is elicited when a noxious stimulus is applied produce a strong and long-lasting gill response which, if but these effects are promptly relieved (gated off) once the unabated, may mask the responses to subsequent stimuli stimulus is removed. In the case of addiction, initial expo- . In this case, the minimum ISI for producing a sure to an addictive drug gates on a normally latent crav- demonstrable habituation effect is limited by the refrac- ing-suppressing primary pathway thereby setting off the tory period of the gill response. Conversely, a behavioral addiction vicious cycle (Fig. 3). system with negligible refractory in the effector would require little or no ISI. This minimum ISI condition is tacit 4.1.2. Maximum interstimulus interval in studies of nonassociative learning reported in the liter- The notion of input gating has important implications in ature. determining the maximum ISI for nonassociative learning experiments. With a repetitive stimulus the primary mem- 4.3. Extrinsic gating 4.3.1. Phase-dependent gating ory is simultaneously induced and recalled at successive stimulus episodes but is gated off in between. Therefore, In contrast to input and output gating, which are intrinsic for optimal memory recall an ISI should be no longer to any stimulus-response pathway, neurotransmission than the decay time of the primary memory. This maxi- gating may also arise from extrinsic factors. In particular, we define phase-dependent gating as the on-off switching of Page 10 of 21 (page number not for citation purposes) Behavioral and Brain Functions 2006, 2:29 http://www.behavioralandbrainfunctions.com/content/2/1/29 a stimulus-response pathway by a phasic command signal 4.3.2. Learning-dependent gating independent of the pathway's input and output. This type Gating may also be triggered by activity-dependent plas- of extrinsic gating is exemplified by the mammalian ticity rather than a phasic command. This type of extrinsic carotid chemoreflex modulation of the respiratory gating is exemplified by Aplysia tail-elicited siphon with- rhythm in which separate STP and STD chemoreflex affer- drawal reflex where a modulatory network that normally ent pathways are temporally gated to either the inspira- inhibits the sensitization of contralateral siphon response tory or expiratory phase of the respiratory pattern is relieved after habituation (see Sect. 2.3.3). Such learn- generator (Fig. 4). Such phase-dependent gating allows ing-dependent gating has been suggested to account for the the chemoreceptor input to selectively modulate each res- bilateral expression of dishabituation vis-à-vis ipsilateral piratory phase in an orderly manner via separate STP or expression of sensitization in this experimental prepara- STD pathways, much like the on-off switching of two-way tion [69,71]. traffic lights at an intersection [74,138]. 4.4. Nonassociative gating as Boolean 'toggle switch' 4.4.1. Nonassociative gating: a new behavioral paradigm Input/output gating and extrinsic gating are instances of Pons nonassociative gating. As with nonassociative learning, the Carotid STD induction of such gating effects is activity-dependent and nonassociative, and their expressions may be intrinsic or extrinsic to the neurotransmission pathway. Furthermore, nonassociative gating displays certain computational Fast characteristics that are complementary to nonassociative learning. CSN 4.4.2. Boolean on-off switching and temporal filtering NTS In input gating, the stimulus itself provides a logic 'on' sig- nal that enables memory recall whereas in output gating, the effector response serves as a logic 'off' signal that momentarily disables or attenuates memory recall. Simi- larly, in phase-dependent or learning-dependent gating I-PMN + an extrinsic signal independent of the current input or output provides the on-off command for the memory trace. Thus, nonassociative gating operates like a Boolean L toggle switch that may turn the memory trace on or off Slow Carotid depending on the logic value of the command signal. STP Alternatively, nonassociative gating may be viewed as a temporal filter that selectively passes or stops memory recall within specific time windows during nonassociative learning. Such signal filtering in the time domain con- Slow trasts with the signal filtering in the frequency domain by nonassociative learning. Pha b p rhythm in rats Figure 4 ilphasic) ified by se-dependent g the integration carotid chemoref ating a and differ nd prenti imary/secondary (mon lex mo ation mechanisms as exem- dulation of respophasic/ iratory Phase-dependent gating and primary/secondary (monophasic/ biphasic) integration and differentiation mechanisms as exem- 5. Frequency filtering by nonassociative learning plified by the carotid chemoreflex modulation of respiratory Based on the above, we propose a theory of gated integral- rhythm in rats. The chemoafferent input from the carotid differential neural computation (or low-pass and high- sinus nerve (CSN) is habituated by a monophasic (input pass frequency filtering) by nonassociative learning. Pres- gated) differentiator in the nucleus tractus solitarius (NTS). cott  has proposed a mathematical model that mimics The output from NTS is relayed by parallel pathways to I the kinetics of habituation and intrinsic sensitization (inspiratory) or E (expiratory) neurons of the respiratory development and their interaction using linear first-order pattern generator or to I-PMN (inspiratory premotor neu- differential equations. Dragoi  has proposed a simi- ron). Switches denote gating to either I or E phase. Each lar model of suppressive and facilitatory interactions dur- pathway is modulated by two biphasic integrators (∫ with fast ing nonassociative learning but with nonlinear first-order or slow time constant) which either add or subtract to pro- differential equations in order to simulate the rate sensi- duce net short-term potentiation (STP) or depression (STD) effects. Adapted from . tivity property of habituation. Staddon and Higa  have proposed a feedback/feedforward integrator model Page 11 of 21 (page number not for citation purposes) Behavioral and Brain Functions 2006, 2:29 http://www.behavioralandbrainfunctions.com/content/2/1/29 of habituation. Shen  has proposed a STP model of Integrator Differentiator neural integrator. The present theory differs from the pre- vious models in that it is structurally-based and includes 3 3 all four modes of nonassociative learning (Sect. 2.4.1) as well as nonassociative gating (Sect. 3.1.3), which provide a complete mathematical basis for gated integral-differen- 1 1 tial computation. 060 120 0 60 120 Ti me ( sec) Time (sec) 5.1. Definitions of neural integrator and differentiator 5.1.1. Leaky integrator and differentiator Numeric integration and differentiation are elemental cal- culus operations. They also underlie all temporal dynam- ics and kinematics phenomena in Nature. An analog integrator/differentiator is a physical process that demon- strates integral/differential input-output transformation in real time. Analog integrator and differentiator are sub- 0.1 0.1 0.1 1 10 100 ject to response-limiting leakages. Leaky integrators are 0. 1 1 1 0 1 00 Frequency (cpm) Freq uen cy ( cpm) commonly used in electrophysiology experiments to obtain a moving-average estimate of neuronal firing fre- quency called 'neurogram.' C 2 5.1.2. Integrator and differentiator response characteristics In the time domain, a leaky integrator's response to a con- I I C R V R R s R s 1 1 3 o stant-step input exhibits exponential saturation during on-transient and exponential decay during off-transient, whereas the corresponding response of a leaky differenti- Time and ( Figure 5 left panelsfrequency response ch ) and differentiator (right aracteristics of panels) integrator ator demonstrates exponential decay from an initial over- Time and frequency response characteristics of integrator shoot and exponential recovery from rebound (left panels) and differentiator (right panels). A. The temporal undershoot (Fig. 5A; Eq. 2 in Appendix I). An integrator or response of a leaky integrator to a constant-step stimulus (horizontal bar) consists of abrupt reflex increase/decrease differentiator that sustains an off-transient response is of the response at stimulus onset/cessation followed by said to be biphasic (or else, monophasic); it is said to be exponentially increasing/decaying (potentiation/afterdis- inverted if the gain is negative (Eq. 3 in Appendix I). The charge) on/off transients. A leaky differentiator has similar dynamical order of a compound integrator/differentiator is reflex components but with exponentially decaying (accom- the number of integrators/differentiators it is composed modation) on-transients and rebound off-transients, which of, and its memory order is the number of component inte- are opposite to those of an integrator (overlaying dotted grators/differentiators that are biphasic. Under these lines). In both cases the off-transients may be rectified, with broad definitions, a neural system that displays such inte- the response becoming monophasic (not shown) instead of gral/differential neurotransmission characteristics is biphasic. The time scales chosen are typical of oculomotor called a neural integrator/differentiator. integrator and respiratory integrator. B. In the frequency domain, an integrator/differentiator behaves like a low-pass/ high-pass filter. The pass-band in both cases is the frequency 5.1.3. Low-pass and high-pass frequency filter characteristics range where the neurotransmission gain (normalized to From linear systems theory , integrator/differentia- unity) is highest and relatively constant. The high and low tor response characteristics in the time domain corre- cut-off frequencies (vertical dotted lines) of these filters are spond to low-pass/high-pass filter characteristics in the inversely proportional to the time constants of the corre- frequency domain (Eq. 4 in Appendix I). The time con- sponding integrator and differentiator shown in A. C. Exam- stant of a leaky integrator or differentiator is inversely pro- ples of RC integrator (C = 3.77, R = 1.60, R = 24.0, R = 1 2 3 portional to the cut-off frequency of the equivalent low- 0.73) and differentiator (C = 1.0, R = 1.75, R = 24.0, R = 1 2 3 pass or high-pass filter, respectively (Fig. 5B). In addition 10.2) circuits with a current source (I ) input and voltage (V ) S 0 to frequency filtering, a leaky integrator/differentiator also output. Units are arbitrary and RC values correspond to introduces phase shift (phase-lag/phase-lead) in the parameter values as defined in Eq. 1 (Appendix I) for integra- input-output relationship. tor (a = 0.125; b = 0.125; c = 1; d = 0.5) and differentiator (a = 0.125; b = 0.125; c = -1; d = 1.5). 5.1.4. Complementarities of neural integrator and differentiator Mathematically, a neural differentiator is an additive com- plement of an integrator, i.e., the response of a differentia- Page 12 of 21 (page number not for citation purposes) Relative Gain Norm. Response Behavioral and Brain Functions 2006, 2:29 http://www.behavioralandbrainfunctions.com/content/2/1/29 tor is complementary to that of an integrator with similar 5.3. Nonassociative learning models of neural integrator time constants (Fig. 5A). The frequency characteristics of a and differentiator 5.3.1. Nonassociative learning hypothesis of neural integrator and low-pass and high-pass filter with matched cut-off fre- quencies are also complementary to one another (Fig. differentiator 5B). Indeed, combination of such complementary filters Although the above models of neural integrator are all in parallel approximates an all-pass filter with constant plausible, none of them can explain neural differentiator. throughput gain at all frequencies. In contrast, nonassociative learning is based on activity- dependent changes in synaptic efficacy [51,139,140,158] 5.2. Reverberation models of neural integrator or neuronal excitability [10,159] that are well docu- 5.2.1. Reverberating neural network hypothesis mented in single neurons. These neural mechanisms are A widespread hypothesis of neural integrator is that of highly stable and robust with short- or long-term memo- reverberation in a recurrent neural network. This hypoth- ries ranging from seconds to days or months, and provide esis has been studied most extensively in two experimen- a plausible explanation of both neural integrator tal models: the "afterdischarge" phenomenon in the [2,139,144] and differentiator [2,140]. For example, syn- chemoreflex control of breathing  and the oculomo- aptic STD or LTD in brainstem NTS [160-162] may pro- tor integrator [147-149]. The proposed mechanism vide the habituation or monophasic differentiator effects involves two steps: intrinsic membrane properties of a in various cardiorespiratory reflexes [3,138] (see Fig. 4). neuron provide a trace capacitance that acts as a seed for 5.3.2. Primary and secondary integrator/differentiator the integrator, and positive feedbacks via a recurrent net- work allow continual refreshment of the seed. The net- To a first approximation, the integrator and differentiator work reverberation hypothesis is bolstered by the finding characteristics defined in Figure 5 are mimicked by the that the goldfish oculomotor integrator during normal augmenting characteristics of primary and secondary sen- saccadic movements could not be reproduced by saccade- sitization and decrementing characteristics of habituation like changes in neuronal firing induced by intracellular and desensitization, respectively. In particular, primary current injection, suggesting that the integrator effect is sensitization/habituation represents a primary integrator/ dependent on persistent changes in synaptic inputs . differentiator with monophasic characteristics whereas sec- It has been proposed that such a recurrent network can be ondary sensitization/desensitization represents a second- made robust by certain bistable neuronal processes ary integrator/differentiator with biphasic characteristics [151,152] or recurrent synaptic excitation with asynchro- (see Appendix II for mathematical details). nous transmitter release , or by external sensory error feedback . The monophasic characteristics of primary sensitization and habituation are due to input gating (Sect. 3.1). The 5.2.2. Reverberating neuronal ion-channels hypothesis biphasic characteristic of desensitization [3,72] may be Alternatively, reverberation of excitatory activity could ascribed to tonic activity in the secondary pathway, which also occur at the single-neuron level via a cascade of mem- provides a continual recall of the secondary memory brane ion channels [155,156]. The persistent activity can (Sect. 2.5). In contrast, in secondary sensitization the roles be elicited bi-directionally by excitatory and inhibitory of the primary and secondary pathways are often reversed inputs in a graded fashion, similar to a biphasic integra- (sensitization in the primary pathway induced by a strong tor. secondary stimulus), and thus a biphasic integrator response would be sustained by continued repetitive 5.2.3. Dendritic calcium self-amplification hypothesis application of the primary stimulus itself. Figure 4 shows A recent mathematical model  posits that temporal examples of primary and secondary integrator and differ- integration in a single neuron may result from self-ampli- entiator demonstrated in the mammalian carotid chem- fying calcium dynamics through a cellular process called oreflex pathways . "calcium induced calcium release." According to this model, synaptic inputs modulate the regenerative propa- Although monophasic integrator and differentiator are gation of calcium waves along dendritic processes, result- driven directly by the primary input, biphasic integrator ing in calcium-dependent currents that vary directly with and differentiator require a secondary input with persist- the temporal sum of prior synaptic inputs. This mecha- ent activity. The latter could come from reverberations at nism of neural integrator is thought to be robust by virtue the neuronal or neural network levels in central neurons of the intrinsic nonlinear spatiotemporal summation of . Alternatively, it may come from tonic central or the calcium waves. peripheral inputs. For example, tonic secondary inputs to the biphasic integrators in the carotid chemoreflex path- ways (Fig. 4) or vagal Hering-Breuer reflex may derive from central chemoreceptors, which provide persistent Page 13 of 21 (page number not for citation purposes) Behavioral and Brain Functions 2006, 2:29 http://www.behavioralandbrainfunctions.com/content/2/1/29 activation of the respiratory pattern generator and its tor and differentiator may combine to form an integrator- afferent pathways . differentiator pair with second-order dynamics and fre- quency characteristics. The simplest example is a primary According to the complementary relationships of neural integrator-differentiator pair in the form of a sensitiza- integrator and differentiator (Sect. 5.1.4), a secondary dif- tion-habituation complex produced by repetitive applica- ferentiator is the combination of two separate processes: a tion of a primary stimulus, as demonstrated in the classic primary reflex and an inverted secondary integrator (Fig. hindlimb flexion reflex of the spinal cat or the rat acoustic 6C, 6D). Similarly, a primary differentiator is comprised startle reflex shown in the dual-process theory [9-11]. The of a primary reflex and an inverted primary integrator combined primary integrator-differentiator pair acts like a (Figs. 6A, 6C). Thus, a primary or secondary neural differ- band-pass or band-stop filter, which selectively admits or entiator is realized by nonassociative learning as the differ- rejects afferent inputs that are fluctuating around certain ence (antagonistic excitation-inhibition combination) mid-frequencies. between a primary reflex and a primary or secondary neu- ral integrator. Nonassociative learning in the primary and secondary pathways may also work in tandem to form second-order 5.3.3. Second-order integrators/differentiators integrator-differentiator pairs. Four different combina- The four basic modes of nonassociative learning – habitu- tions are possible. Habituation in conjunction with sec- ation, desensitization, primary sensitization, secondary ondary sensitization gives a primary differentiator – sensitization – constitute a complete orthogonal (non- secondary integrator pair (Fig. 6A). This is similar to the redundant) mathematical basis that empowers the brain primary integrator-differentiator pair in the acoustic star- to perform basic integral-differential calculus of any tle reflex but with a secondary memory. Similarly, concur- dynamical and memory orders. In particular, an integra- rent primary and secondary sensitization results in a Differentiator and Integrator B Double Integrator Tonic Bias Tonic Bias Secondary Secondary Primary Primary Double Differentiator C D Integrator and Differentiator Tonic Bias Tonic Bias Secondary Secondary Primary Primary Compound neural in Figure 6 tegrator and differentiator models Compound neural integrator and differentiator models. Boxes show model simulations in arbitrary units and parameter values. Conventions are same as Fig. 1. A. Primary differentiator-secondary integrator is realized by activity-dependent habituation- sensitization in corresponding primary-secondary pathways. Step application of primary input at a constant firing rate (inset) induces synaptic STD and STP in primary and secondary pathway, respectively, resulting in temporal differentiation and integra- tion of the transmitted signals (lower and upper boxes). Resultant response (last box) at output neuron shows a compound dif- ferentiator-integrator characteristic. B. A double integrator may arise from STP in both primary and secondary pathways. C. A double differentiator is similar to a double integrator but with STD instead of STP in both pathways. D. A primary integrator- secondary differentiator can be realized in a similar fashion with a STP-STD combination. Structurally, primary differentiator (A, C) and secondary differentiator (B, D) are comprised of the primary reflex in conjunction with an inverted primary and secondary integrator, respectively, demonstrating the complementarities of integrator and differentiator. See text and Appen- dix. Page 14 of 21 (page number not for citation purposes) Behavioral and Brain Functions 2006, 2:29 http://www.behavioralandbrainfunctions.com/content/2/1/29 second-order low-pass filter in the form of a primary inte- 6.1.2. Neural differentiator: possible roles in selective attention, grator and secondary integrator (Fig. 6B). A second-order central resetting, sensory self-organization and fail-safe compensation differentiator/high-pass filter is formed by habituation in the primary pathway and desensitization in the secondary Functionally, a neural differentiator is a high-pass filter pathway (Fig. 6C), as demonstrated in the Hering-Breuer that preferentially admits time-varying signals, rejecting reflex or carotid chemoreflex modulation of expiratory any DC biases that tend to saturate or suppress neuro- duration in the rat [2,3,74,140]. Finally, it is conceivable transmission. This high-pass filtering effect allows the ani- that sensitization-desensitization in the primary-second- mal to automatically recalibrate the sensitivities of the ary pathway may give rise to a second-order integrator-dif- primary and secondary pathways against varying back- ferentiator pair (Fig. 6D) with band-pass or band-stop ground activities thereby extending the dynamic range of filter characteristics similar to those in Figure 6A. Exam- the stimulus-response relationship. Thus, a sustained pri- ples of second-order integrator and differentiator are mary input (e.g., hypertension or bronchopulmonary shown in Figure 4 for the mammalian carotid chemore- afferent hyperactivity) may induce compensatory habitu- flex pathways . ation-desensitization or "central resetting" of primary and secondary pathways [160,169,170], whereas abolition of the primary input (e.g., due to impairment of sensory 6. Nonassociative learning and brain intelligence In addition to performing kinematic transformations, receptors or afferent pathways) may elicit compensatory nonassociative learning may also contribute to the inte- dishabituation of the primary pathway and re-sensitiza- gral-differential calculus and Boolean logic computations tion of the secondary pathway. As such, the secondary that are basic to brain decision processes. These neural pathway provides a reserve surrogate or backup for the integrators, differentiators and logic operators provide primary pathway should it ever fail. Such sensory self- some of the basic building blocks of brain intelligence. organization provides a fail-safe mechanism for optimal compensation against hyper- or hypo-activity of afferent 6. 1. Intelligent roles of neural integrator and differentiator feedback in sensorimotor systems [2,171,172]. 6.1.1. Neural integrator: possible roles in sensory defensiveness, alarm reaction and sensorimotor instability Another useful function of habituation and desensitiza- Behaviorally, a neural integrator can boost an animal's tion is to tune out repetitive inputs that prove to be innoc- responsiveness to a recurrent noxious stimulus and (by uous, thus allowing selective attention to potentially cross-modal transfer) to other inputs even after the pri- important inputs [173-175]. Failure to do so may lead to mary stimulus has ceased. The resultant heightening and sensory defensiveness in some individuals [164,176] and widening of vigilance put the animal on the alert once this in patients with autism , as well as nonassociative self-defense mechanism is triggered. This 'alarm reaction' fear and anxiety  or other forms of hyper-reactivity. instinct sets one free to economize and relax (by staying On the other hand, because habituation and desensitiza- idle and calm) most of the time until fear-arousing epi- tion tend to suppress persistent afferent inputs, their over- sodes (e.g., terrorist attacks) set in. On the other hand, expression may have deleterious effects in certain inordinate sensitization of the primary or secondary path- sensorimotor reflexes. For example, abnormal expression ways could result in hypersensitivity to innocuous sensory of LTD in the NTS of newborn mice devoid of functional stimuli. This mechanism is compatible with certain forms NMDA receptors is implicated in the progressive respira- of sensory integration dysfunction such as sensory defen- tory failure and early death in these mutant animals . siveness  or nonassociative fear or anxiety toward impending adverse stimuli . 6.1.3. Compound neural integrator-differentiator: possible roles in novelty detection and selective attention In sensorimotor control, temporal integration of error A compound integrator-differentiator/differentiator-inte- feedback may help to minimize the resultant steady-state grator is functionally equivalent to a band-pass/band-stop error. On the other hand, low-pass filtering of the feed- filter that preferentially admits/rejects inputs whose tem- back signal may introduce excessive phase lags (phase poral variability falls within some intermediate frequency delays) that tend to destabilize closed-loop control . band or time scale. For example, the acoustic startle reflex It has been suggested that spontaneous oscillations of sen- is sensitized by continuous background noise or novel sorimotor regulation may develop with increased delays inputs but may habituate on discrete repetitive tones . in sensory feedback [166-168]. Such a combined sensitization-habituation or sensitiza- tion-desensitization response pattern allows maximal vig- ilance to unexpected (and potentially alarming) inputs over mundane and insipid ones, thus sharpening novelty detection and selective attention . On the other hand, excessive band-selective filtering may lead to para- Page 15 of 21 (page number not for citation purposes) Behavioral and Brain Functions 2006, 2:29 http://www.behavioralandbrainfunctions.com/content/2/1/29 noia; indeed, increased sensitization and reduced habitu- audio system with unequal tone control). Nonassociative ation are trait markers of patients with schizophrenia learning therefore plays an important role in balancing . The possible role of this band-selective filtering the sensory inputs. This could be the first step in the mechanism in other sensory novelty-detection tasks such brain's putative ability of creating explicit internal models as dynamic predictive coding of unexpected visual infor- of the environment , as implicit in René Des- mation by the retina , or more complex selective cartes' mind-body interactionism . attention tasks such as selective visual attention , deserves further study. 7. Conclusion A general theory of nonassociative learning comprised of 6.2 A sensory firewall for Cartesian mind-body internal habituation, sensitization and desensitization in primary model adaptation or secondary pathways has been presented. The defining The array of low-pass, high-pass and band-pass/band-stop phenotypes of these varying modes of nonassociative frequency filtering effects of nonassociative learning, learning are their distinct integral-differential computa- together with the associated Boolean logic temporal filter- tion capabilities, which are shown to correlate with many ing effects of nonassociative gating, provide a finely-tuned intelligent or maladaptive brain behaviors. In addition, intelligent "firewall" that continuously screens all incom- the notion of nonassociative gating with intrinsic Boolean ing signals into actionable and non-actionable categories logic computation capability has been introduced as a in order to prioritize (Fig. 7). This firewall mechanism basic behavioral paradigm that may act independently or shields the mind from the vast amounts of inundating in tandem with nonassociative learning. Together, nonas- sensory information that constantly compete with one sociative learning and nonassociative gating constitute an another for attention, and spares it the trouble of having intelligent firewall that constantly triages vast amounts of to respond to every tingling except the most salient ones. sensory information into actionable and non-actionable The triage process not only helps to preserve mental sanity categories in order to prioritize. This unified framework of but also conserve physical energy, both of which are nonassociative learning and nonassociative gating sheds important for survival. On the other hand, breakdown of new lights on the ultra secrets of brain intelligence and the nonassociative learning processes may result in mis- brain disorders. The underlying functional and structural tuning of the firewall and hence, distortions in the sensory organization principles  are shown to be generally percept (much like the frequency distortions heard in an applicable to a wide variety of brain systems across animal phyla and sensory modalities in health and in disease states. These system-level principles are fundamental to a systems medicine approach  to the manage- ment of human health and disease at the organ, organism and community level. APPENDIX I. Integrator and differentiator equations A first-order leaky integrator or differentiator (Fig. 5) is described by the following equations: x = -ax + bu (1a) y = cx + du (1b) where y, u are the output and input of the integrator or dif- ferentiator, respectively; x and x are state variable and its rate of change in time; a, b, c, d are parameters and a > 0. The terms cx and du indicate respectively the indirect Nonassociative learnin screens a and priority for internal m interaction Figure 7ll environmenta g as a se l inputs and decides their odel adaptation in mind-body nsory firewall that con salien stant cy ly (adaptive/dynamic) effect and direct (feedforward reflex) Nonassociative learning as a sensory firewall that constantly effects of the input on the output. For a constant-step screens all environmental inputs and decides their saliency and priority for internal model adaptation in mind-body input, u ≡ constant for 0 <t <T where T is the end of input, interaction. This high-pass, low-pass or band-pass/band-stop the solution for Eq. 1 under zero initial condition for x is: signal filtering action is analogous to tone control in an audio system. -at y(t) = du + (cbu/a)(1 - e )for 0 <t ≤ T (2) Page 16 of 21 (page number not for citation purposes) Behavioral and Brain Functions 2006, 2:29 http://www.behavioralandbrainfunctions.com/content/2/1/29 This model represents an integrator (Fig. 5A, left panel) if both terms on the right hand side of Eq. 2 have the same −at yt ()=+ y (01 ) (b c u /a )(−e ) for 0<t<T () 7a 22 321 2 sign, or a differentiator (Fig. 5A, right panel) if they have opposite signs. An integrator or differentiator is said to be and inverted (with negative gain) if the input exerts an oppo- −− at()T yt( )=+ y ()00 [(yT ( )−y ()]e for t>T () 7b 22 2 2 site direct effect on the output, i.e., d < 0. It is called bipha- sic or monophasic depending on the presence or absence of Finally, the resultant response of the dual-process integra- a post-stimulus response (for t >T): tor and/or differentiator is the sum of y and y : 1 2 -a(t-T) Biphasic: y(t) = [y(T) - y(0)]e for t >T (3a) y = y + y (8) 1 2 Monophasic: y = 0 for t >T (3b) Authors' contributions CSP conceived the theory, reviewed and integrated the lit- where y(0), y(T) are respectively the outputs at the begin- erature and wrote the manuscript. DLY performed the ning and end of the step input. mathematical modeling and prepared the illustrations. Both read and approved the final manuscript. From linear systems theory , the equivalent transfer function for the model of Eq. 1 is (Fig. 5B): Acknowledgements We thank Drs. K. Lukowiak, B.R. Dworkin, J.R. DiFranza and members of ds(/ ++ a cb d) the Poon Lab for helpful discussions. This work was supported in part by Ys () = ⋅Us () () sa + National Institutes of Health grants HL067966 and HL072849. DLY was recipient of a National Institute of Mental Health predoctoral fellowship where s is the complex frequency and Y, U are the Laplace MH012697. transforms of y, u, respectively. References 1. McCormick DA: Brain calculus: neural integration and persist- APPENDIX II. Nonassociative-learning ent activity. Nat Neurosci 2001, 4(2):113-114. integrator/differentiator models 2. Poon C-S, Siniaia MS: Plasticity of cardiorespiratory neural From Eq. 2 the response of a primary integrator or differ- processing: Classification and computational functions. Respir Physiol 2000, 122(2-3):83-109. entiator (Fig. 6) to a step input u applied to the primary 3. Siniaia MS, Young DL, Poon C-S: Habituation and desensitization pathway is given by: of the Hering-Breuer reflex in rat. J Physiol (Lond) 2000, 523(2):479-491. 4. 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Ahn AC, Tewari M, Poon CS, Phillips RS: The Limits of Reduction- ism in Medicine: Could Systems Biology Offer an Alterna- Your research papers will be: tive? PLoS Med 2006, 3(6):e208. available free of charge to the entire biomedical community 188. Ahn AC, Tewari M, Poon CS, Phillips RS: The Clinical Applications of a Systems Approach. PLoS Med 2006, 3(7):e209. peer reviewed and published immediately upon acceptance cited in PubMed and archived on PubMed Central yours — you keep the copyright BioMedcentral Submit your manuscript here: http://www.biomedcentral.com/info/publishing_adv.asp Page 21 of 21 (page number not for citation purposes)
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