Uziel Sandler • Lev Tsitolovsky Neural Cell Behavior and Fuzzy Logic Editors UzielSandler LevTsitolovsky Jerusalem College Technology Bar-Ilan University 91 160 Jerusalem Faculty of Life Sciences Israel 52900Ramat-Gan Israel ISBN: 978-0-387-09542-4 e-ISBN: 978-0-387-09543-1 Library of Congress Control Number: 2008926123 © 2008 Springer Science+Business Media, LLC Contents Part I The being of neural cells 1 The operation of memory (a single neuron can learn)...... 11 1.1 Brain straightforward sight.............................. 11 1.2 Prediction of future events after learning ................... 21 1.2.1 Basic types of learning at the neuronal level ......... 21 1.2.2 *How does a neuron reveal, which type of learning tasks it has encountered?........................... 31 1.3 Location of functions in the brain ......................... 35 1.4 Location of memory in the brain .......................... 40 1.5 Memory location in the pre- and postsynaptic structures ..... 46 1.6 Plasticity of excitable membrane .......................... 54 1.7 The chemical nature of memory ........................... 76 1.7.1 Chemical traces of memory and chemical sensitivity of memory.......................................... 76 1.7.2 Biological meaning during habituation is acquired or lost by chemical means............................. 83 1.7.3 The direction to chemical specificity of memory ....... 90 1.7.4 Nontemplate RNA synthesis? ....................... 94 1.8 Preparing of ’a whole’ out of mutual interactions ............100 1.9 *Forward propagation of prediction ........................106 2 The verve of injured neurons (a single neuron tries to survive) ...................................................113 2.1 Neurons and glia operate together .........................113 2.2 Death through necrosis (murder of cells) and apoptosis (suicide of a cell) ........................................114 2.3 Neural and glial cells assist in survival .....................119 2.4 Spread of damage within a tissue ..........................123 2.5 Cell coupling through gap junctions........................124 2.6 Multiple pathways for cell survival.........................127 2.6.1 Damage through excitation and the paradoxical properties of an injured neuron......................127 2.6.2 Second messengers and cell survival..................133 2.6.3 Intercellular protection by retrograde messengers and cytokines.........................................137 2.6.4 Protection through a detoured route .................142 2.7 Nonlinear dependencies of doses, time and reciprocal interactions.............................................144 2.8 Homeostasis as a resetting and reorganization...............147 2.8.1 Homeostasis against death..........................147 2.8.2 Sensors ..........................................152 2.8.3 A bit of injury is sometimes even beneficial ...........156 2.8.4 Can homeostasis be perfected with experience?........161 2.9 Long-term potentiation as a form of cell damage.............165 2.9.1 Is LTP something like an excitotoxicity? .............166 2.9.2 Parallelism between damage-protection and LTP ......166 2.9.3 Development and LTP .............................169 2.9.4 Temporal scopes of damage, LTP and learning ........171 2.9.5 Depotentiation and protection ......................172 2.9.6 Preconditioning of LTP and compensation of damage ..173 2.9.7 Specificity of LTP .................................174 3 Subjective nature of motivation (a single neuron can want) 177 3.1 Motivation as the simplest tool for investigation of the objective roots of a subjective life .........................177 3.1.1 The way a question is formulated....................177 3.1.2 Motivation as a homeostatic recovery ................178 3.2 Chemical nature of motivations ...........................180 3.2.1 Control of motivations by means of motivationally- relevant substances ................................180 3.2.2 Chemical specificity of motivations is not absolute .....183 3.2.3 Motivation reorganizes brain temperature and energy metabolism.......................................186 3.2.4 Localization of metabolic aims of goal-directed behavior in the brain ..............................187 3.3 Elemental motivations emerge in a result of transient cell damage ................................................189 3.3.1 Defensive motivations..............................189 3.3.2 Respiratory motivation.............................192 3.3.3 Temperature regulation ............................193 3.3.4 Drinking motivation ...............................194 3.3.5 Feeding motivation ................................195 3.3.6 Sexual motivation .................................198 3.3.7 Artificial motivations: drug-dependence, self- administration and self-stimulation ..................201 3.3.8 Motivation to sleep ................................205 3.4 Reward protects neurons from damage .....................207 3.4.1 Place of rewards in motivational behavior ............207 3.4.2 Chemical mediators of a conscious reward ............209 3.4.3 Inhibitory actions of rewards........................212 3.4.4 Specialized neurons generate motivations and accept rewards ..........................................216 3.4.5 Protective actions of rewards .......................217 3.5 Goal-directed behavior of single cells.......................219 3.5.1 Motivationally-relevant substances distort properties of an excitable membrane ..........................220 3.5.2 How small may be the brain signal controlling a body?.221 3.5.3 The simplest behavior: chemotaxis...................223 3.5.4 Goal-directed behavior of single neurons..............226 3.6 Paradoxical properties of instrumental reactions .............241 3.7 Trial-and-error at the cellular level during instrumental conditioning ............................................245 4 Goal-directed actions (a single neuron can behave) ........247 4.1 A physiological description of voluntary actions .............247 4.2 An origin of agency and voluntary actions ..................250 4.3 Common decision and the only reaction of the whole brain....252 4.4 Gap junctions enriches a brain with a new quality ...........254 4.5 Choice of alternatives with respect to the output ............257 4.6 Formation of neuronal ensembles during tension .............261 4.7 Physiology of free will....................................266 4.7.1 Instability of neuronal reactions .....................266 4.7.2 Instability and trial-and-error .......................269 4.7.3 Organization of choice .............................275 4.7.4 Free will without mysticism.........................277 4.8 The emergence of higher-level organizations from the interactions of lower-level units............................280 5 Death as an awareness-rising factor (a single neuron can suffer and delight) .........................................287 5.1 Physiological access to consciousness .......................288 5.2 Merging of odd information in aware perception .............293 5.3 Changeability of consciousness ............................295 5.4 Recurring change of consciousness during bipolar disorder ....297 5.5 Properties of the alive, but unconscious brain ...............298 5.6 Inhibition in the brain and consciousness ...................299 5.7 Chemical modulation of consciousness......................302 5.8 Materialization of the SELF ..............................304 5.9 Discrete time steps in perception ..........................308 5.10 Common currency for choice: between displeasure and pleasure309 5.11 What is bad and good for a neuron? .......................311 Part II Mathematics of feeling 6 Introduction to fuzzy logic.................................317 6.1 Phenomenology of a neural cell’s behavior and fuzzy logic ....317 6.2 Perceptions as a Mathematical Object .....................319 6.2.1 Possibility and Fuzzy Set...........................319 6.2.2 Logical Connectives and Triangular Norms ...........321 6.2.3 *Consistent t-norms ...............................324 6.3 Mathematical Operations with Fuzzy Quantities and Zadeh’s Extensional Principle .............................325 6.3.1 Extensional Principle of L.Zadeh ....................326 6.3.2 Fuzzy functions ...................................327 6.3.3 Fuzzy differential inclusions.........................328 6.3.4 *Fuzzy integral....................................330 7 Evolution of Perceptions...................................335 7.1 Fuzzy Dynamics: Evolution of a System with Vague Parameters and Uncertainty in the Dynamics law............335 7.1.1 Fuzzy logic setup of the evolution problems...........337 7.2 Master-Equation of fuzzy dynamics ........................339 7.3 Fuzzy trajectories .......................................341 7.3.1 The most possible and impossible trajectories of the fuzzy evolution....................................344 7.3.2 *Fuzzy dynamics of “oscillator” .....................345 7.3.3 *Splitting of the fuzzy trajectory into a bundle........347 7.3.4 *Some fundamental solutions of the fuzzy dynamics equations.........................................349 7.3.5 *Behavior of fuzzy system near critical points.........354 7.4 Evolution of uncertainty..................................356 7.5 Evolution of perceptions..................................358 8 Fuzzy dynamics of a neuronal behavior ....................361 8.1 Linguistic variables and linguistic rules of a neuron’s behavior.361 8.2 Fuzzy dynamics of a neural cell’s learning ..................367 8.2.1 A simplified model of the neuron’s learning ...........369 8.2.2 Solutions of fuzzy dynamics model of a neural cell’s behavior ..........................371 9 Conclusion: Is real neuron a primary fuzzy unit? ..........383 9.1 The operation of memory.................................383 9.2 The verve of injured neurons..............................386 9.3 Subjective nature of motivation ...........................390 9.4 Goal-directed actions ....................................399 9.5 Death as an awareness-rising factor ........................403 9.6 Fuzzy dynamics model of neuronal behavior ................403 9.7 Fuzzy logic of a neural cell................................405 9.8 Artificial motivational neurons and feeling robots............411 A Appendix..................................................413 A.1 *Model of a chemical memory of a neuron ..................413 A.2 *An alternative type of fuzzy dynamics equations............423 References.....................................................429 Index..........................................................471 List of symbols ................................................475 List of definitions ..............................................477 Introduction: Brain as a unique object Brain is the most complex, puzzling and attractive object in the universe. Everybodyknowsthatbrainisresponsibleforcontrolofourlearning,memory, motivations, consciousness, etc. Moreover, a brain by a certain mysterious way produces the Subject (or Self, Person, Ego, Observer - whatever you like), which tries to look into brain and understand the Subject itself. The means for the objective observation of a subjective world are absent, but we can observe the consequences of objective existence. Neurobiology is the only science that considers the subtle facet between substance and mind. Besidesthefactthatbraingeneratesgoalsanddoesnotneedexternalpro- gramming, it possesses many particular properties that make it an appealing objectforresearch.Brainworksusingfuzzylawsontheonehandandproduces fuzzylogicontheotherhand[1269].Thebrainhasthehighestmetabolicrate ofallbodilyorgansanddependspredominantlyonoxidativemetabolismasa source of energy [755]. The brain spends 20% of total body oxygen consump- tion, although its mass is less than 2% of the total body and a brain does not produces mechanical efforts, as does a muscle, does not synthesize enzymes for food digestion, as does a liver and does not pump overlarge volumes of blood, as does a heart. Energy-consuming processes include maintenance of ion equilibriums, generation of the basal electrical activity, neurotransmitter uptake, etc. There are two main consumers of cellular energy, protein synthe- sis(55%)andNa+,K+-ATPase(45%),butduringhypoxiaNa+,K+-ATPase becomes dominant (80%) [158]. The Na+,K+-ATPase, or the sodium pump, is a transmembrane protein accountable for maintaining electrochemical gra- dients across the membrane in all cells. However, even in the resting awake state,around80%ofenergyusedbythebrainsupportseventsassociatedwith cycling of glutamate and gamma-aminobutyric acid (GABA) neurotransmit- ters[1139,541],themaintransmittersofexcitationandinhibition,connected alsowithcelldamageandprotection.Therefore,equilibriumbetweenneuronal damage and protection plays an important role in the normal brain function. In the brain, at any one moment, a lot of neurons, although not every one, are active. Brainy activity is perceptible even when it appears to be 2 Contents doing absolutely nothing. The basic diversity of chemical reactions in a body also belongs to brain. Properties of neurons are much more complex than for any other cell. This is partially concerned with the excitability of neurons. Brain has infinite memory in a finite volume (in the sense that nobody sees as memory come to an end). Physical damage of brain structure causes only subtleimpairmentofmemory,whichisusuallylessforremote,importantand learned-by-heartmemory[1252,1255].Bysomeevaluations,amassiveparallel processing capacity permits our visual system to successfully decode complex imagesin100ms,andourbraintostoreinformationthatmanytimesexceeds the text contained in the US Library of Congress [794]. Neuronal memory is not reversible, but brain scarcely contains any empty storage medium. The capability to recognize exceeds the capability to recollect. Sometimes, one cannot recall required information from one’s past experience, but images in thelong-termmemoryareneverdestroyed:forexample,onedoesn’tremember onlyhalfofthefaceofafriend,andonedoesn’trememberavacationinblack and white but in color. Brain does not contain moving parts or valves, works exclusively and consistently, and memory stays intact after a short-term shut down of all dynamic processes. Signals in the brain are spread slowly (ten milliontimesslowerthanelectricalsignals),buttimeresponseformanytasks isexceptionallyshort.Braincontainsbillionsofneurons,tenormoretrillions ofsynapticconnections,andprocessesinformationduringmilliseconds.Ithas a highly parallel organization, but does not suffer from the dictates of a few processors. Brainisauniqueobject.However,isbrainasubject?Areyouyourbrain? Is one the activity of his brain? When brain produces thinking, neurons and glial cells generate electrical fields, the distribution of ionic concentrations alters, various substances are synthesized and degraded, numerous enzymes are activated or inhibited, gases spread through nerve tissue, etc. How, when and where is physiology converted into sense and what kind of physiological activityisdecisive?Thisisthecrucialproblem.Canwesomedaysolveit?For sure, problems that are inaccessible to our brain do exist. Just as a crocodile cannot be timed and a dog can not speak, the human mind also has borders. Our brain can’t read two texts simultaneously, can’t remember its prenatal life,can’timaginehowtheelectronrunsthroughtwoholesatonceandmaybe nevercancomprehendhowtheouterenvironmentisconvertedintoaninside, subjectiveword.Infact,thereareenvironmentalfeaturesthatourbraincan’t perceive,ourmemoryisnotidealandimaginationisnotinfinite.However,our capability to realize is exceptionally powerful. For instance, we can’t imagine four-dimensional space but can comprehend that in four-dimensional space, thelossofone’skeysfromyoursafeisnotworrying:onealwayscanpenetrate through the fourth dimension. If we never understand consciousness, this will be the first problem that humanity cannot manage. The foremost mission of neurobiology is the cognition of subjective phe- nomena and this includes the disproving of supernatural or mystic expla- nations for this extremely hard problem. Thermodynamics teaches us that Contents 3 disorder in closed-loop systems increases, but the brain gives a kind of an object,whichintroducesorderintheworld.OnemayimagineMaxwell’sdae- mon, (that little homunculus!) controlling microscopic damper in the vessel. Whena high-speed molecule in the environmentdrawsnear to the vessel,the homunculusopensslightlythedamperandaccumulatesenergy,thusviolating thermodynamic laws. If we mark on the cerebral cortex the points receiving information from the body (face, knees, belly, etc.) we will observe an ugly dwarfatthesurfaceofthecortexwithitshugejaws,widelyspreadfingersand colossal genitals (the more sensitivity, the more cortical representation). This homunculus has only technical, ancillary meaning. However, sometimes one imaginedone’sSelfastheHomunculuslivinginthebrain.Anyproblemiseasy to explain by means of a homunculus, but this is an inadmissible explanation in science. If one says that the theory may work only with the contribution of the homunculus (that is as being run by a Homunculus inside), this means that the theory is not scientific theory. At present, we poorly comprehend a brain. Sometimes comprehension of an object is identified with the skill to recreate and/or to improve this ob- ject. This is not our goal. Animals recreate brain naturally and improve it in evolution without any comprehension. To be more accurate, we want to understand some brain functions. Among them there are some so intricate that even vague explanations are absent. Neurobiologists run into several hard problems: 1. After learning, the reaction to a specific signal depends upon its sig- nificance, which was acquired during learning. Reactions become specific to input, and one signal may increase its effect, whereas another signal turns out to be ineffective. Why are some signals preferred? It is not the rule that a stronger impact evokes a stronger reaction. Gentle footsteps in one’s bare apartment may exert a stronger impression than the harsh noise of one’s TV. A specific reaction to a given signal may be both innate and acquired during experience.Thus,ataskisrelatedtothenatureofmemory:reactiondepends onpastexperience.Moreover,isthephysicalappearanceofmemoryelements predeterminedbytheirrealappearanceintheenvironment?Iftheresponseis ”yes”andsimilarimagesoreventsretainsimilarmaterialtracesofmemoryin different brains, a one-to-one correspondence exists between possible events andmemoryelements,evenifyouwillnevermeettheseeventsinyourlife:for instance, the image corresponding to the face of my grandmother preexists in any brain in a passive form (”grandmother” cells, synapses or pathways). It is scarcely likely that whole world’s diversity may be squeezed into the brain. However,iftheresponseis”no”andthememoryelementsarespecificforeach brain, who decides that an activated memory trace corresponds to a specific image or event? Therefore, the puzzle is how neurons recognize the represen- tations they keep. Should we suppose the existence of a certain mysterious homunculus, living at the skull, which observes the environment through our senses and executes his wishes by means of our muscles? Some people think that we are our homunculi.