In search of a neuronal correlate of the human mind: new concepts from "topological neurochemistry"

Erhard Bieberich

Department of Biochemistry and Molecular Biophysics

Medical College of Virginia Campus of Virginia Commonwealth University

1101 E. Marshall Str. P.O.Box 614

Richmond, VA 23298

Phone: 804-828-9217

Fax: 804-828-1473


Key words: consciousness, neurochemistry, mind-body problem, topology


Neurochemistry is a powerful discipline of modern neuroscience based on a description of neuronal function in terms of molecular reaction and interaction. This study aims at a neurochemical approach to the "hard" philosophical mind-body problem: the search for a neuronal correlate of consciousness. The scattered pattern of remote areas in the human brain simultaneously busy with single perceptions has left us with the unanswered questions why, where, and how the neuronal activity gives rise to a unified conscious observation of the outer world in a space inside of the human brain. In this study, conscious perception of temporally and spatially distinct events by an inner observer, the self, is treated as a topological problem demanding for a correlation of the self with a particular orchestration of neuronal or neurochemical activity triggered by action potentials. According to a novel concept of "topological neurochemistry" it is assumed that three features of the human brain are necessary in order to generate consciousness: 1) A network of neurons with dendritic branching structure and re-entry signaling of action potentials. 2) A macromolecular lattice structure as part of the neuron which is excitable or affected by action potentials. 3) A spatial superposition of action potentials which underlies conscious perception but reveals not necessarily the same topology as the space perceived in consciousness. Several molecular models for the generation of consciousness and the self will be discussed, and a new concept, the "fractal approach", will be introduced. Mathematical theory and experimental methods for investigation of human consciousness will be presented.


The most exceptional and enigmatic property of the human brain is given by its ability to generate a mind inside of itself. By the virtue of being conscious, the human mind experiences a "world" of objects, sensations, and emotions. This world is a product of informational processing and resides completely inside of the brain. Any conscious experience, however, appears to arise from a world projected to the outside of the brain. The mind then merges the perception of the world with an inner quality of emotion and a feeling of being an ontogenetic unity. This inner observer is aware of itself, it is self-concious with an impression of being a perpetual entity with memories and a unique identity, the "self" (Baars, 1997; Cotterill, 1994; Feinberg, 1997; Strawson, 1997).

Neurochemistry is a scientific discipline which attempts to explain the informational processing within the brain by the molecular biochemistry of neuronal cells. The description of brain computational processes by molecular interaction on the cellular or subcellular level has made tremendous progress and is almost complete. The conscious experience arising from this processing, however, still eludes scientific explanation. The objective of this study is to approach the description of consciousness by neurochemistry. This will be achieved by first defining a semantics and symbolic notation for "world", "inner observer", and "self" which treats these expressions as physical entities in space and time. Thereby, a scientific explanation of consciousness has to cope with the principles of group topology. Provided that a topologically consistent model can be found it will be correlated to a mechanistic process based on molecular interaction. Eventually, the concepts arising from this "topological neurochemistry" will be rendered physically accessible and methods for their experimental verification will be discussed.

Computation and imagination: Brain structure and the topological center of consciousness

The detection of processes generating consciousness within the brain is dependent on the ability to monitor its neuronal activity. Several techniques to detect the electrical or physiological activity of brain centers or even single neuronal cells have been developed. I) Invasive techniques record the generation of electrical potentials either by implantation of electrodes or patch-clamping of single nerve cells. II) Non-invasive techniques are used to localize electrical or physiological activity in the entire brain based on encephalographic or tomographic methods. The application of these techniques has resulted in the precise description of computational processes in the brain during active and conscious thinking. The experimental observations, however, are in sharp contrast to the description of a consciously experienced world as deduced from inner observation (meditation):

1) The brain activity during perception or thinking is dissipated throughout several remote centers. These centers appear to be functionally dissociated and specialized according to the quality or property of perception or mental operation (Courtney et al., 1997; Epstein and Kanwisher, 1998). In contrast to the impression of a unified experience during conscious perception of the world, there is no permanent center of awareness detectable.

2) The neuronal processing of information transmitted from different perceptive organs involves the same neurochemical reactions irrespective of an apparently functional specialization. This, however, is in contrast to the vast variety of conscious experiences emerging from these reactions.

In brief, the dissipation of information in the brain contradicts a unified conscious experience whereas the variety of experienced qualities contradicts the uniformity of neuronal processing. This inconsistency impairs a classical attempt of scientific analysis by deconstruction of brain structure and its functional correlation with consciousness. A deconstructive approach is based on the assumption that a specific function observed for an entire structure can be assigned to one or several of its parts. This approach would imply that if the brain is conscious then there is a center localized within the brain that is conscious. In consequence, a cluster of brain cells or even a single cell may also be conscious. Eventually, we will end up with "conscious molecules" or even "conscious subatomar structures". We will see in one of the following sections that recent attempts to find a neurophysical theory of consciousness just claim its generation within a macromolecular structure (e.g., microtubules). However, the more we dissect and deconstruct the brain the less we are able to find a specific structure which makes the brain so special for the generation of consciousness.

Daniel C. Dennett once stated that a center of consciousness is as abstract as the center of a gravitational field (Hardcastle, 1995). The "non-locality" of the self tempted others to describe consciousness as a mental force field causally interacting with neuronal structures (Libet, 1994, 1996; Lindahl and Arhem, 1994, 1996; Popper et al., 1993). Consciously experienced objects and situations, however, are perceived as local events in space and time. This locality implicates a putative correlation with localized processing of information by a neuronal substrate. In turn, it entails an assignment to a particular site within the brain where the neuronal processing takes place. It is obvious, that we will end up in a circulus vitiosus of inconsistent conclusions resulting from the localization of an inner perception and the non-local quality of the perceiving entity. The main fallacy of a deconstructive or reductionistic approach arises from the objective to define a specific neuronal structure or process as a functional atom of consciousness. Deconstruction works perfectly for the description of neuronal computation as a flow of information throughout a sequence of processing centers within the brain (Hildreth and Koch, 1987; Knudsen et al., 1987). An atomistic description, however, will fall into a paradox if applied to conscious experience arising from neuronal computation. If computational processing of information is localized then the conscious experience is contributed by several distinct processing centers. On the other hand, if conscious experience is localized then the variety of information perceived must be integrated into a single processing center. In the first case we would have to accept a "spooky" connectedness between remote centers in the brain. In the second case we would have to deal with an immense compression of information by a rather limited number of different neurochemical processes.

Neurochemistry and signal processing: Organisation of matter and glimpse of a newborn mind

Signal processing on the level of single neurons is mediated by transduced membrane potentials (Johannsson and Arhem, 1994; Koch, 1997). The neurochemical reactions involved are uniform. A local summation of electrical input signals induces the opening of an ion channel protein when reaching a threshold potential. The transmembrane ion flux generates an output potential which propagates along the cell membrane to the next ion channel, where again a signal summation takes place. Eventually, the electrical signal reaches the synaptic cleft upon which a chemical transmitter is released. The neurotransmitter binds to a receptor on the surface of the adjacent cell thereby triggering the opening of an ion channel protein, and so forth. A certain variation of this theme is only given by the types of neurotransmitters, receptors, and ion channels involved. It remains absolutely enigmatic, however, how this process is able to generate consciousness:

1) None of the neurochemical processes or cellular structures involved is confined to the brain or even to neuronal cells. Membrane potentials, receptors and ion channels are ubiquitous and characteristic for any cell type.

2) The multicellular organization of any organism starts with a single cell. Cell division and differentiation then generate neuronal tissue which apparently acquires consciousness during its development. The underlying neurochemistry, however, is already active in the first of all neuronal cells. It is completely unclear, which "critical mass" of neurons eventually ignites consciousness.

These considerations appear to be in contrast to the notion that there is a specific structure or molecule accounting for conscious experience. Recently, Hameroff and Penrose developed a model for the generation of consciousness by certain cytoskeleton molecules termed microtubules (Hameroff and Penrose, 1996; Jibu et al., 1994). It is well known that microtubules are ubiquitous whereas the occurrence of consciousness is confined to the brain. This argument is consistent with the considerations mentioned before and was held against the microtubule theory. It should be noted, however, that the counter-argument holds also true for all those neuronal cells in the brain which are apparently inactive and not participating in the generation of consciousness. In brief, a certain cellular structure or process, e.g., microtubules, may be necessary for the generation of consciousness but is not necessarily conscious. And if it is conscious, then not necessarily all the time. Any molecular theory of consciousness, however, has to cope with the arguments discussed in the previous section. Molecules, no matter how small they are, are local in distribution and internal structure. Accordingly, the inner observer aware of the world must be non-locally distributed over one or several molecules. If the inner observer is localized onto one part of a conscious molecule it is again hard to understand how the vast variety of consciously experienced information is integrated into this part. We have again to deal either with connectedness or extreme compression of information. According to the microtubule model the non-local characteristic of the mind arises from a quantum mechanical behavior of the quasi-crystalline tubule structure. The mind is correlated to a probabilistic wave function directing the assembly mechanics of the microtubules. The assembly of microtubules, however, is well investigated and does not reveal experimentally observable quantum mechanical behavior (Nedelec et al., 1997). Furthermore, the assembly process is confined to the tip of a microtubule and hardly able to account for the integration of consciously experienced information. Nevertheless, the microtubule theory gives an idea how to approach a description of consciousness by molecular biochemistry.

Laws of thought and topology of the mind: Semantics for a description of consciousness

The examples discussed in the previous sections have demonstrated that it is unlikely to find an explanation for the generation of consciousness by the discovery of a new molecule or brain structure. It is rather a new concept of molecular interaction which may provide a scientific basis for the investigation of consciousness. Molecular interaction in general is mechanistic, regardless whether classical or quantum-mechanical. Recently, a critical analysis of physical concepts presumably involved in the generation of consciousness has ruled out any preference for classical (particle like) or quantum (wave like) mechanics (Ludwig, 1995). This is consistent with the present analysis which will attempt to integrate both concepts into a single model. Any mechanistic approach to explain the generation of consciousness, however, has first to cope with the critical discussion of a mechanistic description of the human mind by Robert Rosen (Rosen, 1993). A putative algorithm underlying a certain mind mechanics will always develop from discrete cause-effect transitions. Our mind, however, is able to think of paradoxical situations in which a given physical state is undone by the simultaneous conception of a contradictory state. The mind is self-referential. The scientific value of these paradoxes is still matter of an ongoing discussion which is beyond the scope of this study. Eventually, it will probably melt down to an argument about the validity of Goedel's incompleteness theorem for an algorithmic description of the human mind. We may conclude from these discussions that new clues for a description of the human mind are rather expected from mathematics than from neuroscience. Unfortunately, theoretical mathematics is just not the forte of most neurochemists. Admittantly, I will myself not exclude from this group. The least effort, however, a neurochemist may attempt is to render the subject of her/his research experimentally accessible. Experimental investigation requires measurement of parameters in space and time. A description of the entities: "world" and "self" thus necessitates the definition of representative parameters with a specific spatio-temporal topology (see also Bounias and Bonaly, 1997):

1) The "self" is defined as the inner observer aware of the consciously experienced "world". The "self" itself is experienced as irreducible or non-deconstructable unity. It will be represented as topological group with one element "S" distributed onto the consciously experienced inner space "X".

2) The "world" is defined as all the objects, sensations, and emotions the "self" is aware of. These entities are distinct and reducible, or even denumerable. They form a topological group with elements "Ni" distributed onto the experienced inner space "X".

From these definitions the topological "whole-part dilemma" of an atomistic description of consciousness becomes clear: any product group "S x Ni" renders either "S" reducible onto a single and distinct "Ni" or all "Ni" irreducible and thus indistinguishable. In other words: the topological group "S x Ni" cannot be consistently described by the left distributive law "S x (Nm + Nn) = S x Nm + S x Nn". The dilemma arises from a treatment of the inner space "X" according to the Cartesian principles of the space in which we investigate neuronal structure. This space can be disjoint by dissection and thus elements in it reduced onto subspaces. In brief, most neuroscientists treat the cortex like the retina. A perceived pixel of information is assumed to be correlated with a structural pixel somewhere in the brain. This holds true for the projection of the outer world onto the retina in the beholder's physical eye, but is wrong for the projection of the inner world onto the beholder's mind's eye.

The self and the neuron: Current concepts for a substrate of the mind

Several models have been proposed presenting a mechanism by which consciousness may be generated as a result of brain function. I will not discuss mechanisms explaining only neuronal computation. The processing of transduced and computed neuronal signals will only be examplified if taking into consideration the generation of conscious experience. The current approaches will be characterized by the definition of a "representation group". The mind consciously experiences a visual world as being composed of particle-like and denumerable structural elements undergoing motion operation by changing shape or position. The visual inner world is thus a classical representation group of point elements in a Cartesian space. This world inevitably includes the topology of neuronal elements and signal processing in the brain since these elements are perceived by an inner observer while being investigated. The experimentally accessible representation group is thus consistent with that of the neuron. The inner observer or the "self", however, is more difficult to define as a representation group. Recently, T.E. Feinberg has put it in a very clear way: "...neural states are spatio-temporally distributed when observed from the outside, while mental states are unified when experienced from the inside ... (Feinberg, 1997). The "self" is experienced as perpetual and irreducible pseudo-particulate element. The definition of the space in which the "self" is located is unclear and may be not at all similar to that of the neuron (McGinn, 1995). It is obvious, however, that there is a product space with that of the neuron in which the "self" experiences the world.

As can be seen from these basic considerations, the problem with explanation of consciousness involves much more mathematics than neurobiology. A simple representation group for the "self" should be irreducible and topologically invariant by division into subgroups, but more than one-dimensional in order to allow a correlation to a topological space filled by the neuronal substrate. Such a group can be figurized as invariant triangular module in a two-dimensional space or may be represented by a non-factorizable polynomal function. (Alexandroff, 1961; Burrow, 1965; Dixon, 1973). In practice, irreducible reprentations will be encountered by vibrational and electronic wavefunctions which makes the concept of fields attractive for description of the self (Bishop, 1973). The bottom line is that a representation group for the "self" will define a topological operation on a space-filling but irreducible or even non-decomposable entity. The following description summarizes briefly different models for representation groups of the self and their correlation with a neurophysiological substrate:

1) The representation of a non-localized self is derived from a construction path with signal integration by wave like superposition of internal states in a Cartesian space (Clarke, 1995; Globus, 1995; Stapp, 1995). Field models describe the self as mental force field (e.g., electromagnetic) or holographic construct (holographic paradigm) interacting with a neuronal substrate (Libet, 1994, 1996; Lindahl and Arhem, 1994,1996; Popper et al., 1993; Pribram, 1981,1982; Psaltis et al., 1990). A probabilistic field-interaction is suggested for models of the self based on quantum coherence of single molecular states (Arhem, 1996). The wave function describes either the probability for synaptic transmitter release or ion channel opening (microsite or Beck-Eccles model) or the assembly or interaction mechanics of molecular ensembles or macromolecules (Jibu-Hameroff-Penrose model or molecular automaton theory) (Beck and Eccles, 1992; Conrad and Liberman, 1982; Eccles, 1986, 1992; Hameroff and Penrose, 1996; Jibu et al., 1994; Liberman et al., 1989; Liberman and Minima, 1995).

2) The representation of a localized self is derived from a construction path with signal integration by superposition of internal states onto a particle like structure. Valuable contributions for a description of the self have been provided by molecular automaton theory, in particular the microsite ion channel model (Arhem, 1996).

A brief look at the list above reveals that non-localized, quantum-mechanical models are preferred in current publications. This apparently arises from the ability of quantum-mechanics to determine the evolution of a system as a whole by encoding the present state in each part of it (Ludwig, 1995; Stapp, 1995). The dilemma of a quantum-mechanical system is that it only works non-locally as long as the system does not come to a decision by collapse of the wave function or decoherence. Perceptions in our mind, however, are decisions on spatiotemporal neural states. Accordingly, any representation group of the neuron is strictly classical. We will again encounter the previously discussed inconsistency arising from an irreducible mental state, this time described by a coherent quantum-mechanical operation, and its attempted correlation with a reducible neural state. The holistic character of a quantum-mechanical system, however, may be utilized by a combination with a model which allows a temporary collapse without losing the integrity of the system. In this regard, a novel approach by fractal representation of the self may provide a solution for an entanglement of classical and quantum-mechanical holistic behavior (Bieberich, 1998).

A fractal or self-similar structure contains the construction principle of the whole in each part. A fractal representation is thus irreducible by division into subgroups. Any path mapping the self onto subspaces inevitably entails a correlation to a proportionally downscaled whole. Nevertheless, the construction principle of a fractal follows an iterative mapping operation on its distinct elements. Thereby, a fractal construction maintains a particular correlation between size and number of its elements which is given by a power law equivalent to the fractal dimension (Peitgen et al., 1992; Schroeder, 1991). The construction principle and the path is directed by intrinsic properties of the neuronal substrate which renders the fractal non-local and self-referential (Dubois, 1997). The neuronal substrate in which the fractal is imprinted may be given by any cooperative or coherent molecular ensemble or lattice, and may also involve quantum coherent states. Fractal behavior has been described for neuronal morphology, the opening characteristic of membrane bound ion channel proteins, the internal structure of the cytoplasm, the assembly of macromolecules, and the quantal rate of neurotransmitter release (Aon and Cortassa, 1994; Liebovitch and Toth, 1990; Lowen et al., 1997; Rabouille et al., 1992; Takeda et al., 1992). As discussed in the following section, the most likely substrate for a fractal organization is given by the molecular composition of the neuronal cell membrane, in particular its lipid components. Membrane lipids form extended quasi-crystalline lattices at body temperature, their spatial distribution and orientation is sensitive towards ion fluxes, and they modulate the conformation of ion channel proteins. Superposition of laterally transduced electrical currents may generate a fractal or multi-fractal structure throughout the entire neuronal cell membrane. Regardless, however, where a fractal is realized, it is its topology coping with the whole-part dilemma that makes this concept attractive (Bieberich, 1998).

The mind in a test tube: Experimental analysis by topological neurochemistry

A potential candidate for a neurophysiological substrate of the mind should provide a sufficient degree of structural organization in order to allow the representation of a variety of consciously experienced situations. Macromolecular structures like microtubules or patches and components of the cell membrane may have this level of organization. The brain was suggested to be a "quantum inflated" system (Stapp, 1995). Unfortunately, the brain is certainly rather a heat-inflated organ which naturally interferes with a potential quantum character. There are, however, particular neuronal elements which show exceptional structural properties just at the body temperature of 37 C. Certain lipid components of the cell membrane undergo transition from a solid to a liquid crystalline appearance at this temperature (Becker and Rahmann, 1995; Perillo et al., 1994). This molecular interaction is cooperative in an ensemble of lipid molecules and results in a coherent orientation around ion channel proteins. It has been shown that the coherence length is maximal at a narrow range around body temperature (Sperotto and Mouritson; 1991). Quantum bulk computation by coherent arrays of membrane lipids may thus form an alternative (or supplementation) to the microtubule automaton for the generation of consciousness.

However, for any potential macromolecular representation it has to be experimentally demonstrated that a particular structural organization or topology actually results in the generation of consciousness. This can only be achieved by analyzing a neuronal system that is under influence of signal transduction and remains at least partially intact when experimentally investigated. At present, the most promising methods for investigation are the multi-electrode patch-clamping technique or the biochip or hybrid-element method with isolated neuronal cells or cell clusters attached to a semiconducting support (Fromherz et al., 1991; Jimbo et al., 1993; Neher and Sakman, 1976; Tononi and Edelman, 1998). This experimental set-up allows monitoring of the activity of macromolecular structures (e.g., microtubules, ion channels, membrane patches) in dependence of a spatio-temporally varied signal currents. If the macromolecular topology is not directly observable it may be possible to conclude indirectly from the output current on the structural organization. This assumption is based on the consideration that the overall behavior of the macromolecular system is decided by an intrinsic property which usually partakes in the generation of consciousness. This property is correlated with a microevent in conscious perception which may be active even without the presence of an inner observer. It is very likely that this microevent acts as processing interface between input and output signals somewhere on the neuron. A conscious microevent causally affecting the spatiotemporal processing of input-signals would then be recognized as a selective filter for the generation of specific output signals. Feedback-coupling of output to input currents and re-entry signaling may constitute a device which reveals harmonic or disharmonic oscillator characteristics just for attractive or repulsive internal decision situations (Bieberich, 1998; Sporns et al., 1989). The harmonic resonance characteristics is suggested from the assumption that an attractor tends to stabilize itself by minimizing the net flux (energy loss) of the resonant system (Flanigan, 1972). The computational process will very likely involve the dendritic tree and trunk of neuronal cells (Orpwood, 1994). Signal summation in the dendritic membrane is suggested to generate a pass-filter for percolation and transduction of action potentials (Chen et al., 1997; Segev, 1998; Stuart et al., 1997).

From these observations and assumptions it is concluded that a neuronal, hybrid, or electronic device for generation and investigation of consciousness must have the following characteristics:

1) Single computational elements form a dendritic network with re-entry signaling. This is necessary in order to distribute and integrate a population of spatio-temporally distinct signal potentials. Furthermore, dendritic networks reveal an intrinsic ability to generate fractally organized signal patterns (Bieberich, 1998).

2) The computational element contains a macromolecular lattice that can be affected by action-potentials or signal currents. This is the most difficult technical part for construction of a conscious device. Most likely, a prototype can be realized by neuron-silicon junction or by use of parts of the cell (e.g., a patch-clamped membrane) in a neuronal switch (Bieberich, 1998, Fromherz et al., 1991, Jimbo, 1993). Coating of semiconductor elements with a reconstituted cell membrane may be another way to construct a bio-electronic transistor. Field-effect transistors have been reported to reveal fractal behavior and the coating technology is already in use for the production of biosensors (Fromhold, 1997).

3) The internal topology of the computational event can be neurochemically or neurophysiologically analyzed and modulated. A particular oscillation or resonance frequency of input to reentrant output signals in a bio-electronic element that is under influence of drugs known to produce or modulate sensations (e.g., anaesthetics) may reveal a conscious decision process in the computational device (Bieberich, 1998; Tennigkeit et al., 1997). The electrophysiological characteristics of the neuron-silicon junction may be specifically altered by supplementation with receptor proteins involved in emotional response (e.g., serotonin receptor).

Conclusive remarks

Topological neurochemistry is a new discipline of neuroscience which attempts to devolop concepts for a topology of human consciousness and its correlation with neuronal activity. These concepts are based on the assumption that a particular molecular interaction forms the interface between consciousness and neurochemical reaction. A novel mathematical analysis has to develop a logic or "topologic" which inevitably entails the emergence of consciousness from molecular interaction. Quantum mechanical or fractal approaches are first steps in this direction. The respective neurochemistry is already available and after having developed the theoretical concepts it may take less than a decade that first prototypes of conscious computational elements will be constructed. Their application may not only promote the investigation of consciousness but also found the basis for its artificial creation in a computer-like device. It is necessary that we accept consciousness as a characteristic of specialized living matter. Consciousness is physical after all and just appropriately unfolded by the particular organization of matter in our brain. Topological neurochemistry will contribute to the investigation of this organization.


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