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Cellular computing

Cellular computing and information processing in microtubules and cytoskeleton

Many years ago (1990-92) I was a post-doctoral fellow working with Stuart Hameroff at the University of Arizona (Tucson, USA). According to Hameroff microtubules and cytoskeleton are subneural components that could be the basic units of information processing rather than the neurons themselves [7]. Furthermore, they could be responsible for consciousness. Adaptive behaviors and dynamic activities within living cells are organized by the cytoskeleton: intracellular networks of interconnected protein polymers which include microtubules (MTs), actin, intermediate filaments, microtubule associated proteins (MAPs) and other protein structures. Cooperative interactions among cytoskeletal protein subunit conformational states have been used to model using cellular automata, signal transmission and information processing. I participated of severeal research projects based on cellular automata. Cellular automata may be implemented in the conformational relationships among neighboring protein subunits of cytoskeletal polymers including microtubules, and microtubule conformational automata networks may signal, adapt, recognize, and subserve neural-level learning. The potential capacity of information processing in microtubules and cytoskeleton was studied in the context of molecular computing [4].  

Top photo (1991. From left to right) .- Djuro Koruga, me, Alexei Samsonovich and Stuart Hameroff. Microtubule transition rule and tubulin subunits with hexagonal neighborhood. Conway's Game of Life automata patterns in microtubules.

Bottom caption
.- First  issue of Nanobiology journal.  

We related the above model with neural networks in the context of currently recognized cellular structures within neurons. Neural network models and paradigms require adaptation of synapses for learning to occur in the network. Some models of learning paradigms require information to move from axon to dendrite. This motivated us to examine the possibility of intracellular signaling to mediate such signals. The cytoskeleton forms a substrate for intracellular signaling via material transport and other putative mechanisms. Furthermore, many experimental results suggest a link between the cytoskeleton and cognitive processing. In these papers [5, 6, 9] we review research on intracellular signaling in the context of neural network learning. The work justifies a possible role of microtubules in the learning rule back-propagation, and thus the possibility that this rule take place in biological neurons. This work was conducted in collaboration with J.E. Dayhoff (Margaret O. Dayhoff's daughter, pioneer in the field of bioinformatics).

Also we conducted a theoretical model [8] for molecular computing in which Boolean logic was implemented in parallel networks of individual MTs interconnected by MAPs. Conformational signals propagate on MTs as in data buses and in the model MAPs are considered as Boolean operators, either as bit-lines (like MTs) where a signal can be transported unchanged between MTs (‘BUS-MAP’), or as bit-lines where a Boolean operation is performed in one of the two MAP-MT attachments (‘LOGIC-MAP’). Three logic MAPs have been defined (‘NOT-MAP’, ‘AND-MAP’, ‘XOR-MAP’) and used to demonstrate addition, subtraction and other arithmetic operations. Although our choice of Boolean logic is arbitrary, the simulations demonstrated symbolic manipulation in a connectionist system and suggest that MT-MAP networks can perform computation in living cells and are candidates for future molecular computing devices.

A possible impact of the Hameroff's theories was published in 1993 in two chapters [6, 7] of the book Rethinking Neural Networks: Quantum Fields and Biological Data (Eds. K.H. Pribram y Sir J. Eccles).

Modeling and simulation of quantum coherent superposition and decoherence in cytoskeletal microtubules

Although experimental evidence suggests the influence of quantum effects in living organisms, one of the most critical problems in quantum biology is the explanation of how those effects that take place in a microscopic level can manifest in the macroscopic world of living beings. At present, quantum decoherence associated with the wave function collapse is one of the most accepted mechanisms explaining how the classical world of living beings emerges from the quantum world. Whatever is  the cause of wave function collapses, there exist biological systems where a biological function arises as a result of this collapse (e.g. birds navigation, plants photosynthesis, sense of smell, etc.), as well as the opposite examples (e.g. release of energy from ATP molecules at actomyosin muscle) where a biological function takes place in a quantum coherent environment. In this paper [27] we report the modelling and simulation of quantum coherent superposition in cytoskeletal microtubules including decoherence, thus the effect of the collapse of the microtubule coherent state wave function. Our model is based on a new class of hybrid cellular automata (QvN), capable of performing as either a quantum cellular automata (QCA) or as a classical von Neumann automata (CA). These automata are able to simulate the transition or reduction from a quantum microscopic level with superposition of several quantum states, to a macroscopic level with a single stable state. Our results illustrate the significance of quantum biology explaining the emergence of some biological functions. We believe that in the future quantum biology will have a deep effect on the design of new devices, e.g. quantum hardware, in electrical engineering.

Even when Nanobiology disappeared long ago, it was a very exciting journal. In 1992 we published a paper [3] (vol. 1(1): 61-74) with Steen Rasmussen (at that time he was working in Los Alamos National Laboratory) describing the results of laboratory experiments in combination with a simulation model. This paper described my 'first simulation model and it has a sentimental value. The laboratory experiment was conducted by Hirokazu Hotani in Japan (ERATO Molecular Dynamic Assembly, Kyoto), consisting in the assembly of liposomes or artificial cells. Liposomes contained inside tubulin subunits, which assembly into a microtubule pressed inside the liposome membrane, changing the liposome shape. It was an example of artificial morphogenesis. The results were compared with the cellular automata simulation model of microtubule assemby/disassembly.

It was a good time, not only because we were young, but by the lively atmosphere and intellectually exciting environment  in Tucson with Stuart Hameroff.

From cytoskeleton to neural networks

The study of neuronal cytoskeleton led us to study how neurons modulate the strength of the synapse [10]. Using the neural network of Aplysia we constructed an artificial neural network [11] in which the weight of the connections between neurons was obtained from numerous molecular and cellular mechanisms.

One more step: Bacterial computing

The capability to establish adaptive relationships with the environment is an essential characteristic of living cells. Both bacterial computing [26] and bacterial intelligence [15]  are two general traits manifested along adaptive behaviors that respond to surrounding environmental conditions. These two traits have generated a variety of theoretical and applied approaches. Since the different systems of bacterial signaling and the different ways of genetic change are better known and more carefully explored, the whole adaptive possibilities of bacteria may be studied under new angles. For instance, there appear instances of molecular “learning” along the mechanisms of evolution. More in concrete, and looking specifically at the time dimension, the bacterial mechanisms of learning and evolution appear as two different and related mechanisms for adaptation to the environment; in somatic time the former and in evolutionary time the latter. In this paper [26]  we reviewed the possible application of both kinds of mechanisms to prokaryotic molecular computing [23] schemes as well as to the solution of real world problems [25].

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