Intraneuronal dynamics as a substrate for evolutionary learning

Kirby, Kevin G.; Conrad, Michael

doi:10.1016/0167-2789(86)90241-1

Cited by 32 publications

(9 citation statements)

References 8 publications

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“…(i) Although we exclusively study transport, our model can serve as a platform for reaction-diffusion-based biocomputing devices [4,5,6,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34]. In particular, our work is applicable to studies of the reaction-diffusion neuron [28,29,30,31,32,33,34].…”

Section: Discussionmentioning

confidence: 99%

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Diffusive transport in networks built of containers and tubes

Lizana

Konkoli

2005

Phys. Rev. E

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We developed analytical and numerical methods to study a transport of non-interacting particles in large networks consisting of M d-dimensional containers C1, . . . , CM with radii Ri linked together by tubes of length lij and radii aij where i, j = 1, 2, . . . , M . Tubes may join directly with each other forming junctions. It is possible that some links are absent. Instead of solving the diffusion equation for the full problem we formulated an approach that is computationally more efficient. We derived a set of rate equations that govern the time dependence of the number of particles in each container N1(t), N2(t), . . . , NM (t). In such a way the complicated transport problem is reduced to a set of M first order integro-differential equations in time, which can be solved efficiently by the algorithm presented here. The workings of the method have been demonstrated on a couple of examples: networks involving three, four and seven containers, and one network with a three-point junction. Already simple networks with relatively few containers exhibit interesting transport behavior. For example, we showed that it is possible to adjust the geometry of the networks so that the particle concentration varies in time in a wave-like manner. Such behavior deviates from simple exponential growth and decay occurring in the two container system.

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Section: Discussionmentioning

confidence: 99%

“…In particular, our work is applicable to studies of the reaction-diffusion neuron [28,29,30,31,32,33,34]. The reaction-diffusion neuron is an 2D array of compartments that exchange chemicals by diffusion.…”

Section: Discussionmentioning

confidence: 99%

Diffusive transport in networks built of containers and tubes

Lizana

Konkoli

2005

Phys. Rev. E

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“…And just as Leibniz's panpsychism did not lead him to deny the importance of physics, our pan-computationalism (still of the metaphorical variety) does not mean there is no role for matter in computation. Indeed the physical substrate in natural computing is crucial (Kirby and Conrad, 1986), and there is a complementarity between Turing's tape-based state machine and his morphogenesis model. Exploration of the latter continues (see e.g.…”

Section: The Great Chains Of Computingmentioning

confidence: 99%

The Great Chains of Computing: Informatics at Multiple Scales

Kirby

Walden

Garns

et al. 2011

tripleC

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“…The setup of the reaction schemes is inspired by the work done on prebiotic evolution, genome-based evolution and random reaction networks [27,28,29,30,31,32,33,34], and diffusioncontrolled reactions in bulk phase [35,36,37,38,39,40] and in restricted geometries [41,42,43,44]. The geometrical setup of the model is motivated by the experimental studies given in [20,21,22,23,24,25,26] and theoretical study of reaction-diffusion neuron and enzymatic neuron [45,46,47,48,49,50,51].…”

Section: Introductionmentioning

confidence: 99%

“…For example, when there is a need for that, one can use a method described in refs. [45,46,47,48,49,50,51]. This optimization method mimics process of evolution and belongs to the class of genetic optimization algorithms.…”

Section: Introductionmentioning

confidence: 99%

Interplay between chemical reactions and transport in structured spaces

Konkoli

2005

Phys. Rev. E

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There are many instances in nature where geometry of the system that sustains chemical reactions is structured and the living cell is a typical example. There is a high degree of compartmentalization in the living cell where various compartments sustain different chemical reactions and transport reactants among themselves. In order to avoid storage facilities reactants are routed in orderly fashion between various places in the cell interior with large degree of synchronization. It is exactly such situation that is investigated here. The main motivation behind this study is to understand interplay between reactions and transport in a geometries that are not compact. Typical examples of compact geometries are box, sphere, etc. On the other hand, a network made of containers C1, C2, . . . , CN and tubes is a typical example of space that is structured, and such non compact space is main focus on this study. The whole space is divided into a two regions. First, in containers particles react with rate λ. Second, tubes connecting containers allow for exchange of chemicals with transport rate D. In such a way the two most important processes are isolated in the problem, reactions and transport. By varying topology of such network and details of chemical reactions it is possible to gain some understanding of interplay between chemical reactions and transport in structured spaces. It assumed that the number of reactants in the system is so small that kinetics is noise dominated. Two methods for solving corresponding master equation are discussed. The computer simulation is easy to implement, but leads to the results that are not that accurate. In here, a method is presented that can be used to calculate average, variance, and higher moments of the time reaction needs to finish. The method relies on a matrix representation of the master equation and is in principle exact. It works for an arbitrary reaction scheme and network topology. A number of different chemical reactions were studied and their performance compared in a various ways. Reactions are grouped into two ensembles, Reaction on a Fixed Geometry Ensemble (ROGE) and Geometry on a Fixed Reaction Ensemble (GORE). The ROGE and GORE are used to classify reactions in order to gain some understanding of which types of chemical reactions draw most benefit from the structured spaces. Most important findings are as follows. (i) There is a large number of reactions that run faster in a network like geometry. Such reactions contain antagonistic catalytic influences in the intermediate stages of a reaction scheme that is best dealt with in a network like structure. (ii) Antagonistic catalytic influences are hard to identify since they are strongly connected to the pattern of injected molecules (inject pattern) and depend on the choice of molecules that have to be synthesized at the end (task pattern). (iii) The reaction time depends strongly on the details of the inject and task patterns.

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Intraneuronal dynamics as a substrate for evolutionary learning

Cited by 32 publications

References 8 publications

Diffusive transport in networks built of containers and tubes

Diffusive transport in networks built of containers and tubes

The Great Chains of Computing: Informatics at Multiple Scales

Interplay between chemical reactions and transport in structured spaces

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