The efficacy of genetic algorithms in the design of models that model specific and experimental aspects of action potentials in a wide variety of organisms is proven. A specific example of a plant action potential is used to illustrate the use of genetic algorithms in the search for parameters of models. The efficiency of the genetic algorithms as a search method is in the short generation span of the convergence of the algorithm.
We use the genesis simulator to simulate a single compartmental model of a plant cell. The plant cell has a delayed rectification K channel, a Ca channel and a Ca dependent Cl channel. We have omitted the H+ ATPase pump from the model. The depolarization is by the release of Ca from stores and due to a Ca channel and due to the chloride channel that depends on Calcium. There is an IP3 mediated calcium release mechanism which we have simplified in a model of calcium concentration that decays exponentially with time. The genesis package comes inbuilt with search algorithms that include the genetic algorithm. We use this to run a simulation to search for many parameters including the gbar for the chloride and calcium channels and the time constant and middle point of the potassium channel parameters, Ninf and tauN. The simulations have a time step of 20 micro seconds and are responses of the single compartmental model to current injections of .1 nanoampere to 1.0 nano ampere.
Table of Contents
1. Introduction
2. Genetic algorithms
2.1 A simple genetic algorithm
2.2 The simple operator definitions.
2.3 How do genetic algorithms work?
2.4 Limitations of "static" schema analysis
2.5 Iterated hill climbing techniques
2.5.1 a. Steepest ascent hill climbing(SAHC)
2.5.2 b. Next-ascent hill climbing(NAHC)
2.5.3 c. Random-mutation hill climbing(RMHC)
2.6 Genetic algorithms: Implementation issues.
2.7 Encoding the problem for a genetic algorithm.
2.7.1 Binary encodings
2.7.2 Tree encodings
2.8 Adapting the encoding
2.9 Selection methods
2.9.1 Fitness-Proportionate selection with "Roulette Wheel" and "Stochastic Universal" sampling.
2.9.2 Sigma scaling:
2.9.3 Elitism
2.9.4 Boltzman selection.
2.9.5 Rank selection
2.9.6 Tournament Selection
2.9.7 Steady-State selection
2.10 Genetic Operators
2.11 Parameters for genetic algorithms.
3. Ionic channels
4. Equilibrium potentials.
5. The Hodgkin-Huxley (HH) model
6. The Fitzhug-Nagama model
7. Morris-Lecar model
8. Hindmarsh-Rose model
9. There is a vast diversity of potassium channels.
9.1 Delayed rectifiers keep action potentials short(Hille B. 1984)
9.2 Transient outward currents space repetitive responses(Hille B,1984)
9.3 Ca-dependant K currents make long hyperpolarizing pauses(Hille. B.1984)
9.4 Outward-rectifying
9.5 Inward rectifiers permit long depolarization’s responses(Hille. B. 1984)
9.6 Slowly activating
9.7 Modifier/silencer
10. Plant action potentials.
11. Models of plant neurobiology.
12. Newer approaches:(Beilby M J )
13. The fitness function.(Vainer and Bower 1999)
Research Objectives and Core Themes
The primary objective of this work is to demonstrate the efficacy of genetic algorithms in automating the parameter search for single compartmental neuronal models, specifically focusing on plant action potentials. It investigates how these evolutionary computational methods can mitigate the laborious nature of manual parameter tuning in complex, nonlinear biological models.
- Optimization of parameter search spaces for neuronal modeling using genetic algorithms.
- Comparative analysis of different selection and operator methods within genetic algorithms.
- Physiological characterization of ionic channels and their role in plant membrane excitability.
- Development and validation of quantitative models for plant neurobiology, specifically addressing the IP3-mediated calcium release mechanism.
Excerpt from the Book
Genetic algorithms
Genetic algorithms is a biomimetic science, its origin comes from a computational study of natural evolution. Much of the terminology is borrowed from the field of genetics. We first introduce some of the terminology. All biological organisms consist of cells, these cells contain DNA or genetic information in one or more chromosomes. These chromosomes consist of genes. Each gene encodes a trait. The different settings for a trait are called 'allels'. Each genome is located at a particular locus or position in the gene. The complete collection of all the genes, that is the chromosomes of an organism is called the genome.
The term genotype refers to a set of genes in the genome. Two organisms with the same genes are said to have the same genotype. The genotype gives rise to the phenotype on development. Organisms whose chromosomes are in pairs are called diploid, a single set of chromosomes is haploid. During sexual reproduction, recombination or crossover of genes occurs to create the gamete. The gametes from the two parents combine to form a diploid offspring chromosome.
In haploid organisms, genes are exchanged from single strands of parent chromosome. The offspring genetic material is subject to random mutations owing to copying errors and other factors. The fitness of an individual organism is the probability the organism will live to reproduce(viability) or as a function of the number of offspring that organism has.(fertility)
In genetic algorithms, a chromosome is usually a bit string and denotes a candidate solution to a problem. An allele is usually a bit one or zero at each locus and in more complicated encodings , it can be more complicated. Cross over consists of exchange of genetic material between two haploid parents and mutation consists of inverting a single bit at some locus. Often there is no phenotype but problems like neural networks have both a phenotype and genotype.
Chapter Summaries
1. Introduction: This chapter defines neuronal modeling as a phenomenological approach and explains the necessity of using automated parameter search algorithms to overcome the difficulties of hand-tuning nonlinear, complex neural models.
2. Genetic algorithms: Provides a comprehensive overview of the mechanisms behind genetic algorithms, including terminology, operator definitions, schema theory, and various selection/encoding strategies applied to search problems.
3. Ionic channels: Details the physiological role of ionic channels as fundamental excitable members of membranes and explains how their gating properties dictate the membrane potential and signaling.
4. Equilibrium potentials: Discusses the diffusion-driven charge transfer leading to resting potentials and introduces the Nernst equation in the context of cell membrane potentials.
5. The Hodgkin-Huxley (HH) model: Describes the classical mathematical framework for modeling membrane conductance and ion kinetics, serving as a foundation for understanding excitability.
6. The Fitzhug-Nagama model: Presents a simplified version of the Hodgkin-Huxley model, explaining action potentials through positive and negative feedback factors.
7. Morris-Lecar model: Illustrates a hybrid model that combines Hodgkin-Huxley and FitzHugh-Nagumo concepts to describe voltage-gated calcium channels and delayed rectifier potassium channels.
8. Hindmarsh-Rose model: Introduces a model of neuronal activity based on three first-order differential equations that can simulate rich dynamical behaviors, including chaos.
9. There is a vast diversity of potassium channels.: Explores the functional variety of potassium channels, categorizing them by their gating behavior and physiological roles in stabilizing or regulating cellular activity.
10. Plant action potentials.: Highlights the electric excitability in plants, distinguishing it from animal systems while noting shared physiological phenomena like rapid membrane potential changes.
11. Models of plant neurobiology.: Adapts nerve-based ion transient equations to describe chloride and calcium transients in plant cells, specifically within the context of charophyte algae.
12. Newer approaches:(Beilby M J ): Reviews recent scientific progress concerning IP3-mediated calcium release and the role of internal stores in plant action potential propagation.
13. The fitness function.(Vainer and Bower 1999): Defines the mathematical criteria used to evaluate the similarity between simulated spike trains and experimental data to measure the performance of candidate solutions.
Key Concepts
Genetic Algorithms, Neuronal Modeling, Ionic Channels, Action Potentials, Fitness Function, Parameter Optimization, Charophyte Algae, IP3 Signaling, Crossover, Mutation, Genotype, Phenotype, Hodgkin-Huxley Model, Compartmental Model, Membrane Excitability.
Frequently Asked Questions
What is the core focus of this research?
The work focuses on utilizing genetic algorithms to automate the search for biological parameters in single-compartment neuronal models, with a specific application to studying action potentials in plant cells.
Which specific model systems are investigated?
The research investigates neuronal models derived from charophyte algae, emphasizing their excitability and the mathematical modeling of their ionic current transients.
What is the primary goal of applying genetic algorithms here?
The goal is to replace the time-consuming and laborious process of manual "hand-tuning" parameters in complex, highly nonlinear neural models with an automated, efficient evolutionary search method.
Which scientific methodology is utilized?
The study employs the GENESIS simulator to run genetic algorithms, testing various population sizes, crossover probabilities, and mutation rates to optimize the match between computed and experimental spike trains.
What topics are covered in the main body of the work?
The main body covers the theoretical foundations of genetic algorithms, detailed physiological descriptions of various ion channels, and the construction of mathematical models to describe action potentials in both neural and plant systems.
What are the characterizing keywords of this study?
The study is characterized by terms such as Genetic Algorithms, Neuronal Modeling, Membrane Excitability, Parameter Optimization, and IP3-mediated Calcium release.
How does the work address the limitations of "static" schema analysis?
The author discusses critique regarding collateral convergence and fitness variance, suggesting that a dynamic approach taking into account selection biases is necessary to accurately assess the behavior of GAs.
What is the significance of the "fitness function" in this study?
The fitness function is crucial as it quantitatively evaluates candidate models by comparing simulated spike trains against experimental data using specific metrics, such as spike timing mismatch and waveform variance.
How is the "linkage problem" related to encoding?
The linkage problem concerns the challenge of determining the optimal order of bits in a chromosome so that co-adapted traits remain together during crossover, which is essential for creating fitter chromosomes.
What is the role of A-type potassium channels mentioned in the study?
A-type channels function as dampers in the interspike interval, activating during repolarization to balance depolarization and delay the firing threshold, thus spacing action potential pulses more effectively.
- Quote paper
- Anil Bheemaiah (Author), 2018, Evolutionary computing in neuronal modeling, Munich, GRIN Verlag, https://www.grin.com/document/387764
