Analysis of attractor distances in Random Boolean Networks

We study the properties of the distance between attractors in Random Boolean Networks, a prominent model of genetic regulatory networks. We define three distance measures, upon which attractor distance matrices are constructed and their main statistic parameters are computed. The experimental analysis shows that ordered networks have a very clustered set of attractors, while chaotic networks' attractors are scattered; critical networks show, instead, a pattern with characteristics of both ordered and chaotic networks.Comment: 9 pages, 6 figures. Presented at WIRN 2010 - Italian workshop on neural networks, May 2010. To appear in a volume published by IOS Pres

Neural network computation by in vitro transcriptional circuits

The structural similarity of neural networks and genetic regulatory networks to digital circuits, and hence to each other, was noted from the very beginning of their study [1, 2]. In this work, we propose a simple biochemical system whose architecture mimics that of genetic regulation and whose components allow for in vitro implementation of arbitrary circuits. We use only two enzymes in addition to DNA and RNA molecules: RNA polymerase (RNAP) and ribonuclease (RNase). We develop a rate equation for in vitro transcriptional networks, and derive a correspondence with general neural network rate equations [3]. As proof-of-principle demonstrations, an associative memory task and a feedforward network computation are shown by simulation. A difference between the neural network and biochemical models is also highlighted: global coupling of rate equations through enzyme saturation can lead to global feedback regulation, thus allowing a simple network without explicit mutual inhibition to perform the winner-take-all computation. Thus, the full complexity of the cell is not necessary for biochemical computation: a wide range of functional behaviors can be achieved with a small set of biochemical components

Attraction Basins as Gauges of Robustness against Boundary Conditions in Biological Complex Systems

One fundamental concept in the context of biological systems on which researches have flourished in the past decade is that of the apparent robustness of these systems, i.e., their ability to resist to perturbations or constraints induced by external or boundary elements such as electromagnetic fields acting on neural networks, micro-RNAs acting on genetic networks and even hormone flows acting both on neural and genetic networks. Recent studies have shown the importance of addressing the question of the environmental robustness of biological networks such as neural and genetic networks. In some cases, external regulatory elements can be given a relevant formal representation by assimilating them to or modeling them by boundary conditions. This article presents a generic mathematical approach to understand the influence of boundary elements on the dynamics of regulation networks, considering their attraction basins as gauges of their robustness. The application of this method on a real genetic regulation network will point out a mathematical explanation of a biological phenomenon which has only been observed experimentally until now, namely the necessity of the presence of gibberellin for the flower of the plant Arabidopsis thaliana to develop normally

Quantum Genetics, Quantum Automata and Quantum Computation

The concepts of quantum automata and quantum computation are studied in the context of quantum genetics and genetic networks with nonlinear dynamics. In a previous publication (Baianu,1971a) the formal concept of quantum automaton was introduced and its possible implications for genetic and metabolic activities in living cells and organisms were considered. This was followed by a report on quantum and abstract, symbolic computation based on the theory of categories, functors and natural transformations (Baianu,1971b). The notions of topological semigroup, quantum automaton,or quantum computer, were then suggested with a view to their potential applications to the analogous simulation of biological systems, and especially genetic activities and nonlinear dynamics in genetic networks. Further, detailed studies of nonlinear dynamics in genetic networks were carried out in categories of n-valued, Lukasiewicz Logic Algebras that showed significant dissimilarities (Baianu, 1977) from Bolean models of human neural networks (McCullough and Pitts,1945). Molecular models in terms of categories, functors and natural transformations were then formulated for uni-molecular chemical transformations, multi-molecular chemical and biochemical transformations (Baianu, 1983,2004a). Previous applications of computer modeling, classical automata theory, and relational biology to molecular biology, oncogenesis and medicine were extensively reviewed and several important conclusions were reached regarding both the potential and limitations of the computation-assisted modeling of biological systems, and especially complex organisms such as Homo sapiens sapiens(Baianu,1987). Novel approaches to solving the realization problems of Relational Biology models in Complex System Biology are introduced in terms of natural transformations between functors of such molecular categories. Several applications of such natural transformations of functors were then presented to protein biosynthesis, embryogenesis and nuclear transplant experiments. Other possible realizations in Molecular Biology and Relational Biology of Organisms are here suggested in terms of quantum automata models of Quantum Genetics and Interactomics. Future developments of this novel approach are likely to also include: Fuzzy Relations in Biology and Epigenomics, Relational Biology modeling of Complex Immunological and Hormonal regulatory systems, n-categories and Topoi of Lukasiewicz Logic Algebras and Intuitionistic Logic (Heyting) Algebras for modeling nonlinear dynamics and cognitive processes in complex neural networks that are present in the human brain, as well as stochastic modeling of genetic networks in Lukasiewicz Logic Algebras

Effect of noise in intelligent cellular decision making

Similar to intelligent multicellular neural networks controlling human brains, even single cells surprisingly are able to make intelligent decisions to classify several external stimuli or to associate them. This happens because of the fact that gene regulatory networks can perform as perceptrons, simple intelligent schemes known from studies on Artificial Intelligence. We study the role of genetic noise in intelligent decision making at the genetic level and show that noise can play a constructive role helping cells to make a proper decision. We show this using the example of a simple genetic classifier able to classify two external stimuli

The evolutionary origins of hierarchy

Hierarchical organization -- the recursive composition of sub-modules -- is ubiquitous in biological networks, including neural, metabolic, ecological, and genetic regulatory networks, and in human-made systems, such as large organizations and the Internet. To date, most research on hierarchy in networks has been limited to quantifying this property. However, an open, important question in evolutionary biology is why hierarchical organization evolves in the first place. It has recently been shown that modularity evolves because of the presence of a cost for network connections. Here we investigate whether such connection costs also tend to cause a hierarchical organization of such modules. In computational simulations, we find that networks without a connection cost do not evolve to be hierarchical, even when the task has a hierarchical structure. However, with a connection cost, networks evolve to be both modular and hierarchical, and these networks exhibit higher overall performance and evolvability (i.e. faster adaptation to new environments). Additional analyses confirm that hierarchy independently improves adaptability after controlling for modularity. Overall, our results suggest that the same force--the cost of connections--promotes the evolution of both hierarchy and modularity, and that these properties are important drivers of network performance and adaptability. In addition to shedding light on the emergence of hierarchy across the many domains in which it appears, these findings will also accelerate future research into evolving more complex, intelligent computational brains in the fields of artificial intelligence and robotics.Comment: 32 page

The Age of Analog Networks

A large class of systems of biological and technological relevance can be described as analog networks, that is, collections of dynamical devices interconnected by links of varying strength. Some examples of analog networks are genetic regulatory networks, metabolic networks, neural networks, analog electronic circuits, and control systems. Analog networks are typically complex systems which include nonlinear feedback loops and possess temporal dynamics at different timescales. When tackled by a human expert both the synthesis and reverse engineering of analog networks are recognized as knowledge-intensive activities, for which few systematic techniques exist. In this paper we will discuss the general relevance of the analog network concept and describe an evolutionary approach to the automatic synthesis and reverse engineering of analog networks. The proposed approach is called analog genetic encoding (AGE) and realizes an implicit genetic encoding of analog networks. AGE permits the evolution of human-competitive solutions to real-world analog network design and identification problems. This is illustrated by some examples of application to the design of electronic circuits, control systems, learning neural architectures, and to the reverse engineering of biological networks

Neuroevolution with Analog Genetic Encoding

The evolution of artificial neural networks (ANNs) is often used to tackle difficult control problems. There are different approaches to the encoding of neural networks in artificial genomes. Analog Genetic Encoding (AGE) is a new implicit method derived from the observation of biological genetic regulatory networks. This paper shows how AGE can be used to simultaneously evolve the topology and the weights of ANNs for complex control systems. AGE is applied to a standard benchmark problem and we show that its performance is equivalent or superior to some of the most powerful algorithms for neuroevolution in the literature

Fitting Physical Models to Spatiotemporal Observations: Discovering Developmental Regulatory Networks of Drosophila

Deep learning continues to solve significant scientific and engineering problems, but the solutions found are neural networks with thousands of parameters that provide no scientific or engineering insights. A solution to this problem, explored in this work, is to learn mathematical models that represent mechanisms that can be interpreted by scientists and engineers. A challenging learning problem is to discover the genetic regulatory mechanisms that drive pattern formation during early biological development. Using known mathematical models of these processes, consisting of coupled ordinary differential and partial differential equations, we aim to identify the model parameters that describe the biological mechanisms at play. To guide learning, we use raw gene expression data sampled from the model organism Drosophila melanogaster, a fruit fly, which is normalized through a series of processing steps before learning. Our learning method applies the powerful techniques of algorithmic differentiation and gradient descent that underlie deep-learning advances. The results of this study reveal multiple genetic regulatory solutions capable of producing genetic expression patterns that match those observed in the fruit fly embryo. Cluster analysis of these solutions identifies a set of discrete genetic regulatory networks that more closely match those that function in the actual embryo

Analog Genetic Encoding for the Evolution of Circuits and Networks

This paper describes a new kind of genetic representation called analog genetic encoding (AGE). The representation is aimed at the evolutionary synthesis and reverse engineering of circuits and networks such as analog electronic circuits, neural networks, and genetic regulatory networks. AGE permits the simultaneous evolution of the topology and sizing of the networks. The establishment of the links between the devices that form the network is based on an implicit definition of the interaction between different parts of the genome. This reduces the amount of information that must be carried by the genome relatively to a direct encoding of the links. The application of AGE is illustrated with examples of analog electronic circuit and neural network synthesis. The performance of the representation and the quality of the results obtained with AGE are compared with those produced by genetic programming