COLLECTIVE DYNAMICS: TOPICS ON COMPETITION AND COOPERATION IN THE BIOSCIENCES: A Selection of Papers in the Proceedings of the BIOCOMP2007 International Conference
1028(2008); http://dx.doi.org/10.1063/1.2965089View Description Hide Description
Brownian motion was recognized as a scientific research object by R. Brown in 1827, and then many scientists studied the motion within science. Two famous mathematicians, N. Wiener and P. Lévy, studied Browniam motion mainly in mathematics. We appreciate their works and would like to note that their results play very important role in the study of biological phenomena.
1028(2008); http://dx.doi.org/10.1063/1.2965081View Description Hide Description
The article focuses on the different conceptual and philosophical approaches towards the sciences of life operating in the backstage of Early Cybernetics. After a short reconstruction of the main steps characterizing the origins of Cybernetics, from 1940 until 1948, the paper examines the complementary conceptual views between Norbert Wiener and John von Neumann, as a “fuzzy thinking” versus a “logical thinking”, and the marked difference between the “methodological individualism” shared by both of them versus the “methodological collectivism” of most of the numerous scientists of life and society attending the Macy Conferences on Cybernetics. The main thesis sustained here is that these different approaches, quite invisible to the participants, were different, maybe even opposite, but they could provoke clashes, as well as cooperate in a synergic way.
1028(2008); http://dx.doi.org/10.1063/1.2965087View Description Hide Description
I have been kindly asked by the organizers of the BIOCOMP2007 conference to provide a short sketch of Charles Darwin's contribution to science, and of the role mathematics has played in his discoveries and in subsequent developments. I felt flattered by the invitation but rather unfit to it, since I have no particular expertise in evolutionary theory, and even less in its history; eventually, I decided to accept the invitation, appreciating the opportunity to read some more about Darwin, and the importance of making his contribution better known, at a time where teaching at school the theory of evolution is coming under attack also in Italy (perhaps under American influence). I hope to be able here to give a glimpse of the history of Darwinian thought, and of some current research areas, that will lead some readers towards further reading. There are many excellent books available now about Darwin and Darwinian theory, and my presentation is based on many of them, listed in the Bibliography; I found especially illuminating the book by Gayon Darwinism's Struggle for Survival, a history of theoretical Darwinism illustrating the scientific content, and the philosophical implications, of the debates on evolutionary theory at Darwin's time and up to the “modern synthesis”.
1028(2008); http://dx.doi.org/10.1063/1.2965095View Description Hide Description
We review the recent proposal that the most fascinating brain properties are related to the fact that it always stays close to a second order phase transition. In such conditions, the collective of neuronal groups can reliably generate robust and flexible behavior, because it is known that at the critical point there is the largest abundance of metastable states to choose from. Here we review the motivation, arguments and recent results, as well as further implications of this view of the functioning brain.
1028(2008); http://dx.doi.org/10.1063/1.2965101View Description Hide Description
Mathematical models of spreading depression are considered in the form of reaction‐diffusion systems in two space dimensions. The systems are solved numerically. In the two component model with potassium and calcium ion concentrations, we demonstrate, using updated parameter values, travelling solitary waves of increased potassium and decreased calcium. These have circular wavefronts emanating from a region of application of potassium chloride. The collision of two such waves does not, as in one space dimension, result in annihilation but the formation of a unified wave with a large wavefront. For the first time we show that the mathematical model reproduces the actual properties of spreading depression waves in cortical structures. With attention to geometry, timing and location of stimuli we have succeeded in finding reverberating waves matching experiment. By simulating the technique of anodal block, spiral waves have also been demonstrated which parallel those found experimentally. The six‐component model, which contains additionally sodium, chloride, glutamate and GABA, is also investigated in 2 space dimensions, including an experimentally based exchange pump for sodium and potassium. Solutions are obtained without (amplitude 29 mM external ) and with action potentials (amplitude 44 mM external ) with speeds of propagation, allowing for tortuosity, of 1.4 mm/minute and 2.7 mm/minute, respectively. When action potentials are included a somewhat higher pump strength is required to ensure the return to resting state.
1028(2008); http://dx.doi.org/10.1063/1.2965102View Description Hide Description
Schizophrenia may be best understood in terms of abnormal interactions between different brain regions. Tasks such as associative learning that engage different brain regions may be ideal for studying altered brain function in the illness. Preliminary data suggest that the hippocampus is involved in the encoding (learning) and the prefrontal cortex in the retrieval of associative memories. Specific changes in the fMRI activities have also been observed based on comparative studies between stable schizophrenia patients and healthy control subjects. Disconnectivity, observed between brain regions in schizophrenic patients could result from abnormal modulation of N‐methyl‐D‐aspartate (NMDA)‐dependent plasticity implicated in schizophrenia.
1028(2008); http://dx.doi.org/10.1063/1.2965103View Description Hide Description
The structure of the retina suggests that it should be treated (at least from the computational point of view), as a layered computer. Different retinal cells contribute to the coding of the signals down to ganglion cells. Also, because of the nature of the specialization of some ganglion cells, the structure suggests that all these specialization processes should take place at the inner plexiform layer and they should be of a local character, prior to a global integration and frequency‐spike coding by the ganglion cells.
The framework we propose consists of a layered computational structure, where outer layers provide essentially with band‐pass space‐time filtered signals which are progressively delayed, at least for their formal treatment. Specialization is supposed to take place at the inner plexiform layer by the action of spatio‐temporal microkernels (acting very locally), and having a centerperiphery space‐time structure. The resulting signals are then integrated by the ganglion cells through macrokernels structures.
Practically all types of specialization found in different vertebrate retinas, as well as the quasilinear behavior in some higher vertebrates, can be modeled and simulated within this framework.
Finally, possible feedback from central structures is considered. Though their relevance to retinal processing is not definitive, it is included here for the sake of completeness, since it is a formal requisite for recursiveness.
1028(2008); http://dx.doi.org/10.1063/1.2965104View Description Hide Description
This paper presents a method to mathematically analyze the nerve impulse propagation in nonuniform axons. Starting from the general, nonlinear one‐dimensional cable equations with spatially varying cable diameter, the problem is shown to be equivalent (under some variable transformations) to the case of uniform axons. Characterized by the same normal form, six functions for analytically treatable axon diameter variations are determined. For this class of nonuniform axons, exact solutions describing the propagation of the front of the action potential are derived. The results are used to evaluate the impact of geometric non‐uniformity on the properties of propagating action potentials.
1028(2008); http://dx.doi.org/10.1063/1.2965080View Description Hide Description
Silicon neuron is electrical circuit that is analogous to biological neurons. Conventionally, it was designed mainly in the following two attitudes. One is to realize circuitry that is as close to biological neuron as possible, which enlarges circuit size and complexity terribly. Another is to realize simple and compact circuitry that can be utilized to construct large‐scale silicon neural network. Because designers ignore the mechanisms underlying the neuronal phenomena, silicon neurons can be quite different from biological ones. We proposed a new design method that utilizes mathematical knowledge on neuronal phenomena, which allows us to design simple circuitry whose operating mechanism is same as biological neuron. Several types of circuits have been and are being implemented to validate its efficiency.
1028(2008); http://dx.doi.org/10.1063/1.2965082View Description Hide Description
Axon guidance by graded diffusible ligands plays a crucial role in the developing nervous system. In this paper, we extend the mathematical description of the growth cone transduction cascade of  by adding a model of the gradient sensing process related to the theory of . The resulting model is composed by a series of subsystems characterized by suitable input/output relations. The study of the transmission of the noise‐to‐signal ratio allows to predict the variability of the gradient assay as a function of experimental parameters as the ligand concentration, both in the single and in the multiple ligand tests. For this latter condition, we address the biologically relevant case of silencing in commissural axons. We also consider a phenomenological model which reproduces the results of the experiments of . This simple model allows to test hypotheses on receptor functions and regulation in time.
1028(2008); http://dx.doi.org/10.1063/1.2965083View Description Hide Description
We analyze the first phase of information transduction in the model of the olfactory receptor neuron of the male moth Antheraea polyphemus. We predict such stimulus characteristics that enable the system to perform optimally, i.e., to transfer as much information as possible. Few a priori constraints on the nature of stimulus and stimulus‐to‐signal transduction are assumed. The results are given in terms of stimulus distributions and intermittency factors which makes direct comparison with experimental data possible. Optimal stimulus is approximatelly described by exponential or log‐normal probability density function which is in agreement with experiment and the predicted intermittency factors fall within the lowest range of observed values. The results are discussed with respect to electroantennogram measurements and behavioral observations.
1028(2008); http://dx.doi.org/10.1063/1.2965084View Description Hide Description
The interaction among synapses on dendritic tree of pyramidal neurons, combined with the variability of dendritic passive membrane properties, produces a complex system which regulates both the transfer of information among neurons and between different dendritic areas of the same neuron. A non linear mechanism, based on the excitatory reversal potential which behaves like a threshold, can act as a computational system improving the computational ability of the single neuron. Some examples of inter‐synaptic interaction and of synaptic interaction with the dendritic tree are given and the new concept of “Competition for Plasticity ” among synapses is proposed.
Comparison of Statistical Methods for Estimation of the Input Parameters in the Ornstein‐Uhlenbeck Neuronal Model from First‐Passage Times Data1028(2008); http://dx.doi.org/10.1063/1.2965085View Description Hide Description
The Ornstein‐Uhlenbeck neuronal model is reviewed, and estimation of the input parameters from first‐passage times are being discussed. Three methods previously suggested in the literature are compared through simulations; namely what we have denoted the Moment Method, the Laplace Transform method, and the Integral Equation method. Finally the methods are also applied to experimental data, where the membrane potential is also recorded intracellularly. This permits to compare the methods based on the limited information contained in first‐passage times only to evaluations from more complete observations of the otherwise hidden membrane potential.
1028(2008); http://dx.doi.org/10.1063/1.2965086View Description Hide Description
The paper is a case study monitoring the spiking activity of a place cell of hippocampus of a rat moving in an arena. Real data are evaluated using a new statistical methodology. Experimentally observed overdispersion suggests a doubly stochastic spatio‐temporal point process model of the time of spikes and the location of the rat. The inference of the driving intensity leads to a nonlinear filtering problem. Jump processes are used as parametric models of the driving intensity which enables the solution of the filtering problem by means of Bayesian Markov chain Monte Carlo methods. Simultaneously the parameters of the model are estimated. Model selection, numerical results and receptive field plasticity are discussed.
1028(2008); http://dx.doi.org/10.1063/1.2965088View Description Hide Description
We propose a simple stochastic model for the movement of a potentially infective particle in operating room in which the local air contamination level is reduced by using a double laminar flow. Numerical simulation is used to obtain qualitative scenario analysis, in order to prevent infection, i.e. impact of the infective particle with the surgical wound, during the operation.
1028(2008); http://dx.doi.org/10.1063/1.2965090View Description Hide Description
We report a theoretical analysis of protoplasmic streaming driven by peristaltic movement in an elastic tube of an amoeba‐like organism. The Plasmodium of Physarum polycephalum, a true slime mold, is a large amoeboid organism that adopts a sheet‐like form with a tubular network. The network extends throughout the Plasmodium and enables the transport and circulation of chemical signals and nutrients. This tubular flow is driven by periodically propagating waves of active contraction of the tube cortex, a process known as peristaltic movement. We derive the relationship between the phase velocity of the contraction wave and the flow rate, and we discuss the physiological implications of this relationship.
On the Influence of Quorum Sensing in the Competition Between Bacteria and Immune System of Invertebrates1028(2008); http://dx.doi.org/10.1063/1.2965091View Description Hide Description
The competition between bacteria and innate immune system of invertebrate animals is described by means of ODEs. Two different systems are considered corresponding to the absence or the presence of Quorum Sensing (Q.S.) mechanism. Qualitative properties of the solutions of both systems as well as the stability of their meaningful equilibria are analyzed. By constructing suitable Lyapunov functions, global asymptotic stability results have been proved when the quorum sensing is absent. In order to better illustrate the dynamics of competition, some numerical simulations, obtained by means of MATHEMATICA (Wolfram Research, 1989) are presented.
1028(2008); http://dx.doi.org/10.1063/1.2965092View Description Hide Description
Exploitative competition of two cross‐feeding strains is studied. We found that two types of coexistence of two cross‐feeding strains, type‐I coexistence (cultivated type) and type‐II coexistence (self‐sufficiency type) are possible for microbial cross‐feeding strains. In all cases of coexistence, trade‐off in nutrient availability is required. However, trade‐off is necessary but is not sufficient for the coexistence of two strains. Over‐production of metabolite can induce competitive exclusion on one hand (cultivated regime) whereas do support the coexistence of two strain on the other hand (self‐sufficiency regime). Coexistence of two strains is evaluated by invasibility and permanence criteria and numerical simulations.
1028(2008); http://dx.doi.org/10.1063/1.2965093View Description Hide Description
In the past few years a large number of molecular biology problems have been formulated as combinatorial optimization problems, including sequence alignment problems, genome rearrangement problems, string selection and comparison problems, and protein structure prediction and recognition. This paper describes the combinatorial formulation of some among the most interesting molecular biology problems and surveys the most efficient state‐of‐the‐art techniques and algorithms to exactly or approximately solve them.