Organizers:

Julio A. Hernández, and Andrés Pomi

Sección Biofísica, Facultad de Ciencias, Universidad de la República, Montevideo, Uruguay
 
 

Academic Committee:

Luis Acerenza, Ruben Budelli, Hugo Fort, Leonel Gómez, Julio A. Hernández, Eduardo Mizraji, and Andrés Pomi (Universidad de la República, Montevideo, Uruguay)
 
 

Supported by:

Programa de Desarrollo de las Ciencias Básicas (PEDECIBA)

Comisión Sectorial de Investigación Científica de la Universidad de la República, Uruguay.
 
 

Acknowledgements:

Intendencia Municipal de Colonia, Uruguay.

Friday, May 3rd

Dynamics and Control in Cellular Processes

Population Dynamics
 
 

^{1 Seccion Biomatemática, Facultad de Ciencias. Montevideo, Uruguay; 2 División Neuroanatomía Comparada, Instituto de Investigaciones Biológicas Clemente Estable. Montevideo, Uruguay; 3 Institute Alfred Fessard, CNRS Gif sur Yvette, France.}

^{* presenting author (}ruben@biomat.fcien.edu.uy)
 
 
 
 

Electroreceptive fish detect nearby objects by processing the information contained in the pattern of electric currents through the skin. In weakly electric fish, these currents result from a self generated field (the electric organ discharge, EOD). The electric image can be defined as the pattern of transepidermal voltage. Theoretical analysis has yield realistic models that predict with acceptable accuracy the image.

In pulse mormyrids, the electric organ fires almost synchronously. In resistive environments, the unique parameter defining the stimulus is the peak to peak amplitude (PP). A capacitive object may change both, PP and the local EOD waveform. To evaluate the change in waveform, von der Emde introduced the positive negative quotient parameter (P/N). The pair (PP, P/N) generated by a given object moved away from the fish, moves along a straight line passing through the basal (PP, P/N) pair. Different objects, may share the same straight line, defining families of objects. Objects of different families will be discriminated; and objects of the same family will be confused. We hypothesize that such curves define a distance-invariant perceptual property (quale), detectable by electroreceptors. Analogously to vision, the distance-invariant property related to impedance can be denominated "electric color"

In the case of resistive objects, the only parameter that changes with the presence of the object is the PP. In this case, the stimulus can be also measured as the modulation of the transcutaneous voltage, defined as the quotient of PP in the presence of objects and in their absence (basal stimulus). We found by realistic models and experiments that in any case the image has a center-surround opponent "Mexican-hat" shape, whose importance was stressed by Kohonen and Marr.

These fish are able to discriminate distance independently of object size and conductivity. We proposed the relative slope as candidate for coding object distance. Theoretical analysis, experimental recordings of local fields and behavioral studies indicate that the relative slope of the spatial profile is a good candidate for distance discrimination.

Department of Physiology, University of California, Los Angeles, California 90024, USA, and Center for Studies in Physics & Biology, The Rockefeller Univ. New York, N.Y.

dchialvo@ucla.edu
 
 
 
 

Since the earliest interest of Pythagoras and despite the gargantuan literature the problem of how the pitch of complex sounds is extracted remain unsolved. Pitch is a subjective attribute of a sound sensation by which it may be ordered on a scale from low to high. While the pitch of a tuning fork is objective (i.e., its single frequency) most natural sounds are combination of different frequencies. How the brain assigns a single definite pitch to the sound emitted by a string that is plucked in the middle, which contains many frequencies? The purpose of this work is to show that a simple nonlinear neuronal mechanism can account for all relevant features described for the auditory pitch perception. Complex sounds are composed by more than one tone. It is well known that when 2 tones occur together, a 3^rd one, with a pitch corresponding approximately to the difference in their frequencies is often heard. This is referred to as the "missing fundamental illusion" because the perceived pitch is a frequency (fundamental) for which there is not actual vibration. This phenomenon exemplify a larger variety of problems related to how pitch is extracted by the brain from complex tones, music and speech, and thus have been extensively used to test theories of pitch perception. We call attention here to a simple noisy nonlinear process that can be the main neural mechanism able to explain the vast majority of the phenomenology reported in the last five decades and to provide for specific quantitative predictions. The two basic points of the model presented are: (I) the individual tones composing the complex tones are weak and add linearly producing peaks of constructive interference whose amplitude is always insufficient to fire the neuron; and (II): the threshold to fire an spike is only reached randomly thanks to noise, which naturally "picks out" the maxima of these interferences. This results in spikes at a frequency that is exactly the perceived pitch of the complex tone. Analytical arguments as well as the numerical simulations with several models show that these results are largely model-independent and thus relevant to various sensory modalities.

Sección Biofísica, DBCM, Facultad de Ciencias, Universidad de la República, Montevideo, Uruguay.

*presenting author (mizraj@fcien.edu.uy)
 
 
 
 

The logical operations included under the name of "disjunction", have been very important for the development of neural network theory, in particular the exclusive disjunction (XOR). The implementation of XOR was not possible for McCulloch-Pitts single neurons, and it was not also possible for single layer Perceptrons. However, in some models of context-dependent associative memories, we can easily represent all the logical operations, including XOR. We describe here these neural-based representations.

It is a known fact that the classical Boolean version of XOR exhibits insufficiencies as a model of cognitive exclusive disjunctions for more than two variables. In particular, it is well known that XOR is an estimator of the parity of a Boolean string: XOR concatenated to evaluate three (or any odd number of) true variables provides "true" as its outcome. On the contrary, the exclusive disjunction of three propositions is accepted as true by our cognition if only one variable is true. Consequently, the search for alternative mathematical representations of disjunctions valid in general cases, is an important problem. Here we describe a solution to this problem that uses the theory of context-dependent associative memories. This solution produces models where the exclusive disjunction emerges from the dynamics of a decision problem.

The previous models are valid in the Boolean domain, but they can be extended to become useful in the fuzzy domain, where the logical variables are allowed to be real numbers in the interval [0,1]. This extension becomes important in the task of dealing with decisions involving ill-defined situations. In these situations, logical models that use modalities are important tools. This kind of approach using modal-logic can be interesting if we take into account the fact that some logical functions (specially XOR) have strong capacities of generating chaotic dynamics in some 1-dimensional cellular automata. We show that the modal embedding of the elementary 16 Boolean functions of two variables puts in evidence the particular potentialities of XOR and XOR-related functions to generate complex dynamical behaviors.

Universidad Nacional de General Sarmiento, Roca 850, San Miguel (C.P.1663), Buenos Aires, Argentina.

* presenting author (page@ungs.edu.ar)
 
 
 
 

We analyze response time (RT) measurements from experiments where the participant is asked to decide on the relative order between two visual stimuli (e.g., which is smaller, bigger, taller, shorter, etc).

Response time measurements pinpoint three mayor effects. For instance, in comparisons between digits, small distances between them need longer RTs or, the RT pattern observed between digits with equal split depends on the proposed task and, finally, stimuli pairs with a 1 or a 9 have the shortest RT. These behavior is known as the distance, the congruency and the end effect, respectively.

Theoretical response time models usually propose a linear accumulative process, until a threshold is reached. We show that extending a previous phenomenological model it may be reinterpreted as an accumulative process that reaches the threshold at an exponential rate. The model equations and stopping thresholds for the accumulative process have an immediate interpretation in terms of a simple network. Different sets of thresholds may describe alternative experimental paradigms. We find good correlation between the model predictions and other authors experimental data, both in number comparisons, and in an experimental paradigm where the ordering of the symbolic stimuli has been artificially induced.

Preliminary measurements performed at our laboratory show interesting patterns between the observed mean RT for each pair and the corresponding standard deviation. This result is easily achieved with our model.

Centro de Estudios Avanzados, y Facultad de Ciencias Exactas y Naturales, Depto. de Física, Universidad de Buenos Aires. Pabellón 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina.

perazzo@df.uba.ar
 
 
 
 

We develop several models to discuss the effect of acquired characters in biological evolution within the pure Darwinian framework suggested by Baldwin. He proposed that the interaction of the genetic and behavioral systems accelerates the trascription of environmental data into genetic information. The models are extensions of that of Hinton and Nowlan and study the effects of the combination of a learning capability and other (rigid) genetic effects that contribute to the fitness. We separately consider the cases of a fixed and of a changing environment. Evolution is modelled with genetic algorithms.

For a fixed environment we consider a population of adaptive perceptrons in which some of their synapses can be updated through a learning process. The environment is represented by an optimal synaptic pattern and the fitness is measured by comparing the classification performance of each individual with the optimal one. We find that the above mentioned trascription process depends upon the learning profficency. For a high learning effciency we find a hindrance that is the opposite of the usual interpretation of the Baldwin effect.

A changing environment is represented by two optimal synaptic patterns that alternate during the ``life" of the individuals. We consider the cases of a population of replicating strings and of perceptrons. We find that two evolutionary pathways are possible depending upon how difficult (costly) it is to cope with the changes of the environment. In one case the individuals inherit fixed synapses that are optimal in only one of the environmental states. In the other case a flexible subsystem emerges that allows the individuals to adapt to the changes of the environment. The model explains how an adaptive subsystem can emerge as the result of the tradeoff between the exploitation of a congenital structure and the exploration of the adaptive capabilities practiced by learning.

^{1 Sección Biofísica, 2 Sección Biología Celular, Facultad de Ciencias, Montevideo, Uruguay and}

^{3 Centre de Química Teòrica at Parc Científic de Barcelona and Departament de Química Física, Facultat de Química, Universitat de Barcelona, Barcelona, Spain.}

^{*presenting author (}aceren@fcien.edu.uy)
 
 
 
 

Modular organisation appears to be ubiquitous in biological structure and relevant to biological function. Here we present three examples, at three different levels of organisation, where the processes are described using modular models.

Quimiotaxis is the motile response of bacteria to gradients in the concentration of attractants and repellents. Its molecular mechanism includes receptors whose activity responds to changes in the external concentration, returning to the basal activity when a new constant level is attained. Quimiotactic receptors exhibit this adaptive response in a wide range of concentrations. Here we show that this property depends on the existence of successive methylation-demethylation modules, the number of which is directly related to the number of orders of magnitude in which the receptor responds (Arocena & Acerenza).

Metabolic responses depend on the kinetic properties of the component enzyme-catalysed reactions and their interactions. A quantitative description of this relationship has been obtained by the infinitesimal theory of metabolic control. However, due to the complex nature of metabolism, a full analysis of its responses is outside our reach. It was shown that a solution to this problem is to divide the system into two or a few modules (with physiological meaning), the responses of these modules being the ones analysed. We have recently extended this modular approach to large (non-infinitesimal) metabolic responses (Ortega & Acerenza).

E. coli evolution in controlled conditions shows a parallel increase in cell volume and fitness. Genetic decay of unused catabolic functions was also found. To explain these facts, we developed a minimal model. Briefly, changes in volume and fitness are obtained with cellular metabolism divided in a growth and an adaptation module, and genetic decay of the adaptation module by simple population genetics. In a short time scale, the model reproduces relevant features of bacterial physiology. In the evolutionary time scale, it explains the parallel increase in cell volume and fitness from the genetic decay in unused functions (Graña & Acerenza).

^{(1) Centre de Recerca en Química Teòrica (CeRQT-PCB) and Department de Química Física, Universitat de Barcelona (UB), C/ Martí i Franquès, 1. E-08028 Barcelona, (Spain, EU); (2) Sección Biofísica, Fac. de Ciencias, Universidad de la República, Iguá 4225, Montevideo 11400, Uruguay.}

^{* presenting author (fmas@qf.ub.es; fax: (34) 934021231)}
 
 
 
 

A new approach to the study of complex macromolecular binding systems by means of the properties of the global association quotient, , defined as , where  is the free ligand concentration, is presented [1, 2]. In a previous work [1] it was shown that  is the average of the elementary equilibrium constants with the only requirement that there is a one-to-one relationship between free and occupied sites. For systems that fulfill the Adair equation, the average is over the intrinsic equilibrium constants. Here we show that the decomposition in terms of intrinsic and elementary constants are two particular types of a more general decomposition [3]

This relationship consists on expressing the global association quotient as a weighted average of partial association quotients, , each one associated to one of n sub-systems from which the system is composed. The weights  represent the fractions of free sites of the corresponding subsystems. We show that, if the whole system is split into different subsystems according to a binding hierarchy that starts from the lower, microscopic, level of binding and ends at the higher, aggregation level, the global association quotient can be successively decomposed following this hierarchical levels of macromolecular organisation.

Furthermore, we give a thermodynamic interpretation of the traditional Scatchard plot and the global association quotient, , in terms of the excess free energy of the system. It is also discussed that temperature-dependent studies of  can provide direct information about the entropic and enthalpic changes in cooperative binding processes.

References:

[1] L. Acerenza and E. Mizraji, Biochim. Biophys. Acta, 1339 (1997) 155

Sección Biofísica, Facultad de Ciencias, Universidad de la República, Montevideo, Uruguay

jahern@fcien.edu.uy
 
 
 
 

The biological world provides with examples of systems with a high degree of complexity at every level of organization, including the molecular level. The function of a globular protein, such as an enzyme or a transport protein, is generally described by a kinetic diagram that represents intermediate states of the macromolecule and transitions between them. In spite of the highly complex structures of the membrane proteins, the transport processes mediated by them can be usually described in terms of relatively simple kinetic diagrams. These simple "functional" diagrams, obtained from studies of the ligand fluxes and chemical rates under diverse experimental conditions, are generally different from the ones describing the molecular mechanisms in detail. These latter diagrams may contain a significantly larger number of intermediate states and connections. These complex "mechanistic" diagrams emerge from experimental studies designed to comprehend diverse structural and dynamical properties of the macromolecule, in particular, the identification of the different intermediate states.

How do complex membrane proteins, characterized by a possibly very large number of intermediate states, exhibit functional properties that can be described by relatively simple kinetic diagrams? I discuss two possible ways of explanation of this problem:

1) Some kinetic properties are common to a large number of different transporters, and are independent of the degree of complexity of the mechanistic diagram relating all the actual intermediate states of the macromolecule. As an example I show that the simple carrier behavior, exhibited by many biological membrane transporters and originally attributed to a mode of operation represented by an elementary four-state model, can be shared by diverse transporters characterized by complex mechanistic kinetic diagrams.

2) Under particular experimental conditions, an apparent reduction of the mechanistic kinetic diagram of the macromolecule may take place. I show here examples of the application of the reduction technique to complex kinetic models of facilitative transport. In some cases, the reduced models exhibit behaviors that can be described by simple kinetic formulations.
 

^{(1) Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Córdoba, Argentina; (2) Facultad de Ciencias Agropecuarias, Universidad Católica de Córdoba, Córdoba, Argentina; (3) Instituto Nacional de Tecnología Agropecuaria (INTA); Estación Experimental Agropecuaria Bariloche, Bariloche, Argentina.}

^{* presenting author (}cannas@famaf.unc.edu.ar)
 
 
 
 

Organisms spreading outside of their native ranges have been called "invaders". The process by which an invader arrives and spreads into the new territory is called "ecological invasion". This is a worldwide phenomenon that has been recognised as potentially damaging for ecosystems structures and functioning.

We present a model for the population dynamics of several interacting tree species. The model associates to each species a cellular automaton that takes into account life history traits relevant to species dynamics as well as enviromental parameters. Interaction between species is included by coupling the variables associated to each cellular automaton through simple interacting rules.

Through this model we analize different topics of interest to the study of the ecological invasion problem. In particular, we show how different factors of the dynamics, like interactions between species and long range seeds dispersion strategies may led to different types of scale invariant spatial patterns.

^{1 Departamento de Física Teórica, Instituto de Física and 2 Sección Biofísica, Instituto de Biología, Facultad de Ciencias, Montevideo, Uruguay.}

^{*presenting author (}hugo@fisica.edu.uy)
 
 
 
 

The relationship between the patterns of interaction in an ecological system and its fate is still poorly understood. Even in systems with a small number of species there is a complex relationship between structure and dynamics.

To study this problem, we use a very simple three species system governed by Lotka-Volterra differential equations. The inter-specific interactions are of three types: positive (+1), negative (-1) or null (0), leading to 729 different diagrams. Concerning the intra-specific interactions we study two cases: (I) all non-interacting (isolated species remain stationary) and (II) all negatively interacting (isolated species become extinct). We also assume that: a) the initial populations are identical, b) there is a maximum number of individuals that the ecosystem can sustain and c) in the absence of inter and intra-specific interactions the populations remain stationary.

We have performed two types of studies: "microscopic" and "statistical". The microscopic view is based on comparing individual diagrams. Here we see that there appears to be no simple general rules concerning the relationship between pattern of interactions and fate. For instance, even if the increase in the number of positive interactions or the decrease in the number of negative interactions usually increases the number of survivors, there are counterexamples for both. The statistical studies consisted on the calculation of the fraction of species that survive (f_S) as a function of the net balance of signs of the inter-specific interactions (SB) or the number of cycles (of positive: C+, negative: C- and null: Co interactions). We found several "statistical laws". In case (I): f_S vs. SB increase; f_S vs. C+ and f_S vs. Co increase and f_S vs. C- decrease. In case (II): f_S vs. SB increase; f_S vs. C+ increase, f_S vs. Co is non-monotonous and f_S vs. C- decrease. However, in both (I) and (II), the effect of the number of cycles (C+, C- and Co) on f_S at constant SB results, in the great majority of the situations, in an increase in the fraction of survivors.

^(a) Instituto de Fisica, Universidade Federal do Rio de Janeiro, Cidade Universitaria, C.P. 8528 - 21945-970 Rio de Janeiro, Brazil; ^(b) Instituto de Fisica, Facultad de Ciencias, Igua 4225 - 11400 Montevideo, Uruguay

* presenting author (donangel@if.ufrj.br)
 
 
 
 

The ability to evolve is basic to life, and is a consequence of heredity, mutations, and the capacity of life to copy itself so abundantly that it can sustain the high cost of evolutionary attempts.

First, we briefly review some descriptions of biological evolution: The Neutral model of Kimura, the Quasi species model of Eigen, models based on Game theory -and in particular the existence of stable strategies resembling Nash equilibria- and the Bak-Sneppen model of punctuated equilibrium and co-evolution.

Next, we show how this last model, suplemented with random mutations, can be employed to describe the evolution of fitness in the E.coli cultures experiment for over 10,000 generations performed by R. Lenski and co-workers.

In particular, we show that, for a value of the mutation level which coincides with the one estimated from experiments, this model reproduces quite well the measures of mean fitness relative to that of a common ancestor.

The inclusion of random mutations, besides making more realistic the models, is required to get quantitative agreement with the experimental results, both for the transient and the asymptotic regime.

While both fitness driven and random mutations were shown to be needed, their relative importance remains an open question.
 

EVIDENCE OF SELF-ORGANIZATION IN BRAIN ELECTRICAL ACTIVITY USING WAVELET BASED INFORMATIONAL TOOLS. Osvaldo A. Rosso¹, María Teresa Martin², and Angel Plastino²

^{1Instituto de Cálculo, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires. Pabellón II, Ciudad Universitaria. 1428 Buenos Aires, Argentina; 2Instituto de Física, Universidad Nacional de La Plata and Argentina's National Research Council (CONICET). C.C. 727, 1900 La Plata, Argentina.}
 
 

The traditional way of analyzing brain electrical activity, on the basis of EEG records, relies mainly on visual inspection and years of training. Although it is quite useful, of course, one has to acknowledge its subjective nature, that hardly allows for a systematic protocol. In order to overcome this undesirable feature, a quantitative EEG analysis has been developed over the years that introduces objective measures, reflecting not only the characteristics of the brain activity itself but also giving clues concerning the underlying associated neural dynamics. The processing of information by the brain is reflected in dynamical changes of the electrical activity in time, frequency, and space. Therefore, the concomitant studies require methods capable of describing the qualitative variation of the signal in both time and frequency. With the help of the normalized total wavelet entropy (NTWS) and two complexity measures (Shiner-Davison-Landsberg (SDL) and, López Ruiz-Mancini-Calbert (LMC) complexity definitions), we will show that an epileptic-focus generates a special brain-state characterized by both order and maximal complexity. Since the brain electrical activity reflected in EEGs can be associated to a chaotic dynamics, this state could be called an á la Haken "self-organized" one. This would entail that some of the brain's neurons in such a state acquire spatial, or spatio-temporal structures by means of internal processes without specific interference from the outside.
 

SLIP AND LEAK IN A DYNAMIC MODEL OF ENERGY COUPLING IN BIOLOGICAL MEMBRANES. Ernesto Cristina and Julio A. Hernández.

Sección Biofísica, Facultad de Ciencias, Universidad de la República, 11400 Montevideo, Uruguay.
 
 

The purpose of this work is to contribute to understand the roles of ionic leak and enzyme slippage in the processes of energy coupling in biological membranes. For this, we modified a model previously developed by us to study the basic dynamic and stationary properties of such processes. The model considers that a microorganism expresses, in its plasma membrane, two electrogenic enzymes (E₁ and E₂) transporting the same cation C and electrodiffusive paths for C (cation leak) and for an anion A. Under physiological conditions, E₁ couples the transport of C to the energy donor reaction whereas E₂ utilizes the electrochemical gradient of C to produce ATP. As a main difference with the previous work, in the present case the kinetic diagram describing the activity of E₂ includes a slipping transition. The consequence is that the processes of ionic transport and ATP synthesis mediated by the enzyme become incompletely coupled. The mathematical model describing the dynamics of the overall system is employed to study the effects produced by enzyme slippage and cation leak on the electrical potential difference accross the plasma membrane (V_m ) and on the intracellular concentrations of C (C₁) and ATP (ATP).

From the studies, we conclude that either the presence of cation leak or of enzyme sllippage can produce similar non-linear relationships between the cation motive force and the thermodynamic force of the energy donor reaction. Some differences may be observed, however. While an increase in cation permeability always decreases both V_m and (ATP), an increase in the rate constants of the slipping transition may determine a comparable decrease in (ATP) with almost no modification in V_m. We suggest that this property could underlie control responses of bacteria under conditions of low energy requests. Thus, (ATP) could be diminished within certain values without any metabolic consequence, while the electrical potencial difference, that supports diverse other processes of electrogenic transport, may be kept at physiological values.
 

Author Index
 
 
 

Acerenza, L 9, 10, 13

Arocena, M 9

Blanco, SA 16

Budelli, R 4

Cannas, SA 12

Caputi, AA 4

Chialvo, DR 5

Codnia, J 7

Cristina, E 18

Donangelo, R 14

Figliola, A 17

Fort, H 13, 14

Garcés, JL 10

Gómez, L 4

Grant, K 4

Graña, M 9

Hernández, JA 11, 18

Izquierdo, E 7

Marco, DE 12

Martín, MT 15

Mas, F 10

Mizraji, E 6, 10

Montemurro, M 12

Murer, G 16

Ortega, F 9

Páez, SA 12

Page, R 7

Perazzo, RPJ 8

Plastino, A 15

Pomi, A 6
 
 

Reali, F 6

Riquelme, LA 16

Rosso, O 17

Rosso, OA 15

Rother, D 4

Saal, A 7

Valle-Lisboa, JC 6

Yankilevich, P 16