On the representation of multi-input systems: Computational properties of polynomial algorithms

This paper introduces a theoretical framework for characterizing and classifying simple parallel algorithms and systems with many inputs, for example an array of photoreceptors. The polynomial representation (Taylor series development) of a large class of operators is introduced and its range of validity discussed. The problems involved in the polynomial approximation of systems are also briefly reviewed. Symmetry properties of the input-output map and their implications for the system structure (i.e. its kernels) are studied. Finally, the computational properties of polynomial mappings are characterized.     

Structural classification of multi-input nonlinear systems

We present new structural classification and parameter estimation results that are applicable to multi-input nonlinear systems. The mathematical relationships between the self- and cross-(Volterra and Wiener) kernels are derived for a basic two-input nonlinear structure. These results are then used to develop classification methods for more complicated two-input structures. Algorithms for estimating the parameters (linear and nonlinear subsystems) of these structures are also presented.     

Modelling within-host spatiotemporal dynamics of invasive bacterial disease

Mechanistic determinants of bacterial growth, death, and spread within mammalian hosts cannot be fully resolved studying a single bacterial population. They are also currently poorly understood. Here, we report on the application of sophisticated experimental approaches to map spatiotemporal population dynamics of bacteria during an infection. We analyzed heterogeneous traits of simultaneous infections with tagged Salmonella enterica populations (wild-type isogenic tagged strains [WITS]) in wild-type and gene-targeted mice. WITS are phenotypically identical but can be distinguished and enumerated by quantitative PCR, making it possible, using probabilistic models, to estimate bacterial death rate based on the disappearance of strains through time. This multidisciplinary approach allowed us to establish the timing, relative occurrence, and immune control of key infection parameters in a true host–pathogen combination. Our analyses support a model in which shortly after infection, concomitant death and rapid bacterial replication lead to the establishment of independent bacterial subpopulations in different organs, a process controlled by host antimicrobial mechanisms. Later, decreased microbial mortality leads to an exponential increase in the number of bacteria that spread locally, with subsequent mixing of bacteria between organs via bacteraemia and further stochastic selection. This approach provides us with an unprecedented outlook on the pathogenesis of S. enterica infections, illustrating the complex spatial and stochastic effects that drive an infectious disease. The application of the novel method that we present in appropriate and diverse host–pathogen combinations, together with modelling of the data that result, will facilitate a comprehensive view of the spatial and stochastic nature of within-host dynamics.     

Modelling the spatiotemporal dynamics of chemovirotherapy cancer treatment

Chemovirotherapy is a combination therapy with chemotherapy and oncolytic viruses. It is gaining more interest and attracting more attention in the clinical setting due to its effective therapy and potential synergistic interactions against cancer. In this paper, we develop and analyse a mathematical model in the form of parabolic non-linear partial differential equations to investigate the spatiotemporal dynamics of tumour cells under chemovirotherapy treatment. The proposed model consists of uninfected and infected tumour cells, a free virus, and a chemotherapeutic drug. The analysis of the model is carried out for both the temporal and spatiotemporal cases. Travelling wave solutions to the spatiotemporal model are used to determine the minimum wave speed of tumour invasion. A sensitivity analysis is performed on the model parameters to establish the key parameters that promote cancer remission during chemovirotherapy treatment. Model analysis of the temporal model suggests that virus burst size and virus infection rate determine the success of the virotherapy treatment, whereas travelling wave solutions to the spatiotemporal model show that tumour diffusivity and growth rate are critical during chemovirotherapy. Simulation results reveal that chemovirotherapy is more effective and a good alternative to either chemotherapy or virotherapy, which is in agreement with the recent experimental studies.     

On the existence of 'fast' and 'slow' directionally sensitive motion detector neurons in insects.

In a fly, butterfly, locust and dragonfly we examined the responses of a variety of directional motion-sensitive neurons which run from the brain down the ventral cord. The stimulus was a sinusoidally modulated moving pattern of regular stripes presented at a range of velocities in random order for either 0.1 s or 2.0 s. The response was measured as the total number of spikes to each stimulus. The neurons fall into two groups, 'fast' and 'slow'. The responses of the fast type rise progressively to a peak contrast frequency at 15-20 Hz for all four insects, and decline at higher contrast frequencies. The responses of slow neurons rise rapidly to a peak at 1-10 Hz and then decline more slowly across the range where the fast neurons are at their peak. The existence of two groups of neurons with overlapping response ranges to different velocities of the same pattern, presented in exactly the same way, provides the insect with a means of measuring angular velocity irrespective of contrast, spatial frequency or intensity. As an input mechanism it is proposed that there are two types of unit motion detector, fast and slow, the latter being the main input to the optomotor system. It is also argued that even these inputs are not sufficient to provide a mechanism for the whole repertoire of normal insect vision.     

Modelling cellular systems with PySCeS

SUMMARY: The Python Simulator for Cellular Systems (PySCeS) is an extendable research tool for the numerical analysis and investigation of cellular systems. AVAILABILITY: PySCeS is distributed as Open Source Software under the GNU General Public Licence and is available for download from http://pysces.sourceforge.net CONTACT: bgoli@sun.ac.za.     

Modelling spatiotemporal olfactory data in two steps: from binary to Hodgkin-Huxley neurones

Network models of synchronously updated McCulloch-Pitts neurones exhibit complex spatiotemporal patterns that are similar to activities of biological neurones in phase with a periodic local field potential, such as those observed experimentally by Wehr and Laurent (1996, Nature 384, 162-166) in the locust olfactory pathway. Modelling biological neural nets with networks of simple formal units makes the dynamics of the model analytically tractable. It is thus possible to determine the constraints that must be satisfied by its connection matrix in order to make its neurones exhibit a given sequence of activity (see, for instance, Quenet et al., 2001, Neurocomputing 38-40, 831-836). In the present paper, we address the following question: how can one construct a formal network of Hodgkin-Huxley (HH) type neurones that reproduces experimentally observed neuronal codes? A two-step strategy is suggested in the present paper: first, a simple network of binary units is designed, whose activity reproduces the binary experimental codes; second, this model is used as a guide to design a network of more realistic formal HH neurones. We show that such a strategy is indeed fruitful: it allowed us to design a model that reproduces the Wehr-Laurent olfactory codes, and to investigate the robustness of these codes to synaptic noise.     

A model-based approach for the analysis of neuronal information transmission in multi-input and -output systems

We present a new method to characterize multi-input and output neuronal systems using information theory. To obtain a lower bound of transinformation we take three steps: (1) Estimation of the deterministic response to isolate components carrying stimulus information. The deviation of the original response from the deterministic estimate is defined as noise. (2) Coordinate transformation using PCA yields an uncorrelated representation. (3) Partial transinformation values are calculated independently either by Shannon's formula assuming normality or based on density estimation for arbitrary distributions. We investigate the performance of the algorithms using simulated data and discuss suitable parameter settings. The approach allows to evaluate the degree to which stimulus features are encoded. Its potential is illustrated by analyses of neuronal activity in cat primary visual cortex evoked by electrical retina stimulation.     

Modelling metapopulations with stochastic membrane systems

Metapopulations, or multi-patch systems, are models describing the interactions and the behavior of populations living in fragmented habitats. Dispersal, persistence and extinction are some of the characteristics of interest in ecological studies of metapopulations. In this paper, we propose a novel method to analyze metapopulations, which is based on a discrete and stochastic modelling framework in the area of Membrane Computing. New structural features of membrane systems, necessary to appropriately describe a multi-patch system, are introduced, such as the reduction of the maximal parallel consumption of objects, the spatial arrangement of membranes and the stochastic creation of objects. The role of the additional features, their meaning for a metapopulation model and the emergence of relevant behaviors are then investigated by means of stochastic simulations. Conclusive remarks and ideas for future research are finally presented.     

Modelling the sensitivity of cells in the anteroventral cochlear nucleus to spatiotemporal discharge patterns.

This study investigates a potential mechanism for the processing of acoustic information that is encoded in the spatiotemporal discharge patterns of auditory nerve (AN) fibres. Recent physiological evidence has demonstrated that some low-frequency cells in the anteroventral cochlear nucleus (AVCN) are sensitive to manipulations of the phase spectrum of complex sounds (Carney 1990b). These manipulations result in systematic changes in the spatiotemporal discharge patterns across groups of low-frequency AN fibres having different characteristic frequencies (CFS). One interpretation of these results is that these neurons in the AVCN receive convergent inputs from AN fibres with different CFS, and that the cells perform a coincidence detection or cross-correlation upon their inputs. This report presents a model that was developed to test this interpretation.     

Modelling enteric bacteria survival in aquatic systems

We measured the uptake of carbon and inorganic nitrogen in nutrient-enriched water samples during 15-days incubation in summer in Lake Nakanuma, Japan. We calculated daily variations in neutral sugars and amino acids of the phytoplankton and estimated the efficiency of the increases in sugars and amino acids relative to photosynthetic activities. Only a small portion of carbon incorporated via photosynthesis was used for synthesis of sugars and amino acids during the incubation periods. The percentage increase in neutral sugars plus amino acids compared to photosynthetic rates ranged from 3.7 to 26.9% with an average of 12.8%. These findings suggest that large amounts of photosynthates were not used for the synthesis of cell components of phytoplankton and were lost through processes such as excretion and respiration.     

Modelling the mechanical properties of cardiac muscle

A model of passive and active cardiac muscle mechanics is presented, suitable for use in continuum mechanics models of the whole heart. The model is based on an extensive review of experimental data from a variety of preparations (intact trabeculae, skinned fibres and myofibrils) and species (mainly rat and ferret) at temperatures from 20 to 27°C. Experimental tests include isometric tension development, isotonic loading, quick-release/restretch, length step and sinusoidal perturbations. We show that all of these experiments can be interpreted with a four state variable model which includes (i) the passive elasticity of myocardial tissue, (ii) the rapid binding of Ca²⁺ to troponin C and its slower tension-dependent release, (iii) the kinetics of tropomyosin movement and availability of crossbridge binding sites and the length dependence of this process and (iv) the kinetics of crossbridge tension development under perturbations of myofilament length.     

Modelling the dynamic structure of biological state-based systems

The paper discusses the modelling aspects of systems with dynamic processes and dynamic structure. A combination of models bringing together the benefits of two paradigms, Population P Systems and Communicating X-machines, is introduced. A simple case study is used in order to illustrate the potential of the combined use of the two methods.     

SimRoot: Modelling and visualization of root systems

SimRoot, a geometric simulation model of plant root systems, is described. This model employs a data structure titled the Extensible Tree, which is well suited to the type of data required to model root systems. As implemented on Silicon Graphics workstations, the data structure and visualization code provides for continuous viewing of the simulated root system during growth. SimRoot differs from existing models in the explicit treatment of spatial heterogeneity of physiological processes in the root system, and by inclusion of a kinematic treatment of root axes. Examples are provided of the utility of the model in estimating the fractal geometry of simulated root systems in 1, 2, and 3 dimensional space. We envision continued development of the model to incorporate competition from neighboring root systems, linkage with crop simulation models to simulate root-shoot interactions, explicit treatment of soil heterogeneity, and plasticity of root responses to soil factors such as presence of mycorrhizal associations.     

Modelling biological systems from molecules to dynamical networks

A report of the 5^th IEEE International Conference on Systems Biology (IEEE ISB2011), 2-4 September 2011, Zhuhai, China.