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Steady state analysis of metabolic pathways using Petri nets.

Computer assisted analysis and simulation of biochemical pathways can improve the understanding of the structure and the dynamics of cell processes considerably. The construction and quantitative analysis of kinetic models is often impeded by the lack of reliable data. However, as the topological structure of biochemical systems can be regarded to remain constant in time, a qualitative analysis of a pathway model was shown to be quite promising as it can render a lot of useful knowledge, e. g., about its structural invariants. The topic of this paper are pathways whose substances have reached a dynamic concentration equilibrium (steady state). It is argued that appreciated tools from biochemistry and also low-level Petri nets can yield only part of the desired results, whereas executable high-level net models lead to a number of valuable additional insights by combining symbolic analysis and simulation.

Computer Simulation↗

Microevolution of the Chibcha-speaking peoples of lower Central America: rare genes in an Amerindian complex.

Models are developed for the survival, history, and spread of variant alleles, in order to consider what can, and what cannot, be inferred from this type of data. The high variances of the processes involved, and questions of sampling, place severe limitations on inferences. Nonetheless, by combining information on a number of rare variants observed in a group of interrelated populations, reliable qualitative inferences are possible. These ideas and models are developed in the context of data on five rare variants and six private polymorphisms observed in eight Chibcha-speaking tribes of Costa Rica and Panama. The decline and fragmentation of the Amerindian populations of Central America over the last 300 years create considerable difficulties in attempting inference of past genetic events. However, these tribes have been well studied genetically, anthropologically, and linguistically and thus provide an excellent framework for the study of rare-variant spread.

Biological Evolution↗

Statistical analysis of intramembranous particles using freeze fracture specimens.

We studied the point processes of intramembranous particles of mitochondrial membranes from HeLa cells using the freeze fracture technique. Three groups - under normal conditions, after exposition with rotenone, and after exposition with sodium acid - were compared. First, we used several summary statistics in order to study the two-dimensional point patterns of intramembranous particles within each group. Then, we compared the patterns in different groups by bootstrap tests using the K-function and the nearest neighbour distance function G(r). Estimation of the G-function provided significant results but no significant differences between groups were found using the classical K-function; estimation of G(r) should therefore not be omitted when studying observed planar point patterns.

Data Interpretation, Statistical↗

Time and space issues in ecotoxicology: population models, landscape pattern analysis, and long-range environmental chemistry.

Advances in ecotoxicology addressing problems of time and spatial scales are presented and interpreted in the frame of concepts on population/community dynamics and landscape pattern analysis. Example deterministic/probabilistic modeling experiments are used to illustrate key concepts. Space and time scales analyzed are single and multigenerations of local populations, metapopulations, community, and ecosystem/landscape. Most population models used in recent ecotoxicology studies are deterministic and do not include a formal treatment of spatial processes, like migration or local random extinction. Some metapopulation models have been applied with success. Upscaling of ecotoxicological results at the community level is less developed, probably because of the inherent complexity of indirect and direct coactions among organisms. Community and ecosystem toxicity end points that could find a broad use in regulatory applications have not yet been identified. Some practical issues like the estimation of the potential for the natural attenuation of toxicity and the transport of contaminants along food chains must be addressed at these scales/levels of biological complexity. The estimation of ecotoxicological effects has been increasingly evolving to integrate modeling and monitoring contaminant transport and fate, landscape pattern analysis, and spatially explicit population dynamics (including direct and indirect communal interactions).

Agriculture↗

Isolation and characterization of a MHC class II DRB locus in the European water vole (Arvicola terrestris).

In so-called model species, such as human and mouse, genes of the major histocompatibility complex (MHC) are characterized by extremely high levels of polymorphism, and it is considered that such diversity is maintained by balancing selection. ;There is now a recognized need to expand studies into nonmodel species to examine whether high MHC diversity is mirrored in natural populations, and to determine the ecological, ethological, and evolutionary processes that underpin balancing selection. To address such issues, a necessary prerequisite is the ability to characterize diversity at a single, expressed, polymorphic MHC locus on which selection may be acting. Here, we provide the first description of allelic diversity at exon 2 of an MHC class II DRB locus in the European water vole (Arvicola terrestris), characterize variation across four natural populations, and test whether the patterns of variation are consistent with the effects of balancing selection. Using single-strand conformation polymorphism analysis and subsequent DNA sequencing of gel excisions, five DRB alleles were resolved, each with a unique amino acid sequence, among 100 individuals from four geographically distinct populations. Reverse transcription polymerase chain reaction confirmed that the alleles were products from an expressed locus. Intra-allelic amino acid differences were high (10.5-33.3%), and the nonsynonymous substitution rate exceeded the synonymous substitution rate for the functional peptide-binding region (d (N):d (S)=3.91 and P<0.005). Phylogenetic comparison of resolved alleles with closely related homologues indicated that each allele represented a unique lineage preserved across speciation events. These results indicate that balancing selection has maintained diversity of DRB allelic lineages and amino acid function over evolutionary time scales, but may be less effective at preserving alleles in contemporary populations where stochastic microevolutionary processes may dominate.

Alleles↗

Self-optimizing MPC of melt temperature in injection moulding.

The parameters in plastic injection moulding are highly nonlinear and interacting. Good control of plastic melt temperature for injection moulding is very important in reducing operator setup time, assuring consistent product quality, and preventing thermal degradation of the melt. Step response testing was performed on the barrel heating zones on an industrial injection moulding machine (IMM). The open loop responses indicated a high degree of process coupling between the heating zones. From these experimental step responses, a multiple-input-multiple-output model predictive control strategy was developed and practically implemented. The requirement of negligible overshoot is important to the plastics industry for preventing material overheating and wastage, and reducing machine operator setup time. A generic learning and self-optimizing MPC methodology was developed and implemented on the IMM to control melt temperature for any polymer to be moulded on any machine having different electrical heater capacities. The control performance was tested for varying setpoint trajectories typical of normal machine operations. The results showed that the predictive controller provided good control of melt temperature for all zones with negligible oscillations, and, therefore, eliminated material degradation and extended machine setup time.

Computer Simulation↗

Computer simulations reveal motor properties generating stable antiparallel microtubule interactions.

An aster of microtubules is a set of flexible polar filaments with dynamic plus ends that irradiate from a common location at which the minus ends of the filaments are found. Processive soluble oligomeric motor complexes can bind simultaneously to two microtubules, and thus exert forces between two asters. Using computer simulations, I have explored systematically the possible steady-state regimes reached by two asters under the action of various kinds of oligomeric motors. As expected, motor complexes can induce the asters to fuse, for example when the complexes consist only of minus end-directed motors, or to fully separate, when the motors are plus end directed. More surprisingly, complexes made of two motors of opposite directionalities can also lead to antiparallel interactions between overlapping microtubules that are stable and sustained, like those seen in mitotic spindle structures. This suggests that such heterocomplexes could have a significant biological role, if they exist in the cell.

Animals↗

Electrostatic coupling of ion pumps.

In this paper the electrostatic interactions between membrane-embedded ion-pumps and their consequences for the kinetics of pump-mediated transport processes have been examined. We show that the time course of an intrinsically monomolecular transport reaction can become distinctly nonexponential, if the reaction is associated with charge translocation and takes place in an aggregate of pump molecules. First we consider the electrostatic coupling of a single dimer of ion-pumps embedded in the membrane. Then we apply the treatment to the kinetic analysis of light-driven proton transport by bacteriorhodopsin which forms two-dimensional hexagonal lattices. Finally, for the case of nonordered molecules, we also consider a model in which the pumps are randomly distributed over the nodes of a lattice. Here the average distance is equal to that deduced experimentally and the elemental size of the lattice is the effective diameter of one single pump. This latter model is applied to an aggregate of membrane-embedded Na, K- and Ca-pumps. In all these cases the electrostatic potential considered is the exact solution calculated from the method of electrical images for a plane membrane of finite thickness immersed in an infinite aqueous solution environment. The distributions of charges (ions or charged binding sites) are considered homogeneous or discrete in the membrane and/or in the external solution. In the case of discrete distributions we compare the results from a mean field approximation and a stochastic simulation.

Electrophysiology↗

New approach to generalized two-dimensional correlation spectroscopy. II: Eigenvalue manipulation transformation (EMT) for noise suppression.

This paper introduces the concept of eigenvalue manipulating transformation (EMT) of a data matrix for noise suppression in two-dimensional (2D) correlation spectroscopy. The FT-IR spectra of a polystyrene/methyl ethyl ketone/toluene solution mixture during the solvent evaporation process, to which were added a substantial amount of artificial noise, have been analyzed. By uniformly raising the power of a set of eigenvalues, the major eigenvalues become more prominent. As a consequence, minor eigenvectors representing the noise component are no longer strongly represented in the reconstructed data. This EMT operation is similar to the simple truncation of noise-dominated minor factors practiced in standard principal component analysis (PCA), as demonstrated in our preceding paper on PCA-2D correlation spectroscopy. The effect of this new EMT scheme is more gradual, with attractive flexibility to continuously fine-tune the balance between the desired noise reduction effect and the retention of pertinent spectral information.

Algorithms↗

Interpretation of heart rate variability via detrended fluctuation analysis and alphabeta filter.

Detrended fluctuation analysis (DFA), suitable for the analysis of nonstationary time series, has confirmed the existence of persistent long-range correlations in healthy heart rate variability data. In this paper, we present the incorporation of the alphabeta filter to DFA to determine patterns in the power-law behavior that can be found in these correlations. Well-known simulated scenarios and real data involving normal and pathological circumstances were used to evaluate this process. The results presented here suggest the existence of evolving patterns, not always following a uniform power-law behavior, that cannot be described by scaling exponents estimated using a linear procedure over two predefined ranges. Instead, the power law is observed to have a continuous variation with segment length. We also show that the study of these patterns, avoiding initial assumptions about the nature of the data, may confer advantages to DFA by revealing more clearly abnormal physiological conditions detected in congestive heart failure patients related to the existence of dominant characteristic scales.

Adult↗

The maximum likelihood approach to the identification of neuronal firing systems.

The concern of this work is the identification of the (nonlinear) system of a neuron firing under the influence of a continuous input in one case, and firing under the influence of two other neurons in a second case. In the first case, suppose that the data consist of sample values Xt, Yt, t = 0, +/- 1, +/- 2,... with Yt = 1 if the neuron fires in the time interval t to t + 1 and Yt = 0 otherwise, and with Xt denoting the (sampled) noise value at time t. Suppose that Ht denotes the history of the process to time t. Then, in this case the model fit has the form Prob[Yt = 1/Ht] = phi(Ut-theta) where (formula; see text) where gamma t denotes the time elapsed since the neuron last fired and phi denotes the normal cumulative. This model corresponds to quadratic summation of the stimulus followed by a random threshold device. In the second case, a network of three neurons is studied and it is supposed that (formula; see text) with Xt and Zt zero-one series corresponding to the firing times of the two other neurons. The models are fit by the method of maximum likelihood to Aplysia californica data collected in the laboratory of Professor J.P. Segundo. The paper also contains some general comments of the advantages of the maximum likelihood method for the identification of nonlinear systems.

Animals↗

A dual-process integrator-resonator model of the electrically stimulated human auditory nerve.

A phenomenological dual-process model of the electrically stimulated human auditory nerve is presented and compared to threshold and loudness data from cochlear implant users. The auditory nerve is modeled as two parallel processes derived from linearized equations of conductance-based models. The first process is an integrator, which dominates stimulation for short-phase duration biphasic pulses and high-frequency sinusoidal stimuli. It has a relatively short time constant (0.094 ms) arising from the passive properties of the membrane. The second process is a resonator, which induces nonmonotonic functions of threshold vs frequency with minima around 80 Hz. The ion channel responsible for this trend has a relatively large relaxation time constant of about 1 ms. Membrane noise is modeled as a Gaussian noise, and loudness sensation is assumed to relate to the probability of firing of a neuron during a 20-ms rectangular window. Experimental psychophysical results obtained in seven previously published studies can be interpreted with this model. The model also provides a physiologically based account of the nonmonotonic threshold vs frequency functions observed in biphasic and sinusoidal stimulation, the large threshold decrease obtained with biphasic pulses having a relatively long inter-phase gap and the effects of asymmetric pulses.

Auditory Threshold↗

A numerical algorithm for investigating the role of the motor-cargo linkage in molecular motor-driven transport.

We extend the numerical algorithm developed by Wang et al. (2003. J. Theor. Biol. 221, 491-511) for studying biomolecular transport processes to include the linkage that connects molecular motors to their cargo. The new algorithm is used to investigate how the stiffness of the linkage affects the average velocity, effective diffusion coefficient, and randomness parameter. Three different models for molecular motors are considered: (1) a discrete stepping motor (2) a motor moving in a tilted-periodic potential and (3) a motor driven by a flashing potential. We demonstrate that a flexible motor-cargo linkage can make inferences on motor behavior based on measurements of the cargo's position difficult. We also show that even for the case of a tilted-periodic potential there exists an optimal stiffness of the linkage at which transport is maximized. The MATLAB code used in this paper is available at: http://www.unc.edu/approximatelytelston/code/.

Algorithms↗

Sequence-dependent pausing of single lambda exonuclease molecules.

Lambda exonuclease processively degrades one strand of duplex DNA, moving 5'-to-3' in an ATP-independent fashion. When examined at the single-molecule level, the speeds of digestion were nearly constant at 4 nanometers per second (12 nucleotides per second), interspersed with pauses of variable duration. Long pauses, occurring at stereotypical locations, were strand-specific and sequence-dependent. Pause duration and probability varied widely. The strongest pause, GGCGAT TCT, was identified by gel electrophoresis. Correlating single-molecule dwell positions with sequence independently identified the motif GGCGA. This sequence is found in the left lambda cohesive end, where exonuclease inhibition may contribute to the reduced recombination efficiency at that end.

Bacteriophage lambda↗

Statistical analysis of repeated events forming renewal processes.

For each of several individuals a sequence of repeated events, forming a renewal process, is observed up to some censoring time. The object is to estimate the average interevent time over the population of individuals as well as the variation of interevent times within and between individuals. Medical motivation comes from gastroenterology, and concerns the occurrence of certain cyclic movements in the small bowel during the fasting state. Two statistical models are considered: one is the standard variance component model adapted to censored data, and the other is a recent intensity based model with a random proportionality factor representing interindividual variation. These models are applied to the motility data, and their advantages are discussed. The intensity based model allows simple empirical Bayes estimation of the expected interevent times for an individual in the presence of censoring.

Adult↗

Evolutionary dynamics on graphs.

Evolutionary dynamics have been traditionally studied in the context of homogeneous or spatially extended populations. Here we generalize population structure by arranging individuals on a graph. Each vertex represents an individual. The weighted edges denote reproductive rates which govern how often individuals place offspring into adjacent vertices. The homogeneous population, described by the Moran process, is the special case of a fully connected graph with evenly weighted edges. Spatial structures are described by graphs where vertices are connected with their nearest neighbours. We also explore evolution on random and scale-free networks. We determine the fixation probability of mutants, and characterize those graphs for which fixation behaviour is identical to that of a homogeneous population. Furthermore, some graphs act as suppressors and others as amplifiers of selection. It is even possible to find graphs that guarantee the fixation of any advantageous mutant. We also study frequency-dependent selection and show that the outcome of evolutionary games can depend entirely on the structure of the underlying graph. Evolutionary graph theory has many fascinating applications ranging from ecology to multi-cellular organization and economics.

Biological Evolution↗

How we hear what is not there: a neural mechanism for the missing fundamental illusion.

How the brain estimates the pitch of a complex sound remains unsolved. Complex sounds are composed of more than one tone. When two tones occur together, a third lower pitched tone is often heard. This is referred to as the "missing fundamental illusion" because the perceived pitch is a frequency (fundamental) for which there is no actual source vibration. This phenomenon exemplifies a larger variety of problems related to how pitch is extracted from complex tones, music and speech, and thus has been extensively used to test theories of pitch perception. A noisy nonlinear process is presented here as a candidate neural mechanism to explain the majority of reported phenomenology and provide specific quantitative predictions. The two basic premises of this model are as follows: (I) The individual tones composing the complex tones add linearly producing peaks of constructive interference whose amplitude is always insufficient to fire the neuron (II): The spike threshold is reached only with noise, which naturally selects the maximum constructive interferences. The spacing of these maxima, and consequently the spikes, occurs at a rate identical to the perceived pitch for the complex tone. Comparison with psychophysical and physiological data reveals a remarkable quantitative agreement not dependent on adjustable parameters. In addition, results from numerical simulations across different models are consistent, suggesting relevance to other sensory modalities.

Action Potentials↗

Estimation of synaptic conductances.

In order to identify and understand mechanistically the cortical circuitry of sensory information processing estimates are needed of synaptic input fields that drive neurons. From intracellular in vivo recordings one would like to estimate net synaptic conductance time courses for excitation and inhibition, g(E)(t) and g(I)(t), during time-varying stimulus presentations. However, the intrinsic conductance transients associated with neuronal spiking can confound such estimates, and thereby jeopardize functional interpretations. Here, using a conductance-based pyramidal neuron model we illustrate errors in estimates when the influence of spike-generating conductances are not reduced or avoided. A typical estimation procedure involves approximating the current-voltage relation at each time point during repeated stimuli. The repeated presentations are done in a few sets, each with a different steady bias current. From the trial-averaged smoothed membrane potential one estimates total membrane conductance and then dissects out estimates for g(E)(t) and g(I)(t). Simulations show that estimates obtained during phases without spikes are good but those obtained from phases with spiking should be viewed with skeptism. For the simulations, we consider two different synaptic input scenarios, each corresponding to computational network models of orientation tuning in visual cortex. One input scenario mimics a push-pull arrangement for g(E)(t) and g(I)(t) and idealized as specified smooth time courses. The other is taken directly from a large-scale network simulation of stochastically spiking neurons in a slab of cortex with recurrent excitation and inhibition. For both, we show that spike-generating conductances cause serious errors in the estimates of g(E) and g(I). In some phases for the push-pull examples even the polarity of g(I) is mis-estimated, indicating significant increase when g(I) is actually decreased. Our primary message is to be cautious about forming interpretations based on estimates developed during spiking phases.

Adaptation, Physiological↗