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From fluctuations to phenotypes: the physiology of noise.

There are fundamental physical reasons why biochemical processes might be subject to noise and stochastic fluctuations. Indeed, it has long been understood that random molecular-scale mechanisms, such as those that drive genetic mutation, lie at the heart of population-scale evolutionary dynamics. What we can now appreciate is how stochastic fluctuations inherent in biochemical processes contribute to cellular and organismal phenotypes. Advancements in techniques for empirically measuring single cells and in corresponding theoretical methods have enabled the rigorous design and interpretation of experiments that provide incontrovertible proof that there are important endogenous sources of stochasticity that drive biological processes at the scale of individual organisms. Recently, some studies have progressed beyond merely ascertaining the presence of noise in biological systems; they trace its role in cellular physiology as it is passed through and processed by the biomolecular pathways-from the underlying origins of stochastic fluctuations in random biomolecular interactions to their ultimate manifestations in characteristic species phenotypes. These emerging results suggest new biological network design principles that account for a constructive role played by noise in defining the structure, function, and fitness of biological systems. They further show that stochastic mechanisms open novel classes of regulatory, signaling, and organizational choices that can serve as efficient and effective biological solutions to problems that are more complex, less robust, or otherwise suboptimal to deal with in the context of purely deterministic systems. Research in Drosophila melanogaster eye color-vision development and Bacillus subtilis competence induction has elegantly traced the role of noise in vital physiological processes from fluctuations to phenotypes, and is used here to highlight these developments.

Animals↗

Reactive transport of 85Sr in a chernobyl sand column: static and dynamic experiments and modeling.

The effects of nonlinear sorption and competition with major cations present in the soil solution on radioactive strontium transport in an eolian sand were examined. Three laboratory techniques were used to identify and quantify the chemical and hydrodynamic processes involved in strontium transport: batch experiments, stirred flow-through reactor experiments and saturated laboratory columns. The major goal was to compare the results obtained under static and dynamic conditions and to describe in a deterministic manner the predominant processes involved in radioactive strontium transport in such systems. Experiments under dynamic conditions, namely flow-through reactor and column experiments, were in very good agreement even though the solid/liquid ratio was very different. The experimental data obtained from the flow-through reactor study pointed to a nonlinear, instantaneous and reversible sorption process. Miscible displacement experiments were conducted to demonstrate the competition between stable and radioactive strontium and to quantify its effect on the 85Sr retardation factor. The results were modeled using the PHREEQC computer code. A suitable cation-exchange model was used to describe the solute/soil reaction. The model successfully described the results of the entire set of miscible displacement experiments using the same set of parameter values for the reaction calculations. The column study revealed that the stable Sr aqueous concentration was the most sensitive variable of the model, and that the initial state of the sand/solution system had also to be controlled to explain and describe the measured retardation factor of radioactive strontium. From these observations, propositions can be made to explain the discrepancies observed between some data obtained from static (batches) and dynamic (reactor and column) experiments. Desorbed antecedent species (stable Sr) are removed from the column or reactor in the flow system but continue to compete for sorption sites in the batch system. Batch experiments are simple and fast, and provide a very useful means of multiplying data. However, interpretation becomes difficult when different species compete for sorption sites in the soil/solution system. A combination of batches, flow-through reactor and column experiments, coupled with hydrogeochemical modeling, would seem to offer a very powerful tool for identifying and quantifying the predominant processes on a cubic decimeter scale (dm3) and for providing a range of radioactive strontium retardation factor as a function of the geochemistry of the soil/solution system.

Adsorption↗

Identifiability analysis of models for reversible intermolecular two-state excited-state processes coupled with species-dependent rotational diffusion monitored by time-resolved fluorescence depolarization.

A deterministic identifiability analysis of the kinetic model for a reversible intermolecular two-state excited-state process with species-dependent rotational diffusion described by Brownian reorientation is presented. The cases of both spherically and cylindrically symmetric rotors, with no change in the principal axes of rotation on interconversion in the latter case, are specifically considered. The identifiability analysis is carried out in terms of compartmental modeling based on the S(t) identical with I( parallel)(t)+2I( perpendicular)(t) and D(t) identical with I( parallel)(t)-I( perpendicular)(t) functions, where I( parallel)(t) and I( perpendicular)(t) are the delta-response functions for fluorescence, polarized, respectively, parallel and perpendicular to the electric vector of linearly polarized excitation. It is shown that, from polarized time-resolved fluorescence data collected at two concentrations of coreactant and three appropriately chosen emission wavelengths, (a) a unique set of rate constants for the overall excited-state process is always obtained by making use of polarized measurements and (b) the rotational diffusion constants and geometrical factors associated with the different anisotropy decay components can be uniquely determined and assigned to each species. The geometrical factors are determined by the absorption and emission transitions in the two rotating species. For spherical rotors, these factors depend directly on the relative orientations of the transition moments, while for cylindrically symmetric rotors they depend on the orientations with respect to each other and to the symmetry axis.

Algorithms↗

Extinctions in the random replicator model.

The statistical properties of an ecosystem composed of species interacting via pairwise, random interactions and deterministic, concentration limiting self-interactions are studied analytically with tools of equilibrium statistical mechanics of disordered systems. Emphasis is given to the effects of externally induced extinction of a fixed fraction of species at the outset of the evolutionary process. The manner the ecosystem copes with the initial extinction event depends on the degree of competition among the species as well as on the strength of that event. For instance, in the regime of high competition the ecosystem diversity, given by the fraction of surviving species, is practically insensitive to the strength of the initial extinction provided it is not too large, while in the less competitive regime the diversity decreases linearly with the size of the event. In the case of large extinction events we find that no further biotic extinctions take place and, furthermore, that rare species become very unlikely to be found in the ecosystem at equilibrium. In addition, we show that the reciprocal of the Edwards-Anderson order parameter yields a good measure of the diversity of the model ecosystem.

Animals↗

The catalytic power of pyruvate decarboxylase. A stochastic model for the molecular evolution of enzymes.

Pyruvate decarboxylase (PDC) catalyzes the decarboxylation of pyruvate anion by a factor of around 10(12), compared with the non-enzymic decarboxylation by thiamine, under standard state conditions of 1 mM pyruvate and thiamine diphosphate (TDP), pH 6.2. Free-energy diagrams constructed on the basis of earlier measurements for the enzymic and non-enzymic reactions give some information on catalysis by PDC. PDC stabilizes the reactant state preceding TDP addition to pyruvate by 76 kJ mol-1 and the transition state for the addition by 83 kJ mol-1. PDC stabilizes the reactant state preceding decarboxylation (presumably alpha-lactyl-TDP) by 27 kJ mol-1 and the transition state for decarboxylation by 68 kJ mol-1. In addition, the free-energy diagrams reveal a leveling of reactant-state free energies in the enzymic reaction compared with the non-enzymic reaction, in that the former are nearly equal to each other. The enzyme-bound transition-state energies are similarly leveled. The energetic leveling of reactant states has been noted by Albery, Knowles and their coworkers in many enzymic reactions and termed 'matched internal thermodynamics.' They showed that the result would arise naturally (and inevitably) in the 'evolution to perfection' of enzymes, when the evolutionary process was treated by a deterministic model. The critical assumption of this model was the validity of a Marcus-type or Brønsted-type linear free-energy relationship between rate and equilibrium constants for reactions occurring wholly within enzyme complexes. Here a completely stochastic simulation of molecular evolution, with no deterministic assumptions, is shown to reproduce both 'matched internal thermodynamics' and the 'matched internal kinetics' or leveling of transition-state energies noted here. The Albery-Knowles result is thus more general than might have been supposed.

Biological Evolution↗

Rhythmic changes in spike coding in the rat suprachiasmatic nucleus.

The suprachiasmatic nucleus is regarded as the main mammalian circadian pacemaker but evidence for rhythmic firing of single units in vivo has been obtained only recently. The present study was undertaken to determine if rhythms could be seen using measures of activity in addition to the mean spike frequency. We investigated whether there were changes in the irregularity of cell activity measured by the disorder of the interspike interval distribution for neurones recorded in vivo and in vitro. By plotting the entropy of the log interval histogram that quantifies the coding capacity for each action potential against the respective zeitgeber time, we describe oscillations of spike activity in vivo. Entropy measures have the advantage over variances in that they quantify aspects of the shape of the distribution and not just the dispersion. One hundred and sixty-six cell recordings from the suprachiasmatic nucleus showed a significant rhythm in entropy with an oscillatory trend in the data (P < 0.001) showing a trough towards the end of the light period and a peak in the mid-dark period. There was a similar rhythm for the cells recorded from the peripheral zone (n = 209, P = 0.037). In separate experiments in vitro, to investigate the relationship between mean spike frequency and entropy, potassium-induced depolarization of cells recorded during the subjective night was correlated with a significant increase in mean spike frequency (r = 0.259, P = 0.011) and a decrease in entropy (r = -0.296, P = 0.004). The negative correlation between the entropy and mean spike frequency of cells recorded in vitro was significantly different from that seen in vivo (F = 15.5, P < 0.001), which may reflect differences in the balance between deterministic and stochastic influences on spike occurrence. The study shows that while there is a rhythm of mean spike frequency, parameters based on the variability of interspike interval distributions also display rhythmic changes over the day-night cycle.

Action Potentials↗

Instabilities and oscillation in the deterministic Boltzmann machine.

Simulations indicate that the deterministic Boltzmann machine, unlike the stochastic Boltzmann machine from which it is derived, exhibits unstable behavior during contrastive Hebbian learning of nonlinear problems, including oscillation in the learning algorithm and extreme sensitivity to small weight perturbations. Although careful choice of the initial weight magnitudes, the learning rate, and the annealing schedule will produce convergence in most cases, the stability of the resulting solution depends on the parameters in a complex and generally indiscernible way. We show that this unstable behavior is the result of over parameterization (excessive freedom in the weights), which leads to continuous rather than isolated optimal weight solution sets. This allows the weights to drift without correction by the learning algorithm until the free energy landscape changes in such a way that the settling procedure employed finds a different minimum of the free energy function than it did previously and a gross output error occurs. Because all the weight sets in a continuous optimal solution set produce exactly the same network outputs, we define reliability, a measure of the robustness of the network, as a new performance criterion.

Algorithms↗

Renal blood flow regulation and arterial pressure fluctuations: a case study in nonlinear dynamics.

The arterial blood pressure, a physiological variable on which all renal excretory processes depend, fluctuates over a wide range of amplitudes and frequencies. Much of this variation originates in nonrenal vascular beds to support nonrenal tasks, and the fluctuations provide a noisy environment in which the kidney is obliged to operate. Were it not for renal blood flow autoregulation, it would be difficult to regulate renal excretory processes so as to maintain whole body variables within narrow bounds. Autoregulation is the noise filter on which other renal processes depend for maintaining a relatively noise-free environment in which to work. Because of the time-varying nature of the blood pressure, we have concentrated in this review on the now substantial body of work on the dynamics of renal blood flow regulation and the underlying mechanisms. Renal vascular control mechanisms are not simply reactive but have their own spontaneous dynamics. Both TGF and the myogenic mechanism oscillate autonomously. The TGF oscillation is the better understood of the two. There is an oscillation of tubular pressure, proximal tubular flow, early distal Cl- concentration, and efferent arteriolar blood flow at approximately 35 mHz; all these variables are synchronized when the measurements are made in a single tubule. The autonomous nature of the oscillation is supported by simulations of the nephron and its vasculature, which show that for a reasonable representation of the dynamics of these structures and of the parameters that govern their behavior, the solutions of the equation set are periodic at the frequency of the observed oscillation, and with the same phase relationships among its variables. The simulations also show that the critical variables for the development of the oscillation are the open-loop gain of the feedback system, and the various delays in the system of which convective transport in the axis of the thick ascending limb and signal transmission between the macula densa and the afferent arteriole are the most important. The oscillation in TGF is an example of nonlinear dynamical behavior and is yet another in a long list of oscillations and related dynamics arising in the inherently nonlinear properties of living systems. Some nonlinear systems can bifurcate to states known collectively as deterministic chaos, and TGF is a clear example of such a system. Rats with two different and unrelated forms of experimental hypertension provide tubular pressure records that pass statistical tests for ordered structure and sensitive dependence on initial conditions in the reconstructed state space, two of the hallmarks of deterministic chaos. These records also pass recent more stringent tests for chaos. The significance of deterministic chaos in the context of renal blood flow regulation is that the system regulating blood flow undergoes a physical change to a different dynamical state, and because the change is deterministic, there is every expectation that the critical change will yield itself to experimental discovery.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗

Testing of metal bioaccumulation models with measured body burdens in mice.

Estimates of chemical accumulation in prey organisms can contribute considerable uncertainty to predictive ecological risk assessments. Comparing body burdens calculated in food web models with measured tissue concentrations provides essential information about the expected accuracy of risk indices. Estimates of arsenic, cadmium, copper, lead, and nickel body burdens in house mice (Mus musculus) inhabiting a seasonal wetland were generated with two small mammal bioaccumulation models. Published soil-to-small mammal bioaccumulation regression models produced accurate estimates of arsenic and lead body burdens but failed to adequately predict copper and nickel levels in mice. Incorporating conservative prediction intervals in the regression models shows potential for successful applications in screening-level risk assessments. A simple mechanistic cumulative ingestion bioaccumulation model overpredicted lead levels in mice generally by less than one order of magnitude but greatly overpredicted concentrations of arsenic, copper, and nickel. Better estimates of absorption and elimination of ingested metals and knowledge of specific arthropod taxa in house mouse diets are likely to improve the accuracy of the cumulative ingestion model. Applying Monte Carlo simulations to the soil-small mammal regression models generated probabilistic estimates of body burdens that were consistent with deterministic results. However, deterministic minimum and maximum predictions of the ingestion model were excessively conservative (widely spaced) relative to lower and upper probabilistic percentiles. Metal levels predicted in individual mice on the basis of mouse-specific parameter values and exposures were not significantly more accurate than bioaccumulation predictions for the sitewide population.

Animals↗

Links between play and dominance and attachment dimensions of dog-human relationships.

It is often claimed that certain behavioral problems in domestic dogs can be triggered by the games played by dog and caregiver (owner). In this study, we examine possible links between the types of games played and dimensions of the dog-owner relationship that are generally considered to affect such problems. Fifty dog-owner partnerships were filmed during 3-min play sessions in which the owner was allowed to choose the games played. All partnerships then undertook a 1-hr test designed to measure elements of behavior commonly ascribed to "dominance" and "attachment." Principal components analysis of the data produced 2 dominance-related factors (Amenability and Confident Interactivity) and 4 factors describing aspects of attachment (Nonspecific Attention Seeking, Preference for Owner, Preference for Unfamiliar Person, and Separation-Related Behavior). Amenability, in particular, varied significantly between breeds. In the study, we then compared types of games played to each of these factors. Dogs playing rough-and-tumble scored higher for Amenability and lower on Separation-Related Behavior than did dogs playing other types of games. Dogs playing tug-of-war and fetch scored high on Confident Interactivity. Winning or losing these games had no consistent effect on their test scores. If the dog started the majority of the games, the dog was significantly less amenable and more likely to exhibit aggression. The results suggest that how dogs play reflects general attributes of their temperament and relationship with their owner. This study provides no evidence that games play a major deterministic role on dominance dimensions of dog-human relationships, but the results suggest that playing games involving considerable body contact may affect attachment dimensions.

Animals↗

The dynamics of malaria.

Previous studies on dynamic systems of transmission of malaria, and of eradication of infection following the interruption of transmission, have now been adapted for advanced techniques using the facilities offered by computers.The computer programmes have been designed for a deterministic model suitable for a large community and also for a stochastic model relevant to small populations in which infections reach very low finite numbers. In this model, new infections and recoveries are assessed by the daily inoculation rate and are subject to laws of chance. Such a representation is closer than previous models to natural happenings in the process of malaria eradication. Further refinements of the new approach include the seasonal transmission and simulation of mass chemotherapy aimed at a cure of P. falciparum infections.These programmes present models on which the actual or expected results of changes due to various factors can be studied by the analysis of specific malaria situations recorded in the field. The value of control methods can also be tested by the study of such hypothetical epidemiological models and by trying out various procedures.Two specific malaria situations (in a pilot project in Northern Nigeria and in an outbreak in Syria) were studied by this method and provided some interesting results of operational value. The attack measures in the pilot project in Northern Nigeria were carried out according to the theoretical model derived from the basic data obtained in the field.

Disease Outbreaks↗

Understanding widely scattered traffic flows, the capacity drop, and platoons as effects of variance-driven time gaps.

We investigate the adaptation of the time headways in car-following models as a function of the local velocity variance, which is a measure of the inhomogeneity of traffic flow. We apply this mechanism to several car-following models and simulate traffic breakdowns in open systems with an on-ramp as bottleneck and in a closed ring road. Single-vehicle data and one-minute aggregated data generated by several virtual detectors show a semiquantitative agreement with microscopic and flow-density data from the Dutch freeway A9. This includes the observed distributions of the net time headways for free and congested traffic, the velocity variance as a function of density, and the fundamental diagram. The modal value of the time headway distribution is shifted by a factor of about 2 under congested conditions. Macroscopically, this corresponds to the capacity drop at the transition from free to congested traffic. The simulated fundamental diagram shows free, synchronized, and jammed traffic, and a wide scattering in the congested traffic regime. We explain this by a self-organized variance-driven process that leads to the spontaneous formation and decay of long-lived platoons even for a deterministic dynamics on a single lane.

Journal Article↗

Visual signal detection in structured backgrounds. I. Effect of number of possible spatial locations and signal contrast.

Several studies have investigated the effect of signal location uncertainty on the detectability of simple visual signals in uncorrelated Gaussian noise with a deterministic background. For this case, human performance in locating a signal in a forced-choice experiment has been successfully predicted for 2-1800 alternative locations with the use of signal detection theory and the usual assumption that the observer's internal response is Gaussian distributed. Gaussian uncorrelated noise is far from realistic medical image noise, which includes not only fluctuations in intensity of quantum origin but also other anatomical objects lying in the x-ray path (structured backgrounds). Our goal is to determine whether signal detection theory with the Gaussian assumption is adequate for the case of structured backgrounds, or whether other more complex models need to be developed to predict human performance as a function of the number of possible signal locations in structured backgrounds. We present experimental data suggesting that an assumed Gaussian internal response accurately predicts the decrease in observer performance as the number of alternative locations is increased. The one exception is a lower-than-predicted performance for the detection of low-contrast signals for two alternative locations. Performance as measured by the index of detectability d' is also found to be linear with signal contrast. Together these findings extend the applicability of signal detection theory with Gaussian internal response functions to the case of complex structured backgrounds.

Computer Simulation↗

Mathematical models of Neospora caninum infection in dairy cattle: transmission and options for control.

The transmission and control of Neospora caninum infection in dairy cattle was examined using deterministic and stochastic models. Parameter estimates were derived from recent studies conducted in the UK and from the published literature. Three routes of transmission were considered: maternal vertical transmission with a high probability (0.95), horizontal transmission from infected cattle within the herd, and horizontal transmission from an independent external source. Putative infection via pooled colostrum was used as an example of within-herd horizontal transmission, and the recent finding that the dog is a definitive host of N. caninum supported the inclusion of an external independent source of infection. The predicted amount of horizontal transmission required to maintain infection at levels commonly observed in field studies in the UK and elsewhere, was consistent with that observed in studies of post-natal seroconversion (0.85-9.0 per 100 cow-years). A stochastic version of the model was used to simulate the spread of infection in herds of 100 cattle, with a mean infection prevalence similar to that observed in UK studies (around 20%). The distributions of infected and uninfected cattle corresponded closely to Normal distributions, with S.D.s of 6.3 and 7.0, respectively. Control measures were considered by altering birth, death and horizontal transmission parameters. A policy of annual culling of infected cattle very rapidly reduced the prevalence of infection, and was shown to be the most effective method of control in the short term. Not breeding replacements from infected cattle was also effective in the short term, particularly in herds with a higher turnover of cattle. However, the long-term effectiveness of these measures depended on the amount and source of horizontal infection. If the level of within-herd transmission was above a critical threshold, then a combination of reducing within-herd, and blocking external sources of transmission was required to permanently eliminate infection.

Animals↗

Impact of dermal absorption factors in occupational exposure assessment: comparison of two models for agricultural reentry workers exposed to azinphosmethyl.

This analysis compares two deterministic reentry exposure models that differ in their treatment of the time dependence of dermal absorption. The first model, called the "traditional model," assumes that dermal absorption is a fixed fraction of the cumulative load on skin at the end of the workshift and that absorption is independent of residence time on the skin. The second model, called the "time-integrated model," incorporates the time dependence of both exposure and absorption by assuming that absorption begins at the outset of exposure and continues through the workshift and beyond, until an effective washing event occurs. These two models were evaluated using previously collected biological monitoring data from apple thinners exposed to azinphosmethyl. Daily doses predicted by the models were compared to doses estimated from the biological sampling results assuming pseudo steady-state excretion. The geometric mean dose estimated from the biological sampling data was 20 microg/kg/day. Corresponding geometric mean doses produced by the traditional model and the time-integrated model were 79 microg/kg/day and 24 microg/kg/day, respectively. When the doses predicted by the traditional model were plotted against those estimated from the biological measurements, the slope of the regression line was significantly greater than 1 (beta = 1.37). However, when this same analysis was conducted for the doses predicted by the time-integrated model, the confidence interval around the slope encompassed 1 (beta = 1.01). Thus, time-integrated treatment of absorption appeared to provide more realistic dose estimates than did the traditional approach.

Agriculture↗

Unequal cell division, growth regulation and colony size of mammalian cells: a mathematical model and analysis of experimental data.

This work describes mathematically the dynamics of expansion of cell populations from the initial division of single cells to colonies of several hundred cells. This stage of population growth is strongly influenced by stochastic (random) elements including, among others, cell death and quiescence. This results in a wide distribution of colony sizes. Experimental observations of the NIH3T3 cell line as well as for the NIH3T3 cell line transformed with the ras oncogene were obtained for this study. They include the number of cells in 4-day-old colonies initiated from single cells and measurements of sizes of sister cells after division, recorded in the 4-day-old colonies. The sister cell sizes were recorded in a way which enabled investigation of their interdependence. We developed a mathematical model which includes cell growth and unequal cell division, with three possible outcomes of each cell division: continued cell growth and division, quiescence, and cell death. The model is successful in reproducing experimental observations. It provides good fits to colony size distributions for both NIH3T3 mouse fibroblast cells and the same cells transformed with the rasEJ human cancer gene. The difference in colony size distributions could be fitted by assuming similar cell lifetimes (12-13 hr) and similar probabilities of cell death (q = 0.15), but using different probabilities of quiescence, r = 0 for the ras oncogene transformed cells and r = 0.1 for the non-transformed cells. The model also reproduces the evolution of distributions of sizes of cells in colonies, from a single founder cell of any specified size to the stable limit distribution after eight to ten cell divisions. Application of the model explains in what way both random events and deterministic control mechanisms strongly influence cell proliferation at early stages in the expansion of colonies.

Animals↗

Relative biological effectiveness (RBE), quality factor (Q), and radiation weighting factor (w(R)). A report of the International Commission on Radiological Protection.

The effect of ionising radiation is influenced by the dose, the dose rate, and the quality of the radiation. Before 1990, dose-equivalent quantities were defined in terms of a quality factor, Q(L), that was applied to the absorbed dose at a point in order to take into account the differences in the effects of different types of radiation. In its 1990 recommendations, the ICRP introduced a modified concept. For radiological protection purposes, the absorbed dose is averaged over an organ or tissue, T, and this absorbed dose average is weighted for the radiation quality in terms of the radiation weighting factor, w(R), for the type and energy of radiation incident on the body. The resulting weighted dose is designated as the organ- or tissue-equivalent dose, H(T). The sum of the organ-equivalent doses weighted by the ICRP organ-weighting factors, w(T), is termed the effective dose, E. Measurements can be performed in terms of the operational quantities, ambient dose equivalent, and personal dose equivalent. These quantities continue to be defined in terms of the absorbed dose at the reference point weighted by Q(L). The values for w(R) and Q(L) in the 1990 recommendations were based on a review of the biological and other information available, but the underlying relative biological effectiveness (RBE) values and the choice of w(R) values were not elaborated in detail. Since 1990, there have been substantial developments in biological and dosimetric knowledge that justify a re-appraisal of w(R) values and how they may be derived. This re-appraisal is the principal objective of the present report. The report discusses in some detail the values of RBE with regard to stochastic effects, which are central to the selection of w(R) and Q(L). Those factors and the dose-equivalent quantities are restricted to the dose range of interest to radiation protection, i.e. to the general magnitude of the dose limits. In special circumstances where one deals with higher doses that can cause deterministic effects, the relevant RBE values are applied to obtain a weighted dose. The question of RBE values for deterministic effects and how they should be used is also treated in the report, but it is an issue that will demand further investigations. This report is one of a set of documents being developed by ICRP Committees in order to advise the ICRP on the formulation of its next Recommendations for Radiological Protection. Thus, while the report suggests some future modifications, the w(R) values given in the 1990 recommendations are still valid at this time. The report provides a scientific background and suggests how the ICRP might proceed with the derivation of w(R) values ahead of its forthcoming recommendations.

Advisory Committees↗

Modelling of allocation and balance of carbon in walnut (Juglans regia L.) seedlings during heterotrophy-autotrophy transition

A deterministic and dynamic model of carbon allocation in walnut seedlings is described. Two experimental data sets were used to calibrate and validate the model. These data included: time course of the carbon content, chemical and isotope composition (12C and 13C) of the kernel and growing organs (roots, stem, leaves), and gas exchange rates during the first 55 days of the life of the plant with continuous 13CO2 feeding. The plant is modelled as a network with nodal organs acting as sources or sinks for carbohydrates. In a sink organ the demand for carbon is the sum of four elementary demands: maintenance respiration, structural growth, growth-associated respiration and carbon storage. The organs of the plant are assumed to be in exponential growth phase. The supply of carbon readily accessible for the organs is the store of soluble sugars present in a local reservoir. Carbon flow in the network is determined by the source/sink activities of the organs and local levels of demand and supply. Two carbon sources are considered: soluble sugars from the kernel, and gross photosynthesis. The rate of synthesis of soluble sugars in the kernel, and measured photosynthesis in the leaves are inputs for the plant model. The outputs are the predicted fluxes of carbon within the seedling; 13C composition,carbohydrate allocation to the growing organs, starch and soluble sugars accumulation, and respiration. The mathematical equations were translated into PSPICE software instructions. After optimisation of the parameter values, the model provided an accurate description of experimental observations in the seed-plant system during the critical transition from heterotrophy to autotrophy, especially C allocation to organs and C partitioning between storage, structural growth and respiration in each organ. The growth of the young plant is supply-limited, except at the earliest stages. A sensitivity analysis suggests that intense competition for carbohydrates dominates the relations among and within organs. Copyright 1998 Academic Press Limited

Journal Article↗