A stochastic model for the membrane potential of a stimulated neuron

We present a simple model describing the transition between the prefiring, firing and postfiring phases of a single neuron in a large neural net. Using typical values for the physiological parameters that enter the model, we find average interspike times that are close to those reported in experimental measurements.     

Effect of an exponentially decaying threshold on the firing statistics of a stochastic integrate-and-fire neuron

We study a white-noise driven integrate-and-fire (IF) neuron with a time-dependent threshold. We give analytical expressions for mean and variance of the interspike interval assuming that the modification of the threshold value is small. It is shown that the variability of the interval can become both smaller or larger than in the case of constant threshold depending on the decay rate of threshold. We also show that the relative variability is minimal for a certain finite decay rate of the threshold. Furthermore, for slow threshold decay the leaky IF model shows a minimum in the coefficient of variation whenever the firing rate of the neuron matches the decay rate of the threshold. This novel effect can be seen if the firing rate is changed by varying the noise intensity or the mean input current.     

Derivation of stochastic partial differential equations for size- and age-structured populations

Stochastic partial differential equations (SPDEs) for size-structured and age- and size-structured populations are derived from basic principles, i.e. from the changes that occur in a small time interval. Discrete stochastic models of size-structured and age-structured populations are constructed, carefully taking into account the inherent randomness in births, deaths, and size changes. As the time interval decreases, the discrete stochastic models lead to systems of Itô stochastic differential equations. As the size and age intervals decrease, SPDEs are derived for size-structured and age- and size-structured populations. Comparisons between numerical solutions of the SPDEs and independently formulated Monte Carlo calculations support the accuracy of the derivations.     

Identification and comparison of stochastic metabolic/hemodynamic models (sMHM) for the generation of the BOLD signal

This paper extends a previously formulated deterministic metabolic/hemodynamic model for the generation of blood oxygenated level dependent (BOLD) responses to include both physiological and observation stochastic components (sMHM). This adds a degree of flexibility when fitting the model to actual data by accounting for un-modelled activity. We then show how the innovation method can be used to estimate unobserved metabolic/hemodynamic as well as vascular variables of the sMHM, from simulated and actual BOLD data. The proposed estimation method allowed for doing model comparison by calculating the model’s AIC and BIC. This methodology was then used to select between different neurovascular coupling assumptions underlying sMHM. The proposed framework was first validated on simulations and then applied to BOLD data from a motor task experiment. The models under comparison in the analysis of the actual data considered that vascular response was coupled to: (I) inhibition, (II) excitation, (III) both excitation and inhibition. Data was best described by model II, although model III was also supported.     

A comparison of persistence-time estimation for discrete and continuous stochastic population models that include demographic and environmental variability

A discrete-time Markov chain model, a continuous-time Markov chain model, and a stochastic differential equation model are compared for a population experiencing demographic and environmental variability. It is assumed that the environment produces random changes in the per capita birth and death rates, which are independent from the inherent random (demographic) variations in the number of births and deaths for any time interval. An existence and uniqueness result is proved for the stochastic differential equation system. Similarities between the models are demonstrated analytically and computational results are provided to show that estimated persistence times for the three stochastic models are generally in good agreement when the models satisfy certain consistency conditions.     

On a stochastic model of a molecular genetic system capable of differentiation and reproduction of the initial state

A model of the system, consisting of a cyclic 3-operonic subsystem, related to a 2-operonic trigger by direct and feedback connections, is built. The operons of this system are functionally connected by repressers. The basic postulates are: a) the repressers are stable; b) during cell division each molecule of represser and respective mRNA has equal probability to find itself in any daughter cell. Computer simulation demonstrates that after few cell divisions, analogues of somatic cell, maintaining the system for some successive divisions, and of generative cells, where by the system returns to the initial state, appear. A scheme of molecular genetic control system, producing a lot of different cell types in course of successive cell divisions, is proposed.     

A new mathematical model for combining growth and energy intake in animals: The case of the growing pig

A simultaneous model for analysis of net energy intake and growth curves is presented, viewing the animal's responses as a two dimensional outcome. The model is derived from four assumptions: (1) the intake is a quadratic function of metabolic weight; (2) the rate of body energy accretion represents the difference between intake and maintenance; (3) the relationship between body weight and body energy is allometric and (4) animal intrinsic variability affects the outcomes so the intake and growth trajectories are realizations of a stochastic process. Data on cumulated net energy intake and body weight measurements registered from weaning to maturity were available for 13 pigs. The model was fitted separately to 13 datasets. Furthermore, slaughter data obtained from 170 littermates was available for validation of the model. The parameters of the model were estimated by maximum likelihood within a stochastic state space model framework where a transform-both-sides approach was adopted to obtain constant variance. A suitable autocorrelation structure was generated by the stochastic process formulation. The pigs’ capacity for intake and growth were quantified by eight parameters: body weight at maximum rate of intake (149-281 kg); maximum rate of intake (25.7-35.7 MJ/day); metabolic body size exponent (fixed: 0.75); the daily maintenance requirement per kg metabolic body size (0.232-0.303 MJ/(day×kg^0.75)); reciprocal scaled energy density ; a dimensional exponent, θ₆ (0.730-0.867); coefficient for animal intrinsic variability in intake (0.120-0.248 MJ^0.5) and coefficient for animal intrinsic variability in growth (0.029-0.065 kg^0.5). Model parameter values for maintenance requirements and body energy gains were in good agreement with those obtained from slaughter data. In conclusion, the model provides biologically relevant parameter values, which cannot be derived by traditional analysis of growth and energy intake data.     

RATP: a model for simulating the spatial distribution of radiation absorption, transpiration and photosynthesis within canopies: application to an isolated tree crown

The model RATP (radiation absorption, transpiration and photosynthesis) is presented. The model was designed to simulate the spatial distribution of radiation and leaf-gas exchanges within vegetation canopies as a function of canopy structure, canopy microclimate within the canopy and physical and physiological leaf properties. The model uses a three-dimensional (3D) representation of the canopy (i.e. an array of 3D cells, each characterized by a leaf area density). Radiation transfer is computed by a turbid medium analogy, transpiration by the leaf energy budget approach, and photosynthesis by the Farquhar model, each applied for sunlit and shaded leaves at the individual 3D cell-scale. The model typically operates at a 20–30 min time step. The RATP model was applied to an isolated, 20-year-old walnut tree grown in the field. The spatial distribution of wind speed, stomatal response to environmental variables, and light acclimation of leaf photosynthetic properties were taken into account. Model outputs were compared with data acquired in the field. The model was shown to simulate satisfactorily the intracrown distribution of radiation regime, transpiration and photosynthetic rates, at shoot or branch scales.     

A model for the neuronal substrate of dead reckoning and memory in arthropods: a comparative computational and behavioral study

Returning to the point of departure after exploring the environment is a key capability for most animals. In the absence of landmarks, this task will be solved by integrating direction and distance traveled over time. This is referred to as path integration or dead reckoning. An important question is how the nervous systems of navigating animals such as the 1 mm³ brain of ants can integrate local information in order to make global decision. In this article we propose a neurobiologically plausible system of storing and retrieving direction and distance information. The path memory of our model builds on the well established concept of population codes, moreover our system does not rely on trigonometric functions or other complex non-linear operations such as multiplication, but only uses biologically plausible operations such as integration and thresholding. We test our model in two paradigms; in the first paradigm the system receives input from a simulated compass, in the second paradigm, the model is tested against behavioral data recorded from 17 ants. We were able to show that our path memory system was able to reliably encode and compute the angle of the vector pointing to the start location, and that the system stores the total length of the trajectory in a dependable way. From the structure and behavior of our model, we derive testable predictions both at the level of observable behavior as well as on the anatomy and physiology of its underlying neuronal substrate.     

Modulatory effects of parallel fiber and molecular layer interneuron synaptic activity on purkinje cell responses to ascending segment input: a modeling study

Based on anatomical, physiological, and model-based studies, it has been proposed that synapses associated with the ascending segment of granule cell axons provide the principle excitatory drive on Purkinje cells which is then modulated by the more numerous parallel fiber synapses. In this study we have evaluated this idea using a detailed compartmental model of a cerebellar Purkinje cell by providing identical ascending segment synaptic inputs during different levels of random parallel fiber and molecular interneuron input. Results suggest that background inputs from parallel fibers and molecular layer interneurons can have a substantial effect on the response of Purkinje cells to ascending segment inputs. Interestingly, these effects are not reflected in the average firing rate of the Purkinje cell and are thus entirely dendritic in effect. These results are considered in the context of the known segregated spatial distribution of the parallel fibers and ascending segment synapses and a new hypothesis concerning the functional organization of cerebellar cortical circuitry.     

Exploring the spatial distribution of light interception and photosynthesis of canopies by means of a functional-structural plant model

Background and Aims

At present most process-based models and the majority of three-dimensional models include simplifications of plant architecture that can compromise the accuracy of light interception simulations and, accordingly, canopy photosynthesis. The aim of this paper is to analyse canopy heterogeneity of an explicitly described tomato canopy in relation to temporal dynamics of horizontal and vertical light distribution and photosynthesis under direct- and diffuse-light conditions.

Methods

Detailed measurements of canopy architecture, light interception and leaf photosynthesis were carried out on a tomato crop. These data were used for the development and calibration of a functional–structural tomato model. The model consisted of an architectural static virtual plant coupled with a nested radiosity model for light calculations and a leaf photosynthesis module. Different scenarios of horizontal and vertical distribution of light interception, incident light and photosynthesis were investigated under diffuse and direct light conditions.

Key Results

Simulated light interception showed a good correspondence to the measured values. Explicitly described leaf angles resulted in higher light interception in the middle of the plant canopy compared with fixed and ellipsoidal leaf-angle distribution models, although the total light interception remained the same. The fraction of light intercepted at a north–south orientation of rows differed from east–west orientation by 10 % on winter and 23 % on summer days. The horizontal distribution of photosynthesis differed significantly between the top, middle and lower canopy layer. Taking into account the vertical variation of leaf photosynthetic parameters in the canopy, led to approx. 8 % increase on simulated canopy photosynthesis.

Conclusions

Leaf angles of heterogeneous canopies should be explicitly described as they have a big impact both on light distribution and photosynthesis. Especially, the vertical variation of photosynthesis in canopy is such that the experimental approach of photosynthesis measurements for model parameterization should be revised.     

A new mathematical model for the homeostatic effects of sleep loss on neurobehavioral performance

The two-process model of sleep regulation makes accurate predictions of sleep timing and duration for a variety of experimental sleep deprivation and nap sleep scenarios. Upon extending its application to waking neurobehavioral performance, however, the model fails to predict the effects of chronic sleep restriction. Here we show that the two-process model belongs to a broader class of models formulated in terms of coupled non-homogeneous first-order ordinary differential equations, which have a dynamic repertoire capturing waking neurobehavioral functions across a wide range of wake/sleep schedules. We examine a specific case of this new model class, and demonstrate the existence of a bifurcation: for daily amounts of wakefulness less than a critical threshold, neurobehavioral performance is predicted to converge to an asymptotically stable state of equilibrium; whereas for daily wakefulness extended beyond the critical threshold, neurobehavioral performance is predicted to diverge from an unstable state of equilibrium. Comparison of model simulations to laboratory observations of lapses of attention on a psychomotor vigilance test (PVT), in experiments on the effects of chronic sleep restriction and acute total sleep deprivation, suggests that this bifurcation is an essential feature of performance impairment due to sleep loss. We present three new predictions that may be experimentally verified to validate the model. These predictions, if confirmed, challenge conventional notions about the effects of sleep and sleep loss on neurobehavioral performance. The new model class implicates a biological system analogous to two connected compartments containing interacting compounds with time-varying concentrations as being a key mechanism for the regulation of psychomotor vigilance as a function of sleep loss. We suggest that the adenosinergic neuromodulator/receptor system may provide the underlying neurobiology.     

砂生槐种子蜂危害空间格局及理论抽样研究

应用6种聚集度指标、Taylor和Iwao回归分析法对砂生槐种子蜂幼虫的空间分布格局进行了分析,得出砂生槐种子蜂幼虫的空间分布型为聚集分布,田间调查抽样方法为分行取样法,并得出田间幼虫不同密度时的理论抽样数。     

A probabilistic model of biological ageing of the lungs for analysing the effects of smoking,asthma and COPD

Background

Although a large body of literature is available that describes the effects of smoking, asthma and COPD on lung function, most studies are restricted to a small age range and to one factor. As a consequence, available results are incomplete and often difficult to compare, also due to the ways the effects are expressed. Furthermore, current approaches consider one type of measurement only or several types separately.

Methods

We propose a probabilistic model that expresses the effects as number of years added to chronological age or, in other words, that estimates the biological age of the lungs. Using biological age as a measure of the effects has the advantage of facilitating the understanding of their severity and comparison of results. In our model, chronological age and other factors affecting the health status of the lungs generate biological age, which in turn generates lung function measurements. This structure enables the use of multiple types of measurement to obtain a more precise estimate of the effects and parameter sharing for characterization over large age ranges and of co-occurrence of factors with little data. We treat the parameters that model smoking habits and lung diseases as random variables to obtain uncertainty in the estimated effects.

Results

We use the model to investigate the effects of smoking, asthma and COPD on the TwinsUK Registry. Our results suggest that the combination of smoking with lung disease(s) has higher effect than smoking or lung disease(s) alone, and that in smokers, co-occurrence of asthma and COPD is more detrimental than asthma or COPD alone.

Conclusions

The proposed model or other models based on a similar approach could be of help in improving the understanding of factors affecting lung function by enabling characterizations over large age ranges and of co-occurrence of factors with little data and the use of multiple types of measurement. The software implementing the model can be downloaded at the first author’s webpage.     

Effect of polyols on the conformational stability and biological activity of a model protein lysozyme

The purpose of this study was to investigate the stabilizing action of polyols against various protein degradation mechanisms (eg, aggregation, deamidation, oxidation), using a model protein lysozyme. Differential scanning calorimeter (DSC) was used to measure the thermodynamic parameters, mid point transition temperature and calorimetric enthalpy, in order to evaluate conformational stability. Enzyme activity assay was used to corroborate the DSC results. Mannitol, sucrose, lactose, glycerol, and propylene glycol were used as polyols to stabilize lysozyme against aggregation, deamidation, and oxidation. Mannitol was found to stabilize lysozyme against aggregation, sucrose against deamidation both at neutral pH and at acidic pH, and lactose against oxidation. Stabilizers that provided greater conformational stability of lysozyme against various degradation mechanisms also protected specific enzyme activity to a greater extent. It was concluded that DSC and bioassay could be valuable tools for screening stabilizers in protein formulations.