Absorbent Markov chains as a model for the study of the evolution of proteins

The formalism of absorbent Markov chains, previously developed by Kemeny & Snell (1960) is used as a model for the study of the evolution of proteins. Within the limits of statistical analysis used, the amino acid substitution frequencies of McLachlan (1972) are explained by the numerical values derived from the model used. In addition, the amino acid composition of proteins is partially explained and the relative mutability of amino acids receives a new interpretation in the light of the above mentioned stochastic model. The results show that some basic aspect of protein evolution can be predicted by a stochastic model and therefore a significant component of protein evolution is driven by a random element.     

Modelling the spread of European buckthorn in the Region of Waterloo

Established invasive species, such as European buckthorn (Rhamnus cathartica), pose a challenging problem for land managers who must decide when and how to control them. In order to make an informed decision land managers need to be able to predict the spread of these invasive species at local scales and without the need for excessive sampling. Our approach uses a hybrid model, combining habitat suitability and the presence of the invasive in neighbouring cells to predict the probability of a cell being invaded over time. A generalized linear mixed-effects model was used to create a habitat suitability model and a spread model. The habitat suitability model predicts the presence of buckthorn based on environmental characteristics and the results are used in the spread model. The spread model indicates that the invasion of buckthorn is influenced by the suitability of habitat and the presence of buckthorn in neighbouring cells. The success of the spread model suggests that this approach can be used to create a spatiotemporally explicit model with limited sampling effort.     

A musculoskeletal model of the upper extremity for use in the development of neuroprosthetic systems

Upper extremity neuroprostheses use functional electrical stimulation (FES) to restore arm motor function to individuals with cervical level spinal cord injury. For the design and testing of these systems, a biomechanical model of the shoulder and elbow has been developed, to be used as a substitute for the human arm. It can be used to design and evaluate specific implementations of FES systems, as well as FES controllers. The model can be customized to simulate a variety of pathological conditions. For example, by adjusting the maximum force the muscles can produce, the model can be used to simulate an individual with tetraplegia and to explore the effects of FES of different muscle sets. The model comprises six bones, five joints, nine degrees of freedom, and 29 shoulder and arm muscles. It was developed using commercial, graphics-based modeling and simulation packages that are easily accessible to other researchers and can be readily interfaced to other analysis packages. It can be used for both forward-dynamic (inputs: muscle activation and external load; outputs: motions) and inverse-dynamic (inputs: motions and external load; outputs: muscle activation) simulations. Our model was verified by comparing the model calculated muscle activations to electromyographic signals recorded from shoulder and arm muscles of five subjects. As an example of its application to neuroprosthesis design, the model was used to demonstrate the importance of rotator cuff muscle stimulation when aiming to restore humeral elevation. It is concluded that this model is a useful tool in the development and implementation of upper extremity neuroprosthetic systems.     

Classification of Trends Via the Linear State Space Model

A method is presented for classification of trend curves based on the linear state space model. In this approach information about the smoothness of the trend curves is incorporated into the classification model by a nonstationary stochastic trend model and can thereby be used to obtain a better classification. In the case of small data sets the performance of the classification is significantly improved in comparison with the usual cluster analysis. Maximum likelihood estimation can be used to calculate the parameters of this model and to determine the classification. The classification algorithm is described in detail and the results are compared to those of the usual cluster analysis by simulation studies and by an application to tree ring data.     

Flocculation and its effect on the vertical transport of fine-grained sediments

Recent experimental and theoretical work on flocculation and settling speeds of flocs is reviewed. On the basis of this work, an accurate and computationally efficient model of the aggregation and disaggregation of fine-grained sediments is proposed. This model is then used to predict flocculation times and steady-state floc sizes for a wide range of environmental conditions. The predicted flocculation times are smaller, sometimes by as much as two orders of magnitude, than those predicted by mono-disperse theory. The model is also used to show that the disaggregation of flocs due to increased shear near the sediment-water interface may be a possible mechanism for the increased concentrations often observed near this interface.     

Kinetic metabolic modelling for the control of plant cells cytoplasmic phosphate

A previously developed kinetic metabolic model for plant metabolism was used in a context of identification and control of intracellular phosphate (Pi) dynamics. Experimental data from batch flask cultures of Eschscholtiza californica cells was used to calibrate the model parameters for the slow dynamics (growth, nutrition, anabolic pathways, etc.). Perturbation experiments were performed using a perfusion small-scale bioreactor monitored by in vivo³¹P NMR. Parameter identification for Pi metabolism was done by measuring the cells dynamic response to different inputs for extracellular Pi (two pulse-response experiments and a step-response experiment). The calibrated model can describe Pi translocation between the cellular pools (vacuole and cytoplasm). The effect of intracellular Pi management on ATP/ADP and phosphomonoesters concentrations is also described by the model. The calibrated model is then used to develop a control strategy on the cytoplasmic Pi pool. From the identification of the systems dynamics, a proportional-integral controller was designed and tuned. The closed-loop control was implemented in the small-scale NMR bioreactor and experimental results were in accordance with model predictions. Thus, the calibrated model is able to predict cellular behaviour for phosphate metabolism and it was demonstrated that it is possible to control the intracellular level of cytoplasmic Pi in plant cells.     

A comparative method for both discrete and continuous characters using the threshold model

The threshold model developed by Sewall Wright in 1934 can be used to model the evolution of two-state discrete characters along a phylogeny. The model assumes that there is a quantitative character, called liability, that is unobserved and that determines the discrete character according to whether the liability exceeds a threshold value. A Markov chain Monte Carlo algorithm is used to infer the evolutionary covariances of the liabilities for discrete characters, sampling liability values consistent with the phylogeny and with the observed data. The same approach can also be used for continuous characters by assuming that the tip species have values that have been observed. In this way, one can make a comparative-methods analysis that combines both discrete and continuous characters. Simulations are presented showing that the covariances of the liabilities are successfully estimated, although precision can be achieved only by using a large number of species, and we must always worry whether the covariances and the model apply throughout the group. An advantage of the threshold model is that the model can be straightforwardly extended to accommodate within-species phenotypic variation and allows an interface with quantitative-genetics models.     

Confidence bands for cumulative incidence curves under the additive risk model

In the context of competing risks, the cumulative incidence function is often used to summarize the cause-specific failure-time data. As an alternative to the proportional hazards model, the additive risk model is used to investigate covariate effects by specifying that the subject-specific hazard function is the sum of a baseline hazard function and a regression function of covariates. Based on such a formulation, we present an approach to constructing simultaneous confidence intervals for the cause-specific cumulative incidence function of patients with given risk factors. A melanoma data set is used for the purpose of illustration.     

The use of a syncytium model of the crystalline lens of the eye as a new tool to study the light flashes phenomenon seen by astronauts

A syncytium model to study some electrical properties of the eye is proposed to study the phenomenon of anomalous light flashes (LF) perceived by astronauts in orbit. The crystalline lens is modelled as an ellipsoidal syncytium with a variable relative dielectric constant. The corresponding mathematical model is a boundary value problem for a system of two coupled elliptic partial differential equations in the two unknown syncytial electrical potentials. A numerical method to compute an approximate solution of this mathematical model is used, and some numerical results are shown. The model can be regarded as a new tool to study the LF phenomenon. In particular, the energy lost in the syncytium by a transversing cosmic charged particle is calculated and the results obtained with the syncytium model are compared with those obtained using the previously available Geant 3.21 simulation program. In addition, the interaction of antimatter–syncytium is studied, and the Creme96 computer program is used to evaluate the cosmic ray fluxes encountered by the International Space Station in its standard mission.     

Grasp modelling with a biomechanical model of the hand

The use of a biomechanical model for human grasp modelling is presented. A previously validated biomechanical model of the hand has been used. The equilibrium of the grasped object was added to the model through the consideration of a soft contact model. A grasping posture generation algorithm was also incorporated into the model. All the geometry was represented using a spherical extension of polytopes (s-topes) for efficient collision detection. The model was used to simulate an experiment in which a subject was asked to grasp two cylinders of different diameters and weights. Different objective functions were checked to solve the indeterminate problem. The normal finger forces estimated by the model were compared to those experimentally measured. The popular objective function sum of the squared muscle stresses was shown not suitable for the grasping simulation, requiring at least being complemented by task-dependent grasp quality measures.     

Validation of a Photosynthesis Model through the Use of the CO2Balance of a Greenhouse Tomato Canopy

Several leaf photosynthesis models were developed from wellcontrolled experiments in growth chambers. However, only a fewhave been validated under greenhouse conditions for their quantitativeand qualitative adequacy. In this paper, rates of net photosynthesisfor a tomato crop (Lycopersicon esculentum Mill) were measuredin a semi-commercial greenhouse (615 m³) for a significant timeperiod. Concomitant measurements of climatic conditions andLAI were used for simulation of net photosynthesis using theTOMGRO model which integrates Acock's model for photosynthesiscalculations. From simulations and from sensitivity analysis,the prediction of net photosynthesis appeared to be very sensitiveto the quantum use efficiency. The Acock model with originalparameters underestimated the net photosynthesis rate, but anincrease in the quantum use efficiency by 10% gave a good fit.In an effort to generalize the validity of the model, a residualanalysis was performed and showed a systematic bias relatedto light intensity intercepted by the canopy. The Marquardtalgorithm was used to adjust our data to the model but did noteliminate residual heterogeneity of variance with new parametervalues. On the basis of collected data, the criteria of goodnessof fit used showed that the photosynthesis model is inadequatein describing the CO₂-balance of the greenhouse agrosystem.However, it was determined that it could be used as a submodelwithin a more complex model for predicting growth and development.Copyright 1999 Annals of Botany Company Greenhouse, CO₂-balance, photosynthesis, TOMGRO model, Acock's model, residuals, tomato Lycopersicon esculentum Mill.     

A model of heart ventricles for electrocardiographic evaluation of the state of the myocardium

A mathematical model of heart excitation processes has been developed for describing an electrocardiogram. A verified archive of model electrocardiograms has been created with the use of the model. The model has been used to study how electrocardiograms are affected by individual variability in ventricle shape and heart position in the norm, in myocardial infarction of different localizations, and in ventricular hypertrophy. Correspondence of the specific features of real and model electrocardiograms is discussed.     

Accounting for Emissions and Sinks from the Biogeochemical Cycle of Carbon in the U.S. Economic Input‐Output Model

Biogeochemical cycles are essential ecosystem services that continue to degrade as a result of human activities, but are not fully considered in efforts toward sustainable engineering. This article develops a model that integrates the carbon cycle with economic activities in the 2002 U.S. economy. Data about the carbon cycle, including emissions and sequestration flows, is obtained from the greenhouse gas inventory of the U.S. Environmental Protection Agency. Economic activities are captured by the economic input‐output model available from the Bureau of Economic Analysis. The resulting model is more comprehensive in its accounting for the carbon cycle than existing methods for carbon footprint (CF) calculations. Examples of unique flows in this model include the effect of land‐use and land‐cover change on carbon dioxide flow within the U.S. national boundary, carbon sequestration in urban trees, and emissions resulting from liming. This model is used to gain unique insight into the carbon profile of U.S. economic sectors by providing the life cycle emissions and sequestration in each sector. Such insight may be used to support policies, manage supply chains, and be used for more comprehensive CF calculations.     

A dynamic model of the forearm including fatigue

A biomechanical model of the forearm, consisting of 61 muscle-tendon systems or tendons and 8 sections, is presented. The model can be used to calculate the muscle forces when resultant of the external forces and the motion is known. Calculations are based on constraints of muscle forces, joint forces, contact forces, and tendon junctions, and a load sharing principle telling which of the feasible solutions are likely and which are not. Fatigue is accounted for by updating the upper limits of the muscle forces according to the loading history. As an example, the model is used to predict the load sharing between the fingers when they are pressed against a table with a given total force.     

Estimating the rate of evolution of the rate of molecular evolution

A simple model for the evolution of the rate of molecular evolution is presented. With a Bayesian approach, this model can serve as the basis for estimating dates of important evolutionary events even in the absence of the assumption of constant rates among evolutionary lineages. The method can be used in conjunction with any of the widely used models for nucleotide substitution or amino acid replacement. It is illustrated by analyzing a data set of rbcL protein sequences.      

Evaluation of a generalized model of human postural dynamics and control in the sagittal plane

A two-step identification method is used to evaluate a generalized model of human postural control in the sagittal plane. Postural dynamics are represented as a planar open-chain linkage system supported by a triangular foot. The control mechanism is modeled as a state feedback element in which the torque acting at a given link is an arbitrary function of the state variables — angles and angular velocities. To validate the approach, six normal subjects underwent two series of experiments. The first series were used to determine an appropriate model of the system dynamics. The second series were used to estimate the parameters of the feedback model. A computer simulation of the complete system shows that the model predictions closely match the observed responses. These results suggest that the proposed model provides a useful framework for analysis of postural control mechanisms.This work was supported by the National Institutes of Health under Grant NS 21363     

利用混合模型分析地域对国内马尾松生物量的影响

开展全国森林生物量监测和评估,建立适合较大区域范围的通用性立木生物量模型是一项重要的基础工作,而分析森林生物量受不同地域的影响并保证不同尺度范围森林生物量估计值的可靠性,是必须面临的问题。以南方马尾松(Pinus massoniana)地上生物量数据为例,介绍了如何利用混合模型理论来分析地域对马尾松地上生物量的影响以及利用混合模型构建全国通用性立木生物量模型,为得到不同区域尺度范围内可靠的森林生物量评价和估计提供了有效途径。结果表明,混合模型不仅提高了模型的精度和通用性,并且模型中每个参数都有特定的数学含义,通过这些参数很容易分析出随机因子对生物量的影响程度。因此混合模型方法具有较大的灵活性和适应性,可推广到其它通用性模型(如材积方程)的建立。     

Evaluating the nucleus effect on the dynamic indentation behavior of cells

The effect of the nucleus on the cell mechanical behavior was investigated based on the dynamic indentation response of cells under a spherical tip. A “two-component” cell model (including cytoplasm and nucleus) is used, and the dynamic indentation behavior is studied by a semiempirical method, which is established based on fitting the numerical simulation results of the quasi-static indentation response of cells. We found that the “routine analysis” (based on the Hertz’s contact solution of homogeneous model) significantly overestimated the nucleus effect on the overall cell indentation response due to the effects of the Hertz contact radius and the substrate stiffening. These effects are significantly stronger in the “two-component” cell model than in the homogeneous model. The inaccuracy created by the “routine analysis” slightly increases with the modulus ratio of nucleus to cytoplasm and the volume fraction of nucleus. Finally, the error sensitivity to the geometrical parameters used in the model is discussed, which shows the indentation analysis is not very sensitive to these parameters, and the reasonable assumptions for these parameters are effective. This systematic analysis can provide a useful guideline to understanding the mechanical behavior of cells and nuclei.     

Correlation between the osmotic second virial coefficient and the solubility of proteins

A correlation between the osmotic second virial coefficient and the solubility of proteins is derived from classical thermodynamics to support an empirical relation previously found by Wilson and co-workers (1). The model is based on the equality of fugacities of the protein in the equilibrium phases, with the details of the model depending on the standard state used. The parameters in this model have been fitted to data for several systems, mainly with lysozyme as the protein. The model is found to describe experimental data, with variations in protein concentration, salt type and concentration, temperature, and pH, both qualitatively and quantitatively. Agreement between the model and the experimental data is very good for protein solubilities up to 30 mg/mL. Above this value the model underpredicts the experimental data, probably as a result of multibody interactions that are not included in the model here. Variations of the model parameters with protein type, temperature, pH, and salt type are discussed.