Mathematical modeling of pulmonary tuberculosis therapy: Insights from a prototype model with rifampin

There is a critical need for improved and shorter tuberculosis (TB) treatment. Current in vitro models of TB, while valuable, are poor predictors of the antibacterial effect of drugs in vivo. Mathematical models may be useful to overcome the limitations of traditional approaches in TB research. The objective of this study was to set up a prototype mathematical model of TB treatment by rifampin, based on pharmacokinetic, pharmacodynamic and disease submodels.The full mathematical model can simulate the time-course of tuberculous disease from the first day of infection to the last day of therapy. Therapeutic simulations were performed with the full model to study the antibacterial effect of various dosage regimens of rifampin in lungs.The model reproduced some qualitative and quantitative properties of the bactericidal activity of rifampin observed in clinical data. The kill curves simulated with the model showed a typical biphasic decline in the number of extracellular bacteria consistent with observations in TB patients. Simulations performed with more simple pharmacokinetic/pharmacodynamic models indicated a possible role of a protected intracellular bacterial compartment in such a biphasic decline.This modeling effort strongly suggests that current dosage regimens of RIF may be further optimized. In addition, it suggests a new hypothesis for bacterial persistence during TB treatment.     

Simulation of circadian rhythm generation in the suprachiasmatic nucleus with locally coupled self-sustained oscillators

In mammals, circadian rhythms are driven by a pacemaker located in the suprachiasmatic nuclei (SCN) of the anterior hypothalamus. The firing rate of neurons within the SCN exhibits a circadian rhythm. There is evidence that individual neurons within the SCN act as circadian oscillators. Rhythm generation in the SCN was therefore modeled by a system of self-sustained oscillators. The model is composed of up to 10000 oscillatory elements arranged in a square array. Each oscillator has its own (randomly determined) intrinsic period reflecting the widely dispersed periods observed in the SCN. The model behavior was investigated mainly in the absence of synchronizing zeitgebers. Due to local coupling the oscillators synchronized and an overall rhythm emerged. This indicates that a locally coupled system is capable of integrating the output of individual clock cells with widely dispersed periods. The period of the global output (average of all oscillators) corresponded to the average of the intrinsic periods and was stable even for small amplitudes and during transients. Noise, reflecting biological fluctuations at the cellular level, distorted the global rhythm in small arrays. The period of the rhythm could be stabilized by increasing the array size, which thus increased the robustness against noise. Since different regions of the SCN have separate output pathways, the array of oscillators was subdivided into four quadrants. Sudden deviations of periodicity sometimes appeared in one quadrant, while the periods of the other quadrants were largely unaffected. This result could represent a model for splitting, which has been observed in animal experiments. In summary, the multi-oscillator model of the SCN showed a broad repertoire of dynamic patterns, revealed a stable period (even during transients) with robustness against noise, and was able to account for such a complex physiological behavior as splitting.     

A numerical and experimental study of compliance and collapsibility of preterm lamb tracheae

Knowledge of the mechanical behaviour of immature tracheae is crucial in order to understand the effects exerted on central airways by ventilatory treatments, particularly of Total Liquid Ventilation. In this study, a combined experimental and computational approach was adopted to investigate the compliance and particularly collapsibility of preterm lamb tracheae in the range of pressure likely applied during Total Liquid Ventilation (−30 to 30 cmH₂O). Tracheal samples of preterm lambs (n=5; gestational age 120–130 days) were tested by altering transmural pressure from −30 to 30 cmH₂O. Inflation (S_i) and collapsing (S_c) compliance values were calculated in the ranges 0 to 10 cmH₂O and –10 to 0 cmH₂O, respectively. During the tests, an asymmetric behaviour of the ΔV/V₀ vs. P curves at positive and negative pressure was observed, with mean S_i=0.013 cmH₂O⁻¹ and S_c=0.053 cmH₂O⁻¹. A different deformed configuration of the sample regions was observed, depending on the posterior shape of cartilaginous ring. A three-dimensional finite-element structural model of a single tracheal ring, based on histology measurements of the tested samples was developed. The model was parameterised in order to represent rings belonging to three different tracheal regions (craniad, median, caudal) and numerical analyses replicating the collapse test conditions were performed to evaluate the ring collapsibility at pressures between 0 and −30 cmH₂O. Simulation results were compared to experimental data to verify the model's reliability. The best model predictions occurred at pressures −30 to −10 cmH₂O. In this range, a model composed of median rings best interpreted the experimental data, with a maximum error of 2.7%; a model composed of an equal combination of all rings yielded an error of 12.6%.     

Long-term evolution of an ecosystem with spontaneous periodicity of mass extinctions

Twenty years ago, after analysing palaeontological data, Raup and Sepkoski suggested that mass extinctions on Earth appear cyclically in time with a period of approximately 26 million years (My). To explain the 26 My period, a number of proposals were made involving, e.g., astronomical effects, increased volcanic acitivity, or the Earth's magnetic field reversal, none of which, however, has been confirmed. Here we study a spatially extended discrete model of an ecosystem and show that the periodicity of mass extinctions might be a natural feature of the ecosystem's dynamics and not the result of a periodic external perturbation. In our model, periodic changes of the diversity of an ecosystem and some of its other characteristics are induced by the coevolution of species. In agreement with some palaeontological data, our results show that the longevity of a species depends on the evolutionary stage at which the species is created. Possible further tests of our model are also discussed.     

Compartmental neural simulations with spatial adaptivity

Since their inception, computational models have become increasingly complex and useful counterparts to laboratory experiments within the field of neuroscience. Today several software programs exist to solve the underlying mathematical system of equations, but such programs typically solve these equations in all parts of a cell (or network of cells) simultaneously, regardless of whether or not all of the cell is active. This approach can be inefficient if only part of the cell is active and many simulations must be performed. We have previously developed a numerical method that provides a framework for spatial adaptivity by making the computations local to individual branches rather than entire cells (Rempe and Chopp, SIAM Journal on Scientific Computing, 28: 2139–2161, 2006). Once the computation is reduced to the level of branches instead of cells, spatial adaptivity is straightforward: the active regions of the cell are detected and computational effort is focused there, while saving computations in other regions of the cell that are at or near rest. Here we apply the adaptive method to four realistic neuronal simulation scenarios and demonstrate its improved efficiency over non-adaptive methods. We find that the computational cost of the method scales with the amount of activity present in the simulation, rather than the physical size of the system being simulated. For certain problems spatial adaptivity reduces the computation time by up to 80%.     

Learning and coding of concepts in neural networks

Our environment consists of virtually an infinite number of scenarios in which we have to function. In order to respond properly to an incoming stimulus, the brain has first to analyze it, and to find out the basic familiar elements that are part of it. In other words, by using a library which contains a relatively small number of basic concepts, the brain analyzes the multitude of incoming events. Some of those basic concepts are innate, but many of them must be learned, in order to accommodate for the arbitrary environment around us. A classifying box is defined as the neural network that finds out the familiar concepts that are present in an incoming stimulus. Models for classifying boxes are introduced, and possible mechanisms by which they may establish their libraries of concepts are suggested, and then compared and evaluated by computer simulations.     

Estimation of Free Energy Systematic Errors in Molecular Simulations of Globular Proteins Surrounded by Finite Water Clusters. One Center Multipole Expansion of Reaction Field Differences

Free energy calculated in simulations on the atomic level (Monte Carlo or Molecular Dynamics) has a systematic error, if the water shell surrounding a globular protein is finite. The error (“cluster error”) is equal to a difference of free energies obtained in simulations with an infinite and finite water shell. In this work a continuum dielectric model was used to estimate the “cluster error”. A multipole expansion of the estimate was performed for a water shell with a spherical outer boundary. The expansion has very simple form. Each term is a product of two functions, one of them depending only on the charge's conformation, and the other one only on dielectric properties of the system. There are two practical uses of the expansion. First, it may be used to estimate the “cluster error” in a simulation already made; second, it may be used to plan a simulation in such a way that the “cluster error” is minimal. Numerical values of the largest terms in the multipole expansion corresponding to a typical system in simulations of globular proteins are given.     

Studying the Cu binding sites in the PrP N-terminal region: a test case for ab initio simulations

First principle ab initio molecular dynamics simulations of the Car-Parrinello type have proved to be of invaluable help in understanding the microscopic mechanisms of chemical bonding both in solid state physics and in structural biophysics. In this work we present as a test case a study of the Cu coordination mode at the Prion Protein binding sites localized in the N-terminal octarepeat region. Using medium size PC-clusters, we are able to deal with systems with up to about 350 atoms and 10(3) electrons for as long as approximately 2 ps. With a foreseeable forthcoming scaling up of the available CPU times by a factor 10(3), one can hope to be soon able to simulate systems of biological interest of realistic size and for physical times of the order of the nanosecond.     

Testing the predictivity of ecological indicator values. A comparison of real and `virtual' relevés of lichen vegetation

A complex database on the lichens of Italy was used to combine ecological indicator values assigned to each species (pH, eutrophication, light and aridity), in such a way as to simulate `virtual habitats' from a beech forest of northern Italy. For each habitat, a list of species was obtained (`virtual relevé'). A matrix of real and virtual relevés was submitted to classification and ordination, obtaining six main community-types, all of which include both real and virtual relevés. Two ordinations of species were carried out, one on the matrix of real relevés, the other on that of virtual relevés: their comparison shows that the consistency and the resolving power of the indicator values was high, but it also permits to detect and correct some errors. The results indicate a high predictivity of the indicator values for constructing ecological scenarios.     

The ribosome’s energy landscape: Recent insights from computation

Biophysical Reviews - The ever-increasing capacity of computing resources has extended ribosome calculations from the study of small-scale fluctuations to large-scale barrier-crossing processes. As...     

沙化土地封禁保护政策的农户满意度及影响因素分析——以甘肃省为例

农户是生态治理政策的\"践行者\",也是政策效果的\"检验者\",其满意度对政策的可持续实施至关重要。基于甘肃省沙化土地封禁保护区周边1417份农户调查数据,运用帕累托分析方法和Ordered Logit模型,就沙化土地封禁保护政策的农户满意度及影响因素展开分析。研究结果表明:沙化土地封禁保护政策的农户总体满意度介于\"一般\"和\"满意\"之间,均值为3.67(\"非常满意\"为5);外部影响因素分析表明,政策实施效果中风沙危害削减程度、荒漠化逆转程度、家庭收入提升状况、破坏行为减少程度与农户满意度之间存在正相关性;生态变化感知中的风沙强度、水资源紧缺程度对农户满意度起负向作用,降雨(雪)次数变化、荒漠植被盖度对农户满意度起正向作用。农户内部自身因素中,家庭人均收入、耕地、政府补贴、性别、教育程度、健康状况与农户满意度均通过显著性检验。控制变量因素中地方政府治理重视程度与农户满意度呈正相关性,平原地区的农户满意度明显高于山区。从政策角度看,农户生计改善是未来沙化土地封禁保护政策成功实施的关键保障。