Structured proteins and proteins with internal disorder

The point of view that a uniquely folded protein tertiary structure is required for the protein functioning has been prevailing in the literature quite recently. However of lately it has been found that many proteins in a cell have no such structure in an isolated state, though they have a well-defined function in physiological conditions. These proteins were named as proteins with natural or internal disorder. The portion of disordered regions in such proteins may vary from a sequence of several amino acids to a completely disordered sequence containing from tens to hundreds of amino acids. The main difference of these proteins from the structured (globular) ones is that they have no unique tertiary structure in an isolated state and acquire it after interaction with their partners. Their conformation in such a complex depends on the interacting partner and not only on their own amino acid sequence, which is specific for structured (globular) proteins. The problem of structural and functional relations in the structured proteins and proteins with internal disorder is discussed in this review. The complexity of the problem and its potential solutions are illustrated by the example of elongation factors EFlA.     

From inverse problems in mathematical physiology to quantitative differential diagnoses

The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data interpretation and decision making. In particular, the application of mathematical models of experimentally elucidated physiological mechanisms could augment the interpretation of quantitative, patient-specific information and help to better target therapy. Yet, such models are typically complex and nonlinear, a reality that often precludes the identification of unique parameters and states of the model that best represent available data. Hypothesizing that this non-uniqueness can convey useful information, we implemented a simplified simulation of a common differential diagnostic process (hypotension in an acute care setting), using a combination of a mathematical model of the cardiovascular system, a stochastic measurement model, and Bayesian inference techniques to quantify parameter and state uncertainty. The output of this procedure is a probability density function on the space of model parameters and initial conditions for a particular patient, based on prior population information together with patient-specific clinical observations. We show that multimodal posterior probability density functions arise naturally, even when unimodal and uninformative priors are used. The peaks of these densities correspond to clinically relevant differential diagnoses and can, in the simplified simulation setting, be constrained to a single diagnosis by assimilating additional observations from dynamical interventions (e.g., fluid challenge). We conclude that the ill-posedness of the inverse problem in quantitative physiology is not merely a technical obstacle, but rather reflects clinical reality and, when addressed adequately in the solution process, provides a novel link between mathematically described physiological knowledge and the clinical concept of differential diagnoses. We outline possible steps toward translating this computational approach to the bedside, to supplement today's evidence-based medicine with a quantitatively founded model-based medicine that integrates mechanistic knowledge with patient-specific information.     

Deactivation of Src family kinases: hypothesis testing using a Monte Carlo sensitivity analysis of systems-level properties.

Src family tyrosine kinases play a key role in many cellular signalling networks, but due to the high complexity of these networks their precise function remains elusive. Many factors involved in Src regulation, such as specific kinases and phosphatases, are still unknown. Mathematical models have been constructed to improve the understanding of the system and its dynamic behavior. Using a computational random parameter search, we characterized and compared the dynamics of three alternative models in order to assess their likelihoods. For this, we investigated how systems-level properties such as bistability and excitable behavior relate to kinetic and physiological parameters and how robust these properties were. Our results suggest the existence of a putative negative feedback loop in the Src system. A previously suggested role for PTPalpha in the deactivation of Src was not supported by the model.     

Using a cost function based on kinematics and electromyographic data to quantify muscle forces

A reliable evaluation of muscle forces in the human body is highly desirable for several applications in both clinical and research contexts. Several models of muscle force distribution based on non-invasive measurements have been proposed since 1836 (Weber and Weber, 1836), amongst which Crowninshield’s model (Crowninshield and Brand, 1981), which maximizes a cost-function representing the muscle fiber endurance, is the most popular. It is worth noting that Crowninshield’s model is the most widely adopted notwithstanding its major limitations of physiological coherence. Forster et al. (2004) pointed out that “these (conventional) criteria however do not predict co-contraction adequately”. Besides, electromyographic (EMG)-driven models have been proposed to assess individual muscle forces, which have not been broadly adopted due to their complexity and the need for a calibration before each test. In this context, a cost function based on kinematic and electromyographic data could provide the advantage of being physiologically more coherent with muscle activations compared to conventional cost-functions based on kinematics solely, and easier to use than the EMG-driven models. The objective of this study is to propose the first cost-function based on kinematics and electromyographic data to quantify muscle forces. When applying this new cost-function on a database of upper limb motions data of 17 subjects, healthy or with cerebral palsy, the muscle force prediction of the proposed model was 17.74% more coherent with the EMG pattern than the prediction of Crowninshield’s model. And on average, these results were more consistent whether the subjects were healthy or with cerebral palsy. In conclusion, we propose this cost-function for the quantification of muscle forces.     

Aggregation error in nonlinear ecological models

Conditions are presented for accurately representing the dynamics of several components of a nonlinear ecological system by a single state variable. For mass-balance ecosystem models, only two conditions exist that permit such aggregation without introducing error into the model. Under the first condition, components can be lumped if their environmental losses (e.g. respiration or migration) are characterized by identical linear functions. Under the second condition, the components must maintain constant proportionality throughout their transient behavior. If these conditions are violated, it is not possible to aggregate without error. However, it is shown that aggregation error can still be minimized. The theorems developed here extend related results derived for the general theory of systems and have the advantage of generality, being applicable to nonlinear models of considerable complexity.     

Modeling the physiological glucose-insulin dynamic system on diabetics

A novel mathematical model is presented to describe the dynamic behavior of plasma glucose and insulin on diabetic subjects. Though various models have been proposed to simulate the short-term (a variety of intravenous glucose or insulin injection) glucose-insulin dynamics, it is intended to construct a modified delay differential equations (DDEs) model based on the human glucose-insulin metabolic system. Five specific adjustable parameters inside the model are defined as the factors of the major physiological functions. Then several clinical data sets (56 subjects) which includes the information of food ingestion and exogenous insulin injection are verified and the model could practically reflect the dynamics and oscillation behavior on diabetic subjects by varying the adjustable parameters. Moreover, the corresponding parameters are fairly helpful to identify the patient's conditions of major physiological functions. This generic glucose-insulin dynamic model can be expected to develop such advanced therapy strategies for diabetics in the future.     

A Bidomain Model for Lens Microcirculation

There exists a large body of research on the lens of the mammalian eye over the past several decades. The objective of this work is to provide a link between the most recent computational models and some of the pioneering work in the 1970s and 80s. We introduce a general nonelectroneutral model to study the microcirculation in the lens of the eye. It describes the steady-state relationships among ion fluxes, between water flow and electric field inside cells, and in the narrow extracellular spaces between cells in the lens. Using asymptotic analysis, we derive a simplified model based on physiological data and compare our results with those in the literature. We show that our simplified model can be reduced further to the first-generation models, whereas our full model is consistent with the most recent computational models. In addition, our simplified model captures in its equations the main features of the full computational models. Our results serve as a useful link intermediate between the computational models and the first-generation analytical models. Simplified models of this sort may be particularly helpful as the roles of similar osmotic pumps of microcirculation are examined in other tissues with narrow extracellular spaces, such as cardiac and skeletal muscle, liver, kidney, epithelia in general, and the narrow extracellular spaces of the central nervous system, the “brain.” Simplified models may reveal the general functional plan of these systems before full computational models become feasible and specific.     

Equivalence relationships between stage-structured population models

Matrix population models are widely applied in conservation ecology to help predict future population trends and guide conservation effort. Researchers must decide upon an appropriate level of model complexity, yet there is little theoretical work to guide such decisions. In this paper we present an analysis of a stage-structured model, and prove that the model's structure can be simplified and parameterised in such a way that the long-term growth rate, the stable-stage distribution and the generation time are all invariant to the simplification. We further show that for certain structures of model the simplified models require less effort in data collection. We also discuss features of the models which are not invariant to the simplification and the implications of our results for the selection of an appropriate model. We illustrate the ideas using a population model for short-tailed shearwaters (Puffinus tenuirostris). In this example, model simplification can increase parameter elasticity, indicating that an intermediate level of complexity is likely to be preferred.     

Bioimpedancemetry for the assessment of periodontal tissue inflammation: a numerical feasibility study

In dentistry possible inflammatory episodes of oral cavity can be very frequent (periodontitis, mucositis, peri-implantitis) and they can have serious consequences. Indeed, peri-implantitis is still the principal cause of implant failure. Impedance values of biological tissues are related to the physiological/pathological state of the tissue itself. In fact, an inflamed site exhibits an impedance value lower than that of the corresponding healthy tissue. Based on these observations, the aim of this work is to determine if impedancemetric measurements are able to provide information about the inflammatory state of tissues. A numerical 3D model has been realized to simulate the measurement conditions present in the event of inflammation around a dental implant. The aim is to understand if it is possible to determine the presence of an inflamed tissue and to locate its site, so that the treatment could be specifically focused in that specific area. A simplified geometry reproducing the implant has been realized in order to validate the numerical model by means of experimental measurements. The obtained results are satisfactorily accurate, so the model can be considered reliable. Therefore, multiple simulations have been run on the original model to carry out a parametric study in terms of different conductivity values, different volumes of inflamed tissues and different measurement frequencies. The advantages and limits of such a method have been shown to properly define the main constraints for the system design.     

Neural lineage differentiation of human pluripotent stem cells: Advances in disease modeling

Brain diseases affect 1 in 6 people worldwide. These diseases range from acute neurological conditions such as stroke to chronic neurodegenerative disorders such as Alzheimer’s disease. Recent advancements in tissue-engineered brain disease models have overcome many of the different shortcomings associated with the various animal models, tissue culture models, and epidemiologic patient data that are commonly used to study brain disease. One innovative method by which to model human neurological disease is via the directed differentiation of human pluripotent stem cells (hPSCs) to neural lineages including neurons, astrocytes, and oligodendrocytes. Three-dimensional models such as brain organoids have also been derived from hPSCs, offering more physiological relevance due to their incorporation of various cell types. As such, brain organoids can better model the pathophysiology of neural diseases observed in patients. In this review, we will emphasize recent developments in hPSC-based tissue culture models of neurological disorders and how they are being used to create neural disease models.     

Comparison of Gene Regulatory Networks via Steady-State Trajectories

The modeling of genetic regulatory networks is becoming increasingly widespread in the study of biological systems. In the abstract, one would prefer quantitatively comprehensive models, such as a differential-equation model, to coarse models; however, in practice, detailed models require more accurate measurements for inference and more computational power to analyze than coarse-scale models. It is crucial to address the issue of model complexity in the framework of a basic scientific paradigm: the model should be of minimal complexity to provide the necessary predictive power. Addressing this issue requires a metric by which to compare networks. This paper proposes the use of a classical measure of difference between amplitude distributions for periodic signals to compare two networks according to the differences of their trajectories in the steady state. The metric is applicable to networks with both continuous and discrete values for both time and state, and it possesses the critical property that it allows the comparison of networks of different natures. We demonstrate application of the metric by comparing a continuous-valued reference network against simplified versions obtained via quantization.     

Conventional NMA as a better standard for evaluating elastic network models

Normal mode analysis (NMA) is an important tool for studying protein dynamics. Because of the complexity of conventional NMA that uses an all‐atom model and a semi‐empirical force field, many simplified NMA models have been developed, some of which are known as elastic network models. The quality of these simplified NMA models was assessed mostly by evaluating their predictions against experimental B‐factors, and rarely by comparing them with the original NMA. In this work, we take the effort to create a publicly accessible dataset of proteins with their minimized structures, NMA modes, and mean‐square fluctuations. Then, for the first time, we evaluate the quality of individual normal modes of several widely used elastic network models by comparing them with the conventional NMA. Our results demonstrate that the conventional NMA presents a better and more complete evaluation measure of the quality of elastic network models. This realization should be very helpful in improving current or designing new, higher quality elastic network models. Moreover, using the conventional NMA as the standard of evaluation, a number of interesting and significant insights into the elastic network models are gained. Proteins 2015; 83:259–267. © 2014 Wiley Periodicals, Inc.     

Dimensional reductions of a cardiac model for effective validation and calibration

Complex 3D beating heart models are now available, but their complexity makes calibration and validation very difficult tasks. We thus propose a systematic approach of deriving simplified reduced-dimensional models, in “0D”—typically, to represent a cardiac cavity, or several coupled cavities—and in “1D”—to model elongated structures such as muscle samples or myocytes. We apply this approach with an earlier-proposed 3D cardiac model designed to capture length-dependence effects in contraction, which we here complement by an additional modeling component devised to represent length-dependent relaxation. We then present experimental data produced with rat papillary muscle samples when varying preload and afterload conditions, and we achieve some detailed validations of the 1D model with these data, including for the length-dependence effects that are accurately captured. Finally, when running simulations of the 0D model pre-calibrated with the 1D model parameters, we obtain pressure–volume indicators of the left ventricle in good agreement with some important features of cardiac physiology, including the so-called Frank–Starling mechanism, the End-Systolic Pressure–Volume Relationship, as well as varying elastance properties. This integrated multi-dimensional modeling approach thus sheds new light on the relations between the phenomena observed at different scales and at the local versus organ levels.     

Methods of Model Reduction for Large-Scale Biological Systems: A Survey of Current Methods and Trends

Complex models of biochemical reaction systems have become increasingly common in the systems biology literature. The complexity of such models can present a number of obstacles for their practical use, often making problems difficult to intuit or computationally intractable. Methods of model reduction can be employed to alleviate the issue of complexity by seeking to eliminate those portions of a reaction network that have little or no effect upon the outcomes of interest, hence yielding simplified systems that retain an accurate predictive capacity. This review paper seeks to provide a brief overview of a range of such methods and their application in the context of biochemical reaction network models. To achieve this, we provide a brief mathematical account of the main methods including timescale exploitation approaches, reduction via sensitivity analysis, optimisation methods, lumping, and singular value decomposition-based approaches. Methods are reviewed in the context of large-scale systems biology type models, and future areas of research are briefly discussed.     

Conventional and newly developed bioheat transport models in vascularized tissues: A review

Heat transfer in a biological system is a complex process and its analysis is difficult. Heterogeneous vascular architecture, blood flow in the complex network of arteries and veins, varying metabolic heat generation rates and dependence of tissue properties on its physiological condition contribute to this complexity. The understanding of heat transfer in human body is important for better insight of thermoregulatory mechanism and physiological conditions. Its understanding is also important for accurate prediction of thermal transport and temperature distribution during biomedical applications. During the last three decades, many attempts have been made by researchers to model the complex thermal behavior of the human body. These models, viz., blood perfusion, countercurrent, thermal phase-lag, porous-media, perturbation, radiation, etc. have their corresponding strengths and limitations. Along with their biomedical applications, this article reviews various contextual issues associated with these models. After brief discussion of early bioheat models, the newly developed bioheat models are discussed in detail. Dependence of these models on biological properties, viz., thermophysical and optical properties are also discussed.     

Remote Neurodegeneration: Multiple Actors for One Play

Remote neurodegeneration significantly influences the clinical outcome in many central nervous system (CNS) pathologies, such as stroke, multiple sclerosis, and traumatic brain and spinal cord injuries. Because these processes develop days or months after injury, they are accompanied by a therapeutic window of opportunity. The complexity and clinical significance of remote damage is prompting many groups to examine the factors of remote degeneration. This research is providing insights into key unanswered questions, opening new avenues for innovative neuroprotective therapies. In this review, we evaluate data from various remote degeneration models to describe the complexity of the systems that are involved and the importance of their interactions in reducing damage and promoting recovery after brain lesions. Specifically, we recapitulate the current data on remote neuronal degeneration, focusing on molecular and cellular events, as studied in stroke and brain and spinal cord injury models. Remote damage is a multifactorial phenomenon in which many components become active in specific time frames. Days, weeks, or months after injury onset, the interplay between key effectors differentially affects neuronal survival and functional outcomes. In particular, we discuss apoptosis, inflammation, oxidative damage, and autophagy—all of which mediate remote degeneration at specific times. We also review current findings on the pharmacological manipulation of remote degeneration mechanisms in reducing damage and sustaining outcomes. These novel treatments differ from those that have been proposed to limit primary lesion site damage, representing new perspectives on neuroprotection.     

Metabolic syndrome: from epidemiology to systems biology

Metabolic syndrome (MetSyn) is a group of metabolic conditions that occur together and promote the development of cardiovascular disease (CVD) and diabetes. Recent genome-wide association studies have identified several novel susceptibility genes for MetSyn traits, and studies in rodent models have provided important molecular insights. However, as yet, only a small fraction of the genetic component is known. Systems-based approaches that integrate genomic, molecular and physiological data are complementing traditional genetic and biochemical approaches to more fully address the complexity of MetSyn.     

Chemometrics models for overcoming high between subject variability: applications in clinical metabolic profiling studies

In human metabolic profiling studies, between-subject variability is often the dominant feature and can mask the potential classifications of clinical interest. Conventional models such as principal component analysis (PCA) are usually not effective in such situations and it is therefore highly desirable to find a suitable model which is able to discover the underlying pattern hidden behind the high between-subject variability. In this study we employed two clinical metabolomics data sets as the testing grounds, in which such variability had been observed, and we demonstrate that a proper choice of chemometrics model can help to overcome this issue of high between-subject variability. Two data sets were used to represent two different types of experiment designs. The first data set was obtained from a small-scale study investigating volatile organic compounds (VOCs) collected from chronic wounds using a skin patch device and analysed by thermal desorption-gas chromatography-mass spectrometry. Five patients were recruited and for each patient three sites sampled in triplicate: healthy skin, boundary of the lesion and top of the lesion, the aim was to discriminate these three types of samples based on their VOC profile. The second data set was from a much larger study involving 35 healthy subjects, 47 patients with chronic obstructive pulmonary disease and 33 with asthma. The VOCs in the breath of each subject were collected using a mask device and analysed again by GC–MS with the aim of discriminating the three types of subjects based on breath VOC profiles. Multilevel simultaneous component analysis, multilevel partial least squares for discriminant analysis, ANOVA-PCA, and a novel simplified ANOVA-PCA model—which we have named ANOVA-Mean Centre (ANOVA-MC)—were applied on these two data sets. Significantly improved results were obtained by using these models. We also present a novel validation procedure to verify statistically the results obtained from those models.     

From sensor data to animal behaviour: an oystercatcher example

Animal-borne sensors enable researchers to remotely track animals, their physiological state and body movements. Accelerometers, for example, have been used in several studies to measure body movement, posture, and energy expenditure, although predominantly in marine animals. In many studies, behaviour is often inferred from expert interpretation of sensor data and not validated with direct observations of the animal. The aim of this study was to derive models that could be used to classify oystercatcher (Haematopus ostralegus) behaviour based on sensor data. We measured the location, speed, and tri-axial acceleration of three oystercatchers using a flexible GPS tracking system and conducted simultaneous visual observations of the behaviour of these birds in their natural environment. We then used these data to develop three supervised classification trees of behaviour and finally applied one of the models to calculate time-activity budgets. The model based on accelerometer data developed to classify three behaviours (fly, terrestrial locomotion, and no movement) was much more accurate (cross-validation error?=?0.14) than the model based on GPS-speed alone (cross-validation error?=?0.35). The most parsimonious acceleration model designed to classify eight behaviours could distinguish five: fly, forage, body care, stand, and sit (cross-validation error?=?0.28); other behaviours that were observed, such as aggression or handling of prey, could not be distinguished. Model limitations and potential improvements are discussed. The workflow design presented in this study can facilitate model development, be adapted to a wide range of species, and together with the appropriate measurements, can foster the study of behaviour and habitat use of free living animals throughout their annual routine.