A data-driven model of the generation of human EEG based on a spatially distributed stochastic wave equation

We discuss a model for the dynamics of the primary current density vector field within the grey matter of human brain. The model is based on a linear damped wave equation, driven by a stochastic term. By employing a realistically shaped average brain model and an estimate of the matrix which maps the primary currents distributed over grey matter to the electric potentials at the surface of the head, the model can be put into relation with recordings of the electroencephalogram (EEG). Through this step it becomes possible to employ EEG recordings for the purpose of estimating the primary current density vector field, i.e. finding a solution of the inverse problem of EEG generation. As a technique for inferring the unobserved high-dimensional primary current density field from EEG data of much lower dimension, a linear state space modelling approach is suggested, based on a generalisation of Kalman filtering, in combination with maximum-likelihood parameter estimation. The resulting algorithm for estimating dynamical solutions of the EEG inverse problem is applied to the task of localising the source of an epileptic spike from a clinical EEG data set; for comparison, we apply to the same task also a non-dynamical standard algorithm.     

An inverse method for predicting tissue-level mechanics from cellular mechanical input

Extracellular matrix (ECM) provides a dynamic three-dimensional structure which translates mechanical stimuli to cells. This local mechanical stimulation may direct biological function including tissue development. Theories describing the role of mechanical regulators hypothesize the cellular response to variations in the external mechanical forces on the ECM. The exact ECM mechanical stimulation required to generate a specific pattern of localized cellular displacement is still unknown. The cell to tissue inverse problem offers an alternative approach to clarify this relationship. Developed for structural dynamics, the inverse dynamics problem translates measurements of local state variables (at the cell level) into an unknown or desired forcing function (at the tissue or ECM level). This paper describes the use of eigenvalues (resonant frequencies), eigenvectors (mode shapes), and dynamic programming to reduce the mathematical order of a simplified cell–tissue system and estimate the ECM mechanical stimulation required for a specified cellular mechanical environment. Finite element and inverse numerical analyses were performed on a simple two-dimensional model to ascertain the effects of weighting parameters and a reduction of analytical modes leading toward a solution. Simulation results indicate that the reduced number of mechanical modes (from 30 to 14 to 7) can adequately reproduce an unknown force time history on an ECM boundary. A representative comparison between cell to tissue (inverse) and tissue to cell (boundary value) modeling illustrates the multiscale applicability of the inverse model.     

Distributed parameter identification for a label-structured cell population dynamics model using CFSE histogram time-series data

In this work we address the problem of the robust identification of unknown parameters of a cell population dynamics model from experimental data on the kinetics of cells labelled with a fluorescence marker defining the division age of the cell. The model is formulated by a first order hyperbolic PDE for the distribution of cells with respect to the structure variable x (or z) being the intensity level (or the log₁₀-transformed intensity level) of the marker. The parameters of the model are the rate functions of cell division, death, label decay and the label dilution factor. We develop a computational approach to the identification of the model parameters with a particular focus on the cell birth rate α(z) as a function of the marker intensity, assuming the other model parameters are scalars to be estimated. To solve the inverse problem numerically, we parameterize α(z) and apply a maximum likelihood approach. The parametrization is based on cubic Hermite splines defined on a coarse mesh with either equally spaced a priori fixed nodes or nodes to be determined in the parameter estimation procedure. Ill-posedness of the inverse problem is indicated by multiple minima. To treat the ill-posed problem, we apply Tikhonov regularization with the regularization parameter determined by the discrepancy principle. We show that the solution of the regularized parameter estimation problem is consistent with the data set with an accuracy within the noise level in the measurements.      

A power-law rheology-based finite element model for single cell deformation

Physical forces can elicit complex time- and space-dependent deformations in living cells. These deformations at the subcellular level are difficult to measure but can be estimated using computational approaches such as finite element (FE) simulation. Existing FE models predominantly treat cells as spring-dashpot viscoelastic materials, while broad experimental data are now lending support to the power-law rheology (PLR) model. Here, we developed a large deformation FE model that incorporated PLR and experimentally verified this model by performing micropipette aspiration on fibroblasts under various mechanical loadings. With a single set of rheological properties, this model recapitulated the diverse micropipette aspiration data obtained using three protocols and with a range of micropipette sizes. More intriguingly, our analysis revealed that decreased pipette size leads to increased pressure gradient, potentially explaining our previous counterintuitive finding that decreased pipette size leads to increased incidence of cell blebbing and injury. Taken together, our work leads to more accurate rheological interpretation of micropipette aspiration experiments than previous models and suggests pressure gradient as a potential determinant of cell injury.     

Internal models and intermittency: A theoretical account of human tracking behavior

This paper concerns the use of tracking studies to test a theoretical account of the information processing performed by the human CNS during control of movement. The theory provides a bridge between studies of reaction time and continuous tracking. It is proposed that the human CNS includes neuronal circuitry to compute inverse internal models of the multiple input, multiple output, dynamic, nonlinear relationships between outgoing motor commands and their resulting perceptual consequences. The inverse internal models are employed during movement execution to transform preplanned trajectories of desired perceptual consequences into appropriate outgoing motor commands to achieve them. A finite interval of time is required by the CNS to preplan the desired perceptual consequences of a movement and it does not commence planning a new movement until planning of the old one has been completed. This behavior introduces intermittency into the planning of movements. In this paper we show that the gain and phase frequency response characteristics of the human operator in a visual pursuit tracking task can be derived theoretically from these assumptions. By incorporating the effects of internal model inaccuracy and of speed-accuracy trade-off in performance, it is shown that various aspects of experimentally measured tracking behavior can be accounted for.     

A phenomenological approach to modelling collective cell movement in 2D

There are two main approaches to unraveling the mechanisms involved in the regulation of collective cell movement. On the one hand, “in vitro” tests try to represent “in vivo” conditions. On the other hand, “in silico” tests aim to model this movement through the use of complex numerically implemented mathematical methods. This paper presents a simple cell-based mathematical model to represent the collective movement phenomena. This approach is used to better understand the different interactive forces which guide cell movement, focusing mainly on the role of the cell propulsion force with the substrate. Different applications are simulated for 2D cell cultures, wound healing, and collective cell movement in substrates with different degrees of stiffness. The model provides a plausible explanation of how cells work together in order to regulate their movement, showing the significant influence of the propulsive force exerted by the cell to the substrate on guiding the collective cell movement and its interplay with other cell forces.     

Sea urchin primary mesenchyme cells: relation of cell polarity to the epithelial-mesenchymal transformation

In euechinoid sea urchin embryos, a subset of epithelial cells in the wall of the blastula become pulsatile, elongate, lose connections with their neighboring cells, and move into the blastocoel to form the primary mesenchyme cells. The Golgi apparatus and microtubule organizing center (MTOC) are located at the apical end of these epithelial cells. We show that as primary mesenchyme cells begin to move into the blastocoel, the Golgi apparatus and MTOC move to a new position adjacent to the apical side of the nucleus. They do not move to a position between the nucleus and the leading (i.e., basal) end of the cell as they do in cultured fibroblasts undergoing directed migration. In addition, we have inhibited the movement of membranous vesicles to the cell surface by incubating embryos in the ionophore monensin. We have used antibodies to msp130, a primary mesenchyme cell surface-specific glycoprotein, to demonstrate that monensin inhibits the movement of msp130-containing vesicles to the cell surface. Despite the inhibition of membrane shuttling by monensin, primary mesenchyme cells ingress on schedule and display normal cell-shape changes. We draw two conclusions from our data. First, the cellular elongation that characterizes ingression is not due to the local insertion of membrane at the leading (basal) end of the cell. Second, ingression does not depend upon establishment of the same cell polarity required for fibroblasts to carry out directed cell migration.     

A neuromusculoskeletal tracking method for estimating individual muscle forces in human movement

A neuromusculoskeletal tracking (NMT) method was developed to estimate muscle forces from observed motion data. The NMT method combines skeletal motion tracking and optimal neuromuscular tracking to produce forward simulations of human movement quickly and accurately. The skeletal motion tracker calculates the joint torques needed to actuate a skeletal model and track observed segment angles and ground forces in a forward simulation of the motor task. The optimal neuromuscular tracker resolves the muscle redundancy problem dynamically and finds the muscle excitations (and muscle forces) needed to produce the joint torques calculated by the skeletal motion tracker. To evaluate the accuracy of the NMT method, kinematics and ground forces obtained from an optimal control (parameter optimization) solution for maximum-height jumping were contaminated with both random and systematic noise. These data served as input observations to the NMT method as well as an inverse dynamics analysis. The NMT solution was compared to the input observations, the original optimal solution, and a simulation driven by the inverse dynamics torques. The results show that, in contrast to inverse dynamics, the NMT method is able to produce an accurate forward simulation consistent with the optimal control solution. The NMT method also requires 3 orders-of-magnitude less CPU time than parameter optimization. The speed and accuracy of the NMT method make it a promising new tool for estimating muscle forces using experimentally obtained kinematics and ground force data.     

Prediction of ground reaction forces and moments during various activities of daily living

Inverse dynamics based simulations on musculoskeletal models is a commonly used method for the analysis of human movement. Due to inaccuracies in the kinematic and force plate data, and a mismatch between the model and the subject, the equations of motion are violated when solving the inverse dynamics problem. As a result, dynamic inconsistency will exist and lead to residual forces and moments. In this study, we present and evaluate a computational method to perform inverse dynamics-based simulations without force plates, which both improves the dynamic consistency as well as removes the model?s dependency on measured external forces. Using the equations of motion and a scaled musculoskeletal model, the ground reaction forces and moments (GRF&Ms) are derived from three-dimensional full-body motion. The method entails a dynamic contact model and optimization techniques to solve the indeterminacy problem during a double contact phase and, in contrast to previously proposed techniques, does not require training or empirical data. The method was applied to nine healthy subjects performing several Activities of Daily Living (ADLs) and evaluated with simultaneously measured force plate data. Except for the transverse ground reaction moment, no significant differences (P>0.05) were found between the mean predicted and measured GRF&Ms for almost all ADLs. The mean residual forces and moments, however, were significantly reduced (P>0.05) in almost all ADLs using our method compared to conventional inverse dynamic simulations. Hence, the proposed method may be used instead of raw force plate data in human movement analysis using inverse dynamics.     

Probing plant cell structure and function with viral movement proteins.

Virus-encoded movement proteins are the principal strategy by which all plant viruses counter the primary physical defense of the plant to infection - the cell wall - to produce systemic infection and disease. Our understanding of how these proteins act at the molecular and cellular level has increased enormously in the past decade and ushered in an exciting new era of plant virology as an approach to investigating plant cell structure and function. The earliest studies focused on how movement proteins interacted with plasmodesmata, and were an important element in demonstrating the dynamic nature of these intercellular channels. Current efforts are focused on the role of movement proteins in coordinating the replication of viral genomes and the vectorial movement of the progeny genomes through the infected cell, as well as into adjacent cells. Movement proteins are thus providing unique approaches to unravel the fundamental mechanisms by which macromolecular transport is directed and integrated within and between plant cells.     

Extreme pathway analysis of human red blood cell metabolism

The development of high-throughput technologies and the resulting large-scale data sets have necessitated a systems approach to the analysis of metabolic networks. One way to approach the issue of complex metabolic function is through the calculation and interpretation of extreme pathways. Extreme pathways are a mathematically defined set of generating vectors that describe the conical steady-state solution space for flux distributions through an entire metabolic network. Herein, the extreme pathways of the well-characterized human red blood cell metabolic network were calculated and interpreted in a biochemical and physiological context. These extreme pathways were divided into groups based on such criteria as their cofactor and by-product production, and carbon inputs including those that 1) convert glucose to pyruvate; 2) interchange pyruvate and lactate; 3) produce 2,3-diphosphoglycerate that binds to hemoglobin; 4) convert inosine to pyruvate; 5) induce a change in the total adenosine pool; and 6) dissipate ATP. Additionally, results from a full kinetic model of red blood cell metabolism were predicted based solely on an interpretation of the extreme pathway structure. The extreme pathways for the red blood cell thus give a concise representation of red blood cell metabolism and a way to interpret its metabolic physiology.     

Myoglobin cavities provide interior ligand pathway

The myoglobin protein binds oxygen and catalyzes NO oxidation. As a key model protein, its dynamics have been well studied by spectroscopy and by crystallography as well as by simulation. Nonetheless, visualization of the mechanism of movement of ligands within myoglobin has been difficult. Coordinates of the A1 and A3 taxonomic spectral states of myoglobin from the 1 A crystal structure (1a6g) are generated as consistent sets of correlated clusters of residues with A or B crystal alternates. Analysis of cavities in these A1 and A3 conformations clarifies the pathway of ligand motion from distal entry through interior movement to the proximal side of the heme. Cavities opened up by buried alternate conformations link the distal to the proximal side of the heme. Structural conservation highlights the relevance of this pathway to human neuroglobin. Cavity migration via myoglobin crystal alternates provides a specific link of protein structure to protein dynamics and protein function and demonstrates the relevance of substates (discrete disorder) to function for all proteins.     

Building an extensible cell wall

This article recounts, from my perspective of four decades in this field, evolving paradigms of primary cell wall structure and the mechanism of surface enlargement of growing cell walls. Updates of the structures, physical interactions, and roles of cellulose, xyloglucan, and pectins are presented. This leads to an example of how a conceptual depiction of wall structure can be translated into an explicit quantitative model based on molecular dynamics methods. Comparison of the model’s mechanical behavior with experimental results provides insights into the molecular basis of complex mechanical behaviors of primary cell wall and uncovers the dominant role of cellulose–cellulose interactions in forming a strong yet extensible network.

The ordered synthesis and bundling of cellulose microfibrils leads to a strong yet extensible surface network whose organization and physical properties are modulated by pliant matrix polysaccharides.     

Dynamics of granzyme B-induced apoptosis: mathematical modeling

Apoptosis is mediated by an intracellular biochemical system that mainly includes proteins (procaspases, caspases, inhibitors, Bcl-2 protein family as well as substances released from mitochondrial intermembrane space). The dynamics of caspase activation and target cleavage in apoptosis induced by granzyme B in a single K562 cell was studied using a mathematical model of the dynamics of granzyme B-induced apoptosis developed in this work. Also the first application of optimization approach to determination of unknown kinetic constants of biochemical apoptotic reactions was presented. The optimization approach involves solving of two problems: direct and inverse. Solving the direct optimization problem, we obtain the initial (baseline) concentrations of procaspases for known kinetic constants through conditional minimization of a cost function based on the principle of minimum protein consumption by the apoptosis system. The inverse optimization problem is aimed at determination of unknown kinetic constants of apoptotic biochemical reactions proceeding from the condition that the optimal concentrations of procaspases resulting from the solution of the direct optimization problem coincide with the observed ones, that is, those determined by biochemical methods. The Multidimensional Index Method was used to perform numerical solution of the inverse optimization problem.     

Ethylene-induced differential petiole growth in Arabidopsis thaliana involves local microtubule reorientation and cell expansion

? Hyponastic growth is an upward petiole movement induced by plants in response to various external stimuli. It is caused by unequal growth rates between adaxial and abaxial sides of the petiole, which bring rosette leaves to a more vertical position. The volatile hormone ethylene is a key regulator inducing hyponasty in Arabidopsis thaliana. Here, we studied whether ethylene-mediated hyponasty occurs through local stimulation of cell expansion and whether this involves the reorientation of cortical microtubules (CMTs). ? To study cell size differences between the two sides of a petiole in ethylene and control conditions, we analyzed epidermal imprints. We studied the involvement of CMT orientation in epidermal cells using the tubulin marker line as well as genetic and pharmacological means of CMT manipulation. ? Our results demonstrate that ethylene induces cell expansion at the abaxial side of the- petiole and that this can account for the observed differential growth. At the abaxial side, ethylene induces CMT reorientation from longitudinal to transverse, whereas, at the adaxial side, it has an opposite effect. The inhibition of CMTs disturbed ethylene-induced hyponastic growth. ? This work provides evidence that ethylene stimulates cell expansion in a tissue-specific manner and that it is associated with tissue-specific changes in the arrangement of CMTs along the petiole.     

Acute progression of BCR-FGFR1 induced murine B-lympho/myeloproliferative disorder suggests involvement of lineages at the pro-B cell stage

Constitutive activation of FGFR1, through rearrangement with various dimerization domains, leads to atypical myeloproliferative disorders where, although T cell lymphoma are common, the BCR-FGFR1 chimeric kinase results in CML-like leukemia. As with the human disease, mouse bone marrow transduction/transplantation with BCR-FGFR1 leads to CML-like myeloproliferation as well as B-cell leukemia/lymphoma. The murine disease described in this report is virtually identical to the human disease in that both showed bi-lineage involvement of myeloid and B-cells, splenomegaly, leukocytosis and bone marrow hypercellularity. A CD19(+) IgM(-) CD43(+) immunophenotype was seen both in primary tumors and two cell lines derived from these tumors. In all primary tumors, subpopulations of these CD19(+) IgM(-) CD43(+) were also either B220(+) or B220(-), suggesting a block in differentiation at the pro-B cell stage. The B220(-) phenotype was retained in one of the cell lines while the other was B220(+). When the two cell lines were transplanted into syngeneic mice, all animals developed the same B-lymphoblastic leukemia within 2-weeks. Thus, the murine model described here closely mimics the human disease with bilineage myeloid and B-cell leukemia/lymphoma which provides a representative model to investigate therapeutic intervention and a better understanding of the etiology of the disease.     

Unifying heuristic model of transmembrane co-ordinate control for cell growth and cell movement

An unifying dualistic system is proposed as control transmembrane mediator for both cell growth and cell movement. In this system, sparsely distributed membrane units containing allosteric protomers act through long-range co-operative phase transitions, to store or release a growth primary stereospecific initiator at the inner membrane surface. Other mosaic distributed membrane units contain movement modulation promoters; their mobility is controlled by a mechanism based on the microfilament-microtubule assemblage hypothesis. The movement inhibition is graded with the spreading of cell-cell contacts, while the growth control is an all-or-none effect depending on critical level of environmental factors. It is hypothesized that the growth controlling transmembrane effect is reversible in most of normal cultured cells and in mature cells having ability of proliferate, e.g. hepatocytes, but that it permanently promotes growth in the embryonic and tumor cells and is lacking in some highly differentiated cell types. This both mechanistic and metabolic transmembrane co-ordinate control allows to rationalize in an uniform model numerous different cell behavior phenomena, in particular surface modulation events, overlapping, contact inhibition of growth and movement, G,, S phase conversion, embryological development, differentiation in mature organisms, and metastasis. Its plausibility and implications are discussed.     

Parameter Identification in a Generalized Time-Harmonic Rayleigh Damping Model for Elastography

The identifiability of the two damping components of a Generalized Rayleigh Damping model is investigated through analysis of the continuum equilibrium equations as well as a simple spring-mass system. Generalized Rayleigh Damping provides a more diversified attenuation model than pure Viscoelasticity, with two parameters to describe attenuation effects and account for the complex damping behavior found in biological tissue. For heterogeneous Rayleigh Damped materials, there is no equivalent Viscoelastic system to describe the observed motions. For homogeneous systems, the inverse problem to determine the two Rayleigh Damping components is seen to be uniquely posed, in the sense that the inverse matrix for parameter identification is full rank, with certain conditions: when either multi-frequency data is available or when both shear and dilatational wave propagation is taken into account. For the multi-frequency case, the frequency dependency of the elastic parameters adds a level of complexity to the reconstruction problem that must be addressed for reasonable solutions. For the dilatational wave case, the accuracy of compressional wave measurement in fluid saturated soft tissues becomes an issue for qualitative parameter identification. These issues can be addressed with reasonable assumptions on the negligible damping levels of dilatational waves in soft tissue. In general, the parameters of a Generalized Rayleigh Damping model are identifiable for the elastography inverse problem, although with more complex conditions than the simpler Viscoelastic damping model. The value of this approach is the additional structural information provided by the Generalized Rayleigh Damping model, which can be linked to tissue composition as well as rheological interpretations.     

The possible influence of osmotic poration on cell membrane water permeability

It has been hypothesized that pores in the plasma membrane form under conditions of rapid water efflux, allowing extracellular ice to grow into the cytoplasm under conditions of rapid freezing. When cells with intracellular ice are thawed slowly, the transmembrane ice crystal expands through recrystallization causing the cell to lyse. One of the implications of this hypothesis is that osmotic pores will provide an alternative route for water movement under conditions of osmotically induced flow. We show that the plasma membrane water permeability of a fibroblast cell changes as a function of the osmotic pressure gradient that is used to drive water movement. It is further shown that cell volume is more important than the magnitude of water flux in causing this departure from a uniform water permeability. We suggest that these data provide evidence of a transient route for water movement across cell membranes.