Simulating Membrane Systems in Digital Computers

* Work partially supported by contribution of EU commission Under The Fifth Framework Programme, project “MolCoNet” IST-2001-32008.

A novel role of plasma membrane calcium atpase 4 as a negative-regulator of VEGF-induced angiogenesis

Current anti-angiogenic treatments involve the attenuation of signalling via the pro-angiogenic vascular endothelial growth factor/receptor (VEGF/VEGFR) axis. Stimulation of angiogenesis by VEGF requires the activation of the calcineurin/nuclear factor of activated T-cells (NFAT) signal transduction pathway which is inhibited by Plasma Membrane Calcium ATPase 4 (PMCA4), an endogenous calcium extrusion pump. However, PMCA4s role in calcineurin/NFAT-dependent angiogenesis is unknown. Using “gain of function” studies, we show here that adenoviral overexpression of PMCA4 in human umbilical vein endothelial cells (HUVEC) inhibited NFAT activity, decreased the expression of NFAT-dependent pro-angiogenic proteins (regulator of calcineurin 1.4 (RCAN1.4) and cyclooxygenase-2) and diminished in vitro cell migration and tube formation in response to VEGF-stimulation. Furthermore, in vivo blood vessel formation was attenuated in a matrigel plug assay by ectopic expression of PMCA4. Conversely, “loss of function” experiments by si-RNA-mediated knockdown of PMCA4 in HUVEC or isolation of mouse lung endothelial cells from PMCA4−/− mice showed increased VEGF-induced NFAT activity, RCAN1.4 expression, in vitro endothelial cell migration, tube formation and in vivo blood vessel formation. Additionally, in an in vivo pathological angiogenesis model of limb ischemia, the reperfusion of the ischemic limb of PMCA4−/− mice was augmented compared to wild-type. Disruption of the interaction between endogenous PMCA4 and calcineurin by adenoviral overexpression of the region of PMCA4 that interacts with calcineurin (residues 428–651) increased NFAT activity, RCAN1.4 protein expression and in vitro tube formation. These results identify PMCA4 as an inhibitor of VEGF-induced angiogenesis, highlighting its potential as a new therapeutic target for anti-angiogenic treatments.

Immunological synapse: a mathematical model of the bond formation process:mathematical modelling of the immature synapse

The cell:cell bond between an immune cell and an antigen presenting cell is a necessary event in the activation of the adaptive immune response. At the juncture between the cells, cell surface molecules on the opposing cells form non-covalent bonds and a distinct patterning is observed that is termed the immunological synapse. An important binding molecule in the synapse is the T-cell receptor (TCR), that is responsible for antigen recognition through its binding with a major-histocompatibility complex with bound peptide (pMHC). This bond leads to intracellular signalling events that culminate in the activation of the T-cell, and ultimately leads to the expression of the immune eector function. The temporal analysis of the TCR bonds during the formation of the immunological synapse presents a problem to biologists, due to the spatio-temporal scales (nanometers and picoseconds) that compare with experimental uncertainty limits. In this study, a linear stochastic model, derived from a nonlinear model of the synapse, is used to analyse the temporal dynamics of the bond attachments for the TCR. Mathematical analysis and numerical methods are employed to analyse the qualitative dynamics of the nonequilibrium membrane dynamics, with the specic aim of calculating the average persistence time for the TCR:pMHC bond. A single-threshold method, that has been previously used to successfully calculate the TCR:pMHC contact path sizes in the synapse, is applied to produce results for the average contact times of the TCR:pMHC bonds. This method is extended through the development of a two-threshold method, that produces results suggesting the average time persistence for the TCR:pMHC bond is in the order of 2-4 seconds, values that agree with experimental evidence for TCR signalling. The study reveals two distinct scaling regimes in the time persistent survival probability density prole of these bonds, one dominated by thermal uctuations and the other associated with the TCR signalling. Analysis of the thermal fluctuation regime reveals a minimal contribution to the average time persistence calculation, that has an important biological implication when comparing the probabilistic models to experimental evidence. In cases where only a few statistics can be gathered from experimental conditions, the results are unlikely to match the probabilistic predictions. The results also identify a rescaling relationship between the thermal noise and the bond length, suggesting a recalibration of the experimental conditions, to adhere to this scaling relationship, will enable biologists to identify the start of the signalling regime for previously unobserved receptor:ligand bonds. Also, the regime associated with TCR signalling exhibits a universal decay rate for the persistence probability, that is independent of the bond length.

Elastic modulus study of gold thin film for use as an actuated membrane in a superconductive radio frequency (RF) microelectromechanical (MEM) switch

The objective of this research was to find Young's elastic modulus for thin gold films at room and cryogenic temperatures based on the flexional model which has not been previously attempted. Electrical Sonnet simulations and numerical methods using Abacus for the mechanical responses were employed for this purpose. A RF MEM shunt switch was designed and a fabrication process developed in house. The switch is composed of a superconducting YBa2 Cu3O7 coplanar waveguide structure with an Au bridge membrane suspended above an area of the center conductor covered with BaTiO3 dielectric. The Au membrane is actuated by the electrostatic attractive force acting between the transmission line and the membrane when voltage is applied. The value of the actuation force will greatly depend on the switch pull-down voltage and on the geometry and mechanical properties of the bridge material. Results show that the elastic modulus for Au thin film can be 484 times higher at cryogenic temperature than it is at room temperature. ^

Computational modeling of intermediate temperature proton exchange membrane (PEM) fuel cells

A two-phase three-dimensional computational model of an intermediate temperature (120--190°C) proton exchange membrane (PEM) fuel cell is presented. This represents the first attempt to model PEM fuel cells employing intermediate temperature membranes, in this case, phosphoric acid doped polybenzimidazole (PBI). To date, mathematical modeling of PEM fuel cells has been restricted to low temperature operation, especially to those employing Nafion ® membranes; while research on PBI as an intermediate temperature membrane has been solely at the experimental level. This work is an advancement in the state of the art of both these fields of research. With a growing trend toward higher temperature operation of PEM fuel cells, mathematical modeling of such systems is necessary to help hasten the development of the technology and highlight areas where research should be focused.^ This mathematical model accounted for all the major transport and polarization processes occurring inside the fuel cell, including the two phase phenomenon of gas dissolution in the polymer electrolyte. Results were presented for polarization performance, flux distributions, concentration variations in both the gaseous and aqueous phases, and temperature variations for various heat management strategies. The model predictions matched well with published experimental data, and were self-consistent.^ The major finding of this research was that, due to the transport limitations imposed by the use of phosphoric acid as a doping agent, namely low solubility and diffusivity of dissolved gases and anion adsorption onto catalyst sites, the catalyst utilization is very low (∼1--2%). Significant cost savings were predicted with the use of advanced catalyst deposition techniques that would greatly reduce the eventual thickness of the catalyst layer, and subsequently improve catalyst utilization. The model also predicted that an increase in power output in the order of 50% is expected if alternative doping agents to phosphoric acid can be found, which afford better transport properties of dissolved gases, reduced anion adsorption onto catalyst sites, and which maintain stability and conductive properties at elevated temperatures.^

Blood-brain barrier in vitro model: A tissue engineering approach and validation

This dissertation evaluated the feasibility of using commercially available immortalized cell lines in building a tissue engineered in vitro blood-brain barrier (BBB) co-culture model for preliminary drug development studies. Mouse endothelial cell line and rat astrocyte cell lines purchased from American Type Culture Collections (ATCC) were the building blocks of the co-culture model. An astrocyte derived acellular extracellular matrix (aECM) was introduced in the co-culture model to provide a novel in vitro biomimetic basement membrane for the endothelial cells to form endothelial tight junctions. Trans-endothelial electrical resistance (TEER) and solute mass transport studies were engaged to quantitatively evaluate the tight junction formation on the in-vitro BBB models. Immuno-fluorescence microscopy and Western Blot analysis were used to qualitatively verify the in vitro expression of occludin, one of the earliest discovered tight junction proteins. Experimental data from a total of 12 experiments conclusively showed that the novel BBB in vitro co-culture model with the astrocyte derived aECM (CO+aECM) was promising in terms of establishing tight junction formation represented by TEER values, transport profiles and tight junction protein expression when compared with traditional co-culture (CO) model setups and endothelial cells cultured alone. Experimental data were also found to be comparable with several existing in vitro BBB models built from various methods. In vitro colorimetric sulforhodamine B (SRB) assay revealed that the co-cultured samples with aECM resulted in less cell loss on the basal sides of the insert membranes than that from traditional co-culture samples. The novel tissue engineering approach using immortalized cell lines with the addition of aECM was proven to be a relevant alternative to the traditional BBB in vitro modeling.

Elastic modulus study of gold thin film for use as an actuated membrane in a superconductive radio frequency (RF) MicroElectroMechanical (MEM) switch

The objective of this research was to find Young's elastic modulus for thin gold films at room and cryogenic temperatures based on the flexional model which has not been previously attempted. Electrical Sonnet simulations and numerical methods using Abacus for the mechanical responses were employed for this purpose. A RF MEM shunt switch was designed and a fabrication process developed in house. The switch is composed of a superconducting YBa2Cu3O7 coplanar waveguide structure with an Au bridge membrane suspended above an area of the center conductor covered with BaTiO3 dielectric. The Au membrane is actuated by the electrostatic attractive force acting between the transmission line and the membrane when voltage is applied. The value of the actuation force will greatly depend on the switch pull-down voltage and on the geometry and mechanical properties of the bridge material. Results show that the elastic modulus for Au thin film can be 484 times higher at cryogenic temperature than it is at room temperature.

Antimicrobial activity of prodigiosin is attributable to plasma-membrane damage

The bacterial pigment prodigiosin has various biological activities; it is, for instance, an effective antimicrobial. Here, we investigate the primary site targeted by prodigiosin, using the cells of microbial pathogens of humans as model systems: Candida albicans, Escherichia coli, Staphylococcus aureus. Inhibitory concentrations of prodigiosin; leakage of intracellular K+ ions, amino acids, proteins and sugars; impacts on activities of proteases, catalases and oxidases; and changes in surface appearance of pathogen cells were determined. Prodigiosin was highly inhibitory (30% growth rate reduction of C. albicans, E. coli, S. aureus at 0.3, 100 and 0.18 μg ml−1, respectively); caused leakage of intracellular substances (most severe in S. aureus); was highly inhibitory to each enzyme; and caused changes to S. aureus indicative of cell-surface damage. Collectively, these findings suggest that prodigiosin, log Poctanol–water 5.16, is not a toxin but is a hydrophobic stressor able to disrupt the plasma membrane via a chaotropicity-mediated mode-of-action.

Nonlinear Dynamics Near the Cell Membrane of Chara Corallina

The phenomenon of patterned distribution of pH near the cell membrane of the algae Chara corallina upon illumination is well-known. In this paper, we develop a mathematical model, based on the detailed kinetic analysis of proton fluxes across the cell membrane, to explain this phenomenon. The model yields two coupled nonlinear partial differential equations which describe the spatial dynamics of proton concentration changes and transmembrane potential generation. The experimental observation of pH pattern formation, its period and amplitude of oscillation, and also its hysteresis in response to changing illumination, are all reproduced by our model. A comparison of experimental results and predictions of our theory is made. Finally, a mechanism for pattern formation in Chara corallina is proposed.

Quantitative characterization of physico-chemical properties of the active layers of reverse osmosis and nanofiltration membranes, and their relation to membrane performance

The main objectives of this dissertation were: (i) to develop experimental and analytical procedures to quantify different physico-chemical properties of the ultra-thin (~ 100 nm) active layers of reverse osmosis (RO) and nanofiltration (NF) membranes and their interactions with contaminants; (ii) to use such procedures to evaluate the similarities and differences between the active layers of different RO/NF membranes; and (iii) to relate characterization results to membrane performance. Such objectives were motivated by the current limited understanding of the physico-chemical properties of active layers as a result of traditional characterization techniques having limitations associated with the nanometer-scale spatial resolution required to study these ultra-thin films. Functional groups were chosen as the main active layer property of interest. Specific accomplishments of this study include the development of procedures to quantify in active layers as a function of pH: (1) the concentration of both negatively and positively ionized functional groups; (2) the stoichiometry of association between ions (i.e., barium) and ionized functional groups (i.e., carboxylate and sulfonate); and (3) the steric effects experienced by ions (i.e., barium). Conceptual and mathematical models were developed to describe experimental results. The depth heterogeneity of the active layer physico-chemical properties and interactions with contaminants studied in this dissertation was also characterized. Additionally, measured concentrations of ionized functional groups in the polyamide active layers of several commercial RO/NF membranes were used as input in a simplified RO/NF transport model to predict the rejection of a strong electrolyte (i.e., potassium iodide) and a weak acid (i.e., arsenious acid) at different pH values based on rejection results at one pH condition. The good agreement between predicted and experimental results showed that the characterization procedures developed in this study serve as useful tools in the advancement of the understanding of the properties and structure of the active layers of RO/NF membranes, and the mechanisms of contaminant transport through them.

A deformation model of flexible, high area-to-mass ratio debris under perturbations and validation method

A new type of space debris was recently discovered by Schildknecht in near -geosynchronous orbit (GEO). These objects were later identified as exhibiting properties associated with High Area-to-Mass ratio (HAMR) objects. According to their brightness magnitudes (light curve), high rotation rates and composition properties (albedo, amount of specular and diffuse reflection, colour, etc), it is thought that these objects are multilayer insulation (MLI). Observations have shown that this debris type is very sensitive to environmental disturbances, particularly solar radiation pressure, due to the fact that their shapes are easily deformed leading to changes in the Area-to-Mass ratio (AMR) over time. This thesis proposes a simple effective flexible model of the thin, deformable membrane with two different methods. Firstly, this debris is modelled with Finite Element Analysis (FEA) by using Bernoulli-Euler theory called “Bernoulli model”. The Bernoulli model is constructed with beam elements consisting 2 nodes and each node has six degrees of freedom (DoF). The mass of membrane is distributed in beam elements. Secondly, the debris based on multibody dynamics theory call “Multibody model” is modelled as a series of lump masses, connected through flexible joints, representing the flexibility of the membrane itself. The mass of the membrane, albeit low, is taken into account with lump masses in the joints. The dynamic equations for the masses, including the constraints defined by the connecting rigid rod, are derived using fundamental Newtonian mechanics. The physical properties of both flexible models required by the models (membrane density, reflectivity, composition, etc.), are assumed to be those of multilayer insulation. Both flexible membrane models are then propagated together with classical orbital and attitude equations of motion near GEO region to predict the orbital evolution under the perturbations of solar radiation pressure, Earth’s gravity field, luni-solar gravitational fields and self-shadowing effect. These results are then compared to two rigid body models (cannonball and flat rigid plate). In this investigation, when comparing with a rigid model, the evolutions of orbital elements of the flexible models indicate the difference of inclination and secular eccentricity evolutions, rapid irregular attitude motion and unstable cross-section area due to a deformation over time. Then, the Monte Carlo simulations by varying initial attitude dynamics and deformed angle are investigated and compared with rigid models over 100 days. As the results of the simulations, the different initial conditions provide unique orbital motions, which is significantly different in term of orbital motions of both rigid models. Furthermore, this thesis presents a methodology to determine the material dynamic properties of thin membranes and validates the deformation of the multibody model with real MLI materials. Experiments are performed in a high vacuum chamber (10-4 mbar) replicating space environment. A thin membrane is hinged at one end but free at the other. The free motion experiment, the first experiment, is a free vibration test to determine the damping coefficient and natural frequency of the thin membrane. In this test, the membrane is allowed to fall freely in the chamber with the motion tracked and captured through high velocity video frames. A Kalman filter technique is implemented in the tracking algorithm to reduce noise and increase the tracking accuracy of the oscillating motion. The forced motion experiment, the last test, is performed to determine the deformation characteristics of the object. A high power spotlight (500-2000W) is used to illuminate the MLI and the displacements are measured by means of a high resolution laser sensor. Finite Element Analysis (FEA) and multibody dynamics of the experimental setups are used for the validation of the flexible model by comparing with the experimental results of displacements and natural frequencies.

Study of salinity gradients in the Persian Gulf and an experimental model for electric energy extraction from them using nano-membranes

Salinity gradient power (SGP) is the energy that can be obtained from the mixing entropy of two solutions with a different salt concentration. River estuary, as a place for mixing salt water and fresh water, has a huge potential of this renewable energy. In this study, this potential in the estuaries of rivers leading to the Persian Gulf and the factors affecting it are analysis and assessment. Since most of the full water rivers are in the Asia, this continent with the potential power of 338GW is a second major source of energy from the salinity gradient power in the world (Wetsus institute, 2009). Persian Gulf, with the proper salinity gradient in its river estuaries, has Particular importance for extraction of this energy. Considering the total river flow into the Persian Gulf, which is approximately equal to 3486 m3/s, the amount of theoretical extractable power from salinity gradient in this region is 5.2GW. Iran, with its numerous rivers along the coast of the Persian Gulf, has a great share of this energy source. For example, with study calculations done on data from three hydrometery stations located on the Arvand River, Khorramshahr Station with releasing 1.91M/ energy which is obtained by combining 1.26m3 river water with 0.74 m3 sea water, is devoted to itself extracting the maximum amount of extractable energy. Considering the average of annual discharge of Arvand River in Khorramshahr hydrometery station, the amount of theoretical extractable power is 955 MW. Another part of parameters that are studied in this research, are the intrusion length of salt water and its flushing time in the estuary that have a significant influence on the salinity gradient power. According to the calculation done in conditions HWS and the average discharge of rivers, the maximum of salinity intrusion length in to the estuary of the river by 41km is related to Arvand River and the lowest with 8km is for Helle River. Also the highest rate of salt water flushing time in the estuary with 9.8 days is related to the Arvand River and the lowest with 3.3 days is for Helle River. Influence of these two parameters on reduces the amount of extractable energy from salinity gradient power as well as can be seen in the estuaries of the rivers studied. For example, at the estuary of the Arvand River in the interval 8.9 days, salinity gradient power decreases 9.2%. But another part of this research focuses on the design of a suitable system for extracting electrical energy from the salinity gradient. So far, five methods have been proposed to convert this energy to electricity that among them, reverse electro-dialysis (RED) method and pressure-retarded osmosis (PRO) method have special importance in practical terms. In theory both techniques generate the same amount of energy from given volumes of sea and river water with specified salinity; in practice the RED technique seems to be more attractive for power generation using sea water and river water. Because it is less necessity of salinity gradient to PRO method. In addition to this, in RED method, it does not need to use turbine to change energy and the electricity generation is started when two solutions are mixed. In this research, the power density and the efficiency of generated energy was assessment by designing a physical method. The physical designed model is an unicellular reverse electro-dialysis battery with nano heterogenic membrane has 20cmx20cm dimension, which produced power density 0.58 W/m2 by using river water (1 g NaCl/lit) and sea water (30 g NaCl/lit) in laboratorial condition. This value was obtained because of nano method used on the membrane of this system and suitable design of the cell which led to increase the yield of the system efficiency 11% more than non nano ones.

Stability of membrane bound reactions

We present a novel approach to the dynamics of reactions of diffusing chemical species with species fixed in space e.g. by binding to a membrane. The non-diffusing reaction partners are clustered in areas with a diameter smaller than the diffusion length of the diffusing partner. The activated fraction of the fixed species determines the size of an active sub-region of the cluster. Linear stability analysis reveals that diffusion is one of the ma jor determinants of the stability of the dynamics. We illustrate the model concept with Ca²⁺ dynamics in living cells, which has release channels as fixed reaction partners. Our results suggest that spatial and temporal structures in intracellular Ca²⁺ dynamics are caused by fluctuations due to the small number of channels per cluster.

Mode locking in a spatially extended neuron model: active soma and compartmental tree

Understanding the mode-locked response of excitable systems to periodic forcing has important applications in neuroscience. For example it is known that spatially extended place cells in the hippocampus are driven by the theta rhythm to generate a code conveying information about spatial location. Thus it is important to explore the role of neuronal dendrites in generating the response to periodic current injection. In this paper we pursue this using a compartmental model, with linear dynamics for each compartment, coupled to an active soma model that generates action potentials. By working with the piece-wise linear McKean model for the soma we show how the response of the whole neuron model (soma and dendrites) can be written in closed form. We exploit this to construct a stroboscopic map describing the response of the spatially extended model to periodic forcing. A linear stability analysis of this map, together with a careful treatment of the non-differentiability of the soma model, allows us to construct the Arnol'd tongue structure for 1:q states (one action potential for q cycles of forcing). Importantly we show how the presence of quasi-active membrane in the dendrites can influence the shape of tongues. Direct numerical simulations confirm our theory and further indicate that resonant dendritic membrane can enlarge the windows in parameter space for chaotic behavior. These simulations also show that the spatially extended neuron model responds differently to global as opposed to point forcing. In the former case spatio-temporal patterns of activity within an Arnol'd tongue are standing waves, whilst in the latter they are traveling waves.

Caractérisation du fonctionnement d'une hydrolienne à membrane ondulante pour la récupération de l'énergie des courants marins

This manuscript presents three approaches : analytical, experimental and numerical, to study the behaviour of a flexible membrane tidal energy converter. This technology, developed by the EEL Energy company, is based on periodic deformations of a pre-stressed flexible structure. Energy converters, located on each side of the device, are set into motion by the wave-like motion. In the analytical model, the membrane is represented by a linear beam model at one dimension and the flow by a 3 dimensions potential fluid. The fluid forces are evaluated by the elongated body theory. Energy is dissipated all over the length of the membrane. A 20th scale experimental prototype has been designed with micro-dampers to simulate the power take-off. Trials have allowed to validate the undulating membrane energy converter concept. A numerical model has been developed. Each element of the device is represented and the energy dissipation is done by dampers element with a damping law linear to damper velocity. Comparison of the three approaches validates their ability to represent the membrane behaviour without damping. The energy dissipation applied with the analytical model is clearly different from the two other models because of the location (where the energy is dissipated) and damping law. The two others show a similar behaviour and the same order of power take off repartition but value of power take off are underestimated by the numerical model. This three approaches have allowed to put forward key-parameters on which depend the behaviour of the membrane and the parametric study highlights the complementarity and the advantage of developing three approaches in parallel to answer industrial optimization problems. To make the link between trials in flume tank and sea trials, a 1/6th prototype has been built. To do so, the change of scale was studied. The behaviour of both prototypes is compared and differences could be explained by differences of boundary conditions and confinement effects. To evaluated membrane long-term behaviour at sea, a method of ageing accelerated by temperature and fatigue tests have been carried out on prototype materials samples submerged in sea water.