Viscous energy dissipation in a model of the human bronchial tree

The viscous energy dissipation in a two generation model of the human bronchial tree is determined from inspiratory velocity and static pressure data obtained for large Reynolds numbers (10⁴ < Re < 10⁵). This dissipation is found to be an increasing function of both Re and distance downstream from the inlet of the model. The ratio of the dissipation in the model to the energy dissipation in an equivalent straight pipe system is determined. This ratio, Z^*, for the model is compared to values in the literature for lower (laminar) Re. There is more dissipation in the branched model than in a straight pipe (Z^* > 1) and turbulence keeps Z^* at roughly a fixed value for large Reynolds numbers (10⁴ < Re < 10⁵). Z^* values for curved pipes are also compared to the branching system values. It is found that the energy dissipation for the branched model behaves similarly to that in curved pipes.     

The Fokker-Planck approach for the cooperative molecular motor model with finite number of motors

We provide the methodology for the analysis of the cooperative molecular motor model with finite number of motors, which are linearly and rigidly coupled, based on the Fokker-Planck approach. The probability density functions for the position of motors are solved numerically from the stationary Fokker-Planck equations. By using these probability density functions, we provide the analytical expressions, such as the velocity, the rate of the ATP consumption, the energetic efficiency, and the dissipation energy rates. Furthermore, we investigate three specific examples, such as single motor model, 2-motor model, and infinitely coupled motor model. Numerical algorithm to solve the Fokker-Planck equations is also provided.     

Weakly dissipative predator-prey systems

In the presence of seasonal forcing, predator-prey models with quadratic interaction terms and weak dissipation can exhibit infinite numbers of coexisting periodic attractors corresponding to cycles of different magnitude and frequency. These motions are best understood with reference to the conservative case, for which the degree of dissipation is, by definition, zero. Here one observes the familiar mix of “regular” (neutrally stable orbits and tori) and chaotic motion typical of non-integrable Hamiltonian systems. Perturbing away from the conservative limit, the chaos becomes transitory. In addition, the invariant tori are destroyed and the neutrally stable periodic orbits becomes stable limit cycles, the basins of attraction of which are intertwined in a complicated fashion. As a result, stochastic perturbations can bounce the system from one basin to another with consequent changes in system behavior. Biologically, weak dissipation corresponds to the case in which predators are able to regulate the density of their prey well below carrying capacity.     

Quality factor of a plasma waveguide and contraction of laser-induced breakdown waves in gases

A previously developed plasma-waveguide model of a long laser spark in atmospheric-pressure gases is used to describe the evolution of a plasma waveguide produced in the course of electric breakdown and to analyze energy dissipation in it. The requirements are formulated for the plasma density profile to be steep enough in order that the threshold conditions for electric breakdown can be satisfied, and the conditions are determined under which the distortion of the plasma density profile can lead to a decrease in the diameter of the breakdown wave.     

A new concept to reveal protein dynamics based on energy dissipation

Protein dynamics is essential for its function, especially for intramolecular signal transduction. In this work we propose a new concept, energy dissipation model, to systematically reveal protein dynamics upon effector binding and energy perturbation. The concept is applied to better understand the intramolecular signal transduction during allostery of enzymes. The E. coli allosteric enzyme, aspartokinase III, is used as a model system and special molecular dynamics simulations are designed and carried out. Computational results indicate that the number of residues affected by external energy perturbation (i.e. caused by a ligand binding) during the energy dissipation process shows a sigmoid pattern. Using the two-state Boltzmann equation, we define two parameters, the half response time and the dissipation rate constant, which can be used to well characterize the energy dissipation process. For the allostery of aspartokinase III, the residue response time indicates that besides the ACT2 signal transduction pathway, there is another pathway between the regulatory site and the catalytic site, which is suggested to be the β15-αK loop of ACT1. We further introduce the term "protein dynamical modules" based on the residue response time. Different from the protein structural modules which merely provide information about the structural stability of proteins, protein dynamical modules could reveal protein characteristics from the perspective of dynamics. Finally, the energy dissipation model is applied to investigate E. coli aspartokinase III mutations to better understand the desensitization of product feedback inhibition via allostery. In conclusion, the new concept proposed in this paper gives a novel holistic view of protein dynamics, a key question in biology with high impacts for both biotechnology and biomedicine.     

Theoretical evaluation of the distributed power dissipation in biological cells exposed to electric fields

The paper deals with the power dissipation caused by exposure of biological cells to electric fields of various frequencies. With DC and sub-MHz AC frequencies, power dissipation in the cell membrane is of the same order of magnitude as in the external medium. At MHz and GHz frequencies, dielectric relaxation leads to dielectric power dissipation gradually increasing with frequency, and total power dissipation within the membrane rises significantly. Since such local increase can lead to considerable biochemical and biophysical changes within the membrane, especially at higher frequencies, the bulk treatment does not provide a complete picture of effects of an exposure. In this paper, we theoretically analyze the distribution of power dissipation as a function of field frequency. We first discuss conductive power dissipation generated by DC exposures. Then, we focus on AC fields; starting with the established first-order model, which includes only conductive power dissipation and is valid at sub-MHz frequencies, we enhance it in two steps. We first introduce the capacitive properties of the cytoplasm and the external medium to obtain a second-order model, which still includes only conductive power dissipation. Then we enhance this model further by accounting for dielectric relaxation effects, thereby introducing dielectric power dissipation. The calculations show that due to the latter component, in the MHz range the power dissipation within the membrane significantly exceeds the value in the external medium, while in the lower GHz range this effect is even more pronounced. This implies that even in exposures that do not cause a significant temperature rise at the macroscopic, whole-system level, the locally increased power dissipation in cell membranes could lead to various effects at the microscopic, single-cell level.     

An Optimal Free Energy Dissipation Strategy of the MinCDE Oscillator in Regulating Symmetric Bacterial Cell Division

Sustained molecular oscillations are ubiquitous in biology. The obtained oscillatory patterns provide vital functions as timekeepers, pacemakers and spacemarkers. Models based on control theory have been introduced to explain how specific oscillatory behaviors stem from protein interaction feedbacks, whereas the energy dissipation through the oscillating processes and its role in the regulatory function remain unexplored. Here we developed a general framework to assess an oscillator’s regulation performance at different dissipation levels. Using the Escherichia coli MinCDE oscillator as a model system, we showed that a sufficient amount of energy dissipation is needed to switch on the oscillation, which is tightly coupled to the system’s regulatory performance. Once the dissipation level is beyond this threshold, unlike stationary regulators’ monotonic performance-to-cost relation, excess dissipation at certain steps in the oscillating process damages the oscillator’s regulatory performance. We further discovered that the chemical free energy from ATP hydrolysis has to be strategically assigned to the MinE-aided MinD release and the MinD immobilization steps for optimal performance, and a higher energy budget improves the robustness of the oscillator. These results unfold a novel mode by which living systems trade energy for regulatory function.     

Under what conditions signal transduction pathways are highly flexible in response to external forcing? A case study on calcium oscillations

Sensitivity and flexibility are typical properties of biological systems. These properties are here investigated in a model for simple and complex intracellular calcium oscillations. In particular, the influence of external periodic forcing is studied. The main point of the study is to compare responses of the system in a chaotic regime with those obtained in a regular periodic regime. We show that the response to external signals in terms of the range of synchronization is not significantly different in regular and chaotic Ca2+ oscillations. However, both types of oscillation are highly flexible in regimes with weak dissipation. Therefore, we conclude that dissipation of free energy is a suitable index characterizing flexibility. For biological systems this appears to be of special importance since for thermodynamic reasons, notably in view of low free energy consumption, dissipation should be minimized.     

Thermodynamic correlates of evolution

At any given time the ecosystem is roughly describable as an autocatalytic collection of substances in the steady state. The evolutionary behavior of such a system may be studied by making a thermodynamic analysis of the autocatalytic model. our main assumptions are: the energy input is constant; the dissipation is a function of the concentration of catalyst and the rate constants which characterize the reaction (the catalytic capacity); the dissipation function is time independent. Our main result is: the concentration of catalyst and catalytic capacity are complementary. This means that biomass and rate cannot both increase in the course of evolution. The stationary state which fulfills this complementarity condition is stable and unique, in the sense that the dissipation function along with the catalytic capacity is sufficient to determine the quantity of catalyst. Under quite general conditions changes in the catalytic capacity are positively correlated to changes in the turnover frequency of matter and energy and negatively correlated to changes in the free energy of the system. The spatial heterogeneity of the system plays an important role in determining the applicability of these conditions. Spatial heterogeneity stabilizes the catalytic capacity and biomass since it allows for net movements of catalyst which always oppose changes in these quantities.     

Thermal energy dissipation and xanthophyll cycles beyond the Arabidopsis model

Thermal dissipation of excitation energy is a fundamental photoprotection mechanism in plants. Thermal energy dissipation is frequently estimated using the quenching of the chlorophyll fluorescence signal, termed non-photochemical quenching. Over the last two decades, great progress has been made in the understanding of the mechanism of thermal energy dissipation through the use of a few model plants, mainly Arabidopsis. Nonetheless, an emerging number of studies suggest that this model represents only one strategy among several different solutions for the environmental adjustment of thermal energy dissipation that have evolved among photosynthetic organisms in the course of evolution. In this review, a detailed analysis of three examples highlights the need to use models other than Arabidopsis: first, overwintering evergreens that develop a sustained form of thermal energy dissipation; second, desiccation tolerant plants that induce rapid thermal energy dissipation; and third, understorey plants in which a complementary lutein epoxide cycle modulates thermal energy dissipation. The three examples have in common a shift from a photosynthetically efficient state to a dissipative conformation, a strategy widely distributed among stress-tolerant evergreen perennials. Likewise, they show a distinct operation of the xanthophyll cycle. Expanding the list of model species beyond Arabidopsis will enhance our knowledge of these mechanisms and increase the synergy of the current studies now dispersed over a wide number of species.     

Small-scale turbulence and plankton contact rates

Theoretical and empirical studies of plankton trophodynamicsare usually based on some function of the relative density ofpredator-and-prey plankton. Such approaches based only on therelative density of predator and prey generally underestimatepredator-prey contact rates because contact depends on boththe relative density and the relative velocity of predator andprey. We estimate the components of predator-and-prey contactthat are due to small-scale turbulence. The small-scale turbulenceeffect suggests reconsidering estimates of plankton food requirements,energy gain-and-loss from foraging and mechanisms associatedwith patch formation and dissipation.     

Adaptive coarse-grained Monte Carlo simulation of reaction and diffusion dynamics in heterogeneous plasma membranes

Background  

An adaptive coarse-grained (kinetic) Monte Carlo (ACGMC) simulation framework is applied to reaction and diffusion dynamics in inhomogeneous domains. The presented model is relevant to the diffusion and dimerization dynamics of epidermal growth factor receptor (EGFR) in the presence of plasma membrane heterogeneity and specifically receptor clustering. We perform simulations representing EGFR cluster dissipation in heterogeneous plasma membranes consisting of higher density clusters of receptors surrounded by low population areas using the ACGMC method. We further investigate the effect of key parameters on the cluster lifetime.     

Optimization of diameters and bifurcation angles in lung and vascular tree structures

An optimization model is described for lung and vascular tree structures. The model extends Murray's model, which is derived from minimal power dissipation due to the frictional resistance of laminar flow and the volume of the duct system. Instead of just laminar flow, it takes into account all types of steady flow, e.g. turbulent and laminar flow, and predicts which structural changes will occur among different parts of trees having different types of flow. The sensitivity of the optimal values is indicated and the model, predictions are compared with literature data.     

Power Dissipation in the Cochlea Can Enhance Frequency Selectivity

The cochlear cavity is filled with viscous fluids, and it is partitioned by a viscoelastic structure called the organ of Corti complex. Acoustic energy propagates toward the apex of the cochlea through vibrations of the organ of Corti complex. The dimensions of the vibrating structures range from a few hundred (e.g., the basilar membrane) to a few micrometers (e.g., the stereocilia bundle). Vibrations of microstructures in viscous fluid are subjected to energy dissipation. Because the viscous dissipation is considered to be detrimental to the function of hearing—sound amplification and frequency tuning—the cochlea uses cellular actuators to overcome the dissipation. Compared to extensive investigations on the cellular actuators, the dissipating mechanisms have not been given appropriate attention, and there is little consensus on damping models. For example, many theoretical studies use an inviscid fluid approximation and lump the viscous effect to viscous damping components. Others neglect viscous dissipation in the organ of Corti but consider fluid viscosity. We have developed a computational model of the cochlea that incorporates viscous fluid dynamics, organ of Corti microstructural mechanics, and electrophysiology of the outer hair cells. The model is validated by comparing with existing measurements, such as the viscoelastic response of the tectorial membrane, and the cochlear input impedance. Using the model, we investigated how dissipation components in the cochlea affect its function. We found that the majority of acoustic energy dissipation of the cochlea occurs within the organ of Corti complex, not in the scalar fluids. Our model suggests that an appropriate dissipation can enhance the tuning quality by reducing the spread of energy provided by the outer hair cells’ somatic motility.     

Power Dissipation in the Subtectorial Space of the Mammalian Cochlea Is Modulated by Inner Hair Cell Stereocilia

The stereocilia bundle is the mechano-transduction apparatus of the inner ear. In the mammalian cochlea, the stereocilia bundles are situated in the subtectorial space (STS)—a micrometer-thick space between two flat surfaces vibrating relative to each other. Because microstructures vibrating in fluid are subject to high-viscous friction, previous studies considered the STS as the primary place of energy dissipation in the cochlea. Although there have been extensive studies on how metabolic energy is used to compensate the dissipation, much less attention has been paid to the mechanism of energy dissipation. Using a computational model, we investigated the power dissipation in the STS. The model simulates fluid flow around the inner hair cell (IHC) stereocilia bundle. The power dissipation in the STS because of the presence IHC stereocilia increased as the stimulating frequency decreased. Along the axis of the stimulating frequency, there were two asymptotic values of power dissipation. At high frequencies, the power dissipation was determined by the shear friction between the two flat surfaces of the STS. At low frequencies, the power dissipation was dominated by the viscous friction around the IHC stereocilia bundle—the IHC stereocilia increased the STS power dissipation by 50- to 100-fold. There exists a characteristic frequency for STS power dissipation, CF_STS, defined as the frequency where power dissipation drops to one-half of the low frequency value. The IHC stereocilia stiffness and the gap size between the IHC stereocilia and the tectorial membrane determine the characteristic frequency. In addition to the generally assumed shear flow, nonshear STS flow patterns were simulated. Different flow patterns have little effect on the CF_STS. When the mechano-transduction of the IHC was tuned near the vibrating frequency, the active motility of the IHC stereocilia bundle reduced the power dissipation in the STS.     

Functional analysis of Fontan energy dissipation

We formalize the hydrodynamic energy dissipation in the total cavopulmonary connection (TCPC) using dimensional analysis and examine the effect of governing flow variables; namely, cardiac output, flow split, body surface area, Reynolds number, and certain geometric characteristics. A simplistic and clinically useful mathematical model of the dependence of energy dissipation on the governing variables is developed. In vitro energy loss data corresponding to six patients' anatomies validated the predicted dependency of each variable and was used to develop a predictive, semi-empirical energy dissipation model of the TCPC. It is shown that energy dissipation is a cubic function of pulmonary flow split in the physiological range. Furthermore, non-dimensional energy dissipation, which is a measure of resistance of the connection, is dependent on Reynolds number and geometrical factors alone. Non-dimensional energy dissipation decreases with Reynolds number as Re(-0.25) (R(2)>0.95). In addition, for high Reynolds numbers, within physiological exercise limits, dissipation strongly correlates to minimum PA area as a power law decay with an exponent of -5/4 (R(2)>0.88). This study presents a simple analytical form of energy dissipation rate in complex patient-specific TCPCs that accurately captures the effect of cardiac output, flow split, body surface area, Reynolds number, and pulmonary artery size within physiological limits. Further studies with larger sample sizes are necessary for incorporating finer geometrical parameters such as vessel curvatures and offsets.     

Variation of efficiency with free-energy dissipation in models of biological energy transduction

For two models of biological free-energy transducers, it is investigated how free-energy dissipation and efficiency vary as (i) the demand for output free energy, (ii) the input free energy or (iii) the properties of the transducers themselves, are varied. One model is representative of near-equilibrium free-energy transducers in general, the other is a special case of far-from-equilibrium free-energy transduction, reminiscent of proton pumping by bacteriorhodopsin. It turns out that the relationship between efficiency and free-energy dissipation depends strongly on what varies. In some cases, free-energy dissipation increases as the efficiency increases. It is suggested that this is one reason why biological evolution has not resulted in high efficiencies and low rates of free-energy dissipation. For the near-equilibrium free-energy transducer, the free-energy dissipation at the static head steady state is minimal with respect to variations in the output force. For the far-from-equilibrium model (of bacteriorhodopsin), the static head does not correspond to such a minimum, if that free-energy transducer slips.     

Optimum kinetic energy dissipation in blood flow in glass capillaries by flow field determination: Analysis of curvature effect by axial tomographic and image velocimetry techniques

Based on the variation in the optical density due to erythrocyte concentration and movement, the axial tomographic and image velocimetry techniques are respectively applied to determine the flow field, i.e., the distribution of erythrocytes and axial and radial velocity components, in steady blood flow through a curved glass capillary with a diameter of 180 μm. The data at four positions (two straight and two curved segments of the capillary) are recorded by a video-microscopic system on a video cassette. The erythrocyte and velocity distribution profiles change from symmetric at the straight position to an asymmetric shape at the curved sections. These profiles become symmetric again at the straight section of the capillary. The increase in the radial velocity component at curved portions is attributed to the secondary flow. The tomograms obtained by concentration profiles show respective changes in the cellular population at various cross-sectional positions. The kinetic energy dissipation, as calculated based on a determination of the flow field, is the minimum for the observed profiles. Any deviation towards parabolic form leads to the dissipation of a higher amount of energy.     

An energy dissipation and cross shear time dependent computational wear model for the analysis of polyethylene wear in total knee replacements

The cost and time efficiency of computational polyethylene wear simulations may enable the optimization of total knee replacements for the reduction of polyethylene wear. The present study proposes an energy dissipation wear model for polyethylene which considers the time dependent molecular behavior of polyethylene, aspects of tractive rolling and contact pressure. This time dependent – energy dissipation wear model was evaluated, along with several other wear models, by comparison to pin-on-disk results, knee simulator wear test results under various kinematic conditions and knee simulator wear test results that were performed following the ISO 14243-3 standard. The proposed time dependent – energy dissipation wear model resulted in improved accuracy for the prediction of pin-on-disk and knee simulator wear test results compared with several previously published wear models.     

Modeling of the metabolic energy dissipation for restricted tumor growth

Energy dissipation mostly represents unwanted outcome but in the biochemical processes it may alter the biochemical pathways. However, it is rarely considered in the literature although energy dissipation and its alteration due to the changes in cell microenvironment may improve methods for guiding chemical and biochemical processes in the desired directions. Deeper insight into the changes of metabolic activity of tumor cells exposed to osmotic stress or irradiation may offer the possibility of tumor growth reduction. In this work effects of the osmotic stress and irradiation on the thermodynamical affinity of tumor cells and their damping effects on metabolic energy dissipation were investigated and modeled. Although many various models were applied to consider the tumor restrictive growth they have not considered the metabolic energy dissipation. In this work a pseudo rheological model in the form of “the metabolic spring-pot element” is formulated to describe theoretically the metabolic susceptibility of tumor spheroid. This analog model relates the thermodynamical affinity of cell growth with the volume expansion of tumor spheroid under isotropic loading conditions. Spheroid relaxation induces anomalous nature of the metabolic energy dissipation which causes the damping effects on cell growth. The proposed model can be used for determining the metabolic energy “structure” in the context of restrictive cell growth as well as for predicting optimal doses for cancer curing in order to tailor the clinical treatment for each person and each type of cancer.