A critical comparison of different residence time measures in aneurysms

Flow stagnation and residence time (RT) are important features of diseased arterial flows that influence biochemical transport processes and thrombosis. RT calculation methods are classified into Eulerian and Lagrangian approaches where several measures have been proposed to quantify RT. Each of these methods has a different definition of RT, and it is not clear how they are related. In this study, image-based computational models of blood flow in an abdominal aortic aneurysm and a cerebral aneurysm were considered and RT was calculated using different methods. In the Lagrangian methods, discrete particle tracking of massless tracers was used to calculate particle residence time and mean exposure time. In the Eulerian methods, continuum transport models were used to quantify RT using Eulerian RT and virtual ink approaches. Point-wise RT and Eulerian indicator RT were also computed based on measures derived from velocity. A comparison of these methods is presented and the implications of each method are discussed. Our results highlight that most RT methods have a conceptually distinct definition of RT and therefore should be utilized depending on the specific application of interest.     

Three-dimensional focusing of red blood cells in microchannel flows for bio-sensing applications

Three-dimensional (3D) focusing of particles in microchannels has been a long-standing issue in the design of biochemical/biomedical microdevices. Current microdevices for 3D cell or bioparticle focusing involve complex channel geometries in view of their fabrication because they require multiple layers and/or sheath flows. This paper proposes a simple method for 3D focusing of red blood cells (RBCs) in a single circular microcapillary, without any sheath flows, which is inspired from the fluid dynamics phenomenon in that a spherical particle lagging behind a Poiseuille flow migrates toward and along the channel axis. More explicitly, electrophoresis of RBCs superimposed on the pressure-driven flow is utilized to generate an RBC migration mode analogous to this phenomenon. A particle-tracking scheme with a sub-pixel resolution is implemented to spatially position red blood cells flowing through the channel, so that a probability density function (PDF) is constructed to evaluate the tightness of the cell focusing. Above a specific strength of the electric field, approximately 90% of the sheep RBCs laden in the flow are tightly focused within a beam diameter that is three times the cell dimension. Particle shape effect on the focusing is discussed by making comparisons between the RBCs and the spherical particles. The lateral migration velocity, predicted by an existing theoretical model, is in good agreement with the present experimental data. It is noteworthy that 3D focusing of non-spherical particles, such as RBCs, has been achieved in a circular microchannel, which is a significant improvement over previous focusing methodologies.     

Protein-protein interactions, cytoskeletal regulation and neuronal migration

Neuronal migration, like the migration of many cell types, requires an extensive rearrangement of cell shape, mediated by changes in the cytoskeleton. The genetic analysis of human brain malformations has identified several biochemical players in this process, including doublecortin (DCX) and LIS1, mutations of which cause a profound migratory disturbance known as lissencephaly ('smooth brain') in humans. Studies in mice have identified additional molecules such as Cdk5, P35, Reelin, Disabled and members of the LDL superfamily of receptors. Understanding the cell biology of these molecules has been a challenge, and it is not known whether they function in related biochemical pathways or in very distinct processes. The last year has seen rapid advances in the biochemical analysis of several such molecules. This analysis has revealed roles for some of these molecules in cytoskeletal regulation and has shown an unexpected conservation of the genetic pathways that regulate neuronal migration in humans and nuclear movement in simple eukaryotic organisms.     

Septins: cytoskeletal polymers or signalling GTPases?

Septins are a family of conserved proteins that have been implicated in a variety of cellular functions involving specialized regions of the cell cortex and changes in cell shape. The biochemistry and localization of septins suggest that they form a novel cytoskeletal system or that they function as scaffolds for the assembly of signalling complexes. This article discusses septin biochemistry and septin-interacting proteins, focusing on the missing link between the structure and biochemical properties of septin proteins, and on how they function at a molecular level in processes such as cytokinesis and yeast budding.     

In vitro regulatory models for systems biology

The reductionist approach has revolutionized biology in the past 50 years. Yet its limits are being felt as the complexity of cellular interactions is gradually revealed by high-throughput technology. In order to make sense of the deluge of “omic data”, a hypothesis-driven view is needed to understand how biomolecular interactions shape cellular networks. We review recent efforts aimed at building in vitro biochemical networks that reproduce the flow of genetic regulation. We highlight how those efforts have culminated in the rational construction of biochemical oscillators and bistable memories in test tubes. We also recapitulate the lessons learned about in vivo biochemical circuits such as the importance of delays and competition, the links between topology and kinetics, as well as the intriguing resemblance between cellular reaction networks and ecosystems.     

Effect of membrane flow on the capture of receptors by coated pits. Theoretical results.

Coated pits trap cell surface receptors and mediate their internalization. Once internalized, many receptors recycle back to the cell surface. When recycled receptors are inserted into the plasma membrane, they move until they are again trapped in coated pits. The mechanisms for moving receptors from their insertion sites to coated pits are unknown. Unaided diffusion as the transport mechanism is consistent with the observed kinetics of receptor recycling. Another candidate for the transport mechanism is convection. For receptors that recycle to random positions on the cell surface, or to restricted regions about coated pits, we assess the importance of convective flow in the transport of receptors to coated pits. First we consider local flows set up by the formation of coated pits and their transformation into coated vesicles. As coated pits form and round into coated vesicles, surrounding membrane is drawn inward, creating flows directed toward the coated pit centers. We show that unless the lifetime of a coated pit is very short, 10 s or less, such local flows have a negligible effect on the time it takes receptors to reach coated pits. We also show that they are unlikely to be the mechanism that keeps receptors that have reached coated pits trapped within coated pits until they are internalized. Finally we calculate the mean time tau for a diffusing receptor to reach a coated pit in the presence of membrane flow that is constant in magnitude and direction, as may occur on moving cells. We show that for typical membrane flow velocities, tau can be reduced significantly from its value in the absence of flow. For example, a velocity v = 2.8 micron/min cuts the mean transport time in half.     

Full Mode and Attribution Mode in Environmental Analysis

Several tools exist for the analysis of the environmental impacts of chains or networks of processes. These relatively simple tools include materials flow accounting (MFA), substance flow analysis (SFA), life-cycle assessment (LCA), energy analysis, and environmentally extended input-output analysis (IOA), all based on fixed input-output relations. They are characterized by the nature of their flow objects, such as products, materials, energy, substances, or money flows, and by their spatial and temporal characteristics. These characteristics are insufficient for their methodological characterization, and sometimes lead to inappropriate use. More clarity is desirable, both for clearer guidance of applications and for a more consistent methodology development. In addition to the nature of the flow object and to spatial and temporal characteristics, another key feature concerns the way in which processes are included in a system to be analyzed.
The inclusion of processes can be done in two fundamentally different ways: according to a full mode of analysis, with the inclusion of all flows and related processes to their full extent as present in a region in a specific period of time; and according to an attribution mode, taking processes into account insofar as these are required for a given social demand, function, or activity, in principle whenever and wherever these processes take place. This distinction, which cuts across families of tools that traditionally belong together, appears to have significant methodological and practical implications. Thus the distinction between the two modes of analysis, however crucial it may be, strengthens the idea of one coherent family of tools for environmental systems analysis.     

Bio-microrheology: a frontier in microrheology

Cells continuously adapt to changing conditions through coordinated molecular and mechanical responses. This adaptation requires the transport of molecules and signaling through intracellular regions with differing material properties, such as variations in viscosity or elasticity. To determine the impact of regional variations on cell structure and physiology, an approach, termed bio-microrheology, or the study of deformation and flow of biological materials at small length scales has emerged. By tracking the thermal and driven motion of probe particles, organelles, or molecules, the local physical environment in distinct subcellular regions can be explored. On the surface or inside cells, tracking the motion of particles can reveal the rheological properties that influence cell features, such as shape and metastatic potential. Cellular microrheology promises to improve our concepts of regional and integrated properties, structures, and transport in live cells. Since bio-microrheology is an evolving methodology, many specific details, such as how to interpret complex combinations of thermally mediated and directed probe transport, remain to be fully explained. This work reviews the current state of the field and discusses the utility and challenges of this emerging approach.     

Emergent cell and tissue dynamics from subcellular modeling of active biomechanical processes

Cells and the tissues they form are not passive material bodies. Cells change their behavior in response to external biochemical and biomechanical cues. Behavioral changes, such as morphological deformation, proliferation and migration, are striking in many multicellular processes such as morphogenesis, wound healing and cancer progression. Cell-based modeling of these phenomena requires algorithms that can capture active cell behavior and their emergent tissue-level phenotypes. In this paper, we report on extensions of the subcellular element model to model active biomechanical subcellular processes. These processes lead to emergent cell and tissue level phenotypes at larger scales, including (i) adaptive shape deformations in cells responding to slow stretching, (ii) viscous flow of embryonic tissues, and (iii) streaming patterns of chemotactic cells in epithelial-like sheets. In each case, we connect our simulation results to recent experiments.     

A tridomain model for potassium clearance in optic nerve of Necturus

Complex fluids flow in complex ways in complex structures. Transport of water and various organic and inorganic molecules in the central nervous system are important in a wide range of biological and medical processes. However, the exact driving mechanisms are often not known. In this work, we investigate flows induced by action potentials in an optic nerve as a prototype of the central nervous system. Different from traditional fluid dynamics problems, flows in biological tissues such as the central nervous system are coupled with ion transport. They are driven by osmosis created by concentration gradient of ionic solutions, which in turn influence the transport of ions. Our mathematical model is based on the known structural and biophysical properties of the experimental system used by the Harvard group Orkand et al. Asymptotic analysis and numerical computation show the significant role of water in convective ion transport. The full model (including water) and the electrodiffusion model (excluding water) are compared in detail to reveal an interesting interplay between water and ion transport. In the full model, convection due to water flow dominates inside the glial domain. This water flow in the glia contributes significantly to the spatial buffering of potassium in the extracellular space. Convection in the extracellular domain does not contribute significantly to spatial buffering. Electrodiffusion is the dominant mechanism for flows confined to the extracellular domain.     

Mechanics of the Formation,Interaction, and Evolution of Membrane Tubular Structures

Membrane nanotubes, also known as membrane tethers, play important functional roles in many cellular processes, such as trafficking and signaling. Although considerable progresses have been made in understanding the physics regulating the mechanical behaviors of individual membrane nanotubes, relatively little is known about the formation of multiple membrane nanotubes due to the rapid occurring process involving strong cooperative effects and complex configurational transitions. By exerting a pair of external extraction upon two separate membrane regions, here, we combine molecular dynamics simulations and theoretical analysis to investigate how the membrane nanotube formation and pulling behaviors are regulated by the separation between the pulling forces and how the membrane protrusions interact with each other. As the force separation increases, different membrane configurations are observed, including an individual tubular protrusion, a relatively less deformed protrusion with two nanotubes on its top forming a V shape, a Y-shaped configuration through nanotube coalescence via a zipper-like mechanism, and two weakly interacting tubular protrusions. The energy profile as a function of the separation is determined. Moreover, the directional flow of lipid molecules accompanying the membrane shape transition is analyzed. Our results provide new, to our knowledge, insights at a molecular level into the interaction between membrane protrusions and help in understanding the formation and evolution of intra- and intercellular membrane tubular networks involved in numerous cell activities.     

Cell adhesion in embryo morphogenesis

Visualizing and analyzing shape changes at various scales, ranging from single molecules to whole organisms, are essential for understanding complex morphogenetic processes, such as early embryonic development. Embryo morphogenesis relies on the interplay between different tissues, the properties of which are again determined by the interaction between their constituent cells. Cell interactions, on the other hand, are controlled by various molecules, such as signaling and adhesion molecules, which in order to exert their functions need to be spatiotemporally organized within and between the interacting cells. In this review, we will focus on the role of cell adhesion functioning at different scales to organize cell, tissue and embryo morphogenesis. We will specifically ask how the subcellular distribution of adhesion molecules controls the formation of cell-cell contacts, how cell-cell contacts determine tissue shape, and how tissue interactions regulate embryo morphogenesis.     

A Comparison of Computational Models for Eukaryotic Cell Shape and Motility

Eukaryotic cell motility involves complex interactions of signalling molecules, cytoskeleton, cell membrane, and mechanics interacting in space and time. Collectively, these components are used by the cell to interpret and respond to external stimuli, leading to polarization, protrusion, adhesion formation, and myosin-facilitated retraction. When these processes are choreographed correctly, shape change and motility results. A wealth of experimental data have identified numerous molecular constituents involved in these processes, but the complexity of their interactions and spatial organization make this a challenging problem to understand. This has motivated theoretical and computational approaches with simplified caricatures of cell structure and behaviour, each aiming to gain better understanding of certain kinds of cells and/or repertoire of behaviour. Reaction–diffusion (RD) equations as well as equations of viscoelastic flows have been used to describe the motility machinery. In this review, we describe some of the recent computational models for cell motility, concentrating on simulations of cell shape changes (mainly in two but also three dimensions). The problem is challenging not only due to the difficulty of abstracting and simplifying biological complexity but also because computing RD or fluid flow equations in deforming regions, known as a “free-boundary” problem, is an extremely challenging problem in applied mathematics. Here we describe the distinct approaches, comparing their strengths and weaknesses, and the kinds of biological questions that they have been able to address.     

Intracellular signalling as a parallel distributed process

Living cells respond to their environment by means of an interconnected network of receptors, second messengers, protein kinases and other signalling molecules. This article suggests that the performance of cell signalling pathways taken as a whole has similarities to that of the parallel distributed process networks (PDP networks) used in computer-based pattern recognition. Using the response of hepatocytes to glucagon as an example, a procedure is described by which a PDP network could simulate a cell signalling pathway. This procedure involves the following steps: (a) a bounded set of molecules is defined that carry the signals of interest; (b) each of these molecules is represented by a PDP-type of unit, with input and output functions and connection weights corresponding to specific biochemical parameters; (c) a "learning algorithm" is applied in which small random changes are made in the parameters of the cell signalling units and the new network is then tested by a selection procedure in favour of a specific input-output relationship. The analogy with PDP networks shows how living cells can recognize combinations of environmental influences, how cell responses can be stabilized and made resistant to damage, and how novel cell signalling pathways might appear during evolution.     

Particle Transport through Hydrogels Is Charge Asymmetric

Transport processes within biological polymer networks, including mucus and the extracellular matrix, play an important role in the human body, where they serve as a filter for the exchange of molecules and nanoparticles. Such polymer networks are complex and heterogeneous hydrogel environments that regulate diffusive processes through finely tuned particle-network interactions. In this work, we present experimental and theoretical studies to examine the role of electrostatics on the basic mechanisms governing the diffusion of charged probe molecules inside model polymer networks. Translational diffusion coefficients are determined by fluorescence correlation spectroscopy measurements for probe molecules in uncharged as well as cationic and anionic polymer solutions. We show that particle transport in the charged hydrogels is highly asymmetric, with diffusion slowed down much more by electrostatic attraction than by repulsion, and that the filtering capability of the gel is sensitive to the solution ionic strength. Brownian dynamics simulations of a simple model are used to examine key parameters, including interaction strength and interaction range within the model networks. Simulations, which are in quantitative agreement with our experiments, reveal the charge asymmetry to be due to the sticking of particles at the vertices of the oppositely charged polymer networks.     

A New Approach to Epithelial Isotonic Fluid Transport: An Osmosensor Feedback Model

A model for control of the transport rate and osmolarity of epithelial fluid (isotonic transport) is presented by using an analogy with the control of temperature and flow rate in a shower. The model brings recent findings and theory concerning the role of aquaporins in epithelia together with measurements of epithelial paracellular flow into a single scheme. It is not based upon osmotic equilibration across the epithelium but rather on the function of aquaporins as osmotic sensors that control the tonicity of the transported fluid by mixing cellular and paracellular flows, which may be regarded individually as hyper- and hypo-tonic fluids, to achieve near-isotonicity. The system is built on a simple feedback loop and the quasi-isotonic behavior is robust to the precise values of most parameters. Although the two flows are separate, the overall fluid transport rate is governed by the rate of salt pumping through the cell. The model explains many things: how cell pumping and paracellular flow can be coupled via control of the tight junctions; how osmolarity is controlled without depending upon the precise magnitude of membrane osmotic permeability; and why many epithelia have different aquaporins at the two membranes.The model reproduces all the salient features of epithelial fluid transport seen over many years but also indicates novel behavior that may provide a subject for future research and serve to distinguish it from other schemes such as simple osmotic equilibration. Isotonic transport is freed from constraints due to limited permeability of the membranes and the precise geometry of the system. It achieves near-isotonicity in epithelia in which partial water transport by co-transporters may be present, and shows apparent electro-osmotic effects. The model has been developed with a minimum of parameters, some of which require measurement, but the model is flexible enough for the basic idea to be extended both to complex systems of water and salt transport that still await a clear explanation, such as intestine and airway, and to systems that may lack aquaporins or use other sensors.     

Transport effects on surface reaction arrays: biosensor applications

The ubiquity of surface-volume reactions in biological and industrial processes makes knowledge of their kinetics critical. This has spurred technological advances in several biosensors designed to measure rate constants, such as the Flexchip and the dotLab. These biosensors have multiple reacting zones in a single flow channel, and hence they also serve as good model systems for biochemical systems with multiple reacting zones, such as cell membranes. A correct mathematical model for such systems must incorporate the effects of transport and zone position. A basic unidirectional flow model is developed in general and solved for typical experimental parameters using perturbation methods. The effect of zone placement along the channel can be quantified in terms of an effective Damköhler number based upon position. Moreover, it is established that zone placement across the channel does not affect the measurements.