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The plasmodial slime mold Physarum polycephalum exhibits strong, periodic flow of cytoplasm through the veins of its network. In the special case of mesoplasmodia, a newly described starvation-induced, shape-constant morphotype, this periodic endoplasm streaming is the basis of locomotion. Furthermore, we presume that cytoplasm flow is also involved in signal transmission and signal processing. Mesoplasmodia motility resembles amoeboid locomotion. In contrast to other amoebae, however, mesoplasmodia move without extending pseudopods and retain a coherent, fan-shaped morphology throughout their steady locomotion. Attaining sizes of up to 2 mm2, mesoplasmodia are also much bigger than other amoebae. We characterize this particular type of locomotion and identify patterns of movement. By using the analogy between pulsatile fluid flow through a network of elastic tubes and electrical circuits, we build a lumped model that explains observed fluid flow patterns. Essentially, the mesoplasmodium acts as a low-pass filter, permitting only low-frequency oscillations to propagate from back to front. This frequency selection serves to optimize flow and reduces power dissipation. Furthermore, we introduce a distributed element into the lumped model to explain cell polarization during the onset of chemotaxis: Biochemical cues (internal or external) lead to a local softening of the actin cortex, which in turn causes an increased flow of cytoplasm into that area and, thus, a net forward movement. We conclude that the internal actin-enclosed vein network gives the slime mold a high measure of control over fluid transport, especially by softening or hardening, which in turn leads to polarization and net movement., Competing Interests: The authors have declared that no competing interests exist.

Nonadherent polarized cells have been observed to have a pearlike, elongated shape. Using a minimal model that describes the cell cortex as a thin layer of contractile active gel, we show that the anisotropy of active stresses, controlled by cortical viscosity and filament ordering, can account for this morphology. The predicted shapes can be determined from the flow pattern only; they prove to be independent of the mechanism at the origin of the cortical flow, and are only weakly sensitive to the cytoplasmic rheology. In the case of actin flows resulting from a contractile instability, we propose a phase diagram of three-dimensional cell shapes that encompasses nonpolarized spherical, elongated, as well as oblate shapes, all of which have been observed in experiment.

Confined migration plays a fundamental role during several biological phenomena such as embryogenesis, immunity and tumorogenesis. Here, we propose a two-dimensional mechanical model to simulate the migration of a HeLa cell through a micro-channel. As in our previous works, the cell is modelled as a continuum and a standard Maxwell model is used to describe the mechanical behaviour of both the cytoplasm (including active strains) and the nucleus. The cell cyclically protrudes and contracts and develops viscous forces to adhere to the substrate. The micro-channel is represented by two rigid walls, and it exerts an additional viscous force on the cell boundaries. We test four channels whose dimensions in terms of width are i) larger than the cell diameter, ii) sub-cellular, ii) sub-nuclear and iv) much smaller than the nucleus diameter. The main objective of the work is to assess the necessary conditions for the cell to enter into the channel and migrate through it. Therefore, we evaluate both the evolution of the cell morphology and the cell-channel and cell-substrate surface forces, and we show that there exists a link between the two, which is the essential parameter determining whether the cell is permeative, invasive or penetrating.

Eukaryotic chemotaxis is usually mediated by intracellular signals that tend to localize at the front or back of the cell. Such intracellular polarities frequently require no extracellular guidance cues, indicating that spontaneous polarization occurs in the signal network. Spontaneous polarization activity is considered relevant to the persistent motions in random cell migrations and chemotaxis. In this study, we propose a theoretical model that connects spontaneous intracellular polarity and motile ability in a chemoattractant solution. We demonstrate that the intracellular polarity can enhance the accuracy of chemotaxis. Chemotactic accuracy should also depend on chemoattractant concentration through the concentration-dependent correlation time in the polarity direction. Both the polarity correlation time and the chemotactic accuracy depend on the degree of responsiveness to the chemical gradient. We show that optimally accurate chemotaxis occurs at an intermediate responsiveness of intracellular polarity. Experimentally, we find that the persistence time of randomly migrating Dictyostelium cells depends on the chemoattractant concentration, as predicted by our theory. At the optimum responsiveness, this ameboid cell can enhance its chemotactic accuracy tenfold.

Motivated by recent experimental studies, we derive and analyze a two-dimensional model for the contraction patterns observed in protoplasmic droplets of Physarum polycephalum. The model couples a description of an active poroelastic two-phase medium with equations describing the spatiotemporal dynamics of the intracellular free calcium concentration. The poroelastic medium is assumed to consist of an active viscoelastic solid representing the cytoskeleton and a viscous fluid describing the cytosol. The equations for the poroelastic medium are obtained from continuum force balance and include the relevant mechanical fields and an incompressibility condition for the two-phase medium. The reaction-diffusion equations for the calcium dynamics in the protoplasm of Physarum are extended by advective transport due to the flow of the cytosol generated by mechanical stress. Moreover, we assume that the active tension in the solid cytoskeleton is regulated by the calcium concentration in the fluid phase at the same location, which introduces a mechanochemical coupling. A linear stability analysis of the homogeneous state without deformation and cytosolic flows exhibits an oscillatory Turing instability for a large enough mechanochemical coupling strength. Numerical simulations of the model equations reproduce a large variety of wave patterns, including traveling and standing waves, turbulent patterns, rotating spirals and antiphase oscillations in line with experimental observations of contraction patterns in the protoplasmic droplets.

Particle tracking is a widely used and promising technique for elucidating complex dynamics of the living cell. The cytoplasm is an active material, in which the kinetics of intracellular structures are highly heterogeneous. Tracer particles typically undergo a combination of random motion and various types of directed motion caused by the activity of molecular motors and other non-equilibrium processes. Random switching between more and less directional persistence of motion generally occurs. We present a method for identifying states of motion with different directional persistence in individual particle trajectories. Our analysis is based on a multi-scale turning angle model to characterize motion locally, together with a Hidden Markov Model with two states representing different directional persistence. We define one of the states by the motion of particles in a reference data set where some active processes have been inhibited. We illustrate the usefulness of the method by studying transport of vesicles along microtubules and transport of nanospheres activated by myosin. We study the results using mean square displacements, durations, and particle speeds within each state. We conclude that the method provides accurate identification of states of motion with different directional persistence, with very good agreement in terms of mean-squared displacement between the reference data set and one of the states in the two-state model., (Copyright © 2014 Elsevier Inc. All rights reserved.)

A cellular slime mould Physarum polycephalum is a monstrously large single cell visible by an unaided eye. The slime mold explores space in parallel, is guided by gradients of chemoattractants, and propagates toward sources of nutrients along nearly shortest paths. The slime mold is a living prototype of amorphous biological computers and robotic devices capable of solving a range of tasks of graph optimization and computational geometry. When presented with a distribution of nutrients, the slime mold spans the sources of nutrients with a network of protoplasmic tubes. This protoplasmic network matches a network of major transport routes of a country when configuration of major urban areas is represented by nutrients. A transport route connecting two cities should ideally be a shortest path, and this is usually the case in computer simulations and laboratory experiments with flat substrates. What searching strategies does the slime mold adopt when exploring 3-D terrains? How are optimal and transport routes approximated by protoplasmic tubes? Do the routes built by the slime mold on 3-D terrain match real-world transport routes? To answer these questions, we conducted pioneer laboratory experiments with Nylon terrains of USA and Germany. We used the slime mold to approximate route 20, the longest road in USA, and autobahn 7, the longest national motorway in Europe. We found that slime mold builds longer transport routes on 3-D terrains, compared to flat substrates yet sufficiently approximates man-made transport routes studied. We demonstrate that nutrients placed in destination sites affect performance of slime mold, and show how the mold navigates around elevations. In cellular automaton models of the slime mold, we have shown variability of the protoplasmic routes might depends on physiological states of the slime mold. Results presented will contribute toward development of novel algorithms for sensorial fusion, information processing, and decision making, and will provide inspirations in design of bioinspired amorphous robotic devices.

Myosins are motor proteins that drive movements along actin filaments and have long been assumed to be responsible for cytoplasmic streaming in plant cells. This conjecture is now firmly established by genetic analysis in the reference species, Arabidopsis thaliana. This work and similar approaches in the moss, Physcomitrella patens, also established that myosin-driven movements are necessary for cell growth and polarity, organelle distribution and shape, and actin organization and dynamics. Identification of a mechanistic link between intracellular movements and cell expansion has proven more challenging, not the least because of the high level of apparent genetic redundancy among myosin family members. Recent progress in the creation of functional complementation constructs and identification of interaction partners promises a way out of this dilemma.

Behavioural diversity is an indispensable attribute of living systems, which makes them intrinsically adaptive and responsive to the demands of a dynamically changing environment. In contrast, conventional engineering approaches struggle to suppress behavioural diversity in artificial systems to reach optimal performance in given environments for desired tasks. The goals of this research include understanding the essential mechanism that endows living systems with behavioural diversity and implementing the mechanism in robots to exhibit adaptive behaviours. For this purpose, we have focused on an amoeba-like unicellular organism: the plasmodium of true slime mould. Despite the absence of a central nervous system, the plasmodium exhibits versatile spatiotemporal oscillatory patterns and switches spontaneously among these patterns. By exploiting this behavioural diversity, it is able to exhibit adaptive behaviour according to the situation encountered. Inspired by this organism, we built a real physical robot using hydrostatically coupled oscillators that produce versatile oscillatory patterns and spontaneous transitions among the patterns. The experimental results show that exploiting physical hydrostatic interplay—the physical dynamics of the robot—allows simple phase oscillators to promote versatile behaviours. The results can contribute to an understanding of how a living system generates versatile and adaptive behaviours with physical interplays among body parts.

Two-phase flow models have been used previously to model cell motility. In order to reduce the complexity inherent with describing the many physical processes, we formulate a minimal model. Here we demonstrate that even the simplest 1D, two-phase, poroviscous, reactive flow model displays various types of behaviour relevant to cell crawling. We present stability analyses that show that an asymmetric perturbation is required to cause a spatially uniform, stationary strip of cytoplasm to move, which is relevant to cell polarization. Our numerical simulations identify qualitatively distinct families of travelling-wave solutions that coexist at certain parameter values. Within each family, the crawling speed of the strip has a bell-shaped dependence on the adhesion strength. The model captures the experimentally observed behaviour that cells crawl quickest at intermediate adhesion strengths, when the substrate is neither too sticky nor too slippy.

During asymmetric cell division, cytoplasmic components are segregated to opposite sides of the cell. We discuss how the observed segregation can be achieved by a position-dependent phase separation mechanism controlled by a protein concentration gradient. We show that effects of even a weak gradient can be amplified by the phase transition to achieve strong segregation. We compare our theory to the segregation of germ granules observed during the divisions in the C. elegans embryo. Our study demonstrates how liquid-liquid phase separation can play a key role in the organization of the cytoplasm.

Individuals can function as integrated organisms only when information and resources are shared across a body. Signals and substrates are commonly moved using fluids, often channeled through a network of tubes. Peristalsis is one mechanism for fluid transport and is caused by a wave of cross-sectional contractions along a tube. We extend the concept of peristalsis from the canonical case of one tube to a random network. Transport is maximized within the network when the wavelength of the peristaltic wave is of the order of the size of the network. The slime mold Physarum polycephalum grows as a random network of tubes, and our experiments confirm peristalsis is used by the slime mold to drive internal cytoplasmic flows. Comparisons of theoretically generated contraction patterns with the patterns exhibited by individuals of P. polycephalum demonstrate that individuals maximize internal flows by adapting patterns of contraction to size, thus optimizing transport throughout an organism. This control of fluid flow may be the key to coordinating growth and behavior, including the dynamic changes in network architecture seen over time in an individual.

Blebbing occurs when the cytoskeleton detaches from the cell membrane, resulting in the pressure-driven flow of cytosol towards the area of detachment and the local expansion of the cell membrane. Recent interest has focused on cells that use blebbing for migrating through 3D fibrous matrices. In particular, metastatic cancer cells have been shown to use blebs for motility. A dynamic computational model of the cell is presented that includes mechanics of and the interactions between the intracellular fluid, the actin cortex and the cell membrane. The computational model is used to explore the relative roles in bleb formation time of cytoplasmic viscosity and drag between the cortex and the cytosol. A regime of values for the drag coefficient and cytoplasmic viscosity values that match bleb formation timescales is presented. The model results are then used to predict the Darcy permeability and the volume fraction of the cortex.

The cytoplasm is the largest part of the cell by volume and hence its rheology sets the rate at which cellular shape changes can occur. Recent experimental evidence suggests that cytoplasmic rheology can be described by a poroelastic model, in which the cytoplasm is treated as a biphasic material consisting of a porous elastic solid meshwork (cytoskeleton, organelles, macromolecules) bathed in an interstitial fluid (cytosol). In this picture, the rate of cellular deformation is limited by the rate at which intracellular water can redistribute within the cytoplasm. However, direct supporting evidence for the model is lacking. Here we directly validate the poroelastic model to explain cellular rheology at short timescales using microindentation tests in conjunction with mechanical, chemical and genetic treatments. Our results show that water redistribution through the solid phase of the cytoplasm (cytoskeleton and macromolecular crowders) plays a fundamental role in setting cellular rheology at short timescales.

We study how the net transport and mixing of chemicals occur in a relatively large amoeba, the true slime mold Physarum polycephalum. The shuttle streaming of the amoeba is characterized by a rhythmic flow of the order of 1 μm/s in which the protoplasm streams back and forth. To explain the experimentally observed transport of chemicals, we formulate a simplified model to consider the mechanism by which net transport can be induced by shuttle (or periodic) motion inside the amoeba. This model is independent from the details of fluid property as it is based on the mass conservation law only. Even in such a simplified model, we demonstrate that sectional oscillations play an important role in net transport and discuss the effects of the sectional boundary motion on net transport in the microorganism.

Microdosimetric models for biological cells have assumed increasing significance in the development of nanosecond pulsed electric field technology for medical applications. In this paper, novel passive element circuits, able to take into account the dielectric dispersion of the cell, are provided. The circuital analyses are performed on a set of input pulses classified in accordance with the current literature. Accurate data in terms of transmembrane potential are obtained in both time and frequency domains for different cell models. In addition, a sensitivity study of the transfer function for the cell geometrical and dielectric parameters has been carried out. This analysis offers a new, simple, and efficient tool to characterize the nsPEFs' action at the cellular level.

We present a computer simulation study, via lattice Boltzmann simulations, of a microscopic model for cytoplasmic streaming in algal cells such as those of Chara corallina. We modelled myosin motors tracking along actin lanes as spheres undergoing directed motion along fixed lines. The sphere dimension takes into account the fact that motors drag vesicles or other organelles, and, unlike previous work, we model the boundary close to which the motors move as walls with a finite slip layer. By using realistic parameter values for actin lane and myosin density, as well as for endoplasmic and vacuole viscosity and the slip layer close to the wall, we find that this simplified view, which does not rely on any coupling between motors, cytoplasm and vacuole other than that provided by viscous Stokes flow, is enough to account for the observed magnitude of streaming velocities in intracellular fluid in living plant cells.

The commonly recognized mechanisms for spatial regulation inside the cell are membrane-bounded compartmentalization and biochemical association with subcellular organelles. We use computational modeling to investigate another spatial regulation mechanism mediated by the microtubule network in the cell. Our results demonstrate that the mitotic spindle can impose strong sequestration and concentration effects on molecules with binding affinity for microtubules, especially dynein-directed cargoes. The model can recapitulate the essence of three experimental observations on distinct microtubule network morphologies: the sequestration of germ plasm components by the mitotic spindles in the Drosophila syncytial embryo, the asymmetric cell division initiated by the time delay in centrosome maturation in the Drosophila neuroblast, and the diffusional block between neighboring energids in the Drosophila syncytial embryo. Our model thus suggests that the cell cycle-dependent changes in the microtubule network are critical for achieving different spatial regulation effects. The microtubule network provides a spatially extensive docking platform for molecules and gives rise to a "structured cytoplasm", in contrast to a free and fluid environment.

This Teaching Resource provides lecture notes, slides, and a student assignment for a two-part lecture on mathematical modeling using the Virtual Cell environment. The lectures discuss the steps involved in developing and running simulations using Virtual Cell, with particular focus on spatial partial differential equation models. We discuss how to construct both ordinary differential equation models, in which the cytoplasm is considered a well-mixed cellular compartment, and partial differential equation models, which calculate how chemical species change as a function of both time and location. The Virtual Cell environment is especially well suited for models that explore spatial specificity of cellular reactions. Partial differential equation models in Virtual Cell can give rise to simulations using predefined cellular geometries, which enable direct comparison with imaging data. These models address questions regarding the regulatory capability arising from spatial organization of the cell. Examples are provided of studies that have successfully exploited the Virtual Cell software to address the spatial contribution to signaling.

Background: The inheritance of cellular material between parent and daughter cells during mitosis is highly influential in defining the properties of the cell and therefore the population lineage. This is of particular relevance when studying cell population evolution to assess the impact of a disease or the perturbation due to a drug treatment. The usual technique to investigate inheritance is to use time-lapse microscopy with an appropriate biological marker, however, this is time consuming and the number of inheritance events captured are too low to be statistically meaningful., Results: Here we demonstrate the use of a high throughput fluorescence measurement technique e.g. flow cytometry, to measure the fluorescence from quantum dot markers which can be used to target particular cellular sites. By relating, the fluorescence intensity measured between two time intervals to a transfer function we are able to deconvolve the inheritance of cellular material during mitosis. To demonstrate our methodology we use CdTe/ZnS quantum dots to measure the ratio of endosomes inherited by the two daughter cells during mitosis in the U2-OS, human osteoscarcoma cell line. The ratio determined is in excellent agreement with results obtained previously using a more complex and computational intensive bespoke stochastic model., Conclusions: The use of a transfer function approach allows us to utilise high throughput measurement of large cell populations to derive statistically relevant measurements of the inheritance of cellular material. This approach can be used to measure the inheritance of organelles, proteins etc. and also particles introduced to cells for drug delivery.

Present-day cellular systems biology is producing data on an unprecedented scale. This field has generated a renewed interest in the holistic, "system" character of cell structure-and-function. Underlying the data deluge, however, there is a clear and present need for a historical foundation. The origin of the "system" view of the cell dates to the birth of the protoplasm concept. The 150-year history of the role of "protoplasm" in cell biology is traced. It is found that the "protoplasmic theory," not the "cell theory," was the key 19th-century construct that drove the study of the structure-and-function of living cells and set the course for the development of modern cell biology. The evolution of the "protoplasm" picture into the 20th century is examined by looking at controversial issues along the way and culminating in the current views on the role of cytological organization in cellular activities. The relevance of the "protoplasmic theory" to 21st-century cellular systems biology is considered.

Cytoplasmic transport of organelles, nucleic acids and proteins on microtubules is usually bidirectional with dynein and kinesin motors mediating the delivery of cargoes in the cytoplasm. Here we combine live cell microscopy, single virus tracking and trajectory segmentation to systematically identify the parameters of a stochastic computational model of cargo transport by molecular motors on microtubules. The model parameters are identified using an evolutionary optimization algorithm to minimize the Kullback-Leibler divergence between the in silico and the in vivo run length and velocity distributions of the viruses on microtubules. The present stochastic model suggests that bidirectional transport of human adenoviruses can be explained without explicit motor coordination. The model enables the prediction of the number of motors active on the viral cargo during microtubule-dependent motions as well as the number of motor binding sites, with the protein hexon as the binding site for the motors.

Therapeutic ultrasound of low to medium intensity is known to induce alterations in structure and functioning of cells and tissues, both in vivo and in vitro. Such effects, including excitation or inhibition of action potentials, enhanced angiogenesis rate, increased membrane permeability and changes in molecular expression, cannot be attributed in many cases to rising temperatures or the presence of gas bubbles. This study attempts to find a possible alternative explanation for the cases where neither thermal effects nor cavitation mechanisms count. We focus our attention on the complex and dense structure of cell cytoplasm, looking for periodic separating forces and relative motion between intracellular elements, such as the nucleus, and the structure in which they are embedded. It is hypothesized that relative oscillatory displacements between intracellular elements of different densities might appear in cells in response to low intensity therapeutic ultrasound (LITUS). Those displacements might induce alterations in cell structure and functioning. A linear model is constructed and solved for a spherical object, representing a typical organelle such as the nucleus, within a homogenous viscoelastic medium that vibrates uniformly. The structure in which the object is embedded is described by four different rheologic models, including viscous fluid, elastic solid, and Voigt and Maxwell viscoelastic constructs. It is found that cyclic intracellular displacements comparable with and even larger than the mean thermal fluctuations may be obtained due to LITUS irradiation in conditions where the relative motion of organelles is dominated by elastic response, or where the effective viscosity of the cytoplasm is low. Resonance frequency at which intracellular vibration of maximal amplitude is obtained is found to lie within the low LITUS frequency range, i.e., tens to hundreds of kHz. Local intracellular strain on the order of 0.5% is found for 1 microm organelle in 10 microm cell under typical LITUS settings. It is suggested that fatigue-like, cumulative effect underlie the transfer of the intracellular strain into biologic alterations.

A mathematical model of the active transport of main ions in cells of archaebacteria has been constructed. A set of equations has been developed and solved for ion fluxes through the bacterium membrane. The model is based on the principle "one ion-one transport system." Considering experimental data, the major transport mechanism was determined for each ion and the balance equation was written on the basis of this mechanism in the stationary state. This allowed calculating values of the membrane potential and intracellular concentrations of the ions independently. The calculated values of the intracellular concentrations and resting potential are in qualitative agreement with the corresponding experimental values for cells of extremely halophilic archaea.

Cytoplasmic streaming circulates the contents of large eukaryotic cells, often with complex flow geometries. A largely unanswered question is the significance of these flows for molecular transport and mixing. Motivated by "rotational streaming" in Characean algae, we solve the advection-diffusion dynamics of flow in a cylinder with bidirectional helical forcing at the wall. A circulatory flow transverse to the cylinder's long axis, akin to Dean vortices at finite Reynolds numbers, arises from the chiral geometry. Strongly enhanced lateral transport and longitudinal homogenization occur if the transverse Péclet number is sufficiently large, with scaling laws arising from boundary layers.

Dielectric spectroscopy (DS) of living biological cells is based on the analysis of the complex dielectric permittivity of cells suspended in a physiological medium. It provides knowledge on the polarization-relaxation response of cells to external electric field as function of the excitation frequency. This response is strongly affected by both structural and molecular properties of cells and therefore, can reveal rare insights on cell physiology and behaviour. This study demonstrates the mapping potential of DS after cytoplasmatic and membranal markers for cell-based screening analysis. The effect of membrane permittivity and cytoplasm conductivity was examined using tagged MBA and MDCK cell lines respectively. Comparing the permittivity spectra of tagged and native cell lines reveals clear differences between the analyzed suspensions. In addition, differences on the matching dielectric properties of cells were obtained. Those findings support the high distinction resolution and sensitivity of DS after fine molecular and cellular changes, and hence, highlight the high potential of DS as non invasive screening tool in cell biology research.

The one-cell amphibian embryo is modeled as a rigid spherical shell containing equal volumes of two immiscible fluids with different densities and viscosities and a surface tension between them. The fluids represent denser yolk in the bottom hemisphere and clearer cytoplasm and the germinal vesicle in the top hemisphere. The unstable equilibrium configuration of the inverted system (the heavier fluid on top) depends on the value of the contact angle. The theoretically calculated normal modes of perturbation and the instability of each mode are in agreement with the results from ComFlo computational fluid dynamic simulations of the same system. The two dominant types of modes of perturbation give rise to axisymmetric and asymmetric sloshing of the cytoplasm of the inverted embryos, respectively. This work quantifies our hypothesis that the axisymmetric mode corresponds to failure of development, and the asymmetric sloshing mode corresponds to development proceeding normally, but with reversed pigmentation, for inverted embryos.

We investigate how an amoeba mechanically moves its own center of gravity using the model organism Physarum plasmodium. Time-dependent velocity fields of protoplasmic streaming over the whole plasmodia were measured with a particle image velocimetry program developed for this work. Combining these data with measurements of the simultaneous movements of the plasmodia revealed a simple physical mechanism of locomotion. The shuttle streaming of the protoplasm was not truly symmetric due to the peristalsis-like movements of the plasmodium. This asymmetry meant that the transport capacity of the stream was not equal in both directions, and a net forward displacement of the center of gravity resulted. The generality of this as a mechanism for amoeboid locomotion is discussed.

In 1889 Abderhalden reported his discovery that there is no (or as shown later, little) sodium ion (Na+) in human red blood cells even though these cells live in a medium rich in Na+. History shows that all major theories of the living cell are built around this basic phenomenon seen in all the living cells that have been carefully examined. One of these theories has been steadily evolving but is yet-to-be widely known. Named the association-induction hypothesis (AIH), it has been presented thus far in four books dated 1962, 1984, 1992 and 2001 respectively. In this theory, the low Na+ in living cells originates from (i) an above-normal molecule-to-molecule interaction among the bulk-phase cell water molecules, in consequence of (ii) their (self-propagating) polarization-orientation by the backbone NHCO groups of (fully-extended) cell protein(s), when (iii) the protein(s) involved is under the control of the electron-withdrawing cardinal adsorbent (EWC), ATP. A mature human red blood cell (rbc) has no nucleus, nor other organelle. 64% of the rbc is water; 35% belongs to a single protein, hemoglobin (Hb). This twofold simplicity allows the concoction of an ultra-simple model (USM) of the red blood cell's cytoplasmic protoplasm, which comprises almost entirely of hemoglobin, water, K+ and ATP. Only in the USM, the ATP has been replaced by an artificial but theoretically authentic EWC, H+ (given as HCl). To test the theory with the aid of the USM, we filled dialysis sacs with a 40% solution of pure (ferri-) hemoglobin followed by incubating the sacs till equilibrium in solutions containing different amounts of HCI (including zero) but a constant (low) concentration of NaCl. We then determined the equilibrium ratio of the Na+ concentration inside the sac over that in the solution outside and refer to this ratio as qNaCl. When no H+ was added, the qNaCl stayed at unity as predicted by the theory. More important (and also predicted by the theory,) when the right amount of H+ had been added, qNaCl fell to the 0.1- 0.3 range found in living red blood (and other) cells. These and other findings presented confirm the AIH's theory of life at the most basic level: in the resting living state, microscopic, or nano-protoplasm, is the ultimate physical basis of life. (See Post Script on page 111.)

Osmotic loading of cells has been used to investigate their physicochemical properties as well as their biosynthetic activities. The classical Kedem-Katchalsky framework for analyzing cell response to osmotic loading, which models the cell as a fluid-filled membrane, does not generally account for the possibility of partial volume recovery in response to loading with a permeating osmolyte, as observed in some experiments. The cell may be more accurately represented as a hydrated gel surrounded by a semi-permeable membrane, with the gel and membrane potentially exhibiting different properties. To help assess whether this more elaborate model of the cell is justified, this study investigates the response of spherical gels to osmotic loading, both from experiments and theory. The spherical gel is described using the framework of mixture theory. In the experimental component of the study alginate is used as the model gel, and is osmotically loaded with dextran solutions of various concentrations and molecular weight, to verify the predictions from the theoretical analysis. Results show that the mixture framework can accurately predict the transient and equilibrium response of alginate gels to osmotic loading with dextran solutions. It is found that the partition coefficient of dextran in alginate regulates the equilibrium volume response and can explain partial volume recovery based on passive transport mechanisms. The validation of this theoretical framework facilitates future investigations of the role of the protoplasm in the response of cells to osmotic loading.

A biomechanical approach in modelling the growth and division of a single fully deformable cell by using an immersed boundary method with distributed sources is presented, and its application to model the early tumour development is discussed. This mathematical technique couples a continuous description of a viscous incompressible cytoplasm with the dynamics of separate elastic cells, containing their own point nuclei, elastic plasma membranes with membrane receptors, and individually regulated cell processes. This model enables one to focus on the biomechanical properties of individual cells and on communication between cells and their microenvironment, simultaneously allowing for the formation of clusters or sheets of cells that act together as one complex tissue. Several examples of early tumours growing in various geometrical configurations and with distinct conditions of their initiation and progression are also presented to show the strength of our approach in modelling different topologies of the growing tissues in distinct biochemical conditions of the surrounding media.

In the large amoeboid organism Physarum, biochemical oscillators are spatially distributed throughout the organism and their collective motion exhibits phase waves, which carry physiological signals. The basic nature of this wave behaviour is not well-understood because, to date, an important effect has been neglected, namely, the shuttle streaming of protoplasm which accompanies the biochemical rhythms. Here we study the effects of self-consistent flow on the wave behaviour of oscillatory reaction-diffusion models proposed for the Physarum plasmodium, by means of numerical simulation for the dispersion relation and weakly nonlinear analysis for derivation of the phase equation. We conclude that the flow term is able to increase the speed of phase waves (similar to elongation of wave length). We compare the theoretical consequences with real waves observed in the organism and also point out the physiological roles of these effects on control mechanisms of intracellular communication.

The ability to adjust reproductive output to environmental conditions is important to the fitness of a species. The semelparous, chordate, Oikopleura dioica, is particularly adept in producing a highly variable number of oocytes in its short life cycle. Here we show that this entails an original reproductive strategy in which the entire female germline is contained in a single multinucleate cell, the "coenocyst". After an initial phase of syncytial nuclear proliferation half of the nuclei entered meiosis whereas the other half became highly polyploid. The inner F-actin network, with associated plasma membranes, formed a highly ramified infrastructure in which each meiotic nucleus was contained in a pseudo-compartmentalized pro-oocyte linked to the common cytoplasm via ring canals. At a set developmental time, a subset of the pro-oocytes was selected for synchronous growth and the common coenocyst cytoplasm was equally partitioned by transfer through the ring canals. Examination of related species indicated that the coenocyst arrangement is a conserved feature of Appendicularian oogenesis allowing efficient numerical adjustment of oocyte production. As Appendicularia are the second most abundant class of zooplankton, with a world-wide distribution, the coenocyst is clearly a common and successful reproductive strategy on a global scale.

Melanosomes, pigment granules in melanophores, play a principal role in physiological color adaptation of fish and frog. Melanophores regulate melanosome trafficking on cytoskeletal filaments to generate a range of spatiotemporal patterns. Here, we present the first comprehensive model of spatiotemporal evolution of melanosome patterns. The model encompasses both physical and biochemical aspects of melanosome dynamics. It consists of (i) a kinetic description of biochemical reactions involved in intracellular signaling, (ii) a system of macroscopic reaction-diffusion-convection equations for melanosome concentration, and (iii) a set of constitutive relationships for coupling transport with the biochemical network. The model relates molecular-level regulatory actions to cell-level melanosome distribution, allowing unification of existing experimental observations and qualitative hypotheses into an integrated, consistent framework. The model reproduces salient features of melanosome patterns, both during transient and steady state. It gives useful insights into how cells coordinate motor-assisted transport to maintain and adapt spatial organization of intracellular organelles. In particular, we calculate the optimal transition paths from aggregation to dispersion in fish melanophores. The calculations suggest that fish melanophores optimally control intracellular signaling to maximize the efficiency of motor-assisted transport during dispersion.

With the rapidly accumulating knowledge of biological entities and networks, there is a growing need for a general framework to understand this information at a system level. In order to understand life as system, a formal description of system dynamics with semantic validation will be necessary. Within the context of biological pathways, several formats have been proposed, e.g., SBML, CellML, and BioPAX. Unfortunately, these formats lack the formal definitions of each term or fail to capture the system dynamics behavior. Thus, we have developed a new system dynamics centered ontology called Cell System Ontology (CSO). As an exchange format, the ontology is implemented in the Web Ontology Language (OWL), which enables semantic validation and automatic reasoning to check the consistency of biological pathway models. The features of CSO are as follows: (1) manipulation of different levels of granularity and abstraction of pathways, e.g., metabolic pathways, regulatory pathways, signal transduction pathways, and cell-cell interactions; (2) capture of both quantitative and qualitative aspects of biological function by using hybrid functional Petri net with extension (HFPNe); and (3) encoding of biological pathway data related to visualization and simulation, as well as modeling. The new ontology also predefines mature core vocabulary, which will be necessary for creating models with system dynamics. In addition, each of the core terms has at least one standard icon for easy modeling and accelerating the exchangeability among applications. In order to demonstrate the potential of CSO-based pathway modeling, visualization, and simulation, we present an HFPNe model for the ASEL and ASER regulatory networks in Caenorhabditis elegans.

Based on earlier suggestions that peroxisomes may have arisen from endosymbionts that later lost their DNA, it was expected that protein transport into this organelle would have parallels to systems found in other organelles of endosymbiont origin, such as mitochondria and chloroplasts. This review highlights three features of peroxisomal matrix protein import that make it unique in comparison with these other subcellular compartments - the ability of this organelle to transport folded, co-factor-bound and oligomeric proteins, the dynamics of the import receptors during the matrix protein import cycle and the existence of a peroxisomal quality-control pathway, which insures that the peroxisome membrane is cleared of cargo-free receptors.

Background: The motion and redistribution of intracellular organelles is a fundamental process in cells. Organelle motion is a complex phenomenon that depends on a large number of variables including the shape of the organelle, the type of motors with which the organelles are associated, and the mechanical properties of the cytoplasm. This paper presents a study that characterizes the diffusive motion of mitochondria in chondrocytes seeded in agarose constructs and what this implies about the mechanical properties of the cytoplasm., Method of Approach: Images showing mitochondrial motion in individual cells at 30 s intervals for 15 min were captured with a confocal microscope. Digital image correlation was used to quantify the motion of the mitochondria, and the mean square displacement (MSD) was calculated. Statistical tools for testing whether the characteristic motion of mitochondria varied throughout the cell were developed. Calculations based on statistical mechanics were used to establish connections between the measured MSDs and the mechanical nature of the cytoplasm., Results: The average MSD of the mitochondria varied with time according to a power law with the power term greater than 1, indicating that mitochondrial motion can be viewed as a combination of diffusion and directional motion. Statistical analysis revealed that the motion of the mitochondria was not uniform throughout the cell, and that the diffusion coefficient may vary by over 50%, indicating intracellular heterogeneity. High correlations were found between movements of mitochondria when they were less than 2 microm apart. The correlation is probably due to viscoelastic properties of the cytoplasm. Theoretical analysis based on statistical mechanics suggests that directed diffusion can only occur in a material that behaves like a fluid on large time scales., Conclusions: The study shows that mitochondria in different regions of the cell experience different characteristic motions. This suggests that the cytoplasm is a heterogeneous viscoelastic material. The study provides new insight into the motion of mitochondria in chondrocytes and its connection with the mechanical properties of the cytoplasm.

We describe a finite-element model of mast cell calcium dynamics that incorporates the endoplasmic reticulum's complex geometry. The model is built upon a three-dimensional reconstruction of the endoplasmic reticulum (ER) from an electron tomographic tilt series. Tetrahedral meshes provide volumetric representations of the ER lumen, ER membrane, cytoplasm, and plasma membrane. The reaction-diffusion model simultaneously tracks changes in cytoplasmic and ER intraluminal calcium concentrations and includes luminal and cytoplasmic protein buffers. Transport fluxes via PMCA, SERCA, ER leakage, and Type II IP3 receptors are also represented. Unique features of the model include stochastic behavior of IP3 receptor calcium channels and comparisons of channel open times when diffusely distributed or aggregated in clusters on the ER surface. Simulations show that IP3R channels in close proximity modulate activity of their neighbors through local Ca2+ feedback effects. Cytoplasmic calcium levels rise higher, and ER luminal calcium concentrations drop lower, after IP3-mediated release from receptors in the diffuse configuration. Simulation results also suggest that the buffering capacity of the ER, and not restricted diffusion, is the predominant factor influencing average luminal calcium concentrations.

It has not escaped the attention of the plant disease resistance community that the vacuole is rapidly emerging as a central player in the execution of cell death. On the one hand the targeted destruction of the vacuole-from the inside out-by vacuolar processing enzymes (VPE) is required to induce PCD in pathogen-infected cells. On the other hand, an intact vacuole is vital for a functional autophagic response to ensure survival of uninfected cells. At face value, the two responses seem to represent distinct resistance mechanisms that operate at divergent branch points and their use of the vacuole merely coincidental. However, closer examination has led us to propose an interesting hypothesis that accounts for these two opposing roles of the vacuole in both VPE-mediated PCD and autophagydependent cell survival. During initial infection, we propose a mechanism similar to the CPY transport pathway in yeast wherein a select set of genes, including several which encode a phosphatidylinositol 3-kinase complex that is needed for autophagy, are needed for VPE transport, vacuolar processing and initiation of PCD. Later during infection, autophagyspecific genes are needed for autophagosome formation, sequestration of VPE preproteins and VPE degradation.

Cytoplasmic incompatibility (CI) is induced in arthropods by the maternally inherited bacterium Wolbachia. When infected males mate with uninfected females or with females bearing a different Wolbachia variant, paternal chromosomes behave abnormally and embryos die. This pattern can be interpreted as resulting from two bacterial effects: One (usually termed mod, for modification) would affect sperm and induce embryo death, unless Wolbachia is also present in the egg, which implies the existence of a second effect, usually termed resc, for rescue. The fact that CI can occur in crosses between males and females infected by different Wolbachia shows that mod and resc interact in a specific manner. In other words, different compatibility types, or mod/resc pairs seem to have diverged from one (or a few) common ancestor(s). We are interested in the process allowing the evolution of mod/resc pairs. Here this question is addressed experimentally after cytoplasmic injection into a single host species (Drosophila simulans) by investigating compatibility relationships between closely related Wolbachia variants naturally evolving in different dipteran hosts: D. simulans, Drosophila melanogaster, and Rhagoletis cerasi. Our results suggest that closely related bacteria can be totally or partially incompatible. The compatibility relationships observed can be explained using a formal description of the mod and resc functions, implying both qualitative and quantitative variations.

Mechanical stimulation is known to cause alterations in the behaviour of cells adhering to a substrate. The mechanisms by which forces are transduced into biological responses within the cell remain largely unknown. Since cellular deformation is likely involved, further understanding of the biomechanical origins of alterations in cellular response can be aided by the use of computational models in describing cellular structural behaviour and in determining cellular deformation due to imposed loads of various magnitudes. In this paper, a finite element modelling approach that can describe the biomechanical behaviour of adherent eukaryotic cells is presented. It fuses two previous modelling approaches by incorporating, in an idealised geometry, all cellular components considered structurally significant, i.e. prestressed cytoskeleton, cytoplasm, nucleus and membrane components. The aim is to determine if we can use this model to describe the non-linear structural behaviour of an adherent cell and to determine the contribution of the various cellular components to cellular stability. Results obtained by applying forces (in the picoNewton range) to the model membrane nodes suggest a key role for the cytoskeleton in determining cellular stiffness. The model captures non-linear structural behaviours such as strain hardening and prestress effects (in the region of receptor sites), and variable compliance along the cell surface. The role of the cytoskeleton in stiffening a cell during the process of cell spreading is investigated by applying forces to five increasingly spread cell geometries. Parameter studies reveal that material properties of the cytoplasm (elasticity and compressibility) also have a large influence on cellular stiffness. The computational model of a single cell developed here is proposed as one that is sufficiently complex to capture the non-linear behaviours of the cell response to forces whilst not being so complex that the parameters cannot be specified. The model could be very useful in computing cellular structural behaviour in response to various in vitro mechanical stimuli (e.g. fluid flow, substrate strain), or for use in algorithms that attempt to simulate mechanobiological processes.

This paper shows the importance of using realistic cell shapes with the proper geometry and orientation to study the mechanisms of direct cellular effects from radiofrequency (RF) exposure. For this purpose, the electric field distribution within erythrocyte, rod and ellipsoidal cell models is calculated by using a finite element technique with adaptive meshing. The three cell models are exposed to linearly polarized electromagnetic plane waves of frequencies 900 and 2450 MHz. The results show that the amplification of the electric field within the membrane of the erythrocyte shape cell is more significant than that observed in other cell geometries. The results obtained show the dependence of the induced electric field distribution on frequency, electrical properties of membrane and cytoplasm and the orientation of the cell with respect to the applied field. The analysis of the transition of an erythrocyte shape to an ellipsoidal one shows that a uniformly shelled ellipsoid model is a rough approximation if a precise simulation of bioeffects in cells is desired.

Muscles are ideal models with which to examine the relationship between structure and metabolism because they are some of the most highly structured cells, and are capable of the largest and most rapid metabolic transitions as well as the highest metabolic rates known. Studies of metabolism have traditionally been conducted within what can considered as the kinetic paradigm provided by 'solution biochemistry'; i.e. the rates of enzymatic reactions are studied in terms of their regulation by mass-action and allosteric effectors and, most recently, metabolic control analysis of pathways. This approach has served biology well and continues to be useful. Here, we consider the diffusion of small and large molecules in muscles and energy metabolism in the context of intracellular space. We find that in attempting to explain certain phenomena, a purely kinetic paradigm appears insufficient. Instead, phenomena such as the 'shuttling' of high-energy phosphate donors and acceptors and the binding of metabolic enzymes to intracellular structures or to each other are better understood when metabolic rates and their regulation are considered in the context of intracellular compartments, distances, gradients and diffusion. As in all of biology, however, complexity dominates, and to such a degree that one pathway may consist of several reactions that each behave according to different rules. 'Soluble' creatine kinase operates at or near equilibrium, while mitochondrial and myofibrillar creatine kinases directly channel substrate to (or from) the adenine nucleotide translocase and actomyosin-ATPase, their operation being thus displaced from equilibrium. Hexose 6-phosphate metabolism appears to obey the rules of solution biochemistry, e.g. phosphoglucoisomerase behaves as Haldane would have predicted in 1930. In contrast, given low steady-state substrate and product concentrations and high flux rates, a number of glycolytic reactions further downstream must be catalyzed by enzymes localized in close proximity to each other. Metabolites may be channeled within these complexes. When observed, mechanistic differences between species in the same steps or processes should not be surprising, considering how animals vary so much in structures, mechanical properties, mitochondrial contents and metabolic rates. This analysis suggests that declarations of the triumph of one mechanism or paradigm over all others, as well as calls for the abandonment of solution biochemistry, are unwarranted. Rather, metabolic biochemistry would seem better served by reconciling the old and the new.

The exchange of macromolecules between the cytoplasm and the nucleus of eukaryotic cells takes place through the nuclear pore complex (NPC), which contains a selective permeability barrier. Experiments on the physical properties of this barrier appear to be in conflict with current physical understanding of the rheology of reversible gels. This paper proposes that the NPC gel is anomalous and characterized by connectivity fluctuations. It develops a simplified model to demonstrate the possibility of enhanced diffusion constants of macromolecules trapped in such a gel.

The cell nucleus plays a central role in the response of the endothelium to mechanical forces, possibly by deforming during cellular adaptation. The goal of this work was to precisely quantify the mechanical properties of the nucleus. Individual endothelial cells were subjected to compression between glass microplates. This technique allows measurement of the uniaxial force applied to the cell and the resulting deformation. Measurements were made on round and spread cells to rule out the influence of cell morphology on the nucleus mechanical properties. Tests were also carried out with nuclei isolated from cell cultures by a chemical treatment. The non-linear force-deformation curves indicate that round cells deform at lower forces than spread cells and nuclei. Finite-element models were also built with geometries adapted to actual morphometric measurements of round cells, spread cells and isolated nuclei. The nucleus and the cytoplasm were modeled as separate homogeneous hyperelastic materials. The models simulate the compression and yield the force-deformation curve for a given set of elastic moduli. These parameters are varied to obtain a best fit between the theoretical and experimental data. The elastic modulus of the cytoplasm is found to be on the order of 500N/m(2) for spread and round cells. The elastic modulus of the endothelial nucleus is on the order of 5000N/m(2) for nuclei in the cell and on the order of 8000N/m(2) for isolated nuclei. These results represent an unambiguous measurement of the nucleus mechanical properties and will be important in understanding how cells perceive mechanical forces and respond to them.

We present an analytical equation for the transmembrane voltage (Deltaphi) induced by a homogeneous AC field on arbitrarily oriented cells of the general ellipsoidal shape. The equation generalizes the Schwan equation for spherical cells and describes the dependence of Deltaphi on field frequency, cell size and shape, membrane capacitance, conductivities of cytoplasm, membrane and external medium, the location of the membrane site under consideration, and on the orientation of the cell with respect to the field. The derivation is based on the fact that the cytoplasm and the Maxwellian equivalent body of the whole cell are both of a general ellipsoidal shape and must thus exhibit constant local fields. The constant fields allow for a relatively simple description of the potentials on the internal and external membrane sides, leading to Deltaphi. For this, the properties of cytoplasm, membrane, and external medium have been introduced into a special, finite element model. We found that Deltaphi can be unambiguously defined for non-spherical cells, provided that the membrane thickness is thin in comparison to the cell dimensions.

The motion of amoeboid cells is characterized by cytoplasmic streaming and by membrane protrusions and retractions which occur even in the absence of interactions with a substratum. Cell translocation requires, in addition, a transmission mechanism wherein the power produced by the cytoplasmic engine is applied to the substratum in a highly controlled fashion through specific adhesion proteins. Here we present a simple mechano-chemical model that tries to capture the physical essence of these complex biomolecular processes. Our model is based on the continuum equations for a viscous and reactive two-phase fluid model with moving boundaries, and on force balance equations that average the stochastic interactions between actin polymers and membrane proteins. In this paper we present a new derivation and analysis of these equations based on minimization of a power functional. This derivation also leads to a clear formulation and classification of the kinds of boundary conditions that should be specified at free surfaces and at the sites of interaction of the cell and the substratum. Numerical simulations of a one-dimensional lamella reveal that even this extremely simplified model is capable of producing several typical features of cell motility. These include periodic 'ruffle' formation, protrusion-retraction cycles, centripetal flow and cell-substratum traction forces.