Evolutionary dynamics within and among competing groups.

Biological and social systems are structured at multiple scales, and the incentives of individuals who interact in a group may diverge from the collective incentive of the group as a whole. Mechanisms to resolve this tension are responsible for profound transitions in evolutionary history, including the origin of cellular life, multicellular life, and even societies. Here, we synthesize a growing literature that extends evolutionary game theory to describe multilevel evolutionary dynamics, using nested birth-death processes and partial differential equations to model natural selection acting on competition within and among groups of individuals. We analyze how mechanisms known to promote cooperation within a single group-including assortment, reciprocity, and population structure-alter evolutionary outcomes in the presence of competition among groups. We find that population structures most conducive to cooperation in multiscale systems can differ from those most conducive within a single group. Likewise, for competitive interactions with a continuous range of strategies we find that among-group selection may fail to produce socially optimal outcomes, but it can nonetheless produce second-best solutions that balance individual incentives to defect with the collective incentives for cooperation. We conclude by describing the broad applicability of multiscale evolutionary models to problems ranging from the production of diffusible metabolites in microbes to the management of common-pool resources in human societies.

Front propagation in the shadow wave-pinning model.

In this paper we consider a non-local bistable reaction-diffusion equation which is a simplified version of the wave-pinning model of cell polarization. In the small diffusion limit, a typical solution u(x, t) of this model approaches one of the stable states of the bistable nonlinearity in different parts of the spatial domain [Formula: see text], separated by an interface moving at a normal velocity regulated by the integral [Formula: see text]. In what is often referred to as wave-pinning, feedback between mass-conservation and bistablity causes the interface to slow and approach a fixed limit. In the limit of a small diffusivity [Formula: see text], we prove that for any [Formula: see text] the interface can be estimated within [Formula: see text] of the location as predicted using formal asymptotics. We also discuss the sharpness of our result by comparing the formal asymptotic results with numerical simulations.

On the role of myosin-induced actin depolymerization during cell migration.

Mammalian cell migration in open spaces requires F-actin polymerization and myosin contraction. While many studies have focused on myosin's coupling to focal adhesion and stress fibers, the indirect effect of myosin contraction on cell migration through actin depolymerization is not well studied. In this work, we quantified how cell velocity and effective power output are influenced by the rate of actin depolymerization, which is affected by myosin contraction. In addition, we derived scaling laws to provide physical insights into cell migration. Model analysis shows that the cell migration velocity displays a biphasic dependence on the rate of actin depolymerization and myosin contraction. Our model further predicts that the effective cell energy output depends not only on the cell velocity but also on myosin contractility. The work has implications on in vivo processes such as immune response and cancer metastasis, where cells overcome barriers imposed by the physical environment.

Optimality of intercellular signaling: Direct transport versus diffusion.

Intercellular signaling has an important role in organism development, but not all communication occurs using the same mechanism. Here, we analyze the energy efficiency of intercellular signaling by two canonical mechanisms: Diffusion of signaling molecules and direct transport mediated by signaling cellular protrusions. We show that efficient contact formation for direct transport can be established by an optimal rate of projecting protrusions, which depends on the availability of information about the location of the target cell. The optimal projection rate also depends on how signaling molecules are transported along the protrusion, in particular the ratio of the energy cost for contact formation and molecule synthesis. Also, we compare the efficiency of the two signaling mechanisms, under various model parameters. We find that direct transport is favored over diffusion when transporting a large amount of signaling molecules. There is a critical number of signaling molecules at which the efficiencies of the two mechanisms are the same. The critical number is small when the distance between cells is far, which helps explain why protrusion-based mechanisms are observed in long-range cellular communications.

Long-time behavior of a PDE replicator equation for multilevel selection in group-structured populations.

In many biological systems, natural selection acts simultaneously on multiple levels of organization. This scenario typically presents an evolutionary conflict between the incentive of individuals to cheat and the collective incentive to establish cooperation within a group. Generalizing previous work on multilevel selection in evolutionary game theory, we consider a hyperbolic PDE model of a group-structured population, in which members within a single group compete with each other for individual-level replication; while the group also competes against other groups for group-level replication. We derive a threshold level of the relative strength of between-group competition such that defectors take over the population below the threshold while cooperation persists in the long-time population above the threshold. Under stronger assumptions on the initial distribution of group compositions, we further prove that the population converges to a steady state density supporting cooperation for between-group selection strength above the threshold. We further establish long-time bounds on the time-average of the collective payoff of the population, showing that the long-run population cannot outperform the payoff of a full-cooperator group even in the limit of infinitely-strong between-group competition. When the group replication rate is maximized by an intermediate level of within-group cooperation, individual-level selection casts a long shadow on the dynamics of multilevel selection: no level of between-group competition can erase the effects of the individual incentive to defect. We further extend our model to study the case of multiple types of groups, showing how the games that groups play can coevolve with the level of cooperation.

A reduced 1D stochastic model of bleb-driven cell migration.

Blebs are pressure-driven protrusions that have been observed in cells undergoing apoptosis, cytokinesis, or migration, including tumor cells that use blebs to escape their organs of origin. Here, we present a minimal 1D model of bleb-driven cell motion that combines a simple mechanical model with turnover kinetics of the actin cortex and adhesions between the membrane and the cortex. The deterministic version of this model is used to study the properties of individual blebbing events. We further introduce stochastic turnover of the adhesions, which allows for spontaneous initiation of repeated blebbing events, thus leading to sustained cell travel. We explore how the main parameters of the system control the properties of the blebbing events and the speed of cell travel. Finally, we derive a further simplification by deriving a Langevin approximation to this stochastic model.

Evolution of prosocial behaviours in multilayer populations.

Human societies include diverse social relationships. Friends, family, business colleagues and online contacts can all contribute to one's social life. Individuals may behave differently in different domains, but success in one domain may engender success in another. Here, we study this problem using multilayer networks to model multiple domains of social interactions, in which individuals experience different environments and may express different behaviours. We provide a mathematical analysis and find that coupling between layers tends to promote prosocial behaviour. Even if prosociality is disfavoured in each layer alone, multilayer coupling can promote its proliferation in all layers simultaneously. We apply this analysis to six real-world multilayer networks, ranging from the socio-emotional and professional relationships in a Zambian community, to the online and offline relationships within an academic university. We discuss the implications of our results, which suggest that small modifications to interactions in one domain may catalyse prosociality in a different domain.

Strong intracellular signal inactivation produces sharper and more robust signaling from cell membrane to nucleus.

For a chemical signal to propagate across a cell, it must navigate a tortuous environment involving a variety of organelle barriers. In this work we study mathematical models for a basic chemical signal, the arrival times at the nuclear membrane of proteins that are activated at the cell membrane and diffuse throughout the cytosol. Organelle surfaces within human B cells are reconstructed from soft X-ray tomographic images, and modeled as reflecting barriers to the molecules' diffusion. We show that signal inactivation sharpens signals, reducing variability in the arrival time at the nuclear membrane. Inactivation can also compensate for an observed slowdown in signal propagation induced by the presence of organelle barriers, leading to arrival times at the nuclear membrane that are comparable to models in which the cytosol is treated as an open, empty region. In the limit of strong signal inactivation this is achieved by filtering out molecules that traverse non-geodesic paths.

The importance of water and hydraulic pressure in cell dynamics.

All mammalian cells live in the aqueous medium, yet for many cell biologists, water is a passive arena in which proteins are the leading players that carry out essential biological functions. Recent studies, as well as decades of previous work, have accumulated evidence to show that this is not the complete picture. Active fluxes of water and solutes of water can play essential roles during cell shape changes, cell motility and tissue function, and can generate significant mechanical forces. Moreover, the extracellular resistance to water flow, known as the hydraulic resistance, and external hydraulic pressures are important mechanical modulators of cell polarization and motility. For the cell to maintain a consistent chemical environment in the cytoplasm, there must exist an intricate molecular system that actively controls the cell water content as well as the cytoplasmic ionic content. This system is difficult to study and poorly understood, but ramifications of which may impact all aspects of cell biology from growth to metabolism to development. In this Review, we describe how mammalian cells maintain the cytoplasmic water content and how water flows across the cell surface to drive cell movement. The roles of mechanical forces and hydraulic pressure during water movement are explored.

A computational study on the role of glutamate and NMDA receptors on cortical spreading depression using a multidomain electrodiffusion model.

Cortical spreading depression (SD) is a spreading disruption of ionic homeostasis in the brain during which neurons experience complete and prolonged depolarizations. SD is the basis of migraine aura and is increasingly associated with many other brain pathologies. Here, we study the role of glutamate and NMDA receptor dynamics in the context of an ionic electrodiffusion model. We perform simulations in one (1D) and two (2D) spatial dimension. Our 1D simulations reproduce the "inverted saddle" shape of the extracellular voltage signal for the first time. Our simulations suggest that SD propagation depends on two overlapping mechanisms; one dependent on extracellular glutamate diffusion and NMDA receptors and the other dependent on extracellular potassium diffusion and persistent sodium channel conductance. In 2D simulations, we study the dynamics of spiral waves. We study the properties of the spiral waves in relation to the planar 1D wave, and also compute the energy expenditure associated with the recurrent SD spirals.

On the energy efficiency of cell migration in diverse physical environments.

In this work, we explore fundamental energy requirements during mammalian cell movement. Starting with the conservation of mass and momentum for the cell cytosol and the actin-network phase, we develop useful identities that compute dissipated energies during extensions of the cell boundary. We analyze 2 complementary mechanisms of cell movement: actin-driven and water-driven. The former mechanism occurs on 2-dimensional cell-culture substrate without appreciable external hydraulic resistance, while the latter mechanism is prominent in confined channels where external hydraulic resistance is high. By considering various forms of energy input and dissipation, we find that the water-driven cell-migration mechanism is inefficient and requires more energy. However, in environments with sufficiently high hydraulic resistance, the efficiency of actin-polymerization-driven cell migration decreases considerably, and the water-based mechanism becomes more efficient. Hence, the most efficient way for cells to move depends on the physical environment. This work can be extended to higher dimensions and has implication for understanding energetics of morphogenesis in early embryonic development and cancer-cell metastasis and provides a physical basis for understanding changing metabolic requirements for cell movement in different conditions.

waveCSD: A method for estimating transmembrane currents originated from propagating neuronal activity in the neocortex: Application to study cortical spreading depression.

BACKGROUND: Recent years have witnessed an upsurge in the development of methods for estimating current source densities (CSDs) in the neocortical tissue from their recorded local field potential (LFP) reflections using microelectrode arrays. Among these, methods utilizing linear arrays work under the assumption that CSDs vary as a function of cortical depth; whereas they are constant in the tangential direction, infinitely or in a confined cylinder. This assumption is violated in the analysis of neuronal activity propagating along the neocortical sheet, e.g. propagation of alpha waves or cortical spreading depression. NEW METHOD: Here, we developed a novel mathematical method (waveCSD) for CSD analysis of LFPs associated with a planar wave of neocortical neuronal activity propagating at a constant velocity towards a linear probe. RESULTS: Results show that the algorithm is robust to the presence of noise in LFP data and uncertainties in knowledge of propagation velocity. Also, results show high level of accuracy of the method in a wide range of electrode resolutions. Using in vivo experimental recordings from the rat neocortex, we employed waveCSD to characterize transmembrane currents associated with cortical spreading depressions. COMPARISON WITH EXISTING METHOD(S): Simulation results indicate that waveCSD has a significantly higher reconstruction accuracy compared to the widely-used inverse CSD method (iCSD), and the regularized kernel CSD method (kCSD), in the analysis of CSDs originating from propagating neuronal activity. CONCLUSIONS: The waveCSD method provides a theoretical platform for estimation of transmembrane currents from their LFPs in experimental paradigms involving wave propagation.

Eversion stripping of the esophagus with intraesophageal insufflation-A case report.

INTRODUCTION: Patients with esophageal cancer frequently cannot tolerate thoracotomy due to their overall debilitated condition. Moreover, some patients have severe adhesions in the thoracic cavity. Eversion stripping of the esophagus is an option for resection in these patients. PRESENTATION OF CASE: A 64-year-old man was admitted to our institution with the chief complaint of epigastric pain. Endoscopic examination showed a protruding lesion 22cm from the incisors, with a superficial and circumferential mucosal irregularity on the distal side of the lesion. Biopsy revealed squamous cell carcinoma. Clinical stage was T1b(sm)N0M0, cStage I. In addition to the poor pulmonary status of the patient, adhesions in the intrathoracic cavity were predicted. The decision was made to perform esophageal resection without a thoracotomy. In order to ensure complete invagination of the esophagus, the esophagus was insufflated prior to stripping. The stripping process was observed with a gastroscope. During the stripping, the esophagus did not bunch up, and stripping was smooth and with minimal resistance. DISCUSSION: The stripping resection of the esophagus is an important option for the esophageal surgeon. In this case report, we describe a new eversion stripping method of the esophagus. This easy and reliable stripping method incorporates intraesophageal insufflation. CONCLUSION: The indications for blunt esophageal dissection without thoracotomy have been decreasing. On the other hand, our method seems to be useful in optimal case of stripping of esophagus.

Resection of the Gastric Tube Reconstructed through the Retrosternal Route without Sternotomy.

With advances of combined modality therapy, prognoses in esophageal cancer have been improving. After resection of esophageal cancer, the development of gastric tube cancer is a risk. While such cancer in an early stage can be cured endoscopically, total gastric tube resection is indicated in advanced stages. A 68-year-old man underwent subtotal esophagectomy reconstructed with a gastric tube through the retrosternal route. Gastric cancer was found one and a half years postoperatively. The gastric tube was resected without sternotomy. This is the first report of a patient undergoing resection of the gastric tube reconstructed through the retrosternal route without sternotomy.

Effects of Glia in a Triphasic Continuum Model of Cortical Spreading Depression.

Cortical spreading depression (SD) is a spreading disruption in brain ionic homeostasis during which neurons experience complete and prolonged depolarizations. SD is generally believed to be the physiological substrate of migraine aura and is associated with many other brain pathologies. Here, we perform simulations with a model of SD treating brain tissue as a triphasic continuum of neurons, glia and the extracellular space. A thermodynamically consistent incorporation of the major biophysical effects, including ionic electrodiffusion and osmotic water flow, allows for the computation of important physiological variables including the extracellular voltage (DC) shift. A systematic parameter study reveals that glia can act as both a disperser and buffer of potassium in SD propagation. Furthermore, we show that the timing of the DC shift with respect to extracellular [Formula: see text] rise is highly dependent on glial parameters, a result with implications for the identification of the propagating mechanism of SD.

The dual effect of ephaptic coupling on cardiac conduction with heterogeneous expression of connexin 43.

Decreased and heterogeneous expression of connexin 43 (Cx43) are common features in animal heart failure models. Ephpatic coupling, which relies on the presence of junctional cleft space between the ends of adjacent cells, has been suggested to play a more active role in mediating intercellular electrical communication when gap junctions are reduced. To better understand the interplay of Cx43 expression and ephaptic coupling on cardiac conduction during heart failure, we performed numerical simulations on our model when Cx43 expression is reduced and heterogeneous. Under severely reduced Cx43 expression, we identified three new phenomena in the presence of ephaptic coupling: alternating conduction, in which ephaptic and gap junction-mediated mechanisms alternate; instability of planar fronts; and small amplitude action potential (SAP), which has a smaller potential amplitude than the normal action potential. In the presence of heterogeneous Cx43 expression, ephaptic coupling can either prevent or promote conduction block (CB) depending on the Cx43 knockout (Cx43KO) content. When Cx43KO content is relatively high, ephaptic coupling reduces the probabilities of CB. However, ephaptic coupling promotes CB when Cx43KO and wild type cells are mixed in roughly equal proportion, which can be attributed to an increase in current-to-load mismatch.

The role of short term memory and conduction velocity restitution in alternans formation.

Alternans is the periodic beat-to-beat short-long alternation in action potential duration (APD), which is considered to be a precursor of ventricular arrhythmias and sudden cardiac death. In extended cardiac tissue, electrical alternans can be either spatially concordant (SCA, all cells oscillate in phase) or spatially discordant (SDA, cells in different regions oscillate out of phase). SDA gives rise to an increase in the spatial dispersion of repolarization, which is thought to be proarrhythmic. In this paper, we investigated the effect of two aspects of short term memory (STM) (α, τ) and their interplay with conduction velocity (CV) restitution on alternans formation using numerical simulations of a mapping model with two beats of memory. Here, α quantifies the dependence of APD restitution on pacing history and τ characterizes APD accommodation, which is an exponential change of APD over time once basic cycle length (BCL) changes. Our main findings are as follows: In both single cell and spatially coupled homogeneous cable, the interplay between α and τ affects the dynamical behaviors of the system. For the case of large APD accommodation (τ ≥ 290 ms), increase in α leads to suppression of alternans. However, if APD accommodation is small (τ ≤ 250 ms), increase in α leads to appearance of additional alternans region. On the other hand, the slope of CV restitution does not change the regions of alternans in the cable. However, steep CV restitution leads to more complicated dynamical behaviors of the system. Specifically, SDA instead of SCA are observed. In addition, for steep CV restitution and sufficiently large τ, we observed formations of type II conduction block (CB2), transition from type I conduction block (CB1) to CB2, and unstable nodes.

Flow-Driven Cell Migration under External Electric Fields.

Electric fields influence many aspects of cell physiology, including various forms of cell migration. Many cells are sensitive to electric fields, and they can migrate toward a cathode or an anode, depending on the cell type. In this Letter, we examine an actomyosin-independent mode of cell migration under electrical fields. Our theory considers a one-dimensional cell with water and ionic fluxes at the cell boundary. Water fluxes through the membrane are governed by the osmotic pressure difference across the cell membrane. Fluxes of cations and anions across the cell membrane are determined by the properties of the ion channels as well as the external electric field. Results show that without actin polymerization and myosin contraction, electric fields can also drive cell migration, even when the cell is not polarized. The direction of migration with respect to the electric field direction is influenced by the properties of ion channels, and are cell-type dependent.