A qualitative model is presented, suggesting gravitational information is transduced into biological systems primarily by its effect on spatially organised membrane and cytoplasmic flows. Continuous low affinity interactions between membrane bound cytoskeletal proteins and phospholipid flows that are undergoing forced convective and shear driven flows are shown to convert this information into spatial protein patterns, and hence cell shape. As applied here to plant cells, the feedback mechanism is shown capable not only of establishing the strict nanometer scale parallelism that exists between proteins running on the inside and outside of the cell membrane, but also to predict its maintainance and the angle of fibre realignment observed during tropic responses.
Biological systems are influenced by fluid mechanics at nearly all spatiotemporal scales. This broad relevance of fluid mechanics to biology has been increasingly appreciated by engineers and biologists alike, leading to continued expansion of research in the field of biological fluid dynamics. While this growth is exciting, it can present a barrier to researchers seeking a concise introduction to key challenges and opportunities for progress in the field. Rather than attempt a comprehensive review of the literature, this article highlights a limited selection of classic and recent work. In ad…
John Blake (1947--2016) was a leader in fluid mechanics, his two principal areas of expertise being biological fluid mechanics on microscopic scales and bubble dynamics. He produced leading research and mentored others in both Australia, his home country, and the UK, his adopted home. This article reviews John Blake's contributions in biological fluid mechanics, as well as giving the author's personal viewpoint as one of the many graduate students and researchers who benefitted from his supervision, guidance and inspiration. The key topics from biological mechanics discussed are: `squirmer' mo…
In the past decade the volvocine green algae, spanning from the unicellular $Chlamydomonas$ to multicellular $Volvox$, have emerged as model organisms for a number of problems in biological fluid dynamics. These include flagellar propulsion, nutrient uptake by swimming organisms, hydrodynamic interactions mediated by walls, collective dynamics and transport within suspensions of microswimmers, the mechanism of phototaxis, and the stochastic dynamics of flagellar synchronization. Green algae are well suited to the study of such problems because of their range of sizes (from 10 $μ$m to several m…
Mechanical characteristics of single biological cells are used to identify and possibly leverage interesting differences among cells or cell populations. Fluidity---hysteresivity normalized to the extremes of an elastic solid or a viscous liquid---can be extracted from, and compared among, multiple rheological measurements of cells: creep compliance vs. time, complex modulus vs. frequency, and phase lag vs. frequency. With multiple strategies available for acquisition of this nondimensional property, fluidity may serve as a useful and robust parameter for distinguishing cell populations, and f…
The flow of fluids at branching junctions plays important kinematic and dynamic roles in most biological and industrial flow systems. The present paper highlights some key issues related to the flow of fluids at these junctions with special emphasis on the biological flow networks particularly blood transportation vasculature.
The rheology of biological tissues is important for their function, and we would like to better understand how single cells control global tissue properties such as tissue fluidity. A confluent tissue can fluidize when cells diffuse by executing a series of cell rearrangements, or T1 transitions. In a disordered 2D vertex model, the tissue fluidizes when the T1 energy barriers disappear as the target shape index approaches a critical value ($s^*_{0} \sim 3.81$), and the shear modulus describing the linear response also vanishes at this same critical point. However, the ordered ground states of…
A mechanism of memories, especially biological memories, is studied in terms of quantum fluids. Two-dimensional flows in central potentials $V_a(ρ)=-a^2g_aρ^{2(a-1)}$ ($a\not=0$ and $ρ=\sqrt{x^2+y^2}$) have zero-energy eigenstates that degenerate infinitely for all $a$. It is shown that stable standing waves constructed from the zero-energy flows are confined in various types of polygons which can be the minimum units of memory systems. Vortex patterns awoken in the units by stimuli correspond to the memories of the stimuli. This memory system is not a system for preserving memories as usual b…
Many cells exploit the bending or rotation of flagellar filaments in order to self-propel in viscous fluids. While appropriate theoretical modelling is available to capture flagella locomotion in simple, Newtonian fluids, formidable computations are required to address theoretically their locomotion in complex, nonlinear fluids, e.g.~mucus. Based on experimental measurements for the motion of rigid rods in non-Newtonian fluids and on the classical Carreau fluid model, we propose empirical extensions of the classical Newtonian resistive-force theory to model the waving of slender filaments in n…
The Cellular Potts Model (CPM) is a robust, cell-level methodology for simulation of biological tissues and morphogenesis. Both tissue physiology and morphogenesis depend on diffusion of chemical morphogens in the extra-cellular fluid or matrix (ECM). Standard diffusion solvers applied to the cellular potts model use finite difference methods on the underlying CPM lattice. However, these methods produce a diffusing field tied to the underlying lattice, which is inaccurate in many biological situations in which cell or ECM movement causes advection rapid compared to diffusion. Finite difference…
The nanoscopic isothermal machines are not only energy but also information transducers. We show that the generalized fluctuation theorem with information creation and entropy reduction can be fulfilled for the enzymatic molecular machines with the stochastic dynamics, which offers a choice of the work performance in a variety of ways. A model of such dynamics, specified by a critical complex network, is investigated. The main conclusion of the study is that the processing of free energy has to be distinguished from the processing of organization, which we identify with an adequately defined t…
Fluid deformable surfaces are ubiquitous in cell and tissue biology, including lipid bilayers, the actomyosin cortex, or epithelial cell sheets. These interfaces exhibit a complex interplay between elasticity, low Reynolds number interfacial hydrodynamics, chemistry, and geometry, and govern important biological processes such as cellular traffic, division, migration, or tissue morphogenesis. To address the modelling challenges posed by this class of problems, in which interfacial phenomena tightly interact with the shape and dynamics of the surface, we develop a general continuum mechanics an…
Short-term physico-chemical reactions at the interface between bioactive glass particles and biological fluids are studied and we focus our attention on the measurements of O/Si atomic ratio. The studied bioactive glass is in the SiO2-Na2O-CaO-P2O5-K2O-Al2O3-MgO system. The elemental analysis is performed at the submicrometer scale by STEM associated with EDXS and EELS. We previously developed an EDXS quantification method based on the ratio method and taking into account local absorption corrections. In this way, we use EELS data to determine, by an iterative process, the local mass thickness…
Although there are theoretical studies on the thermodynamics of ion channels, an investigation involving the thermodynamics of coupled channels has not been proposed. To overcome this issue, we developed calculations to present a thermodynamic scenario associated with mechanoelectrical transduction channels as a single and coupling of two-state channels. The modeling was inspired by the Tsallis theory, in which we derived the open and closed probability distributions, the joint probability distribution, the Tsallis entropy, and the Shannon mutual information. Despite being well studied in many…
Animals have evolved distinctive survival strategies in response to constant selective pressure. In this review, we highlight how animals exploit complex flow phenomena by manipulating their habitat or by producing complex fluids. In particular, we outline different strategies evolved for movement, defense from predators, attacking of prey, and reproduction and breeding. From the slimy defense of the notorious hagfish to the circus-like mating spectacle of leopard slugs, we unveil remarkable correlations within the flow behavior and biological purpose of biological complex fluids. We discuss r…
Meso-scale turbulence is an innate phenomenon, distinct from inertial turbulence, that spontaneously occurs at zero-Reynolds number in fluidized biological systems. This spatio-temporal disordered flow radically changes nutrient and molecular transport in living fluids and can strongly affect the collective behaviour in prominent biological processes, including biofilm formation, morphogenesis and cancer invasion. Despite its crucial role in such physiological processes, understanding meso-scale turbulence and any relation to classical inertial turbulence remains obscure. Here, we show how the…
The locomotion of microorganisms and spermatozoa in complex viscoelastic fluids is of critical importance in many biological processes such as fertilization, infection, and biofilm formation. Depending on their propulsion mechanisms, microswimmers display various responses to a complex fluid environment: increasing or decreasing their swimming speed and efficiency, modifying their propulsion kinematics and swimming gaits, and experiencing different hydrodynamic interactions with their surroundings. In this article, we review the fundamental physics of locomotion of biological and synthetic mic…
Fluid pumping and the generation of electric current by living tissues are required during morphogenetic processes and for maintainance of homeostasis. How these flows emerge from active and passive ion transport in cells has been well established. However, the interplay between flow and current generation is not well understood. Here, we study the electro-hydraulic coupling that arises from cell ion pumping. We develop a one-dimensional continuum model of fluid and ion transport across active cell membranes. Solving the Nernst-Planck and Poisson equations in the limit of weak charge imbalance…
The biological fluids encountered by self-propelled cells display complex microstructures and rheology. We consider here the general problem of low-Reynolds number locomotion in a complex fluid. {Building on classical work on the transport of particles in viscoelastic fluids,} we demonstrate how to mathematically derive three integral theorems relating the arbitrary motion of an isolated organism to its swimming kinematics {in a non-Newtonian fluid}. These theorems correspond to three situations of interest, namely (1) squirming motion in a linear viscoelastic fluid, (2) arbitrary surface defo…
The biological membrane, which compartmentalizes the cell and its organelles, exhibit wide variety of macroscopic shapes of varying morphology and topology. A systematic understanding of the relation of membrane shapes to composition, external field, environmental conditions etc. have important biological relevance. Here we review the triangulated surface model, used in the macroscopic simulation of membranes and the associated Monte Carlo (DTMC) methods. New techniques to calculate surface quantifiers, that will facilitate the study of additional in-plane orientational degrees of freedom, has…
Microscopic robots could perform tasks with high spatial precision, such as acting on precisely-targeted cells in biological tissues. Some tasks may benefit from robots that change shape, such as elongating to improve chemical gradient sensing or contracting to squeeze through narrow channels. This paper evaluates the energy dissipation for shape-changing (i.e., metamorphic) robots whose size is comparable to bacteria. Unlike larger robots, surface forces dominate the dissipation. Theoretical estimates indicate that the power likely to be available to the robots, as determined by previous stud…
Metastatic tumors often invade healthy neighboring tissues by forming multicellular finger-like protrusions emerging from the cancer mass. To understand the mechanical context behind this phenomenon, we here develop a minimalist fluid model of a self-propelled, growing biological tissue. The theory involves only four mechanical parameters and remains analytically trackable in various settings. As an application of the model, we study the evolution of a 2D circular droplet made of our active and expanding fluid, and embedded in a passive non-growing tissue. This system could be used to model th…
In a variety of biological situations, swimming cells have to move through complex fluids. Similarly, mucociliary clearance involves the transport of polymeric fluids by beating cilia. Here, we consider the extent to which complex fluids could be exploited for force generation on small scales. We consider a prototypical reciprocal motion (i.e. identical under time-reversal symmetry): The periodic flapping of a tethered semi-infinite plane. In the Newtonian limit, such motion cannot be used for force generation according to Purcell's scallop theorem. In a polymeric fluid (Oldroyd-B, and its gen…
In vertebrates, insufficient availability of calcium and phosphate ions in extracellular fluids leads to loss of bone density and neuronal hyper-excitability. To counteract this problem, calcium ions are present at high concentrations throughout body fluids -- at concentrations exceeding the saturation point. This condition leads to the opposite situation where unwanted mineral sedimentation may occur. Remarkably, ectopic or out-of-place sedimentation into soft tissues is rare, in spite of the thermodynamic driving factors. This fortunate fact is due to the presence of auto-regulatory proteins…
Transport networks are typically optimized, either by evolutionary pressures in biological systems or by human design in engineered structures. In the case of systems such as the animal vasculature, the transport of fluids is hindered by the inherent viscous resistance to flow while being kept in a dynamic state by the pulsatile nature of the heart and elastic properties of the vessel walls. While this imparted pulsatility necessarily increases the dissipation of energy caused by the resistance, the vessel elasticity helps to reduce overall dissipation by attenuating the amplitude of the pulsa…
Models for confluent biological tissues often describe the network formed by cells as a triple-junction network, similar to foams. However, higher order vertices or multicellular rosettes are prevalent in developmental and {\it in vitro} processes and have been recognized as crucial in many important aspects of morphogenesis, disease, and physiology. In this work, we study the influence of rosettes on the mechanics of a confluent tissue. We find that the existence of rosettes in a tissue can greatly influence its rigidity. Using a generalized vertex model and effective medium theory we find a …
Surface tension governed by differential adhesion can drive fluid particle mixtures to sort into separate regions, i.e., demix. Does the same phenomenon occur in confluent biological tissues? We begin to answer this question for epithelial monolayers with a combination of theory via a vertex model and experiments on keratinocyte monolayers. Vertex models are distinct from particle models in that the interactions between the cells are shape-based, as opposed to distance-dependent. We investigate whether a disparity in cell shape or size alone is sufficient to drive demixing in bidisperse vertex…
Experimental evidence shows that there is a feedback between cell shape and cell motion. How this feedback impacts the collective behavior of dense cell monolayers remains an open question. We investigate the effect of a feedback that tends to align the cell crawling direction with cell elongation in a biological tissue model. We find that the alignment interaction promotes nematic patterns in the fluid phase that eventually undergo a non-equilibrium phase transition into a quasi-hexagonal solid. Meanwhile, highly asymmetric cells do not undergo the liquid-to-solid transition for any value of …
Lipid bilayers forming biological membranes are known to behave as viscous 2D fluids on submicrometer scales; usually they contain a large number of active protein inclusions. Recently, it has been shown [Proc. Nat. Acad. Sci. USA 112, E3639 (2015)] that such active proteins should in- duce non-thermal fluctuating lipid flows leading to diffusion enhancement and chemotaxis-like drift for passive inclusions in biomembranes. Here, a detailed analytical and numerical investigation of such effects is performed. The attention is focused on the situations when proteins are concentrated within lipid …
Recent \emph{in vivo} experiments have illustrated the importance of understanding the hemodynamics of heart morphogenesis. In particular, ventricular trabeculation is governed by a delicate interaction between hemodynamic forces, myocardial activity, and morphogen gradients, all of which are coupled to genetic regulatory networks. The underlying hemodynamics at the stage of development in which the trabeculae form is particularly complex, given the balance between inertial and viscous forces. Small perturbations in the geometry, scale, and steadiness of the flow can lead to changes in the ove…
In a world without inertia, Purcell's scallop theorem states that in a Newtonian fluid a time-reversible motion cannot produce any net force or net flow. Here we consider the extent to which the nonlinear rheological behavior of viscoelastic fluids can be exploited to break the constraints of the scallop theorem in the context of fluid pumping. By building on previous work focusing on force generation, we consider a simple, biologically-inspired geometrical example of a flapper in a polymeric (Oldroyd-B) fluid, and calculate asymptotically the time-average net fluid flow produced by the recipr…
Microscopic robots could perform tasks with high spatial precision, such as acting in biological tissues on the scale of individual cells, provided they can reach precise locations. This paper evaluates the feasibility of in vivo locomotion for micron-size robots. Two appealing methods rely only on surface motions: steady tangential motion and small amplitude oscillations. These methods contrast with common microorganism propulsion based on flagella or cilia, which are more likely to damage nearby cells if used by robots made of stiff materials. The power potentially available to robots in tis…
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 [C. Nicholson, and S. Hrabětová, Biophysical Journal, 113(10), 2133(2017)]. However, the exact driving mechanisms are often not known. In this paper, we investigate flows induced by action potentials in an optic nerve as a prototype of the central nervous system (CNS). Different from traditional fluid dynamics problems, flows in biological tissues such as the CNS are coupled with…
Interactions between microorganisms and their complex flowing environments are essential in many biological systems. We develop a model for microswimmer dynamics in non-Newtonian Poiseuille flows. We predict that swimmers in shear-thickening (-thinning) fluids migrate upstream more (less) quickly than in Newtonian fluids and demonstrate that viscoelastic normal stress differences reorient swimmers causing them to migrate upstream at the centreline, in contrast to well-known boundary accumulation in quiescent Newtonian fluids. Based on these observations, we suggest a sorting mechanism to selec…
