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The locomotion of microorganisms in fluids is ubiquitous and plays an important role in numerous biological processes. In this chapter we present an overview of theoretical modeling for low-Reynolds-number locomotion.
Microorganisms such as bacteria often swim in fluid environments that cannot be classified as Newtonian. Many biological fluids contain polymers or other heterogeneities which may yield complex rheology. For a given set of boundary conditions on a moving organism, flows can be substantially different in complex fluids, while non-Newtonian stresses can alter the gait of the microorganisms themselves. Heterogeneities in the fluid may also be characterized by length scales on the order of the organism itself leading to additional dynamic complexity. In this chapter we present a theoretical overview of small-scale locomotion in complex fluids with a focus on recent efforts quantifying the impact of non-Newtonian rheology on swimming microorganisms.
The study of configurational parameters of deformed DNA is a relevant problem in research of such important biological process as double helix compactization in cell. The deformations accompanied with local disruptions of the regular macromolecule structure cause significant bending of the double helix, or kinks. In this paper an approach for Kratky-Porod model to calculate persistence length of DNA macromolecule with kinks is developed. The presented approach considers kinks of arbitrary configuration, including two basic types of kinks, type 1 - sharp kink caused by unstacking a single base pair step, and type 2 - intrinsic-induced kink that involves several base pairs. Within developed approach analytical expressions for persistence length, coil size and gyration radius of kinky double helix were obtained.
Biological hydrogels have been increasingly sought after as e.g. wound dressings or scaffolds for regenerative medicine, due to their inherent biofunctionality in biological environments. Especially in moist wound healing, the ideal material should absorb large amounts of wound exudate whilst remaining mechanically competent in-situ. Despite their large hydration, however, current biological hydrogels still leave much to be desired in terms of mechanical properties in physiological conditions. To address this challenge, a multi-scale approach is presented for the synthetic design of cyto-compatible collagen hydrogels with tunable mechanical properties (from nano- up to the macro-scale), uniquely high swelling ratios and retained (>70%) triple-helical features. Type I collagen was covalently functionalized with three different monomers, i.e. 4 vinylbenzyl chloride, glycidyl methacrylate and methacrylic anhydride, respectively. Backbone rigidity, hydrogen-bonding capability and degree of functionalization ( F : 16±12 &ndash 91±7 mol.-%) of introduced moieties governed the structure-property relationships in resulting collagen networks, so that the swelling ratio ( SR : 707±51 &ndash 1996±182 wt.-%), bulk compressive modulus ( E c : 30±7 &ndash 168±40 kPa) and Atomic Force Microscopy elastic modulus ( E AFM : 16±2 &ndash 387±66 kPa) were readily adjusted. In light of their remarkably high swelling and mechanical properties, these tunable collagen hydrogels may be further exploited for the design of advanced dressings for chronic wound care.
A multicomponent multiphase reactive transport simulator has been developed to facilitate the investigation of a large variety of phenomena in porous media including component transport, diffusion, microbiological growth and decay, cell attachment and detachment and phase exchange. The coupled problem is solved using operator splitting. This approach allows a flexible adaptation of the solution strategy to the concrete problem. Moreover, the individual submodels were optimised to be able to describe behaviour of Escherichia coli (HB101 K12 pGLO) in the capillary fringe in the presence or absence of dissolved organic carbon and oxygen under steady-state and flow conditions. Steady-state and flow through experiments in a Hele-Shaw cell, filled with quartz sand, were conducted to study eutrophic bacterial growth and transport in both saturated and unsaturated porous media. As E. coli cells can form the green fluorescent protein (GFP), the cell densities, calculated by evaluation of measured fluorescence intensities (in situ detection) were compared with the cell densities computed by numerical simulation. The comparison showed the laboratory experiments can be well described by our mathematical model.
In systems biology effective models are widely used due to the complexity of biological system. They result from a coarse-graining process which employs specific assumptions. Frequently one does not start with a model taking all details into account and then performs a coarse-graining process, but rather one starts right away with the effective equations and often the underlying assumptions remain hidden or unclear. We exemplify the analysis of an effective model by analyzing a time delay equation for the JAK/STAT5 signaling pathway and show how one can avoid wrong conclusions and obtain a deeper understanding of the biological system . By analyzing the assumptions leading to a coarse-grained model one might be able to gain new insight into the involved biological processes. Further, the compliance of the model with experimental data can be considered as a validation of the assumptions made in the derivation of the mathematical equations.
Sperm traverse their microenvironment through viscous fluid by propagating flagellar waves; the waveform emerges as a consequence of elastic structure, internal active moments, and low Reynolds number fluid dynamics. Engineered microchannels have recently been proposed as a method of sorting and manipulating motile cells; the interaction of cells with these artificial environments therefore warrants investigation. A numerical method is presented for the geometrically nonlinear elastohydrodynamic interaction of active swimmers with domain features. This method is employed to examine hydrodynamic scattering by a model microchannel backstep feature. Scattering is shown to depend on backstep height and the relative strength of viscous and elastic forces in the flagellum. In a 'high viscosity' parameter regime corresponding to human sperm in cervical mucus analogue, this hydrodynamic contribution to scattering is comparable in magnitude to recent data on contact effects, being of the order of 5-10 degrees. Scattering can be positive or negative depending on the relative strength of viscous and elastic effects, emphasising the importance of viscosity on the interaction of sperm with their microenvironment. The modulation of scattering angle by viscosity is associated with variations in flagellar asymmetry induced by the elastohydrodynamic interaction with the boundary feature.
Techniques for recording large-scale neuronal spiking activity are developing very fast. This leads to an increasing demand for algorithms capable of analyzing large amounts of experimental spike train data. One of the most crucial and demanding tasks is the identification of similarity patterns with a very high temporal resolution and across different spatial scales. To address this task, in recent years three time-resolved measures of spike train synchrony have been proposed, the ISI-distance, the SPIKE-distance, and event synchronization. The Matlab source codes for calculating and visualizing these measures have been made publicly available. However, due to the many different possible representations of the results the use of these codes is rather complicated and their application requires some basic knowledge of Matlab. Thus it became desirable to provide a more user-friendly and interactive interface. Here we address this need and present SPIKY, a graphical user interface which facilitates the application of time-resolved measures of spike train synchrony to both simulated and real data. SPIKY includes implementations of the ISI-distance, the SPIKE-distance and SPIKE-synchronization (an improved and simplified extension of event synchronization) which have been optimized with respect to computation speed and memory demand. It also comprises a spike train generator and an event detector which makes it capable of analyzing continuous data. Finally, the SPIKY package includes additional complementary programs aimed at the analysis of large numbers of datasets and the estimation of significance levels.
The formation of a collectively moving group benefits individuals within a population in a variety of ways such as ultra-sensitivity to perturbation, collective modes of feeding, and protection from environmental stress. While some collective groups use a single organizing principle, others can dynamically shift the behavior of the group by modifying the interaction rules at the individual level. The surface-dwelling bacterium Myxococcus xanthus forms dynamic collective groups both to feed on prey and to aggregate during times of starvation. The latter behavior, termed fruiting-body formation, involves a complex, coordinated series of density changes that ultimately lead to three-dimensional aggregates comprising hundreds of thousands of cells and spores. This multi-step developmental process most likely involves several different single-celled behaviors as the population condenses from a loose, two-dimensional sheet to a three-dimensional mound. Here, we use high-resolution microscopy and computer vision software to spatiotemporally track the motion of thousands of individuals during the initial stages of fruiting body formation. We find that a combination of cell-contact-mediated alignment and internal timing mechanisms drive a phase transition from exploratory flocking, in which cell groups move rapidly and coherently over long distances, to a reversal-mediated localization into streams, which act as slow-spreading, quasi-one-dimensional nematic fluids. These observations lead us to an active liquid crystal description of the myxobacterial development cycle.
Ionic electrodiffusion and osmotic water flow are central processes in many physiological systems. We formulate a system of partial differential equations that governs ion movement and water flow in biological tissue. A salient feature of this model is that it satisfies a free energy identity, ensuring the thermodynamic consistency of the model. A numerical scheme is developed for the model in one spatial dimension and is applied to a model of cortical spreading depression, a propagating breakdown of ionic and cell volume homeostasis in the brain.
Trying to identify the entropy production within a cell has been part of debates and studies in the last century. First the idea was to make a resemblance of a cell with a Carnot engine, which is the most thermodynamically perfect machine. This approach was clearly not the best, since the yield achieved within a cell cannot be ideal, but can we even measure it? Several models approach the living cell, since the very simple one (e.g. Prigogine model) to more elaborated proposals. The concept of entropy has been the centre of discussions within several scientific fields. To interpret how entropy is produced in the complicated system of a cell is as hard as to understand how life originated at the first place. Understanding the way a cell works is key in biology, medicine, and multiple other scientific fields. Thermodynamics is essential in multitude of processes around us. I give here an insight of what has been done and a personal opinion about the topic, focusing in the results from Himeoka and Kaneko paper.
The ability of uropathogenic Escherichia coli (UPEC) to cause urinary tract infections is dependent on their ability to colonize the uroepithelium. Infecting bacteria ascend the urethra to the bladder and then kidneys by attaching to the uroepithelial cells via the differential expression of adhesins. P pili are associated with pyelonephritis, the more severe infection of the kidneys. In order to find means to treat pyelonephritis, it is therefore of interest to investigate the properties P pili. The mechanical behavior of individual P pili of uropathogenic Escherichia coli has recently been investigated using optical tweezers. P pili, whose main part constitutes the PapA rod, composed of ~1000 PapA subunits in a helical arrangement, are distributed over the bacterial surface and mediate adhesion to host cells. We have earlier studied P pili regarding its stretching/elongation properties where we have found and characterized three different elongation regions, of which one constitute an unfolding of the quaternary (helical) structure of the PapA rod. It was shown that this unfolding takes place at an elongation independent force of 27 pN. We have also recently performed studies on its folding properties and shown that the unfolding/folding of the PapA rod is completely reversible. Here we present a study of the dynamical properties of the PapA rod. We show, among other things, that the unfolding force increases and that the folding force decreases with the speed of unfolding and folding respectively. Moreover, the PapA rod can be folded-unfolded a significant number of times without loosing its characteristics, a phenomenon that is believed to be important for the bacterium to keep close contact to the host tissue and consequently helps the bacterium to colonize the host tissue.
The rapid squirt of a proteinaceous slime jet endows the ancient velvet worms (Onychophora) with a unique mechanism for defense from predators and for capturing prey by entangling them in a disordered web that immobilizes their target. However, to date neither qualitative nor quantitative descriptions have been provided for this unique adaptation. Here we investigate the fast oscillatory motion of the oral papillae and the exiting liquid jet that oscillates with frequencies $f\sim 30-60$ Hz. Using anatomical images, high speed videography, theoretical analysis and a physical simulacrum we show that this fast oscillatory motion is the result of an elastohydrodynamic instability driven by the interplay between the elasticity of oral papillae and the fast unsteady flow during squirting. Our results demonstrate how passive strategies can be cleverly harnessed by organisms, while suggesting future oscillating micro-fluidic devices as well as novel ways for micro and nano fiber production using bioinspired strategies.
Many signs indicate that the graphene could widely occur on the early Earth. Here, we report a new theory that graphene might be an embryo of protocell membrane, and found several evidences. Firstly, the graphene oxide and phospholipid-graphene oxide composite would curl into capsules in strongly acidic saturated solution of Pb(NO3)2 at low temperature, providing a protective space for biochemical reactions. Secondly, L-animi acids exhibit higher reactivity than D-animi acids for graphene oxides in favor of the formation of left-handed proteins. Thirdly, monolayer graphene with nanopores prepared by unfocused 84Kr25+ has high selectivity for permeation of the monovalent metal ions (Rb+ > K+ > Cs+ > Na+ > Li+), but does not allow Cl- through, which could be attributed to the ion exchange of oxygen-containing groups on the rim of nanopores. It is similar to K+ channels, which would cause efflux of some ions from capsule of graphene oxides with the decrease of pH in the primitive ocean, creating a suitable inner condition for the origin of life. Consequently, the strongly acidic, high salinity and strong radiation as well as temperature changes in the early Earth, regarded as negative factors, would be indispensable for the origin of protocell. In short, graphene bred life, but digested gradually by the evolution.
In contrast with ordinary materials, living matter drives its own motion by generating active, out-of-equilibrium internal stresses. These stresses typically originate from localized active elements embedded in an elastic medium, such as molecular motors inside the cell or contractile cells in a tissue. While many large-scale phenomenological theories of such active media have been developed, a systematic understanding of the emergence of stress from the local force-generating elements is lacking. In this paper, we present a rigorous theoretical framework to study this relationship. We show that the medium's macroscopic active stress tensor is equal to the active elements' force dipole tensor per unit volume in both continuum and discrete linear homogeneous media of arbitrary geometries. This relationship is conserved on average in the presence of disorder, but can be violated in nonlinear elastic media. Such effects can lead to either a reinforcement or an attenuation of the active stresses, giving us a glimpse of the ways in which nature might harness microscopic forces to create active materials.
We develop and present an improvement to the conventional technique for solving the Hierarchical Equations of Motion which reduces the memory cost by more than 75% while retaining the same convergence rate and accuracy. This allows for a full calculation of the population dynamics of the 24-site FMO trimer for long timescales with very little effort, and we present the first fully converged, exact results for the 7-site subsystem of the monomer, and for the full 24-site trimer. Owing to this new approach, our numerically exact 24-site, 2-exponential results are the most demanding HEOM calculations performed to date, surpassing the 50-site, 1-exponential results of Strumpfer and Schulten [2012, J. Chem. Thy. & Comp., 8, 2808]. We then show where our exact 7-site results deviate from the approximation of Ishizaki and Fleming [2009, Proc. Natl. Acad. Sci. USA, 106, 17255]. Our exact results are then compared to calculations using the incoherent Forster theory, and it is found that the energy transfer from the antenna to the reaction center occurs more than 50 times faster than the fluorescence lifetime of the excitation, whether or not coherence is considered. This means that coherence is not likely to improve the efficiency of the photosynthesis. In fact, the incoherent theory often tends to over-predict the rates of energy transfer, suggesting that in some cases electronic coherence may actually slow down the photosynthetic process.
This paper provides a collection of mathematical and computational tools for the study of robustness in nonlinear gene regulatory networks, represented by time- and state-discrete dynamical systems taking on multiple states. The focus is on networks governed by nested canalizing functions (NCFs), first introduced in the Boolean context by S. Kauffman. After giving a general definition of NCFs we analyze the class of such functions. We derive a formula for the normalized average $c$-sensitivities of multistate NCFs, which enables the calculation of the Derrida plot, a popular measure of network stability. We also provide a unique canonical parametrized polynomial form of NCFs. This form has several consequences. We can easily generate NCFs for varying parameter choices, and derive a closed form formula for the number of such functions in a given number of variables, as well as an asymptotic formula. Finally, we compute the number of equivalence classes of NCFs under permutation of variables. Together, the results of the paper represent a useful mathematical framework for the study of NCFs and their dynamic networks.
Stochastic resonance induced by external factor is considering to investigate the complex dynamics of tumor. The surrounding environment and the treatment effects on the tumor growth are considered as additive and multiplicative noises in growth model. The adaptability of tumor to treatment is presented by correlation of these two noises. The Fokker-Plank equation is deduced to study the probability distribution function and mean number of tumor cells in different conditions. The mean number of tumor cells can be controlled by the correlation and intensity of noises.