Modelling the mechanical properties of yeast cells

Analytical Models for Measuring the Mechanical Properties of Yeast

The mechanical properties of yeast play an important role in many biological processes, such as cell division and growth, maintenance of internal pressure, and biofilm formation. In addition, the mechanical properties of cells can indicate the degree of damage caused by antifungal drugs, as the mechanical parameters of healthy and damaged cells are different. Over the past decades, atomic force microscopy (AFM) and micromanipulation have become the most widely used methods for evaluating the mechanical characteristics of microorganisms. In this case, the reliability of such an estimate depends on the choice of mathematical model. This review presents various analytical models developed in recent years for studying the mechanical properties of both cells and their individual structures. The main provisions of the applied approaches are described along with their limitations and advantages. Attention is paid to the innovative method of low-invasive nanomechanical mapping with scanning ion-conductance microscopy (SICM), which is currently starting to be successfully used in the discovery of novel drugs acting on the yeast cell wall and plasma membrane.

Osmolyte homeostasis controls single-cell growth rate and maximum cell size of Saccharomyces cerevisiae

Cell growth is well described at the population level, but precisely how nutrient and water uptake and cell wall expansion drive the growth of single cells is poorly understood. Supported by measurements of single-cell growth trajectories and cell wall elasticity, we present a single-cell growth model for yeast. The model links the thermodynamic quantities, such as turgor pressure, osmolarity, cell wall elasto-plasticity, and cell size, applying concepts from rheology and thin shell theory. It reproduces cell size dynamics during single-cell growth, budding, and hyper-osmotic or hypo-osmotic stress. We find that single-cell growth rate and final size are primarily governed by osmolyte uptake and consumption, while bud expansion requires additionally different cell wall extensibilities between mother and bud. Based on first principles the model provides a more accurate description of size dynamics than previous attempts and its analytical simplification allows for easy combination with models for other cell processes.

Discrete element modelling of tomato tissue deformation and failure at the cellular scale

Bruise damage in fruit results from cell wall failure and inter-cellular separation. Despite the importance of the micro-mechanics of plant tissue with respect to its integrity, it remains largely unquantified and poorly understood, due to many difficulties during experimental characterization. In this article, a 3D micro-mechanical plant tissue model that is able to model cell rupture and inter-cellular debonding and thus provide more insight into the micro-mechanics was developed. The model is based on the discrete element method (DEM) and represents the tissue as a mass-spring system. Each plant cell is represented as a deformable visco-elastoplastic triangulated mesh under turgor pressure. To model cell wall rupture, it is assumed that a spring connection in the wall breaks at a certain critical stretch ratio and that a ruptured cell is turgorless. The inter-cellular contact model assumes brittle fracture between a cell's node and an adjacent cell's triangle when their bond distance exceeds a critical value. A high-speed tomato fruit cell compression test was simulated and the modelled force-strain curve compares well with the experimental data, including for strains above the elastic limit. By varying the shape of the cell in the compression simulation it was shown that the force-strain curve is highly dependent on the cell shape and thus parameter fitting procedures based on a spherical cell model will be inaccurate. Furthermore, the wall stiffness and thickness showed a positive linear relationship with the force at cell bursting. Besides simulating compression tests of single cells, we also simulated tensile and compression tests on small tissue specimens. Realistic tissue structures of tomato mesocarp tissue were generated by a novel method using DEM simulations of deformable cells in a shrinking cylinder. The cell area, volume and anisotropy distributions of the virtual tissue compared well with micro-CT images of real tomato mesocarp tissue (normalized root mean square error values smaller than 3%). The tissue compression and tensile test simulations demonstrated an important influence of the inter-cellular bonding energy and tissue porosity on the tissue failure characteristics and elastic modulus.

LILY-lipidome isotope labeling of yeast: in vivo synthesis of 13C labeled reference lipids for quantification by mass spectrometry

Quantification is an essential task in comprehensive lipidomics studies challenged by the high number of lipids, their chemical diversity and their dynamic range of the lipidome. In this work, we introduce lipidome isotope labeling of yeast (LILY) in order to produce (non-radioactive) isotopically labeled eukaryotic lipid standards in yeast for normalization and quantification in mass spectrometric assays. More specifically, LILY is a fast and efficient in vivo labeling strategy in Pichia pastoris for the production of ¹³C labeled lipid library further paving the way to comprehensive compound-specific internal standardization in quantitative mass spectrometry based assays. More than 200 lipid species (from PA, PC, PE, PG, PI, PS, LysoGP, CL, DAG, TAG, DMPE, Cer, HexCer, IPC, MIPC) were obtained from yeast extracts with an excellent ¹³C enrichment >99.5%, as determined by complementary high resolution mass spectrometry based shotgun and high resolution LC-MS/MS analysis. In a first proof of principle study we tested the relative and absolute quantification capabilities of the ¹³C enriched lipids obtained by LILY using a parallel reaction monitoring based LC-MS approach. In relative quantification it could be shown that compound specific internal standardization was essential for the accuracy extending the linear dynamic range to four orders of magnitude. Excellent analytical figures of merit were observed for absolute quantification for a selected panel of 5 investigated glycerophospholipids (e.g. LOQs around 5 fmol absolute; typical concentrations ranging between 1 to 10 nmol per 10⁸ yeast cell starting material; RSDs <10% (N = 4)).

Finite Element Analysis of Single Cell Stiffness Measurements Using PZT-Integrated Buckling Nanoneedles

This paper proposes a new technique for real-time single cell stiffness measurement using lead zirconate titanate (PZT)-integrated buckling nanoneedles. The PZT and the buckling part of the nanoneedle have been modelled and validated using the ABAQUS software. The two parts are integrated together to function as a single unit. After calibration, the stiffness, Young’s modulus, Poisson’s ratio and sensitivity of the PZT-integrated buckling nanoneedle have been determined to be 0.7100 N·m⁻¹, 123.4700 GPa, 0.3000 and 0.0693 V·m·N⁻¹, respectively. Three Saccharomyces cerevisiae cells have been modelled and validated based on compression tests. The average global stiffness and Young’s modulus of the cells are determined to be 10.8867 ± 0.0094 N·m⁻¹ and 110.7033 ± 0.0081 MPa, respectively. The nanoneedle and the cell have been assembled to measure the local stiffness of the single Saccharomyces cerevisiae cells The local stiffness, Young’s modulus and PZT output voltage of the three different size Saccharomyces cerevisiae have been determined at different environmental conditions. We investigated that, at low temperature the stiffness value is low to adapt to the change in the environmental condition. As a result, Saccharomyces cerevisiae becomes vulnerable to viral and bacterial attacks. Therefore, the proposed technique will serve as a quick and accurate process to diagnose diseases at early stage in a cell for effective treatment.

Nitrogen deprivation of microalgae: effect on cell size, cell wall thickness, cell strength, and resistance to mechanical disruption

Nitrogen deprivation (N-deprivation) is a proven strategy for inducing triacylglyceride accumulation in microalgae. However, its effect on the physical properties of cells and subsequently on product recovery processes is relatively unknown. In this study, the effect of N-deprivation on the cell size, cell wall thickness, and mechanical strength of three microalgae was investigated. As determined by analysis of micrographs from transmission electron microscopy, the average cell size and cell wall thickness for N-deprived Nannochloropsis sp. and Chlorococcum sp. were ca. 25% greater than the N-replete cells, and 20 and 70% greater, respectively, for N-deprived Chlorella sp. The average Young’s modulus of N-deprived Chlorococcum sp. cells was estimated using atomic force microscopy to be 775 kPa; 30% greater than the N-replete population. Although statistically significant, these microstructural changes did not appear to affect the overall susceptibility of cells to mechanical rupture by high pressure homogenisation. This is important as it suggests that subjecting these microalgae to nitrogen starvation to accumulate lipids does not adversely affect the recovery of intracellular lipids.

Self-Driven Jamming in Growing Microbial Populations

In natural settings, microbes tend to grow in dense populations [1-4] where they need to push against their surroundings to accommodate space for new cells. The associated contact forces play a critical role in a variety of population-level processes, including biofilm formation [5-7], the colonization of porous media [8, 9], and the invasion of biological tissues [10-12]. Although mechanical forces have been characterized at the single cell level [13-16], it remains elusive how collective pushing forces result from the combination of single cell forces. Here, we reveal a collective mechanism of confinement, which we call self-driven jamming, that promotes the build-up of large mechanical pressures in microbial populations. Microfluidic experiments on budding yeast populations in space-limited environments show that self-driven jamming arises from the gradual formation and sudden collapse of force chains driven by microbial proliferation, extending the framework of driven granular matter [17-20]. The resulting contact pressures can become large enough to slow down cell growth, to delay the cell cycle in the G1 phase, and to strain or even destroy the microenvironment through crack propagation. Our results suggest that self-driven jamming and build-up of large mechanical pressures is a natural tendency of microbes growing in confined spaces, contributing to microbial pathogenesis and biofouling [21-26].

Numerical Analysis of Hydrodynamic Flow in Microfluidic Biochip for Single-Cell Trapping Application

Single-cell analysis has become the interest of a wide range of biological and biomedical engineering research. It could provide precise information on individual cells, leading to important knowledge regarding human diseases. To perform single-cell analysis, it is crucial to isolate the individual cells before further manipulation is carried out. Recently, microfluidic biochips have been widely used for cell trapping and single cell analysis, such as mechanical and electrical detection. This work focuses on developing a finite element simulation model of single-cell trapping system for any types of cells or particles based on the hydrodynamic flow resistance (Rh) manipulations in the main channel and trap channel to achieve successful trapping. Analysis is carried out using finite element ABAQUS-FEA™ software. A guideline to design and optimize single-cell trapping model is proposed and the example of a thorough optimization analysis is carried out using a yeast cell model. The results show the finite element model is able to trap a single cell inside the fluidic environment. Fluid's velocity profile and streamline plots for successful and unsuccessful single yeast cell trapping are presented according to the hydrodynamic concept. The single-cell trapping model can be a significant important guideline in designing a new chip for biomedical applications.

Single cell stiffness measurement at various humidity conditions by nanomanipulation of a nano-needle

This paper presents a method for single cell stiffness measurement based on a nano-needle and nanomanipulation. The nano-needle with a buffering beam was fabricated from an atomic force microscope cantilever by the focused ion beam etching technique. Wild type yeast cells (W303) were prepared and placed on the sample stage inside an environmental scanning electron microscope (ESEM) chamber. The nanomanipulator actuated the nano-needle to press against a single yeast cell. As a result, the deformation of the cell and nano-needle was observed by the ESEM system in real-time. Finally, the stiffness of the single cell was determined based on this deformation information. To reveal the relationship between the cell stiffness and the environmental humidity conditions, the cell stiffness was measured at three different humidity conditions, i.e. 40, 70 and 100%, respectively. The results show that the stiffness of a single cell is reduced with increasing humidity.

Imaging and analyzing the elasticity of vascular smooth muscle cells by atomic force acoustic microscope

Vascular smooth muscle cells (VSMCs) play an important role in the good performance of the vasculature. To study the surface, intracellular structure and elasticity of VSMCs, atomic force acoustic microscope (AFAM) was used for imaging VSMCs from A7r5 rat aorta arteries. The topography images of VSMCs were obtained in contact mode and the acoustic images were obtained by AFAM in sample vibration mode. Then, the force curve measurement derived using Young's modulus of the interested areas was used for evaluating elasticity properties. The acoustic images were found in higher resolution with more information than the topography images. The force curves showed the difference in Young's modulus of the different parts of VSMC. These findings demonstrate that AFAM is useful for displaying the surface, structure and elasticity property of VSMCs clearly, with short scanning time, negligible harm or damage to cell and nanometer-level resolution.

Determining the mechanical properties of yeast cell walls

The intrinsic cell wall mechanical properties of Baker's yeast (Saccharomyces cerevisiae) cells were determined. Force-deformation data from compression of individual cells up to failure were recorded, and these data were fitted by an analytical model to extract the elastic modulus of the cell wall and the initial stretch ratio of the cell. The cell wall was assumed to be homogeneous, isotropic, and incompressible. A linear elastic constitutive equation was assumed based on Hencky strains to accommodate the large stretches of the cell wall. Because of the high compression speed, water loss during compression could be assumed to be negligible. It was then possible to treat the initial stretch ratio and elastic modulus as adjustable parameters within the analytical model. As the experimental data fitted numerical simulations well up to the point of cell rupture, it was also possible to extract cell wall failure criteria. The mean cell wall properties for resuspended dried Baker's yeast were as follows: elastic modulus 185 ± 15 MPa, initial stretch ratio 1.039 ± 0.006, circumferential stress at failure 115 ± 5 MPa, circumferential strain at failure 0.46 ± 0.03, and strain energy per unit volume at failure 30 ± 3 MPa. Data on yeast cells obtained by this method and model should be useful in the design and optimization of cell disruption equipment for yeast cell processing.

Measuring the mechanical properties of single microbial cells

Many cells are considered to be susceptible to mechanical forces or "shear" in bioprocessing, leading to undesirable cell breakage or adverse metabolic effects. However, cell breakage is the aim of some processing operations, in particular high-pressure homogenisation and other cell disruption methods. In either case, the exact mechanisms of damage or disruption are obscure. One reason for this is that the mechanical properties of the cells are generally unknown, which makes investigation or prediction of the damage difficult. There are several methods for measuring the mechanical properties of single microbial cells, and these are reviewed briefly. In the context of bioprocessing research, a powerful method of characterising the mechanical properties of single cells is compression testing using micromanipulation, supplemented by mathematical modelling of the cell behaviour in compression. The method and associated modelling are described, with results mainly from studies on yeast cells. Continuing difficulties in making a priori predictions of cell breakage in processing are identified. In future, compression testing by micromanipulation might also be used in conjunction with other single cell analytical techniques to study mechanisms controlling form, growth and division of cells and their consequential mechanical behaviour. It ought to be possible to relate cell wall mechanics to cell wall composition and structure, and eventually to underlying gene expression, allowing much greater understanding and control of the cell mechanical properties.