On the adhesion-velocity relation and length adaptation of motile cells on stepped fibronectin lanes

The biphasic adhesion-velocity relation is a universal observation in mesenchymal cell motility. It has been explained by adhesion-promoted forces pushing the front and resisting motion at the rear. Yet, there is little quantitative understanding of how these forces control cell velocity. We study motion of MDA-MB-231 cells on microlanes with fields of alternating Fibronectin densities to address this topic and derive a mathematical model from the leading-edge force balance and the force-dependent polymerization rate. It reproduces quantitatively our measured adhesion-velocity relation and results with keratocytes, PtK1 cells, and CHO cells. Our results confirm that the force pushing the leading-edge membrane drives lamellipodial retrograde flow. Forces resisting motion originate along the whole cell length. All motion-related forces are controlled by adhesion and velocity, which allows motion, even with higher Fibronectin density at the rear than at the front. We find the pathway from Fibronectin density to adhesion structures to involve strong positive feedbacks. Suppressing myosin activity reduces the positive feedback. At transitions between different Fibronectin densities, steady motion is perturbed and leads to changes of cell length and front and rear velocity. Cells exhibit an intrinsic length set by adhesion strength, which, together with the length dynamics, suggests a spring-like front-rear interaction force. We provide a quantitative mechanistic picture of the adhesion-velocity relation and cell response to adhesion changes integrating force-dependent polymerization, retrograde flow, positive feedback from integrin to adhesion structures, and spring-like front-rear interaction

Elastic deformation of a fluid membrane upon colloid binding

When a colloidal particle adheres to a fluid membrane, it induces elastic deformations in the membrane which oppose its own binding. The structural and energetic aspects of this balance are theoretically studied within the framework of a Helfrich Hamiltonian. Based on the full nonlinear shape equations for the membrane profile, a line of continuous binding transitions and a second line of discontinuous envelopment transitions are found, which meet at an unusual triple point. The regime of low tension is studied analytically using a small gradient expansion, while in the limit of large tension scaling arguments are derived which quantify the asymptotic behavior of phase boundary, degree of wrapping, and energy barrier. The maturation of animal viruses by budding is discussed as a biological example of such colloid-membrane interaction events.Comment: 14 pages, 9 figures, REVTeX style, follow-up on cond-mat/021242

Inter-laboratory comparison of nanoparticle size measurements using dynamic light scattering and differential centrifugal sedimentation

Nanoparticle in vitro toxicity studies often report contradictory results with one main reason being insufficient material characterization. In particular the characterization of nanoparticles in biological media remains challenging. Our aim was to provide robust protocols for two of the most commonly applied techniques for particle sizing, i.e. dynamic light scattering (DLS) and differential centrifugal sedimentation (DCS) that should be readily applicable also for users not specialized in nanoparticle physico-chemical characterization. A large number of participants (40, although not all participated in all rounds) were recruited for a series of inter-laboratory comparison (ILC) studies covering many different instrument types, commercial and custom-built, as another possible source of variation. ILCs were organized in a consecutive manner starting with dispersions in water employing well-characterized near-spherical silica nanoparticles (nominal 19 nm and 100 nm diameter) and two types of functionalized spherical polystyrene nanoparticles (nominal 50 nm diameter). At first each laboratory used their in-house established procedures. In particular for the 19 nm silica particles, the reproducibility of the methods was unacceptably high (reported results were between 10 nm and 50 nm). When comparing the results of the first ILC round it was observed that the DCS methods performed significantly worse than the DLS methods, thus emphasizing the need for standard operating procedures (SOPs). SOPs have been developed by four expert laboratories but were tested for robustness by a larger number of independent users in a second ILC (11 for DLS and 4 for DCS). In a similar approach another SOP for complex biological fluids, i.e. cell culture medium containing serum was developed, again confirmed via an ILC with 8 participating laboratories. Our study confirms that well-established and fit-for-purpose SOPs are indispensable for obtaining reliable and comparable particle size data. Our results also show that these SOPs must be optimized with respect to the intended measurement system (e.g. particle size technique, type of dispersant) and that they must be sufficiently detailed (e.g. avoiding ambiguity regarding measurand definition, etc.). SOPs may be developed by a small number of expert laboratories but for their widespread applicability they need to be verified by a larger number of laboratories

Mesenchymal cell migration on one-dimensional micropatterns

Quantitative studies of mesenchymal cell motion are important to elucidate cytoskeleton function and mechanisms of cell migration. To this end, confinement of cell motion to one dimension (1D) significantly simplifies the problem of cell shape in experimental and theoretical investigations. Here we review 1D migration assays employing micro-fabricated lanes and reflect on the advantages of such platforms. Data are analyzed using biophysical models of cell migration that reproduce the rich scenario of morphodynamic behavior found in 1D. We describe basic model assumptions and model behavior. It appears that mechanical models explain the occurrence of universal relations conserved across different cell lines such as the adhesion-velocity relation and the universal correlation between speed and persistence (UCSP). We highlight the unique opportunity of reproducible and standardized 1D assays to validate theory based on statistical measures from large data of trajectories and discuss the potential of experimental settings embedding controlled perturbations to probe response in migratory behavior

Parameter estimation for dynamical systems with discrete events and logical operations.

Motivation: Ordinary differential equation (ODE) models are frequently used to describe the dynamic behaviour of biochemical processes. Such ODE models are often extended by events to describe the effect of fast latent processes on the process dynamics. To exploit the predictive power of ODE models, their parameters have to be inferred from experimental data. For models without events, gradient based optimization schemes perform well for parameter estimation, when sensitivity equations are used for gradient computation. Yet, sensitivity equations for models with parameter- and state-dependent events and event-triggered observations are not supported by existing toolboxes. Results: In this manuscript, we describe the sensitivity equations for differential equation models with events and demonstrate how to estimate parameters from event-resolved data using event-triggered observations in parameter estimation. We consider a model for GFP expression after transfection and a model for spiking neurons and demonstrate that we can improve computational efficiency and robustness of parameter estimation by using sensitivity equations for systems with events. Moreover, we demonstrate that, by using event-outputs, it is possible to consider event-resolved data, such as time-to-event data, for parameter estimation with ODE models. By providing a user-friendly, modular implementation in the toolbox AMICI, the developed methods are made publicly available and can be integrated in other systems biology toolboxes. Availability and Implementation: We implement the methods in the open-source toolbox Advanced MATLAB Interface for CVODES and IDAS (AMICI, https://github.com/ICB-DCM/AMICI)

Temporal analysis of active and passive transport in living cells

FWN – Publicaties zonder aanstelling Universiteit Leide

On multistability and constitutive relations of cell motion on Fibronectin lanes

Cell motility on flat substrates exhibits coexisting steady and oscillatory morphodynamics, the biphasic adhesion-velocity relation, and the universal correlation between speed and persistence (UCSP) as simultaneous observations common to many cell types. Their universality and concurrency suggest a unifying mechanism causing all three of them. Stick-slip models for cells on 1dimensional lanes suggest multistability to arise from the non-linear friction of retrograde flow. This study suggests a mechanical mechanism controlled by integrin signalling on the basis of a biophysical model and analysis of trajectories of MDA-MB-231 cells on Fibronectin lanes which additionally explains the constitutive relations. The experiments exhibit cells with steady or oscillatory morphodynamics and either spread or moving with spontaneous transitions between the dynamic regimes, spread and moving and spontaneous direction reversals. Our biophysical model is based on the force balance at the protrusion edge, the noisy clutch of retrograde flow and a response function of friction and membrane drag to integrin signaling. The theory reproduces the experimentally observed cell states, characteristics of oscillations and state probabilities. Analysis of experiments with the biophysical model establishes a stick-slip oscillation mechanism, explains multistability of cell states and the statistics of state transitions. It suggests protrusion competition to cause direction reversal events, the statistics of which explain the UCSP. The effect of integrin signalling on drag and friction explains the adhesion-velocity relation and cell behavior at Fibronectin density steps. The dynamics of our mechanism are non-linear flow mechanics driven by F-actin polymerization and shaped by the noisy clutch of retrograde flow friction, protrusion competition via membrane tension and drag forces. Integrin signalling controls the parameters of the mechanical system

Interaction of similarly charged surfaces mediated by nanoparticles

We study the interaction between two like charged surfaces embedded in a solution of oppositely charged multivalent rod-like counterions. The counterions consist of two rigidly bonded point charges, each of valency Z. The strength of the electrostatic coupling increases with increasing surface charge density or valency of the charges. The system is analyzed by employing a self-consistent field theory, which treats the short and long range interactions of the counterions within different approximations. We find that in the weak coupling limit, the interactions are only repulsive. In the intermediate coupling regime, the multivalent rod-like counterions can mediate attractive interactions between the surfaces. For sufficiently long rods, bridging contributes to the attractive interaction. In the strong coupling limit, the charge correlations can contribute to the attractive interactions at short separations between the charged surfaces. Two minima can then appear in the force curve between surfaces

Inter-laboratory comparison of nanoparticle size measurements using dynamic light scattering and differential centrifugal sedimentation

Nanoparticle in vitro toxicity studies often report contradictory results with one main reason being insufficient material characterization. In particular the characterization of nanoparticles in biological media remains challenging. Our aim was to provide robust protocols for two of the most commonly applied techniques for particle sizing, i.e. dynamic light scattering (DLS) and differential centrifugal sedimentation (DCS) that should be readily applicable also for users not specialized in nanoparticle physico-chemical characterization. A large number of participants (40, although not all participated in all rounds) were recruited for a series of inter-laboratory comparison (ILC) studies covering many different instrument types, commercial and custom-built, as another possible source of variation. ILCs were organized in a consecutive manner starting with dispersions in water employing well-characterized near-spherical silica nanoparticles (nominal 19 nm and 100 nm diameter) and two types of functionalized spherical polystyrene nanoparticles (nominal 50 nm diameter). At first each laboratory used their in-house established procedures. In particular for the 19 nm silica particles, the reproducibility of the methods was unacceptably high (reported results were between 10 nm and 50 nm). When comparing the results of the first ILC round it was observed that the DCS methods performed significantly worse than the DLS methods, thus emphasizing the need for standard operating procedures (SOPs). SOPs have been developed by four expert laboratories but were tested for robustness by a larger number of independent users in a second ILC (11 for DLS and 4 for DCS). In a similar approach another SOP for complex biological fluids, i.e. cell culture medium containing serum was developed, again confirmed via an ILC with 8 participating laboratories. Our study confirms that well-established and fit-for-purpose SOPs are indispensable for obtaining reliable and comparable particle size data. Our results also show that these SOPs must be optimized with respect to the intended measurement system (e.g. particle size technique, type of dispersant) and that they must be sufficiently detailed (e.g. avoiding ambiguity regarding measurand definition, etc.). SOPs may be developed by a small number of expert laboratories but for their widespread applicability they need to be verified by a larger number of laboratories