3D magnetically controlled spatiotemporal probing and actuation of collagen networks from a single cell perspective

Cells continuously sense and react to mechanical cues from their surrounding matrix, which consists of a fibrous network of biopolymers that influences their fate and behavior. Several powerful methods employing magnetic control have been developed to assess the micromechanical properties within extracellular matrix (ECM) models hosting cells. However, many of these are limited to in-plane sensing and actuation, which does not allow the matrix to be probed within its full 3D context. Moreover, little attention has been given to factors specific to the model ECM systems that can profoundly influence the cells contained there. Here we present methods to spatiotemporally probe and manipulate extracellular matrix networks at the scale relevant to cells using magnetic microprobes (μRods). Our techniques leverage 3D magnetic field generation, physical modeling, and image analysis to examine and apply mechanical stimuli to fibrous collagen matrices. We determined shear moduli ranging between hundreds of Pa to tens of kPa and modeled the effects of proximity to rigid surfaces and local fiber densification. We analyzed the spatial extent and dynamics of matrix deformation produced in response to magnetic torques on the order of 10 pNm, deflecting fibers over an area spanning tens of micrometers. Finally, we demonstrate 3D actuation and pose extraction of fluorescently labelled μRods.

Magnetic tweezers with magnetic flux density feedback control

In this work, we present a single-pole magnetic tweezers (MT) device designed for integration with substrate deformation tracking microscopy and/or traction force microscopy experiments intended to explore extracellular matrix rheology and human epidermal keratinocyte mechanobiology. Assembled from commercially available off-the-shelf electronics hardware and software, the MT device is amenable to replication in the basic biology laboratory. In contrast to conventional solenoid current-controlled MT devices, operation of this instrument is based on real-time feedback control of the magnetic flux density emanating from the blunt end of the needle core using a cascade control scheme and a digital proportional-integral-derivative (PID) controller. Algorithms that compensate for a spatially non-uniform remnant magnetization of the needle core that develops during actuation are implemented into the feedback control scheme. Through optimization of PID gain scheduling, the MT device exhibits magnetization and demagnetization response times of less than 100 ms without overshoot over a wide range of magnetic flux density setpoints. Compared to current-based control, magnetic flux density-based control allows for more accurate and precise magnetic actuation forces by compensating for temperature increases within the needle core due to heat generated by the applied solenoid currents. Near field calibrations validate the ability of the MT device to actuate 4.5 μm-diameter superparamagnetic beads with forces up to 25 nN with maximum relative uncertainties of ±30% for beads positioned between 2.5 and 40 µm from the needle tip.

Effect of the C-terminal amino acid of the peptide on the structure and mechanical properties of alginate-peptide hydrogels across length-scales

Alginate is a natural anionic polysaccharide that exhibits excellent biocompatibility and biodegradability. Alginate hydrogels have many different applications in the field of regenerative medicine especially when peptides are conjugated to the alginate backbone. Here, we systematically investigate the effect of six arginine-glycine-aspartic acid (RGD)-containing peptides, G6KRGDY/S, A6KRGDY/S and V6KRGDY/S, on the macroscopic and microscopic physical properties and spatial organization of alginate-peptides hydrogels. Using rheology, small angle X-ray scattering and nanoindentation measurements we show a strong correlation between the macroscopic-bulk properties and the microscopic-local properties of the alginate-peptide hydrogels. Furthermore, our results indicate that the identity of the amino acid at the C-terminal of the peptide plays a major role in determining the structure and mechanical properties of the hydrogel across length-scales, where the presence of tyrosine (Y) terminated peptides introduce more junction-zones and consequently larger stiffness than those terminated with serine (S).

Magnetic wire-based sensors for the microrheology of complex fluids

We propose a simple microrheology technique to evaluate the viscoelastic properties of complex fluids. The method is based on the use of magnetic wires of a few microns in length submitted to a rotational magnetic field. In this work, the method is implemented on a surfactant wormlike micellar solution that behaves as an ideal Maxwell fluid. With increasing frequency, the wires undergo a transition between a steady and a hindered rotation regime. The study shows that the average rotational velocity and the amplitudes of the oscillations obey scaling laws with well-defined exponents. From a comparison between model predictions and experiments, the rheological parameters of the fluid are determined.

Characterization of uniaxial stiffness of extracellular matrix embedded with magnetic beads via bio-conjugation and under the influence of an external magnetic field

In this paper, we study the deformation, and experimentally quantify the change in stiffness, of an extracellular matrix (ECM) embedded with magnetic beads that are bio-conjugated with the collagen fibers and under the influence of an external magnetic field. We develop an analytical model of the viscoelastic behavior of this modified ECM, and design and implement a stretch test to quantify (based on statistically meaningful experiment data) the resulting changes in its stiffness induced by the external magnetic field. The analytical results are in close agreement with that obtained from the experiments. We discuss the implication of these results that point to the possibility of creating desired stiffness gradients in an ECM in vitro to influence cell behavior.

Complete mechanical characterization of soft media using nonspherical rods

Hydrogels have been used as substrates for studying the cellular processes by many researchers. The stiffness of such gels was also characterized previously. However, in most of the cases, these soft Poisson's ratio was assumed incompressible and Poisson's ratio is assumed to be one-half. This may not be true in many cases, and might alter the calculation of the stiffness of the gels. In this study, we present equations for the complete characterization of soft media, i.e., calculation of Young's modulus, shear modulus, and Poisson's ratio. The method involves the individual measurement of either the displacement or rotation of cylindrical rods embedded in the soft media, under the application of an external force or torque. Equations involving shear modulus and Poisson's ratio for rotation of the rod and Young's modulus and Poisson's ratio for the displacement of the rod are independently derived. In addition, the displacement and rotation of the rods embedded in an elastic medium, under the application of either a force or a torque, respectively, were also calculated using finite element analysis. These values compared well with the displacements and rotations obtained using closed form equations.