Mathematical modeling of microscale biology: Ion pairing, spatially varying permittivity, and Born energy in glycosaminoglycan brushes.

Biological macromolecules including nucleic acids, proteins, and glycosaminoglycans are typically anionic and can span domains of up to hundreds of nanometers and even micron length scales. The structures exist in crowded environments that are dominated by multivalent electrostatic interactions that can be modeled using mean-field continuum approaches that represent underlying molecular nanoscale biophysics. We develop such models for glycosaminoglycan brushes using steady state modified Poisson-Boltzmann models that incorporate important ion-specific (Hofmeister) effects. The results quantify how electroneutrality is attained through ion electrophoresis, spatially-varying permittivity hydration forces, and ion-specific pairing. Brush-salt interfacial profiles of the electrostatic potential as well as bound and unbound ions are characterized for imposed jump conditions across the interface. The models should be applicable to many intrinsically-disordered biophysical environments and are anticipated to provide insight into the design and development of therapeutics and drug-delivery vehicles to improve human health.

DNA adsorption to and elution from silica surfaces: influence of amino acid buffers.

Solid phase extraction and purification of DNA from complex samples typically requires chaotropic salts that can inhibit downstream polymerase amplification if carried into the elution buffer. Amino acid buffers may serve as a more compatible alternative for modulating the interaction between DNA and silica surfaces. We characterized DNA binding to silica surfaces, facilitated by representative amino acid buffers, and the subsequent elution of DNA from the silica surfaces. Through bulk depletion experiments, we found that more DNA adsorbs to silica particles out of positively compared to negatively charged amino acid buffers. Additionally, the type of the silica surface greatly influences the amount of DNA adsorbed and the final elution yield. Quartz crystal microbalance experiments with dissipation monitoring (QCM-D) revealed multiphasic DNA adsorption out of stronger adsorbing conditions such as arginine, glycine, and glutamine, with DNA more rigidly bound during the early stages of the adsorption process. The DNA film adsorbed out of glutamate was more flexible and uniform throughout the adsorption process. QCM-D characterization of DNA elution from the silica surface indicates an uptake in water mass during the initial stage of DNA elution for the stronger adsorbing conditions, which suggests that for these conditions the DNA film is partly dehydrated during the prior adsorption process. Overall, several positively charged and polar neutral amino acid buffers show promise as an alternative to methods based on chaotropic salts for solid phase DNA extraction.

Multiphasic DNA adsorption to silica surfaces under varying buffer, pH, and ionic strength conditions.

Reversible interactions between DNA and silica are utilized in the solid phase extraction and purification of DNA from complex samples. Chaotropic salts commonly drive DNA binding to silica but inhibit DNA polymerase amplification. We studied DNA adsorption to silica using conditions with or without chaotropic salts through bulk depletion and quartz crystal microbalance (QCM) experiments. While more DNA adsorbed to silica using chaotropic salts, certain buffer conditions without chaotropic salts yielded a similar amount of eluted DNA. QCM results indicate that under stronger adsorbing conditions the adsorbed DNA layer is initially rigid but becomes viscoelastic within minutes. These results qualitatively agreed with a mathematical model for a multiphasic adsorption process. Buffer conditions that do not require chaotropic salts can simplify protocols for nucleic acid sample preparation. Understanding how DNA adsorbs to silica can help optimize nucleic acid sample preparation for clinical diagnostic and research applications.

Mechanical disruption of lysis-resistant bacterial cells by use of a miniature, low-power, disposable device.

Molecular detection of microorganisms requires microbial cell disruption to release nucleic acids. Sensitive detection of thick-walled microorganisms such as Bacillus spores and Mycobacterium cells typically necessitates mechanical disruption through bead beating or sonication, using benchtop instruments that require line power. Miniaturized, low-power, battery-operated devices are needed to facilitate mechanical pathogen disruption for nucleic acid testing at the point of care and in field settings. We assessed the lysis efficiency of a very small disposable bead blender called OmniLyse relative to the industry standard benchtop Biospec Mini-BeadBeater. The OmniLyse weighs approximately 3 g, at a size of approximately 1.1 cm(3) without the battery pack. Both instruments were used to mechanically lyse Bacillus subtilis spores and Mycobacterium bovis BCG cells. The relative lysis efficiency was assessed through real-time PCR. Cycle threshold (C(T)) values obtained at all microbial cell concentrations were similar between the two devices, indicating that the lysis efficiencies of the OmniLyse and the BioSpec Mini-BeadBeater were comparable. As an internal control, genomic DNA from a different organism was spiked at a constant concentration into each sample upstream of lysis. The C(T) values for PCR amplification of lysed samples using primers specific to this internal control were comparable between the two devices, indicating negligible PCR inhibition or other secondary effects. Overall, the OmniLyse device was found to effectively lyse tough-walled organisms in a very small, disposable, battery-operated format, which is expected to facilitate sensitive point-of-care nucleic acid testing.

Modeling of mass transfer limitation in biomolecular assays.

Many biomolecular assays involve the capture of an analyte by ligands that are attached or immobilized upon a solid surface. Often the binding kinetics of the ligand and analyte are fast enough that the capture step is limited by diffusion or mass transfer of the analyte from the bulk fluid phase onto the surface. In this contribution, after a brief survey of various mathematical models for mass transfer-limited analyte capture, we analyze one model problem. The model involves the capture of analytes by suspended solid spherical beads on whose surface many ligands are attached. The rate of association of the ligand and analyte molecules is taken to be high enough that the overall rate of the capture process is limited by diffusion. Two distinct limits are examined analytically. In early times, when the analytes near a bead are being captured and the depletion layers in the neighborhood of the individual beads are nonoverlapping, the problem is modeled as a diffusion/surface reaction problem about a single bead, and analytical results are obtained that describe the amount of analyte captured as a function of time. At later times, when the depletion layers from neighboring beads begin to overlap, the problem is modeled by means of generalized Taylor dispersion or macrotransport theory. In each case, scaling laws are derived that characterize the capture efficiency as a function of number density, volume fraction, and radius of beads.

Moment analysis of near-equilibrium binding interactions during electrophoresis.

The electrophoretic transport of three chemically reacting species, two of which can bind reversibly to form the third, is analyzed mathematically. The species are assumed to move horizontally through a long channel with different electrophoretic mobilities and diffusion coefficients. By considering small perturbations of the system about equilibrium or when one of the two binding species is much more abundant than the other, the governing advection-reaction-diffusion equations can be linearized and studied via the method of moments. The result is a set of coupled ordinary differential equations for the moments that can be solved analytically. Analysis of the long-time evolution of the moments yields mean velocities and dispersion coefficients for each species. The results provide a method for measuring the rate and equilibrium constants of binding reactions using capillary electrophoresis.

On deriving lumped models for blood flow and pressure in the systemic arteries.

Windkessel and similar lumped models are often used to represent blood flow and pressure in systemic arteries. The windkessel model was originally developed by Stephen Hales (1733) and Otto Frank (1899) who used it to describe blood flow in the heart. In this paper we start with the onedimensional axisymmetric Navier-Stokes equations for time-dependent blood flow in a rigid vessel to derive lumped models relating flow and pressure. This is done through Laplace transform and its inversion via residue theory. Upon keeping contributions from one, two, or more residues, we derive lumped models of successively higher order. We focus on zeroth, first and second order models and relate them to electrical circuit analogs, in which current is equivalent to flow and voltage to pressure. By incorporating effects of compliance through addition of capacitors, windkessel and related lumped models are obtained. Our results show that given the radius of a blood vessel, it is possible to determine the order of the model that would be appropriate for analyzing the flow and pressure in that vessel. For instance, in small rigid vessels ( R < 0.2 cm) it is adequate to use Poiseuille's law to express the relation between flow and pressure, whereas for large vessels it might be necessary to incorporate spatial dependence by using a one-dimensional model accounting for axial variations.

Resolution of multiple ssDNA structures in free solution electrophoresis.

By using high concentrations of buffer, electroosmotic flow within uncoated channels of a microfluidic chip was minimized, allowing the free solution electrophoretic separation of DNA. More importantly, because of the ability to efficiently dissipate heat within these channels, field strengths as high as 600 V/cm could be applied with minimal Joule heating (<2 degrees C). As a result of the higher field strengths, separations within an 8-cm-long channel were achieved within a few minutes. However, when the electrophoretic separation of single-stranded DNA (ssDNA) less than 22 bases in length was performed, containing the fluorophore Texas Red as an end label, more than the expected single peak was observed at this high electric field. On the other hand, the free solution electrophoresis of a double-stranded DNA (dsDNA) consisting of a random sequence did exhibit the expected single peak. The appearance of these multiple peaks for ssDNA is shown to be dependent upon the base content and sequence of the ssDNA as well as on the chemical structure of the fluorophore used to tag the DNA for detection. Specifically, the peaks can be attributed to different secondary structures that result either from hydrophobic interactions between the DNA bases and an uncharged fluorescent dye or from G-quadruplexes within guanine-rich strands.

Dynamics of cerebral blood flow regulation explained using a lumped parameter model.

The dynamic cerebral blood flow response to sudden hypotension during posture change is poorly understood. To better understand the cardiovascular response to hypotension, we used a windkessel model with two resistors and a capacitor to reproduce beat-to-beat changes in middle cerebral artery blood flow velocity (transcranial Doppler measurements) in response to arterial pressure changes measured in the finger (Finapres). The resistors represent lumped systemic and peripheral resistances in the cerebral vasculature, whereas the capacitor represents a lumped systemic compliance. Ten healthy young subjects were studied during posture change from sitting to standing. Dynamic variations of the peripheral and systemic resistances were extracted from the data on a beat-to-beat basis. The model shows an initial increase, followed approximately 10 s later by a decline in cerebrovascular resistance. The model also suggests that the initial increase in cerebrovascular resistance can explain the widening of the cerebral blood flow pulse observed in young subjects. This biphasic change in cerebrovascular resistance is consistent with an initial vasoconstriction, followed by cerebral autoregulatory vasodilation.

A numerical study of the effect of insoluble surfactants on the stability of a viscous drop translating in a Hele-Shaw cell.

A circular drop is a linearly stable solution for the buoyancy-driven motion of drops in a Hele-Shaw cell [Gupta et al. J. Colloid Interface Sci.218(1), 338 (1999)]. In the absence of surface-active agents, an initially prolate drop always goes to a steady circular shape while initially oblate drops exhibit complex dynamics [Gupta et al. J. Colloid Interface Sci.222, 107 (2000)]. In this study, the effect of insoluble surfactant impurities on the critical conditions for drop breakup is explored by using the Langmuir adsorption framework in conjunction with a physically based expression for the depth-averaged tangential stress exerted on a two-phase interface in a Hele-Shaw cell. It is shown that the presence of surfactants can have both a stabilizing and a destabilizing effect on the shape of the drop, depending on the Bond number, the magnitude of the initial perturbation, and the strength of surface convection. Similar to the clean drop dynamics, two marginally stable branches are found. Increasing the surface Peclet number results in the stabilization of the main branch while the secondary branch shifts to higher Bond numbers. The mode of breakup is also found to be strongly influenced by the strength of surface convection.