1
|
Puleri DF, Randles A. The role of adhesive receptor patterns on cell transport in complex microvessels. Biomech Model Mechanobiol 2022; 21:1079-1098. [PMID: 35507242 PMCID: PMC10777541 DOI: 10.1007/s10237-022-01575-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2020] [Accepted: 02/26/2022] [Indexed: 01/13/2023]
Abstract
Cell transport is governed by the interaction of fluid dynamic forces and biochemical factors such as adhesion receptor expression and concentration. Although the effect of endothelial receptor density is well understood, it is not clear how the spacing and local spatial distribution of receptors affect cell adhesion in three-dimensional microvessels. To elucidate the effect of vessel shape on cell trajectory and the arrangement of endothelial receptors on cell adhesion, we employed a three-dimensional deformable cell model that incorporates microscale interactions between the cell and the endothelium. Computational cellular adhesion models are systematically altered to assess the influence of receptor spacing. We demonstrate that the patterns of receptors on the vessel walls are a key factor guiding cell movement. In straight microvessels, we show a relationship between cell velocity and the spatial distribution of adhesive endothelial receptors, with larger receptor patches producing lower translational velocities. The joint effect of the complex vessel topology seen in microvessel shapes such as curved and bifurcated vessels when compared to straight tubes is explored with results which showed the spatial distribution of receptors affecting cell trajectory. Our findings here represent demonstration of the previously undescribed relationship between receptor pattern and geometry that guides cellular movement in complex microenvironments.
Collapse
Affiliation(s)
- Daniel F Puleri
- Department of Biomedical Engineering, Duke University, Durham, NC, 27708, USA
| | - Amanda Randles
- Department of Biomedical Engineering, Duke University, Durham, NC, 27708, USA.
| |
Collapse
|
2
|
Massaro EK, Goswami I, Verbridge SS, von Spakovsky MR. Electro-chemo-mechanical model to investigate multi-pulse electric-field-driven integrin clustering. Bioelectrochemistry 2020; 137:107638. [PMID: 33160180 DOI: 10.1016/j.bioelechem.2020.107638] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2020] [Revised: 08/18/2020] [Accepted: 08/18/2020] [Indexed: 11/28/2022]
Abstract
The effect of pulsed electric fields (PEFs) on transmembrane proteins is not fully understood; how do chemo-mechanical cues in the microenvironment mediate the electric field sensing by these proteins? To answer this key gap in knowledge, we have developed a kinetic Monte Carlo statistical model of the integrin proteins that integrates three components of the morphogenetic field (i.e., chemical, mechanical, and electrical cues). Specifically, the model incorporates the mechanical stiffness of the cell membrane, the ligand density of the extracellular environment, the glycocalyx stiffness, thermal Brownian motion, and electric field induced diffusion. The effects of both steady-state electric fields and transient PEF pulse trains on integrin clustering are studied. Our results reveal that electric-field-driven integrin clustering is mediated by membrane stiffness and ligand density. In addition, we explore the effects of PEF pulse-train parameters (amplitude, polarity, and pulse-width) on integrin clustering. In summary, we demonstrate a computational methodology to incorporate experimental data and simulate integrin clustering when exposed to PEFs for time-scales comparable to experiments (seconds-minutes). Thus, we propose a blueprint for understanding PEF/electric field effects on protein induced signaling and highlight key impediments to incorporating experimental values into computational models such as the kinetic Monte Carlo method.
Collapse
Affiliation(s)
- Evan K Massaro
- Center for Computational Science and Engineering, Massachusetts Institute of Technology, MA, USA
| | - Ishan Goswami
- California Institute for Quantitative Biosciences, University of California Berkeley, CA, USA.
| | - Scott S Verbridge
- Department of Biomedical Engineering and Applied Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA
| | - Michael R von Spakovsky
- Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA
| |
Collapse
|
3
|
Surface deformation and shear flow in ligand mediated cell adhesion. J Math Biol 2016; 73:1035-52. [PMID: 26965247 DOI: 10.1007/s00285-016-0983-7] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2015] [Revised: 01/22/2016] [Indexed: 10/22/2022]
Abstract
We present a unified, multiscale model to study the attachment/detachment dynamics of two deforming, charged, near spherical cells, coated with binding ligands and subject to a slow, homogeneous shear flow in a viscous, ionic fluid medium. The binding ligands on the surface of the cells experience both attractive and repulsive forces in an ionic medium and exhibit finite resistance to rotation via bond tilting. The microscale drag forces and couples describing the fluid flow inside the small separation gap between the cells, are calculated using a combination of methods in lubrication theory and previously published numerical results. For a selected range of material and fluid parameters, a hysteretic transition of the sticking probability curves (i.e., the function [Formula: see text]) between the adhesion phase (when [Formula: see text]) and the fragmentation phase (when [Formula: see text]) is attributed to a nonlinear relation between the total nanoscale binding forces and the separation gap between the cells. We show that adhesion is favoured in highly ionic fluids, increased deformability of the cells, elastic binders and a higher fluid shear rate (until a critical threshold value of shear rate is reached). Within a selected range of critical shear rates, the continuation of the limit points (i.e., the turning points where the slope of [Formula: see text] changes sign) predict a bistable region, indicating an abrupt switching between the adhesion and the fragmentation regimes. Although, bistability in the adhesion-fragmentation phase diagram of two deformable, charged cells immersed in an ionic aqueous environment has been identified by some in vitro experiments, but until now, has not been quantified theoretically.
Collapse
|
4
|
Statistically-based DLVO approach to the dynamic interaction of colloidal microparticles with topographically and chemically heterogeneous collectors. J Colloid Interface Sci 2015; 449:443-51. [DOI: 10.1016/j.jcis.2015.02.031] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2014] [Revised: 02/08/2015] [Accepted: 02/11/2015] [Indexed: 11/22/2022]
|
5
|
Rocheleau AD, Sumagin R, Sarelius IH, King MR. Simulation and Analysis of Tethering Behavior of Neutrophils with Pseudopods. PLoS One 2015; 10:e0128378. [PMID: 26091091 PMCID: PMC4474963 DOI: 10.1371/journal.pone.0128378] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2015] [Accepted: 04/29/2015] [Indexed: 11/30/2022] Open
Abstract
P-selectin and P-selectin glycoprotein ligand-1 (PSGL-1) play important roles in mediating the inflammatory cascade. Selectin kinetics, together with neutrophil hydrodynamics, regulate the fundamental adhesion cascade of cell tethering and rolling on the endothelium. The current study uses the Multiscale Adhesive Dynamics computational model to simulate, for the first time, the tethering and rolling behavior of pseudopod-containing neutrophils as mediated by P-selectin/PSGL-1 bonds. This paper looks at the effect of including P-selectin/PSGL-1 adhesion kinetics. The parameters examined included the shear rate, adhesion on-rate, initial neutrophil position, and receptor number sensitivity. The outcomes analyzed included types of adhesive behavior observed, tether rolling distance and time, number of bonds formed during an adhesive event, contact area, and contact time. In contrast to the hydrodynamic model, P-selectin/PSGL-1 binding slows the neutrophil’s translation in the direction of flow and causes the neutrophil to swing around perpendicular to flow. Several behaviors were observed during the simulations, including tethering without firm adhesion, tethering with downstream firm adhesion, and firm adhesion upon first contact with the endothelium. These behaviors were qualitatively consistent with in vivo data of murine neutrophils with pseudopods. In the simulations, increasing shear rate, receptor count, and bond formation rate increased the incidence of firm adhesion upon first contact with the endothelium. Tethering was conserved across a range of physiological shear rates and was resistant to fluctuations in the number of surface PSGL-1 molecules. In simulations where bonding occurred, interaction with the side of the pseudopod, rather than the tip, afforded more surface area and greater contact time with the endothelial wall.
Collapse
Affiliation(s)
- Anne D. Rocheleau
- Department of Biomedical Engineering, Cornell University, Ithaca, New York, United States of America
| | - Ronen Sumagin
- Department of Pathology, Feinberg School of Medicine, Northwestern University, Chicago, Illinois, United States of America
| | - Ingrid H. Sarelius
- Department of Pharmacology and Physiology, University of Rochester Medical Center, Rochester, New York, United States of America
| | - Michael R. King
- Department of Biomedical Engineering, Cornell University, Ithaca, New York, United States of America
- * E-mail:
| |
Collapse
|
6
|
|
7
|
Mitchell MJ, King MR. Computational and experimental models of cancer cell response to fluid shear stress. Front Oncol 2013; 3:44. [PMID: 23467856 PMCID: PMC3587800 DOI: 10.3389/fonc.2013.00044] [Citation(s) in RCA: 136] [Impact Index Per Article: 12.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2013] [Accepted: 02/18/2013] [Indexed: 11/14/2022] Open
Abstract
It has become evident that mechanical forces play a key role in cancer metastasis, a complex series of steps that is responsible for the majority of cancer-related deaths. One such force is fluid shear stress, exerted on circulating tumor cells by blood flow in the vascular microenvironment, and also on tumor cells exposed to slow interstitial flows in the tumor microenvironment. Computational and experimental models have the potential to elucidate metastatic behavior of cells exposed to such forces. Here, we review the fluid-generated forces that tumor cells are exposed to in the vascular and tumor microenvironments, and discuss recent computational and experimental models that have revealed mechanotransduction phenomena that may play a role in the metastatic process.
Collapse
Affiliation(s)
- Michael J Mitchell
- Department of Biomedical Engineering, Cornell University Ithaca, NY, USA
| | | |
Collapse
|
8
|
Geng Y, Marshall JR, King MR. Glycomechanics of the metastatic cascade: tumor cell-endothelial cell interactions in the circulation. Ann Biomed Eng 2011; 40:790-805. [PMID: 22101756 DOI: 10.1007/s10439-011-0463-6] [Citation(s) in RCA: 57] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2011] [Accepted: 11/02/2011] [Indexed: 02/07/2023]
Abstract
Hydrodynamic shear force plays an important role in the leukocyte adhesion cascade that involves the tethering and rolling of cells along the endothelial layer, their firm adhesion or arrest, and their extravasation or escape from the circulatory system by inducing passive deformation, or cell flattening, and microvilli stretching, as well as regulating the expression, distribution, and conformation of adhesion molecules on leukocytes and the endothelial layer. Similarly, the dissemination of circulating tumor cells (CTCs) from the primary tumor sites is believed to involve tethering, rolling, and firm adhesion steps before their eventual extravasation which leads to secondary tumor sites (metastasis). Of particular importance to both the leukocyte adhesion cascade and the extravasation of CTCs, glycoproteins are involved in all three steps (capture, rolling, and firm adhesion) and consist of a variety of important selectin ligands. This review article provides an overview of glycoprotein glycosylation associated with the abnormal glycan expression on cancer cell surfaces, where well-established and novel selectin ligands that are cancer related are discussed. An overview of computational approaches on the effects of fluid mechanical force on glycoprotein mediated cancer cell rolling and adhesion is presented with a highlight of recent flow-based and selectin-mediated cell capturing/enriching devices. Finally, as an important branch of the glycoprotein family, mucins, specifically MUC1, are discussed in the context of their aberrant expression on cancer cells and their role as cancer cell adhesion molecules. Since metastasis relies heavily on glycoprotein interactions in the bloodstream where the fluid shear stress highly regulates cell adhesion forces, it is important to study and understand the glycomechanics of all relevant glycoproteins (well-established and novel) as they relate to the metastatic cascade.
Collapse
Affiliation(s)
- Yue Geng
- Department of Biomedical Engineering, Cornell University, Ithaca, NY 14853, USA
| | | | | |
Collapse
|
9
|
Geng Y, Narasipura S, Seigel GM, King MR. Vascular Recruitment of Human Retinoblastoma Cells by Multi-Cellular Adhesive Interactions with Circulating Leukocytes. Cell Mol Bioeng 2010; 3:361-368. [PMID: 25110524 DOI: 10.1007/s12195-010-0145-8] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
Retinoblastoma (RB) is a retinal cancer of childhood. RB survivors tend to develop additional tumors later in life, although the physical mechanisms of RB metastatic spread are largely unknown. One step in metastasis through the blood stream is tumor cell adherence to the blood vessel wall through specific receptor:ligand interactions. Yet, human RB cell lines RB143 and WERI-Rb27 do not express selectin ligands or beta-2 integrins and cannot directly interact with inflamed endothelium. In this study, we show that RB cells express ICAM-1, a beta-2 integrin ligand that correlates with metastasis and is preferentially co-expressed on RB cells that also express ABCG2, a stem cell marker associated with chemoresistance and metastasis. Based on the presence of ICAM-1+ RB cells, we tested the hypothesis that RB cells could be recruited to an E-selectin surface via attachment to activated polymorphonuclear cells (PMNs). We characterized the dynamic adhesion between RB cells and PMNs within E-selectin coated microtubes under a physiological range of wall shear stress values (0.2-5 dyn/cm2). We show that activated PMNs are necessary for the recruitment of RB cells through ICAM-1:LFA-1 binding. Results from this work may lead to new strategies that target the metastatic spread of tumor cells.
Collapse
Affiliation(s)
- Yue Geng
- Department of Biomedical Engineering, Cornell University, 205 Weill Hall, 14853 Ithaca, NY, USA
| | - Srinivas Narasipura
- Department of Biomedical Engineering, Cornell University, 205 Weill Hall, 14853 Ithaca, NY, USA
| | - Gail M Seigel
- Center for Hearing and Deafness, University at Buffalo, Buffalo, NY, USA
| | - Michael R King
- Department of Biomedical Engineering, Cornell University, 205 Weill Hall, 14853 Ithaca, NY, USA
| |
Collapse
|
10
|
Adhesive dynamics simulations of the mechanical shedding of L-selectin from the neutrophil surface. J Theor Biol 2009; 260:27-30. [PMID: 19486904 DOI: 10.1016/j.jtbi.2009.05.014] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2009] [Revised: 04/13/2009] [Accepted: 05/18/2009] [Indexed: 12/12/2022]
Abstract
Here we accurately recreate the mechanical shedding of L-selectin and its effect on the rolling behavior of neutrophils in vitro using the adhesive dynamics simulation by incorporating the shear-dependent shedding of L-selectin. We have previously shown that constitutively expressed L-selectin is cleaved from the neutrophil surface during rolling on a sialyl Lewis x-coated planar surface at physiological shear rates without the addition of exogenous stimuli. Utilizing a Bell-like model to describe a shedding rate which presumably increases exponentially with force, we were able to reconstruct the characteristics of L-selectin-mediated neutrophil rolling observed in the experiments. First, the rolling velocity was found to increase during rolling due to the mechanical shedding of L-selectin. When most of the L-selectin concentrated on the tips of deformable microvilli was cleaved by force exerted on the L-selectin bonds, the cell detached from the reactive plane to join the free stream as observed in the experiments. In summary, we show through detailed computational modeling that the force-dependent shedding of L-selectin can explain the rolling behavior of neutrophils mediated by L-selectin in vitro.
Collapse
|
11
|
Duffadar RD, Davis JM. Dynamic adhesion behavior of micrometer-scale particles flowing over patchy surfaces with nanoscale electrostatic heterogeneity. J Colloid Interface Sci 2008; 326:18-27. [DOI: 10.1016/j.jcis.2008.07.004] [Citation(s) in RCA: 76] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2008] [Revised: 07/01/2008] [Accepted: 07/03/2008] [Indexed: 10/21/2022]
|
12
|
A computational study of leukocyte adhesion and its effect on flow pattern in microvessels. J Theor Biol 2008; 254:483-98. [DOI: 10.1016/j.jtbi.2008.05.020] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2008] [Revised: 05/08/2008] [Accepted: 05/19/2008] [Indexed: 11/18/2022]
|
13
|
Dyugovskaya L, Polyakov A, Lavie P, Lavie L. Delayed Neutrophil Apoptosis in Patients with Sleep Apnea. Am J Respir Crit Care Med 2008; 177:544-54. [DOI: 10.1164/rccm.200705-675oc] [Citation(s) in RCA: 93] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
|
14
|
The systemic inflammatory response syndrome induces functional changes and relative hyporesponsiveness in neutrophils. J Crit Care 2008; 23:542-9. [PMID: 19056020 DOI: 10.1016/j.jcrc.2007.09.004] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2007] [Revised: 08/28/2007] [Accepted: 09/24/2007] [Indexed: 11/24/2022]
Abstract
PURPOSE To study the effects of systemic inflammatory response syndrome (SIRS) on polymorhonuclear neutrophil (PMN) function and phenotype by comparing neutrophils from critically ill patients with SIRS against those from healthy blood donors. MATERIAL AND METHODS Intensive care unit patients (n = 110) who met at least one SIRS criterion were recruited to the study. One hundred healthy blood donors were recruited as normal controls. RESULTS Polymorphonuclear cells from critically ill patients with SIRS were more resistant to activation than PMNs from healthy donors, but when stimulated had an exaggerated microbicidal response. Buffer-treated PMNs from patients with SIRS had significantly higher CD43 surface expression that may inhibit heterotypic cellular contact or ligand stimulation of membrane receptors, had significantly lower expression of IgG receptor CD16, demonstrated resistance to shedding of L-selectin when primed by platelet-activating factor which could be pro-inflammatory, and had reduced respiratory burst when primed by platelet-activating factor than activated by formyl-Met-Leu-Phe. CONCLUSION The phenotypic and functional changes observed in neutrophils in the critically ill indicate that they require a higher level of stimulus to become activated. This may represent an auto-protective mechanism where the neutrophils in the already inflamed host may, by this mechanism, avoid excessive inflammation reducing the risk of further host cell injury and death.
Collapse
|
15
|
Schaff U, Mattila PE, Simon SI, Walcheck B. Neutrophil adhesion to E-selectin under shear promotes the redistribution and co-clustering of ADAM17 and its proteolytic substrate L-selectin. J Leukoc Biol 2007; 83:99-105. [DOI: 10.1189/jlb.0507304] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
|
16
|
Lee D, King MR. Shear-induced capping of L-selectin on the neutrophil surface during centrifugation. J Immunol Methods 2007; 328:97-105. [PMID: 17915247 PMCID: PMC2121613 DOI: 10.1016/j.jim.2007.08.011] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2007] [Revised: 07/30/2007] [Accepted: 08/20/2007] [Indexed: 01/06/2023]
Abstract
L-selectin on leukocytes is critical in leukocyte tethering and adhesion to inflamed endothelium and lymphocyte homing to lymphoid organs. The spatial distribution of L-selectin on leukocytes controls cellular adhesive function in hydrodynamic shear. How L-selectin changes its position on the cell membrane remains an open question, but a possible candidate is shear stress encountered on the cell surface. Here we demonstrate shear-induced L-selectin polarization on the membrane during the process of centrifugation of resting neutrophils via immunofluorescent microscopy. It was found that randomly distributed L-selectin on neutrophils moves to a polar cap at one end of the cell after centrifugation (300 x g for 2 min) without inflammatory stimuli. This L-selectin redistribution under shear was predicted by Monte Carlo simulations that show how convection dominates over diffusion, leading to L-selectin cap formation during centrifugation at 280 x g or during leukocyte adhesion to the endothelial wall at 1 dyn/cm(2). Those results point to a role for shear stress in the modulation of L-selectin distribution, and suggest a possible alternate mechanism and reinterpretation of previous in vitro studies of L-selectin mediated adhesion of neutrophils isolated via centrifugation.
Collapse
Affiliation(s)
- Dooyoung Lee
- Department of Chemical Engineering, University of Rochester, Rochester, NY 14627
| | - Michael R. King
- Department of Chemical Engineering, University of Rochester, Rochester, NY 14627
- Department of Biomedical Engineering, University of Rochester, Rochester, NY 14627
- *To whom correspondence should be addressed. Michael R. King, Ph.D., Department of Biomedical Engineering, University of Rochester, 218 Goergen Hall, RC 270168, Rochester, NY 14627, , Phone: 585-275-3285, Fax: 585-276-1999
| |
Collapse
|
17
|
Schaff UY, Xing MMQ, Lin KK, Pan N, Jeon NL, Simon SI. Vascular mimetics based on microfluidics for imaging the leukocyte--endothelial inflammatory response. LAB ON A CHIP 2007; 7:448-56. [PMID: 17389960 DOI: 10.1039/b617915k] [Citation(s) in RCA: 99] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
We describe the development, validation, and application of a novel PDMS-based microfluidic device for imaging leukocyte interaction with a biological substrate at defined shear force employing a parallel plate geometry that optimizes experimental throughput while decreasing reagent consumption. The device is vacuum bonded above a standard 6-well tissue culture plate that accommodates a monolayer of endothelial cells, thereby providing a channel to directly observe the kinetics of leukocyte adhesion under defined shear flow. Computational fluid dynamics (CFD) was applied to model the shear stress and the trajectory of leukocytes within the flow channels at a micron length scale. In order to test this model, neutrophil capture, rolling, and deceleration to arrest as a function of time and position was imaged in the transparent channels. Neutrophil recruitment to the substrate proved to be highly sensitive to disturbances in flow streamlines, which enhanced the rate of neutrophil-surface collisions at the entrance to the channels. Downstream from these disturbances, the relationship between receptor mediated deceleration of rolling neutrophils and dose response of stimulation by the chemokine IL-8 was found to provide a functional readout of integrin activation. This microfluidic technique allows detailed kinetic studies of cell adhesion and reveals neutrophil activation within seconds to chemotactic molecules at concentrations in the picoMolar range.
Collapse
Affiliation(s)
- Ulrich Y Schaff
- Department of Biomedical Engineering, University of California, Davis, 451 E. Health Sciences Drive, Davis, CA 95616, USA
| | | | | | | | | | | |
Collapse
|