Biophysical journal.
`v. 103. no. 1 (July 3 2012)
`General Collection
`W1 Bl8765
`2012-07-16 09:43:56
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`l
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`
`Volume 103
`Number 1
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`I-I-u
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`for the Biophysical Society
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`

`

`Biophysical Journal
`Contents
`
`July 2012
`
`Volume 103
`
`Number 1
`
`Editorial
`
`Biophysical Journal 60 Years after Hodgkin-Huxley.
`Leslie M. Loew ....................................................... E01-E02
`
`Gaurav M. Shah, Xin-ping Xu, Amber R. Hackett,
`Changan Xie, Sabisha Shrestha, Lin Liu, Qinglian Liu,
`and Lei Zhou............................................................... 19-28
`
`Biophysical Letters
`
`Membranes
`
`LeuT Conformational Sampling Utilizing Accelerated
`Molecular Dynamics and Principal Component Analysis.
`James R. Thomas, Patrick C. Gedeon, Barry J. Grant,
`and Jeffry D. Madura .............................................. L01-L03
`
`The Highly Processive Kinesin-8, Kip3, Switches
`Microtubule Protofilaments with a Bias toward the Left.
`Volker Bormuth, Bert Nitzsche, Felix Ruhnow,
`Aniruddha Mitra, Marko Storch, Burkhard Rammner
`Jonathon Howard, and Stefan Diez....................... L.04-L06
`
`NADH Distribution in Live Progenitor Stem Cells
`by Phasor-Fluorescence Lifetime Image Microscopy.
`Belinda K. Wright, Laura M. Andrews, Julie Markham,
`Mark R. Jones, Chiara Stringari, Michelle A. Digman,
`and Enrico Gratton .................................................. L07-L09
`
`Hydration Dynamics of Hyaluronan and Dextran.
`Johannes Hunger, Anja Bernecker, Huib J. Bakker,
`Mischa Bonn, and Ralf P. Richter.......................... L 10-L 12
`
`Myofilament Length-Dependent Activation Develops
`within 5 ms in Guinea-Pig Myocardium.
`Ryan D. Mateja and Pieter P. de Tambe............... L 13-L 15
`
`Cell Biophysics
`
`How Malaria Parasites Reduce the Deformability
`of Infected Red Blood Cells. S. Majid Hosseini
`and James J. Feng....................................................... 1-1 o
`
`Label-Free Imaging of Membrane Potential Using
`Membrane Electromotility. Seungeun Oh,
`Christopher Fang-Yen, Wonshik Choi, Zahid Yaqoob,
`Dan Fu, YongKeun Park, Ramachandra R. Dassari,
`and Michael S. Feld.................................................... 11-18
`
`Supramolecular Structure of Membrane-Associated
`Polypeptides by Combining Solid-State NMR
`and Molecular Dynamics Simulations. Markus Weingarth,
`Christian Ader, Adrien J. S. Melquiond, Deepak Nand,
`Olaf Pangs, Stefan Becker, Alexandre M. J. J. Bonvin,
`and Marc Baldus......................................................... 29-37
`
`Dynamic Force Spectroscopy on Supported Lipid Bilayers:
`Effect of Temperature and Sample Preparation.
`Andrea Alessandrini, Heiko M. Seeger,
`Tommaso Caramaschi, and Paolo Facci ................... 38-47
`
`Molecular Machines, Motors, and Nanoscale Biophysics
`
`Force-Dependent Detachment of Kinesin-2 Biases
`Track Switching at Cytoskeletal Filament Intersections.
`Harry W. Schroeder Ill, Adam G. Hendricks, Kazuho Ikeda,
`Henry Shuman, Vladimir Rodionov, Mitsuo lkebe,
`Yale E. Goldman, and Erika L. F. Holzbaur............... 48-58
`
`Negative-Stain Electron Microscopy of Inside-Out FtsZ
`Rings Reconstituted on Artificial Membrane Tubules
`Show Ribbons of Protofilaments. Sara L. Milam,
`Masaki Osawa, and Harold P. Erickson .. .. .. .... .... .. .. .. 59-68
`
`Weak Interactions Govern the Viscosity of Concentrated
`Antibody Solutions: High-Throughput Analysis Using the
`Diffusion Interaction Parameter. Brian D. Connolly,
`Chris Petry, Sandeep Yadav, Barthelemy Demeule,
`Natalie Ciaccio, Jamie M. R. Moore, Steven J. Shire,
`and Yatin R. Gokarn ................................................... 69-78
`
`The Dynamic Structure of Thrombin in Solution.
`Brian Fuglestad, Paul M. Gasper, Marco Tonelli,
`J. Andrew McCammon, Phineus R. L. Markwick,
`and Elizabeth A. Komives .. .. .. .. .. .. .. ...... .... .. .. .. .. .. .. .... .. 79-88
`
`Channels and Transporters
`
`Proteins and Nucleic Acids
`
`Normal-Mode-Analysis-Guided Investigation of Crucial
`!ntersubunit Contacts in the cAMP-Dependent Gating
`1n HCN Channels. Farzana Marni, Shengjun Wu,
`
`Predicting the Effect of Ions on the Conformation of the
`H-NS Dimerization Domain.
`Jocelyne Vreede
`and Remus Th. Dame .. .. .. .. .. .. .. .. .... .. .. .. .. .. .... .. .... .... .. .. 89-98
`
`Page 4 of 15
`
`

`

`Contents ( continued)
`
`Folding a Protein with Equal Probability of Being Helix
`or Hairpin. Chun-Yu Lin, Nan-Yow Chen,
`and Chung Yu Mou .................................................... 99-108
`
`Electron Paramagnetic Resonance Characterization
`of Tetrahydrobiopterin Radical Formation in Bacterial Nitric
`Oxide Synthase Compared to Mammalian Nitric Oxide
`Synthase. A/bane Brunel, Jerome Santolini,
`and Pierre Dor/et...................................................... 109-117
`
`Competition between Supercoils and Toroids in Single
`Molecule DNA Condensation. David Argudo
`and Prashant K. Purohit ... . . . . ... . . . . . . . . . . . . . ... . . . . . ... . . . . . . .. 118-128
`
`Dynamical Coupling of Intrinsically Disordered Proteins
`and Their Hydration Water: Comparison with Folded
`F. -X. Gal/at,
`Soluble and Membrane Proteins.
`A. Laganowsky, K. Wood, F. Gabel, L. van Eijck,
`J. Wuttke, M. Moulin, M. Hartlein, D. Eisenberg,
`J. -P. Colletier, G. Zaccai, and M. Weik.................. 129-136
`
`Systems Biophysics
`
`Effect of Viscoelasticity on the Analysis of Single-Molecule
`Force Spectroscopy on Live Cells.
`V. K. Gupta,
`K. B. Neeves, and C. D. Eggleton ........................... 137-145
`
`Flow Directs Surface-Attached Bacteria to Twitch
`Upstream. Yi Shen, Albert Siryaporn, Sigolene Lecuyer,
`Zemer Gitai, and Howard A. Stone......................... 146-151
`
`Mapping of Mechanical Strains and Stresses around
`Quiescent Engineered Three-Dimensional Epithelial
`Tissues. Niko/ce Gjorevski and Celeste M. Nelson 152-162
`
`Comments to the Editor
`
`Electron Microscopy of Biological Specimens in Liquid
`Water. Robert M. Glaeser.................................... 163-164
`
`Response to "Electron Microscopy of Biological Specimens
`in Liquid Water". Utkur M. Mirsaidov, Haimei Zheng,
`Yosune Casana, and Paul Matsudaira ................... 165-166
`
`Corrections .................................................................... · 167
`
`Cover picture: The structural ensemble of thrombin determined by NMR combined with accelerated molecular dynamics. The
`structure is superimposed on the TROSY spectrum of thrombin. The combined computational and experimental approaches have
`revealed a broad range of dynamic motions on multiple timescales in this important serine protease. See the article by Fuglestad
`et al. on page 79.
`
`Page 5 of 15
`
`

`

`Biophysical Journal Volume 103 July 2012 69-78
`
`69
`
`Weak Interactions Govern the Viscosity of Concentrated Antibody
`Solutions: High-Throughput Analysis Using the Diffusion Interaction
`Parameter
`
`Brian D. Conno11.r,t Chris Petry,t Sandeep Yadav,t Barthelemy Demeule,t Natalie Ciaccio,+ Jamie M. R. Moore,t
`Steven J. Shire, and Yatin R. Gokarnt*
`tPharmaceutical Development, Genentech, Inc., South San Francisco, California; and *Department of Bioengineering and Therapeutic
`Sciences, University of California, San Francisco, California
`
`ABSTRACT Weak protein-protein interactions are thought to modulate the viscoelastic properties of concentrated antibody
`solutions. Predicting the viscoelastic behavior of concentrated antibodies from their dilute solution behavior is of significant
`interest and remains a challenge. Here, we show that the diffusion interaction parameter (k0 ), a component of the osmotic
`second virial coefficient (82 ) that is amenable to high-throughput measurement in dilute solutions, correlates well with the
`viscosity of concentrated monoclonal antibody (mAb) solutions. We measured the ko of 29 different mAbs (lgG 1 and lgG4 ) in
`four different solvent conditions (low and high ion normality) and found a linear dependence between k0 and the exponential
`coefficient that describes the viscosity concentration profiles (IRI 2: 0.9). Through experimentally measured effective charge
`measurements, under low ion normality where the electroviscous effect can dominate, we show that the mAb solution viscosity
`is poorly correlated with the mAb net charge (IRI :::; 0.6). With this large data set, our results provide compelling evidence in
`support of weak intermolecular interactions, in contrast to the notion that the electroviscous effect is important in governing
`the viscoelastic behavior of concentrated mAb solutions. Our approach is particularly applicable as a screening tool for selecting
`mAbs with desirable viscosity properties early during lead candidate selection.
`
`INTRODUCTION
`
`The study of weak (i.e., nonspecific) protein-protein interac(cid:173)
`tions is of significant interest given its immense relevance
`in
`terms of biological action, biochemical processes,
`and disease. Weak protein-protein interactions have been
`shown to influence protein aggregation, solution viscosity,
`and phase transitions (1-3). Intermolecular interactions
`coupled with conformational factors have been implicated
`in diseases such as cataract formation (4) and sickle-cell
`anemia (5), and in amyloid diseases such as systemic
`amyloidosis, amyotrophic lateral sclerosis, Alzheimer's
`disease, Parkinson's disease, and Huntington's disease
`(6,7). From a biopharmaceutical perspective, protein(cid:173)
`protein interactions often become important during the
`development of concentrated monoclonal antibody (mAb)(cid:173)
`based drug solutions.
`mAbs are the most rapidly growing class of protein ther(cid:173)
`apeutics being developed for the treatment of a wide spec(cid:173)
`trum of diseases ranging from cancer to arthritis (8).
`Currently >20 mAb drugs have been approved, and >400
`are in clinical development worldwide (8). The increasing
`success of therapeutic mAbs can be attributed to their
`high target specificity, superior safety profiles compared
`with traditional small-molecule drugs, and long in vivo
`half-lives (9). Even with these unique advantages, high
`mAb doses (several mg/kg) are often necessary to achieve
`an adequate clinical effect. For some diseases, such as
`
`S11b111i11ed Fehnttll)' /0, 20/2, and accepted}<!rp11!,/icatio11 April 24, 20/2.
`*Correspondence: gokarn.yatin@gene.com or yatin_gokarn@yahoo.com
`Editor: George Makhatadze.
`ID 2012 by the Biophysical Society
`0006-3495/12/07/0069/10 $2.00
`
`cancer, that are often treated in hospital settings, large doses
`(I 00-300 mg) of low- to moderate-concentration mAb solu(cid:173)
`tions can be administered via intravenous injection/infusion.
`However, home-use applications for treating chronic inflam(cid:173)
`matory diseases, such as rheumatoid arthritis, necessitate
`the development of high-concentration mAb formulations
`( < 1-1.5 mL) for patient self-administration (10). The devel(cid:173)
`opment of suitable high-concentration mAb formulations
`can pose unique manufacturing and delivery challenges re(cid:173)
`sulting from the high viscosity of such solutions.
`mAbs exhibit peculiar and diverse viscosity-concentra(cid:173)
`tion profiles that reveal a sharp exponential increase in solu(cid:173)
`tion viscosity with increasing mAb concentration. Previous
`studies (2,3) that focused on understanding the origin of
`high viscosity in some high-concentration mAb solutions
`suggested that intermolecular interactions may be respon(cid:173)
`sible for the sharp increases in solution viscosity in addition
`to excluded volume effects. It was proposed that in concen(cid:173)
`trated mAb solutions (> I 50 mg/mL), where intermolecular
`distances can be comparable to or even smaller than molec(cid:173)
`ular dimensions, localized, weak intermolecular interactions
`between mAb molecules occur through exposed charged
`and hydrophobic patches. It was hypothesized that such
`interactions lead to the formation of long-range mAb
`networks, which suboptimally affect the mAb packing
`volume fraction and result in high solution viscosity.
`However, Salinas et al. (11) proposed that the increase in
`solution viscosity of mAbs may simply be a result of the
`electroviscous effect, in similarity to the effect observed in
`dilute solutions of charged colloids, wherein the high net
`
`doi: I0.1016/j.bpj.2012.04.047
`
`Page 6 of 15
`
`

`

`70
`
`surface charge (or s'-potential) of particles under low ion
`normality can dominate viscoelastic behavior.
`Here, we posed the following question: If the increase in
`viscosity of concentrated mAb solutions is caused by weak
`intermolecular interactions, to what extent would such inter(cid:173)
`actions persist in low-concentration conditions, and could
`we detect them? The osmotic second virial coefficient
`(B2) is an excellent measure of weak pairwise interactions;
`however, its measurement can be cumbersome and time(cid:173)
`consuming (12). Although automated methods are emerging
`that may be able to increase throughput for B2 determination
`( 13), previous work showed that the diffusion interaction
`parameter (k0 ), which is related to B2 by the sedimentation
`interaction parameter (ks), the partial specific volume (v),
`and the molecular mass (M) using the equation (14)
`ks+ kv + v
`2M
`
`(1)
`
`and is amenable to high-throughput measurement, is an
`equivalent measure of pairwise intermolecular interactions
`(I, 15). To determine if high viscosity in concentrated
`mAb solutions can be explained by weak intermolecular
`interactions present under dilute conditions, we measured
`the k0 of 29 mAbs under four solvent conditions and exam(cid:173)
`ined its correlation to high-concentration mAb viscosity
`data. We also measured the effective charge of 19 mAbs
`in low-ion-normality solutions to determine whether the
`high viscosity of mAbs can be explained by the net charge
`(or (-potential) as incorporated in models describing the
`electroviscous effect.
`In addition to probing the role of interactions as the
`general underlying mechanism that governs the viscosity
`of concentrated antibody solutions, our work has significant
`practical utility. Not only can high-concentration viscosities
`be severely limiting to the design of efficient ultrafiltration/
`diafiltration unit operations, they may also necessitate
`prohibitively high injection forces for delivery through
`a needle (16). Further, in the high-viscosity regime, small
`changes in mAb concentrations can lead to large changes
`in solution viscosity, causing additional process control
`challenges. Although it is possible to select for molecules
`with desirable (i.e., low) viscosity early in development, ob(cid:173)
`taining measurements with concentrated protein solutions
`by conventional techniques is time-consuming and often
`requires quantities of material that are not readily available
`during discovery and lead optimization. There remains
`a critical need for high-throughput methods that can facili(cid:173)
`tate rapid screening of molecules.
`
`MATERIALS AND METHODS
`
`Solution preparation procedures
`
`Connolly et al.
`
`M-3) with unique complementarity determining region (CDR) sequences
`were cloned, expressed in Chinese hamster ovary cell lines, and purified
`at Genentech (South San Francisco, California). The mAbs were con(cid:173)
`structed with an IgG 1 framework and K light chains, with the following
`exceptions: mAb-4 and mAb-11 contained }. light chains, and mAb-13
`was constructed with an lgG.1 framework. The numbering or these mAbs
`is related to the decreasing value or the interaction parameter (kn) in
`low-ion-normality solution. Some or these mAbs, including the charge(cid:173)
`swap mutants, were used in previous studies and arc related to the previous
`nomenclature as follows: mAb-7 and mAb-15 arc MAb2 and MAb I,
`respectively, in Liu et al. ( 16). Yadav ct al. (17) described the sequence posi(cid:173)
`tion and amino acids involved in the charge-swap mutations. The charge(cid:173)
`swap mutants discussed previously are related to the current nomenclature
`as follows: mAb-15 (M-1) was labeled as M-7, mAb-15 (M-2) as M-5,
`mAb-15 (M-3) as M-6, and mAb-7 (M-2) as M-10 in Table 1 of Yadav
`ct al. (17). The isoclcctric points (pl) of the mAbs ranged from 7.7 to 9.6
`as determined by capillary imaged isoelcctric focusing experiments (data
`not shown). Antibody solutions were stored at 2-8°C before analysis.
`The 20 mM histidine-acetate (His-OAc), 20 mM His-OAc with
`200 mM arginine-chloride (Arg-CI), 200 mM argininc-succinate (Arg(cid:173)
`Succ), and 30 mM histidine-chloride (His-Cl) buffers were prepared with
`compendia-grade (USP, NP, El') chemicals, and purified with deionized
`water via an Elga PURELAB Ultra (Celle, Germany) water purification
`system. The His-OAc buffer was prepared by adjusting a solution of
`20 mM histidine to pH 5.5 with 18 mM acetic acid. The His-Cl solution
`was adjusted to pH 6.0 by combining 16.6 mM histidine-hydrochloride
`monohydratc and 13.3 mM histidine free-base. The Arg-CI buffer was
`prepared by adjusting a solution of 20 mM histidine and 200 mM arginine
`to pH 5.0 with 218 mM hydrochloric acid. The Arg-Succ buffer was
`prepared by adjusting a solution of 200 mM arginine to pH 5.5 with
`121 mM succinic acid.
`The 29 mAbs were exhaustively dialyzed into His-OAc, His-Cl, Arg-Cl,
`and Arg-Succ buffers with the use of Pierce Slide-A-Lyzcr dialysis cassettes
`or Millipore (Billerica, MA) Amicon Ultra centrifugation tubes (IO kD
`molecular mass cutoff), and the mAb stock solution pH was verified for
`each dialyzed sample. After dialysis, the samples were concentrated by
`ultrafiltration with the use of Amicon Ultra centrifugal filtration devices
`(IO kD molecular mass cutoff). We diluted the mAb stock solutions to
`the desired concentration with the respective buffer and filtered them
`through 0.1 µm Anopore membranes using Anotop 10 (Cat. No. 6809-
`1112) sterile syringe filters (Whatman International, Maidstone, UK) before
`obtaining viscosity and dynamic light scattering (DLS) measurements.
`
`Determination of antibody concentration by UV
`spectroscopy
`
`The mAb concentration in the stock solutions(> 175 mg/mL) was measured
`without dilution by slope spectroscopy on a Varian Solo VPE (Bridgewater,
`NJ) spectrophotometer equipped with SoloVPE software (Bridgewater,
`NJ). The UV absorbance of a given sample was measured at 279 11111 in
`a quartz cuvette as a function of pathlength using an initial pathlength of
`150 µrn and a terminal path length or IO µm in 5-µm increments. Each
`sample measurement was corrected for absorbancc at 320 nm and blanked
`against the appropriate buffer. SoloVPE software was used to detcnnine an
`optimal (R2 > 0.998) slope (m) of absorbance (A) as a function of path(cid:173)
`length (/) for each sample using six absorbance values between 0.5 and
`1.0 AU. The slope and the absorptivity (a) were used to calculate mAb
`concentration (c) for each sample using the Beer-Lambert law:
`
`111
`
`d(A)
`d(l)
`
`lY X C.
`
`(2)
`
`Twenty-nine full-length mAbs (mAb-1 through mAb-23) and charge-swap
`mutants for mAb-7 (M-1, M-2, and M-3), and mAb-15 (M-1, M-2, and
`
`The mAb concentration in the diluted antibody solutions was mea(cid:173)
`sured with a SpectraMax M2° microplatc spectrophotometer (Molecular
`
`Biophysical Journal 103(1) 69-78
`
`Page 7 of 15
`
`

`

`Weak Interactions and mAb Viscosity
`
`Devices, Sunnyvale, CA) equipped with SoftMax Pro software (Molecular
`Devices, Sunnyvale, CA). The UV absorbance or each sample was
`measured at 279 and 320 111111 on a CoStar UV transparent 96-well plate.
`Protein concentration was calculated using the absorptivity of each anti(cid:173)
`body molecule. The absorptivitics or the 29 mAbs ranged from 1.41 to
`1.70 (mg/mL)- 1 cm- 1.
`
`Determination of antibody effective charge by
`capillary zone electrophoresis
`
`The elcctrophorctic mobility (µ) of 15 mAbs (mAb-1 to mAb-15) was
`measured with the use of a Beckman Coulter PA 800 plus Pharmaceutical
`Analysis System (18). The instrument was equipped with a Beckman
`Coulter eCAP amine capillary (65 cm, 50 µm inner diameter) and a UV
`detector module. Samples were prepared al I mg/mL concentrations in
`the 20 mM His-OAc, pH 5.5, solution. Dimethylsulfoxide (DMSO) was
`used as a neutral marker representing clectroosmotic llow (EOF). The
`DMSO was prepared at a concentration of0.02% (v/v) in water and injected
`immediately before the mAb sample using an applied pressure of0.5 psi for
`3 s. Detection was p.:rfonned al 214 nm. Measun;ments were made in dupli(cid:173)
`cate under applied voltages of 5000, 7000, and 10,000 Vin reverse polarity.
`The apparent electrophoretic mobility of each protein (J.ip*) was determined
`from the slope of a graph that plotted the analyte velocity (Vp) as a function
`of the electric field (E) ( 18):
`
`E
`
`V
`L,'
`
`(3)
`
`(4)
`
`where Ld is the distance in centimeters from the capillary inlet to the
`detector, Ip is the sample migration time in seconds, Vis the applied voltage,
`and L, is the total length of the capillary. The same method was used
`to calculate the elcctrophorctic mobility of the EOF (µEoFl from the
`DMSO data. A corrected electrophoretic mobility (µp) was then deter(cid:173)
`mined for each sample by simply subtracting J.LEoF from µp*· The effective
`charge or apparent valence (z*) was determined by using the following
`relation ( 19):
`
`Z'
`
`(5)
`
`where kn is Boltzmann's constant (1.3087 x I0- 16 crgl°K), Tis the abso(cid:173)
`lute temperature (292 K), !)0 is the diffusion codlicient (average value of
`4 x I0- 7 cm 2/s for an IgG antibody at infinite dilution as determined
`by DLS in low-ion-normality solution), and e is the elementary charge
`(1.60 x I0- 19 coulombs).
`
`Determination of antibody effective charge by
`electrophoretic light scattering
`
`The clectrophorctic mobility (1-i) of 8 mAbs (mAb-2, mAb-7, mAb-7
`(M-2), mAb-14, mAb-15, and mAb-15 (M-1, M-2, and M-3)) was
`measured with the use of a Malvern Zetasizer Nano Series (Worcester(cid:173)
`shire, UK). Samples were prepared at 5 mg/mL in the 30 mM His-Cl,
`pH 6.0, solution. The electrophoretic mobility measurements were made
`using laser Doppler vclocimetry in a DTS I 060 clear disposable folded
`capillary cell in fast field reversal mode. The (-potential (() and effective
`net molecular charge (z*) were determined by using Henry's equation
`(Eq. 6) and a Dcbye-Hiickcl approximation of the Poisson-Boltzmann
`equation (Eq. 7) (20,21 ):
`
`I; =
`
`3riµp
`2ef(Ka)
`
`z·· = 4mm(l + Ka)/;
`
`e
`
`71
`
`(6)
`
`(7)
`
`where 7] is the viscosity of the solvent (().89 centip ·. .
`•
`2 o
`I
`,
`.
`.
`Oise at 5 C IS used for
`t 1e purpose oJ tlm work),µ" is the electrophoretic mobil"t
`, ..
`· .
`1
`I y, l IS t 1e d1elcc-
`t .
`f I
`, ·
`·
`.
`nc const,mt o
`t 1e medium, e 1s the e·leineilt·iry 1
`c 1arge (1.60 x IO- 9
`1
`..
`'
`,
`.
`coulombs), K 1s the Debye-Huckel parameter it is th
`. 1·
`,
`.
`e r,1t 1us of a sphenc·il
`.
`'
`·
`.
`.
`particle, and }(Ka) 1s Henry's function. The Debye-'I'" k I
`'
`r uc e parameter ( K)
`.
`.
`.
`which describes the distance (in units or inverse Ien ti )
`.
`·
`'
`, ,
`.. ,
`g 1 across which two
`,
`.
`.
`,
`·
`charged pa1 t1clcs can interact, 1s a I unction of th,
`I· . ·
`·
`(/) of the buffer:
`e mo ,ll iomc strength
`
`K
`
`(8)
`
`h
`·
`where e is the solution dielectric const·mt ,, 1·s tl1c elect·
`I 011IC C arnc. T is
`,
`'
`'"
`'
`·
`temperature, kn 1s Boltzmann's constant