BioSystems 59 2001 35 – 51
A single-fractal analysis of cellular analyte – receptor binding kinetics utilizing biosensors
Anand Ramakrishnan, Ajit Sadana
Chemical Engineering Department, Uni6ersity of Mississippi,
134
Anderson Hall, Mississippi, MS
38677
-
9740
, USA Received 18 January 2000; received in revised form 16 October 2000; accepted 30 October 2000
Abstract
A fractal analysis of a confirmative nature only is presented for cellular analyte – receptor binding kinetics utilizing biosensors. Data taken from the literature can be modeled by using a single-fractal analysis. Relationships are
presented for the binding rate coefficient as a function of the fractal dimension and for the analyte concentration in solution. In general, the binding rate coefficient is rather sensitive to the degree of heterogeneity that exists on the
biosensor surface. It is of interest to note that examples are presented where the binding coefficient, k exhibits an increase as the fractal dimension D
f
or the degree of heterogeneity increases on the surface. The predictive relationships presented provide further physical insights into the binding reactions occurring on the surface. These
should assist in understanding the cellular binding reaction occurring on surfaces, even though the analysis presented is for the cases where the cellular ‘receptor’ is actually immobilized on a biosensor or other surface. The analysis
suggests possible modulations of cell surfaces in desired directions to help manipulate the binding rate coefficient or affinity. In general, the technique presented is applicable for the most part to other reactions occurring on different
types of biosensor or other surfaces. © 2001 Elsevier Science Ireland Ltd. All rights reserved.
Keywords
:
Cellular analyte – receptor binding; Fractals; Biosensors; Binding rate coefficient www.elsevier.comlocatebiosystems
1. Introduction
Sensitive detection systems or sensors are re- quired to distinguish a wide range of substances.
Sensors find application in the areas of biotech- nology, physics, chemistry, medicine, aviation,
oceanography and environmental control. These sensors or biosensors can be used to monitor
analyte – receptor reactions in real time Myszka et al., 1997. The importance of providing a better
understanding of the mode of operation of biosensors to improve their sensitivity, stability
and specificity has been emphasized Scheller et al., 1991. A particular advantage of this method
is that no reactant labeling is required. However, for the binding interaction to occur, one of the
components has to be bound or immobilized on a solid surface. This solid surface may, for example,
be a biosensor or cell surface. This often leads to mass
transfer limitations
and subsequent
complexities.
Corresponding author. Tel.fax: + 1-601-232-7023. E-mail address
:
cmsadanaolemiss.edu A. Sadana. 0303-264701 - see front matter © 2001 Elsevier Science Ireland Ltd. All rights reserved.
PII: S 0 3 0 3 - 2 6 4 7 0 0 0 0 1 4 2 - 8
Weiping et al. 1999 have very recently indi- cated that the assembly and architecture of
molecules at an interface will significantly influ- ence the reactions at the surfaces of biosensors
and other biomaterials. The solid-phase im- munoassay technique represents a convenient
method for the separation andor detection of reactants e.g., antigen in a solution because the
binding of antigen to an antibody-coated surface or vice versa is sensed directly and rapidly.
There is a need to characterize the reactions oc- curring at the biosensor surface as well as other
receptor-coated surfaces such as cell surfaces in the presence of diffusional limitations that are
inevitably present in these types of systems. It is our intention to further develop the knowledge on
analyte – receptor binding kinetics for biosensor applications, and to extend and apply it to
provide insights into cellular analyte – receptor re- actions. Some examples where analyte – receptor
reactions
are analyzed
by biosensors
are presented.
van Cott et al. 1994 emphasize that there is a critical need to develop serologic tools predictive
of antibody function. This applies both to in vitro as well as to in vivo studies. For example, these
authors emphasize that antibodies directed to- wards the V3 loop of the envelope glycoprotein
gp 20 of HIV-1 is of importance due to its preva- lence in natural infection and its ability to neutral-
ize HIV-1 in vitro. Thus, these authors utilized surface plasmon resonance and biosensor technol-
ogy to analyze the binding and dissociation kinet- ics of V3-specific antibodies with biosensor matrix
immobilized recombinant-gp 120. They emphasize that biosensor immobilized V3 peptides were
found to mimic their conformational structure in solution.
Alphaviruses pose a significant threat to human health and cause a wide variety of diseases, such
as arthralgia, myalgia, and encephalitis Brynes and Griffin, 1998. These authors emphasize that
a better understanding of the cellular receptors used by the alphaviruses would provide a clearer
insight into the pathogenesis of these viruses, besides leading to the design of effective ‘live-at-
tenuated’ vaccines against them. The binding of Sindbis virus to cell surface heparan sulfate im-
mobilized on a biosensor surface was analyzed. They indicate that glycosaminoglycan heparan
sulfate participates in the binding of Sindbis virus to cells. In its absence, the binding of virus to the
cell is diminished, though it still does occur.
The influence of a synthetic peptide adhesion epitope as an antimicrobial agent has been ana-
lyzed recently using a biosensor Kelly et al., 1999. These authors indicate that an early step in
microbial infection is the adherence of binding of specific microbial adhesins to the mucosa of dif-
ferent tracts, such as oro-intestinal, nasorespira- tory,
or genitourinary.
Utilizing a
surface plasmon resonance biosensor they attempted to
inhibit the binding of cell surface adhesin of Streptococcus mutans to salivary receptors in
vitro. They utilized a synthetic peptide, p1025, which corresponded to residues 1025 – 1044 of the
adhesin. The two residues Q1025 and E1037 that contributed to the binding were identified by site-
directed mutagenesis. They indicate that this tech- nique of utilizing peptide inhibitors of adhesion
may be utilized to control other microorganisms in which adhesins are involved.
Though in the analysis to be presented, we will emphasize cellular reactions occurring on biosen-
sor surfaces, the analysis is in general applicable to ligand – receptor and analyte – receptorless sys-
tems for biosensor and other applications. Exter- nal diffusional limitations play a role in the
analysis of immunodiagnostic assays Giaver, 1976; Bluestein et al., 1987; Eddowes, 1987, 1988;
Place et al., 1991; Glaser, 1993; Fischer et al., 1994. The influence of diffusion in such systems
has been analyzed to some extent Stenberg and Nygren, 1982; Nygren and Stenberg, 1985; Sten-
berg et al., 1986; Place et al., 1991; Sadana and Sii, 1992; Sadana and Beelaram, 1994, 1995.
Kopelman 1988 indicates that surface diffu- sion-controlled reactions that occur on clusters or
islands are expected to exhibit anomalous and fractal-like kinetics. These kinetics exhibit anoma-
lous reaction orders and time-dependent e.g., binding rate coefficients. Fractals are disordered
systems and the disorder is described by non-inte- gral dimensions Pfeifer and Obert, 1989. These
authors further indicate that as long as surface irregularities show scale invariance that is dilata-
tional symmetry they can be characterized by a single number, the fractal dimension. This means
that the surface exhibits self-similarity over cer- tain length scales. In other words, the structure
exhibited at the scale of the basic building blocks is reproduced at the level of larger and larger
conglomerates. The fractal dimension is a global property and is insensitive to structural or mor-
phological details Pajkossy and Nyikos, 1989; Markel et al., 1991. These authors indicate that
fractals are scale self-similar mathematical objects that possess non-trivial geometrical properties.
Furthermore, these authors indicate that rough surfaces, disordered layers on surfaces, and
porous objects all possess fractal structure.
A consequence of the fractal nature is a power- law dependence of a correlation function in our
case the analyte – receptor on the cell or biosensor surface on a coordinate e.g., time. Rizhalla et
al. 1999 have recently analyzed the influence of the fractal character of model substances on their
reactivity at solid – liquid interfaces. These authors emphasize that surface characteristics and com-
plexity significantly determine and control the het- erogeneous
reactions at
interfaces. They
emphasize that fractal systems accommodate structure within structure. They occupy more
space than ordered systems. In effect, the fractal dimension is a measure of the space-filling ability
of a system. It is worth mentioning that fractal growth phenomena are prevalent in natural sys-
tems Viscek, 1989, and the build-up of the ana- lyte – receptor complex on a biosensor cellular
surface is an example of this process.
We present in this paper a fractal analysis of the binding of an analyte in solution to a cellular
receptor immobilized on biosensor and other sur- faces. The emphasis is to promote the understand-
ing of cell-surface reactions. The fractal approach is not new and has been used previously in the
studies of immunosensors and phenomena in membranes Tam and Tremblay, 1993. This is an
early attempt at a more extended application of fractal analysis to the investigation of analyte – re-
ceptor binding kinetics for biosensors with the eventual goal of providing a better understanding
of these reactions on cell surfaces. Similarities with immunoassay kinetics are also discussed
whenever appropriate. Our analysis is performed on data available in the literature. The fractal
analysis is one way by which one may elucidate the time-dependent binding rate coefficients and
the heterogeneity that exists on the biosensor or cell surface.
2. Theory
