Memory in receptor–ligand-mediated cell adhesion
Veronika I. Zarnitsyna*, Jun Huang*, Fang Zhang*, Yuan-Hung Chien
, Deborah Leckband, and Cheng Zhu*,
,
*Coulter Department of Biomedical Engineering and Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0363; and Departments of Chemistry and Chemical and Biomolecular Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801
Edited by Michael L. Dustin, Skirball Institute of Biomolecular Medicine, New York, NY, and accepted by the Editorial Board September 7, 2007 (received for review May 22, 2007)
Single-molecule biomechanical measurements, such as the force to unfold a protein domain or the lifetime of a receptor–ligand bond, are inherently stochastic, thereby requiring a large number of data for statistical analysis. Sequentially repeated tests are generally used to obtain a data ensemble, implicitly assuming that the test sequence consists of independent and identically distributed (i.i.d.) random variables, i.e., a Bernoulli sequence. We tested this assumption by using data from the micropipette adhesion frequency assay that generates sequences of two random outcomes: adhesion and no adhesion. Analysis of distributions of consecutive adhesion events revealed violation of the i.i.d. assumption, depending on the receptor–ligand systems studied. These include Markov sequences with positive (T cell receptor interacting with antigen peptide bound to a major histocompatibility complex) or negative (homotypic interaction between C-cadherins) feedbacks, where adhesion probability in the next test was increased or decreased, respectively, by adhesion in the immediate past test. These molecular interactions mediate cell adhesion and cell signaling. The ability to "remember" the previous adhesion event may represent a mechanism by which the cell regulates adhesion and signaling.
adhesion frequency assay | Markov sequence | single-molecule mechanics | Bernoulli sequence 1). These experiments employ ultrasensitive force techniques, for example, atomic force microscopy (2) and the biomembrane force probe technique (3), to mechanically characterize a single molecule that physically links the force sensor to a sample surface.
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Biomechanical studies of protein, DNA, and RNA at the level of single molecules provide insights that complement information obtained from conventional measurements on ensembles of large numbers of molecules (Fig. 1[and supporting information (SI) Movie 1] illustrate a simple experiment: the micropipette adhesion frequency assay (4). A human red blood cell (RBC) pressurized by micropipette aspiration is used as an adhesion sensor to test interactions between ligands coated on the RBC membrane and receptors expressed on a second cell (Fig. 1A). The receptor-expressing cell is put into contact with the RBC for a given duration (Fig. 1B) and then retracted. If adhesion results, retraction will stretch the RBC (Fig. 1C), otherwise the RBC will smoothly return to its initial shape (Fig. 1D). When adhesion does occur, additional quantities can be measured by using the RBC picoforce transducer or any other ultrasensitive force technique, including rupture force (3), adhesion lifetime (2), molecular elasticity (5), protein unfolding (6), and protein refolding (7).
Single-molecule biomechanical measurements are inherently stochastic because molecular events (e.g., unfolding of a protein domain or unbinding of a receptor–ligand bond) are determined not only by the weak, noncovalent interactions (within a single molecule or between two interacting molecules) but also by thermal excitations from the environment. In a given adhesion test, both positive (adhesion, scored 1) and negative (no adhesion, scored 0) outcomes are possible. When adhesion occurs, its rupture force or lifetime can be any positive value. Estimation of the adhesion probability requires averaging a large number of adhesion scores (
4), and estimation of the probability distribution of single-bond rupture forces or lifetimes requires histogram analysis of a large number of measurements (
2,
3). Experimentally, these data are obtained by sequentially repeating the measurement many times, yielding a sequence of random numbers (e.g., random sequences of 0s and 1s from the micropipette adhesion frequency assay).
A crucial assumption that allows probability to be calculated by using measurements from sequentially repeated tests is that all measurements are identical yet independent from each other, i.e., the "independent and identically distributed" (i.i.d.) assumption. However, no analysis had been done to test this assumption in single-molecule biomechanical experiments.
Various statistical tests could be used to test the i.i.d. assumption. Probability plots can be employed to visually determine whether data are from Bernoulli sequences, an approach that can be subjective (8). Another widely used procedure employs a 
2 statistic of empirical transitional probabilities to test serial independence (9). Here we develop a model for size distribution of the consecutive adhesion events expected for a one-step Markov process. Fitting the model to experimental data allows us to quantify the magnitude and direction of deviation from the i.i.d. assumption in terms of a "memory" index. Here, memory represents the ability of the system to remember the result of the previous test, as evidenced by a change in the likelihood of the outcome in the subsequent test. We found that nature has provided examples for all three theoretically possible scenarios: no memory, positive memory, and negative memory.
Adhesion between K562 cells transfected with lymphocyte function-associated antigen 1 (LFA-1) and RBCs reconstituted with intercellular adhesion molecule 1 (ICAM-1) (10) exhibited the behavior describable by Bernoulli sequences, with no memory. LFA-1/ICAM-1 interaction mediates the adhesion and migration of leukocytes during an inflammatory reaction (11), as well as their formation of immunological synapses with other cells (12).
Markov sequences with positive feedback (adhesion probability increased by adhesion in the immediate past) were observed in adhesion between T lymphocytes expressing T cell receptor (TCR) and RBCs coated with an antigen peptide bound to a major histocompatibility molecule (pMHC). TCR/pMHC interaction is of central importance to adaptive immunity because it determines how T cells discriminate between different pMHC ligands and transduce distinct signals for various downstream effector functions (13).
Markov sequences with negative feedback (adhesion probability decreased by adhesion in the immediate past) were observed in homotypic adhesions between CHO cells transfected with C-cadherin and RBCs coated with C-cadherin. C-cadherin mediates adhesion between Xenopus laevis blastomeres and plays an essential role in the maintenance of embryo integrity (14) and in morphogenetic cell movements (15).
These three molecular interactions mediate cell adhesion and cell signaling. Memory in cell signaling has been reported, e.g., phosphorylation of receptors could modulate their affinity, leading to sensitization or desensitization of cells to soluble hormone ligands (16). However, the memory in cell adhesion reported here may represent a mechanism by which the cell regulates adhesion and signaling.
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