2.79J/3.96J/20.441J/HST.552J Biological Specificity and Cooperativity (From chance to necessity) 1. Adsorption of ligands on most biomaterials surfaces as a random process. Non-interacting sites. (a) Stochastic independence. Outcome of n th trial does not depend on outcome of (n −1)st trial. If Prob. of event = ()and Prob. of event B = () , then Prob. of event APA PB “first A and then B ” is PAB(). PAB ( ) () () × PB if trials are stochastically independent. = PA (b) Independent trials. With two outcomes only: Bernoulli trials. pq1. If+=probabilities remain constant throughout trials, then for a given sequence of heads () and tails ():H T P HHTHT TTH ⋅ ( ⋅⋅⋅ )= ppqpq ⋅⋅qqp . Stochastic independence of successive trials. Casino example: Does Nature have memory? (c) Random walks of different kinds: The 0.5-power rule. 1 11 Kinetic theory of gases: ()=(kT / m)υ22 2; υ∝ T2. 1 11 x22 2 Diffusion: ()=(2Dt )2; x ∝ T . 11 1 Unstretched macromolecule: ()r =( ) r ∝ N22 Nl 2 2; 2. Ligand adsorption onto n identical noninteracting sites of protein molecule: nk A []v = moles bound ligand ÷moles total protein = 1+ kA[].2 2.79J/3.96J/20.441J/HST552J 2. Adsorption on interacting sites. (a) Loss of randomness during various physiochemical or biological processes. Compress a gas. Impose a concentration gradient. Stretch a macromolecule. Adsorb ligand onto protein. Interacting sites. nk A []n v = moles bound ligand ÷moles total protein = n . 1+ kA[] (b) Sigma-shaped curves. Oxygenation of hemoglobin. (c) Micelle formation. Cell membrane formation. (d) How large need n be to achieve cooperativity? Myoglobin vs. hemoglobin. 3. Cooperative processes. (a) Outcome of n th trial depends on outcome of (n −1)st trial. (b) How to choose between a car and a goat. (c) Enzyme-substrate interaction. (d) ECM protein –cell receptor interaction. (e) Reversible melting of quaternary structure of collagen. (f) Simple one-dimensional statistical model of a critical transition as a cooperative process (See below #5). Nearest-neighbor interactions are sufficient for an “all or none” transition provided that the energy cost of the hybrid state is high enough and the sequence is long enough. The classical “lock-and-key” fit is not necessary. (g) A thermodynamic representation of a helix-coil transition: Gibbs free energy and the first-order transition. 4. The unit cell process: Inside and outside the control volume dV . (a) Regulators diffuse into and out of control volume dV . (b) Cell-matrix interaction inside dV is a cooperative process. Another way of putting it: the cell-matrix interaction is biologically specific. 23 2.79J/3.96J/20.441J/HST552J 5. A model of a critical transition from noncooperative to cooperative cell behavior. What is cooperativity in cell biology? Cells cooperate, i.e., communicate with each other and acquire a common phenotype, following formation of condensed states of biological matter. States of this type comprise cells, usually embedded in matrix, that are arranged in close proximity with each other and frequently function as a single unit. Examples of such organized cell structures are contractile cell capsules surrounding tissues in wounded organs, columns of Schwann cells, and cords formed by epithelial cells during skin synthesis. An example of a cooperative functioning unit is the contractile cell capsule that surrounds skin wounds and nerve wounds during spontaneous healing. Cooperative activity can be disrupted by scaffolds with specific biological activity, occasionally resulting in tissue and organ regeneration. How do cells cooperate? Cells cooperate by sending to and receiving signals from other cells that lead to a change in phenotype that eventually leads to similarity in behavior. Signals are typically macromolecules, such as growth factors and cytokines of various types. Cell A sends a signal to a cell B in its vicinity by secreting several macromolecules M that travel by diffusion away from cell A, eventually binding on receptors on cell B. After binding on receptors on cell A these macromolecular signals may modify the phenotype of cell B, which now behaves like cell A. The intensity of communication can be described by I, the rate of binding of macromolecular signals on receptors of cell B. The quantity I is the flux rate of signals transferred to B, i.e., the flux rate of signals that were actually received by B. It may not be possible to detect the cell that has sent out the cells but it is always possible, in principle, to measure the signals that have been received by a cell. The flux rate of signals received can be measured as the number of macromolecules that have become bound per unit surface area of cell B following a defined exposure to cells that emit such macromolecules. Although intensity of communication is required, it does no suffice for cooperative behavior since cells must also modify their phenotype, acquiring a common phenotype that characterizes the entire assembly of cells. Cells that do not cooperate at all are referred to as noncooperative (“isolated”). Noncooperative cells show an intrinsic behavior that is not affected by the presence of other cells in culture or in a tissue site. An operational definition of an isolated cell is the indifference of its behavior to changing levels of cell density in the system. These cells have maintained their original phenotype either because the intensity of communication with neighboring cells was insufficient for conversion to the cooperative phenotype or because conversion was blocked by a sufficiently high conversion energy. Critical transition. The behavior of cooperating cells differs markedly from that of isolated cells. When the cell density, or other parameters that are currently under study, a key experimental parameter, is increased above a threshold, cell behavior undergoes a sharp change. An example is the mechanical force exerted by cells on matrix. Below the density threshold cells apply forces that are independent of cell density and are only characteristic of cell type (and other parameters, such as medium composition). Such behavior is characteristic of point sources of mechanical force that act as if they were 34 2.79J/3.96J/20.441J/HST552J stochastically independent. In contrast, above the threshold, the cells apply their individual forces in unison, developing macroscopic tractions that are