Response to shape emerges in a complex biochemical network and its simple chemical analogue.

Although biology is governed by underlying chemical processes, equations of chemical kinetics do not directly predict many properties that emerge in living systems. For example, cells and organisms can detect and respond to the shape of objects, as observed in endothelial cell attachment to patterned islands, selective phagocytosis in neutrophils, and insect recognition of shape, such as the outline of flowers. Response to shape in these systems probably occurs at a high level of organization (cytoskeleton or neural networks) with no immediate connection to the underlying chemistry. This leaves one to wonder, what level of chemical complexity does the emergence of unanticipated functions require? Is this emergence unique to living organisms or can it occur in more simple chemical systems and be explained by chemical principles? Herein, we show that response to shape can emerge at the level of a biochemical network. We relied on a previously developed mechanism and an experimental system to examine initiation of coagulation of human blood plasma in vitro. We found that this biochemical network responded to shape, that is, the shape of the patch of stimulus controlled whether clotting was initiated. To characterize the response of initiation of the blood clotting cascade (initiation) to the shape of a patch presenting a stimulus of clotting, we detected clotting by monitoring both the formation of fibrin and the formation of thrombin. Fibrin was detected by using brightfield microscopy, and thrombin was detected by using fluorescence microscopy to visualize a blue fluorogenic substrate (Figure 1a). Surface patches of tissue factor (TF), an integral membrane protein that stimulates initiation, were patterned by using photolithography. TF was reconstituted in phospholipid bilayers containing 0.5 mol% of lipid labeled with a red fluorescent dye. We presented various shapes of the TF patches to human blood plasma in a microfluidic chamber. When comparing patches of different shapes, the area of all patches (and therefore the amount of TF) was kept constant (3.14 7 10 mm). When human blood plasma was exposed to patches containing TF, initiation only occurred on specific shapes. Initiation occurred on circular patches above a critical size, which is consistent with previous results. Initiation on other shapes showed a fascinating trend. Wide rectangles, such as a square (aspect ratio= 1:1), initiated in less than four minutes, whereas narrow rectangles (aspect ratio 16:1) did not initiate within 48 minutes (Figure 1b,c). From these experiments, it appeared that there is a critical rectangle width necessary to cause initiation ( 90 mm for the experiments described above). Interestingly, star-shaped patches were on the border for initiation and initiated in only half of the experiments (7 out of 14). These results imply that the shape of vascular damage, and its orientation relative to the direction of blood flow, may be important in determining whether clotting occurs. Additional work in vitro and in vivo is required to establish whether these implications are valid. To examine the mechanism behind this response to shape, we used a 3D numerical simulation that considered a simplified reaction–diffusion system. We previously showed that some properties of hemostasis could be explained by a simple modular mechanism. In those studies, initiation of clotting displayed a threshold response to the concentration Figure 1. The initiation of clotting of human blood plasma responded to the shape of surface patches of identical area and the amount of a clotting stimulus, TF. a) Side-view drawing showing clotting (blue) on a patch (red) of phospholipid bilayer containing TF. b) Chart quantifying the initiation times of human blood plasma on rectangular patches of varying aspect ratio, measured in triplicate. c) Time-lapse fluorescent micrographs (top view) showing clotting on circular and squareshaped patches but not on narrow-rectangular and star-shaped patches of the same area. All scale bars are 150 mm.