Toward Novel Polymer-Based Materials Inspired in Blood Clotting

Perspective pubs.acs.org/Macromolecules

Toward Novel Polymer-Based Materials Inspired in Blood Clotting Alfredo Alexander-Katz* Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Mass. Ave., Room 12-009, Cambridge, Massachusetts 02139, United States ABSTRACT: Blood clotting provides a beautiful playground to explore polymerbased materials used in natural self-healing scaffolds with applications in multiple highly sought-after areas that include rheological modifiers, self-healing materials, and targeted drug delivery. In this Perspective we present an overview of blood clotting with particular emphasis on the dynamics of biopolymers involved during the first stages of the clotting cascade. We cover from single molecule dynamics in multiple types of flows to complete plug assembly. Different interaction models between monomers and between monomers and platelets/colloids are considered. The many-body polymer and colloid dynamics during the assembly of blood-clotting scaffolds is discussed in detail. Throughout this Perspective insights and connections between the natural system and synthetic systems are highlighted. We finalize by presenting a list of emerging areas inspired by the clotting process. These emerging areas not only present new and interesting scientific challenges but also offer the possibility of controlling and tailoring the properties of polymer systems in novel ways.

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elasticity7,8 all the way to the assembly of amyloid fibrils.9,10 As will be clear toward the end of this work, polymers with VWFlike characteristics already exist, yet their properties in the context that we will describe here have not been tested or exploited. As usual, most of the developments in this area have occurred in response to experimental observations that have defied our current understanding of such systems. This has forced us and others working in this field to rethink how such processes can be possible, and we will highlight throughout this Perspective how new properties in the field of polymer dynamics and assembly have emerged while trying to reconcile such behaviors. In particular, we have gained a much better understanding of how one can exploit external flows to “tilt” energy landscapes and induce stationary behavior not present in equilibrium. However, other ingredients are necessary such as kinetic barriers that dictate the time scale for relaxation as well as a competition between the imposed (actuation) rates and the internal relaxation rates. One example where such competition leads to dramatic effects is that of the large nonmonotonic response of self-associating polymers in shear flow. In this system the polymers stretch out at low to moderate amounts of shear, but as the shear increases beyond a “threshold rate”, the system no longer can react and on average starts decreasing in size by as much as 50% compared to the maximum size. At very high shear stresses, however, the system starts unraveling again since the forces are enough to overcome the potential energy barriers. Interestingly, such behavior is tunable and could be employed in many different contexts where a particular response is needed.

INTRODUCTION The dynamics of polymers in solution has very important implications in current technologies such as rheology modifiers, drag reducing agents, electrophoresis, etc. On the biological side, Nature has also utilized polymers and developed systems that display remarkable dynamical properties, as for example the cytoskeleton and muscles. Much work has gone into understanding how these biological systems work and also how to mimic them using synthetic routes.2−4 In this Perspective we wish to introduce a novel polymer-based system used by our body to create plugs that stop bleeding. The (bio)polymer that is at the core of this blood plugging process is called the Von Willebrand factor (or VWF for short), and this macromolecule is interesting not only from the standpoint of self-healing but also because it possesses other highly sought-after properties. In particular, VWF displays three properties that today are highly desirable in synthetic systems: (i) VWF can be activated on demand through a combination of chemistry and mechanics (flow), (ii) it can form reversible self-healing polymer−colloid aggregates with tailored mechanical and chemical properties, and (iii) it dramatically increases the lifetime of a hydrophobic “drug” and delivers it when and where it is needed, which in this case is the injured area. The origins of such rich and interesting behavior from a single molecule are currently being intensely explored due to its implications in medicine and technology. In this Perspective, however, we would like to explore the properties of this system from a conceptual standpoint where “system specifics” are not considered. We do this with the intent of highlighting the important ingredients that enable the wide range of functionalities exhibited by VWF and associated systems with the hope to provide a perspective on how to design synthetic polymers and soft materials that could display at least some of the properties of the naturally occurring ones. We must note that similar approaches have been used in the past with great success as in the case of DNA © 2014 American Chemical Society

Received: April 16, 2013 Revised: December 24, 2013 Published: February 19, 2014 1503

dx.doi.org/10.1021/ma4007768 | Macromolecules 2014, 47, 1503−1513

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Figure 1. Sketch of the stages of blood clotting (see text for details). The different stages have been assigned arbitrarily. The biochemical reaction network that includes proteins such as thrombin has been omitted for clarity, yet such reactions are crucial during blood clotting and work in unison with the mechanistic model described above.

present, chemical and mechanical cues activate it to become perhaps the stickiest molecule in our body, adhering rapidly to the injured substrate as well as platelets. This activation is the start of the clotting cascade.11−14 Before we can start discussing the details of the activation of VWF and the new concepts that have emerged from trying to understand its underpinnings, it is instructive to present in a very simplified form the stages of the clotting cascade at elevated flow rates (see Figure 1): • Stage 1. A normal blood vessel has an intact lining of epithelial cells, and all of the blood constituents including proteins, red blood cells, platelets, and white blood cells flow normally. • Stage 2. A lesion occurs in the vessel wall due to mechanical stresses or simply due to cell death. Note that small vessels, particularly arterioles and capillaries, are always getting injured due to constant mechanical stresses that we are exposed to. Probably everyone has already seen what happens when one hits a hard object; a dark spot appears that is indicative of blood. During the breakage of the vessels, collagen gets exposed; VWF activates due to a complicity of chemical and mechanical forces and starts to cover the exposed collagen. The activation of VWF is essentially an unraveling of the biopolymer exposing a large number of binding sites at once. • Stage 3. Concurrently with the activation and adhesion of VWF to the injured vessel area, platelets start to agglomerate at the site of lesion due to VWF-mediated platelet−platelet attraction. The polymer−platelet physically cross-linked composite that is formed at the site of lesion is known as the plug. This plug seals the leak but is not stable over large periods of time due to VWF degradation. • Stage 4. While the first stages of clotting occur in seconds, the final stage of the clotting process occurs in

While today we know much more how polymers mediate the process of plugging our arteries in regions of high shear stresses, we are still far from having of a complete understanding of this process. Progress in this area truly needs an interdisciplinary approach since it involves working at the interface of biology, medicine, chemistry, materials, and physics. However, we believe that taking such an endeavor is worthwhile as new polymer chemistry and polymer physics concepts are still to be uncovered for this system that can lead to novel polymer systems that have nothing to do with blood clotting but that take advantage of some of its characteristics. Below we will show how this has been the case for most of the theoretical developments, and it is starting to be the case in experimental realizations related to this area. This Perspective is organized as pedagogical as possible trying to introduce the most important concepts toward the beginning and discuss key results afterward. It is by no means a comprehensive review of every work in this area, but rather a summary of what we believe are the most important and interesting results. At the end we present our concluding remarks and an outlook on the future of this field and how it ties to other areas in polymer research.

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THE BLOOD CLOTTING CASCADE AND VON WILLEBRAND FACTOR Our body relies on rather complicated polymers (i.e., proteins) to perform essentially all its functions. The behavior and function of proteins are still far from being completely understood, although we have a good sense in some cases how they fold and work. In the case of blood clotting at elevated shear rates, there exists a protein called the von Willebrand factor that resembles a “complex homopolymer” in the sense that it is a repetitive sequence that can contain as many as a hundred “effective monomers”. VWF is a stimuliresponsive glue, meaning that in its quiescent state the macromolecule is nonsticky and soluble, but when a lesion is 1504


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the absence of VWF activity due to mutations or small overall polymer sizes (fewer than 10 repeat units in the VWF biopolymer). We refer the reader to clinical reviews and references therein for more information on the medical aspects of VWF.24,25 So what makes VWF a “magical” macromolecule? The answer we believe is in its structure, depicted in Figure 2. VWF

minutes. It consists of polymerizing in situ a more stable permanently cross-linked network of fibrin strands. The polymerization proceeds from the monomer fibrinogen and several clotting factors such as thrombin and Factor VIII are necessary in this process. While this stage does not involve VWF directly, it does indirectly. The reason is that VWF carries Factor VIII, a hydrophobic factor that is reversibly linked to one of the domains in VWF. When the polymer is stretched and adheres to the vessel wall and platelets, it releases this factor which is one of the catalysts for the conversion of fibrinogen to fibrin fibers through a complicated biochemical cascade of events called the clotting cascade.12,15 The reader is referred to these classical works if interested in the more biochemical aspects of the clotting process. The particular breakup of the stages as described above is arbitrary, but we have chosen it because it directly corresponds to three highly sought-after properties in polymeric systems, namely (i) during stage 2 the VWF polymer is activated on demand using a combination of flow and chemistry, (ii) during stage 3 VWF is capable of forming self-healing aggregates with presumably tailored mechanical and chemical properties, and (iii) VWF delivers on-site a hydrophobic factor, performing what we call targeted catalyst/drug delivery. It is very important to understand that in conjunction with these stages there are about 80 biochemical reactions occurring in parallel. Such reactions are important not only for the production of the final stable clot but also for our discussion in the sense that they might alter the local pH or chemical nature of VWF by dressing or undressing the polymer. As will be shown later, if the associating units of VWF are strongly pH dependent, then a slight modification of pH may lead to very different activation energies for unfolding, and this together with increased flow rates due to the lesion can trigger the activation of VWF. As the reader might be thinking, if WVF can be activated by mechanical stresses and these vary widely in our circulatory system, then how is it preventable for VWF to not unfold in some parts of the blood vessel system with elevated stresses? The answer is that these unfolding events are rare but do happen. In fact, that is the origin of a disease called thombotic thombocytopenic purpura (TTP).16,17 In this disease a protein of the metalloprotease family called ADAMTS 13 which is in charge of degrading VWF is not present or does not work properly. When this happens, VWF starts sequestering platelets into small aggregates. In order to do so, VWF must stretch, which provides a direct evidence that VWF unravels even in the absence of a lesion. This perhaps is not occurring often, but with sufficient frequency such that most platelets become part of microaggregates and are not available when needed. Thus, a person with this disease will bleed very heavily from the small vessels and eventually can have organ failures or a stroke. It is interesting to note that VWF does not degrade when it is not activated. The reason for this is that the cleavage site where ADAMTS 13 cuts the polymer is cryptic, meaning it is hidden inside one of the domains and is only exposed when the polymer unfolds which coincides with the unfolding of the A2 domain.18−21 Thus, VWF is a protein that simultaneously activates and sends an autodestruction signal. The other side of Von Willebrand malfunction is referred to as Von Willebrand disease (VWD), which is the most common hereditary vascular disease and 1−2% of the population has it.22,23 VWD is due to

Figure 2. Different lengths scales of VWF. At the coarsest length scale, VWF has the structure of a repeating sequence of 4100 amino acids; thus, it is a “complex homopolymer”. Within a single monomer there are approximately 15 domains contained, each with a particular function. At the finest level, each domain has a peculiar 3D structure dictated by the amino acid sequence. The function of most of the domains is to bind to different proteins and factors in the blood as well as to VWF itself. The most important domains that we will be referring to in this work are the A1 domain that binds platelets through the GP1bα receptor as well as collagen. The A3 domain binds collagen and is believed to be its own receptor as well.1 Finally, the D domains bind Factor VIII, which is one of the catalysts in the polymerization of fibrin from fibrinogen.

can be thought as a hierarchical polymer in the sense that it has multiple scales.26 On the largest scale this protein looks like a homopolymer since it consists of multiple repeats of a sequence of 4100 amino acids. This scale is associated with its function, since one needs VWF to be at least 10 repeat units long to be functional. If one inspects each of the repeating units more carefully, one finds that each of these units contains a sequence of about 15 “pearls” that correspond to folded domains. Each of these domains has a name and an associated function. For example, the A1 domain binds to the GP1bα receptor in the surface of platelets as well as to collagen, or the D3 domain binds to Factor VIII. A not complete list of the motifs to which each of the domains binds is described in Figure 2. At an even finer resolution one finds that each of the “pearls” has a tertiary structure, and we refer to this scale as the chemistry scale since it dictates the interactions of VWF with itself and with the environment. Something that we have not discussed here, but that is important in physiological conditions, is that VWF is heavily glycosylated through post-transcriptional modifications. The effect of this sugar “bottle brush” is still not understood to this day, but it is known that it is important for regulating its interaction with platelets and other cell types.26 Such bottlebrush polymers are well-known to polymer scientists, and their properties have been started to be understood systematically in solution and at interfaces.27−29 1505


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MODELS OF VON WILLEBRAND FACTOR

While VWF has a well-defined amino acid sequence, the massive length of each of its “monomers” consisting of 4100 amino acids makes it impossible to be studied at the amino acid level, specially if one is interested in studying long VWF concatemers with 20+ repeating units. Thus, one needs to construct effective models that can reproduce the behavior of VWF to a certain degree. In some sense, we are fortunate that this polymer has a repeating sequence, since this naturally leads us to coarsen the representation of the polymer to the coarsest level which would be a simple homopolymer with N repeat units. The question is, how do we incorporate the interactions occurring at the finer scales? Historically, there have been two ways of doing this. In a first attempt to elucidate the observed unfolding of VWF at high shear rates it was proposed that there was an effective attraction between the “monomers” that resulted in a collapsed state for the polymer.30−33 The particular effective potential was of course not known, so a simple Lennard-Jones potential was considered. The particular potential form is not so important in terms of qualitative behavior and might only be important for exact quantitative predictions. However, at this stage one would be happy if one can obtain the qualitative features. The reason why such a model was introduced was due to the large discrepancies between well-accepted unfolding shear rates for an equivalent DNA molecule of the same length as the experimentally observed VWF chains.31 The rational was that there were some attractive interactions between some VWF domains of either hydrophobic or specific nature, but that after integrating all the degrees of freedom associated with the configurations of the domains, one would end up with a smooth attractive potential. We refer to this model as the potential (of mean force) model (PM) of VWF (see Figure 3b). The other model is based on the fact that VWF has a multitude of domains that are either ligands or receptors for other VWF domains or some external motif. In that regards, the attraction between VWF monomers might not be well captured by a PM as described above that does not have energy barriers and whose interaction length scale is enormous compared to the domain size. Thus, a more palpable model where such ligand−receptor interactions can be explicitly included would be desired. Such a model was described recently for VWF.34,35 This model was originally devised for leukocyte rolling.36 The basic idea of the model is to replace all of the attractive interactions by effective reactions between two or more monomers in which a bond is stochastically formed (or not) depending on the probability of bond formation. The simplest model that describes such reactive model (RM) is the Bell model of ligand−receptor interactions.37,38 In such a model one needs to know a priori the energy landscape including the kinetic barriers for bond formation. Once this is known, it is possible to incorporate this into the model by allowing the formation of a bond (= a stiff spring constraint) between two monomers if they are within an interaction radius rrxn. The probability with which such bonds are formed is proportional to exp(−EB/kT), where EB corresponds to the height of the energy barrier from free to associated. Once the monomers are bound (with the creation of a spring linking them), the probability of unbinding is simply given by exp(−(EUB − f x)/ kT), where EUB is the barrier for unbinding, x is the distance to the transition point, and f is the applied tensile force on the

Figure 3. Coarse-grained representations of VWF: potential vs reactive models. (A) Schematic of two monomers (or beads) of the same chain connected by flexible linkers that represents the backbone of the chain. The relevant distances are denoted by R, σ, and rrxn, which correspond to the distance between the centers of both monomers, the radius of each of the monomers, and the reaction radius within which two monomers may bind, respectively. (B) The potential model depends only on the relative position between beads and is characterized by a single potential curve, e.g., a Lennard-Jones potential. (C) In the reactive model, the beads form a bond only when they are within the reaction radius of the other monomer, and the formation and breakage of the bond proceeds in a stochastic manner. (D) The probability to form a bond once the monomers are within rrxn is dictated by the energy landscape. In this particular case we use the simplest reaction model, the so-called Bell model, that contains a single barrier between the bound and unbound states. See text for more details.

bond. The proportionality constant can be incorporated into the attempt frequency. This model is depicted in Figure 3c,d. The reactive or self-associative model has the advantage that it is possible to coarse grain the molecule to different levels by simply considering more or less interactions. The other advantage is that it can be easily parametrized from experimental findings, especially if the rate constants are obtained from atomic force microscopy, laser tweezers, or some other analytical methods.39,40 Such a direct mapping is not possible in the PM model, although in principle the PM model as used up to now should be reproduced by a RM model with low barriers and a reaction radius similar to the extent of the potential.34 Both models have been very useful to understand different aspects of VWF behavior and have predicted novel polymer phenomena that was not conceived before and that has been experimentally confirmed in some cases very recently. For example, in the original work aiming to understand the 2 orders of magnitude discrepancy between DNA and VWF, it was found that the unraveling pathway in shear and elongational flow for a collapsed polymer compared to an ideal or selfavoiding chain is qualitatively different. In fact, in the former case it was shown that it is an activated process in which a small strand must fluctuate away from the globule to be stretched by the flow.30,32,33,41−43 Such strand fluctuations are thermally activated, and thus the unfolding does not proceed by any 1506


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classical mechanism of drop breakup or polymer elongation in flow. De Gennes pioneered the idea of having a first order transition in elongational flow due to hydrodynamic screening,44 but these new PM models predict this type of unfolding even for Rouse-type dynamics. Experimentally, there is strong evidence that the nucleation path predicted using the PM is correct from studying the unfolding of collapsed DNA by electric fields.45 In recent years our group has preferred to use the RM model, but other groups still use the PM model. At the end of the day, one has to choose a model that can describe as accurately as possible the particular behavior one is interested in understanding. Given the growth in computational capacity in recent years, one can start to think in more microscopic hybrid models in which the domains (or pearls) associated with each monomer can be distinguished.

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DYNAMICS OF VON WILLEBRAND FACTOR AND SELF-ASSOCIATING POLYMERS The dynamics of VWF has been studied experimentally31 and theoretically,5,30,32−34,41−43,46 and new behaviors have been found. In this section, instead of exhibiting all the different behaviors encountered, we would like to highlight the effect of shear flow on self-associating polymers, as is VWF, using the RM. In particular, we would like to show that having the monomers interact through ligand−receptor-like interactions introduces another time scale which competes with the unraveling time scale, yielding very counterintuitive results that could be useful in other systems such as for drag reducing agents. In particular, it was found that even for slightly collapsed polymers where the energy levels of the bound and unbound state are the same, yet they have a barrier in between, the polymer exhibits a giant nonmonotonic response to shear flow. The large nonmonotonicity is shown in Figure 4, where one can clearly see that the average extension of the polymers increases at first for low values of the dimensionless shear rate defined as γ̇τ, where τ is the monomer diffusive time scale τ = a2/D with a being the monomer size and D the monomer diffusion constant. At intermediate values the average size starts to reduce itself by margins as large as 50%. Such nonmonotonicity had been conjectured by de Gennes in a different context related to hydrodynamic interactions44 and had been originally observed by Netz and co-workers in PM systems.47 We have reproduced a curve using a Lennard-Jones potential (black trace and symbols) that corresponds to the RM conditions. As is evident, the nonmonotonicity is strongly amplified in the RM and can be almost completely suppressed at high enough values of the barrier.5 The origin of this nonmonotonicity is clearly not just of hydrodynamic origin. In fact, the origin can be traced back to the relaxation time of the polymer globule. For small values of the barrier the relaxation is controlled by an “effective solvent friction”,48−50 but as the height of the barrier is increased, the barrier starts to dominate and an exponential increase in relaxation times is observed.34 The long relaxation time scales compared to the unraveling attempt frequency from the flow leads to the large nonmonotonicity.5 The reason is in fact easy to understand. In order for the polymer to unfold, one must break essentially all the bonds in the chain within the time scale of unfolding. If the shear stress is not sufficiently large to tilt the binding energy landscape considerably, one is limited by the relaxation time scale of the bond itself. Once this time scale is long enough, the globule will be in a “stuck” conformation within an attempt

Figure 4. Control of the flow response through kinetic microscopic processes: the source for the large nonmonotonic response. (A) Fractional extension of self-associating single polymer in shear flow: simulations (symbols) and theory (continuous lines). The bound and unbound energy levels are equal. The barrier is denoted by EUB (which in this case is equal to EB). (B) Schematic of the two-state model that predicts the behavior observed in (A). The continuous lines in (A) are analytical solutions to this model using transition probabilities dictated by the bonds and the flow (see text for details). Reproduced with permission from ref 5. Copyright 2011 the American Physical Society.

cycle to unfurl the polymer (see Figure 4b). If a part of the chain was stretched, it will be wound again onto the globule due to the tumbling effect in shear. The attempt frequency to unfold as well as refold is dictated by the shear rate γ̇, so above a “critical” γ̇ the polymer will not be able to respond. Given that the system does not have memory, one is faced with the same probability of unfolding during each attempt, and thus the probability of unfolding diminishes rapidly as one increases the barrier. Notice that it is possible even to suppress the unraveling almost completely by increasing the barrier to large values. At high shear rates the stresses on the polymer are large enough to tilt the binding potentials and allow unfolding of the polymer regardless of the height of the barrier. While the first studies in this system have been conducted, there are still unanswered questions in terms of what role does the length of the polymer have in this system or if this process could occur as well in aggregates of these self-associating polymers, implying “physical gel” collapse above certain shear rates. Also, in an originally dispersed solution, it is not known if at low enough concentrations the effect of shear will drive the polymers to form a glob or will it disperse them. The shear flow case described previously is not as intuitive to understand as the elongational case. The logic behind the nonmonotonic response described above in shear is easily transferred to the case of self-associating polymers in elongational flow. In this case we do not expect the molecule to return to the collapsed state through the tumbling mechanism, but rather halt its extension for a period of time until the next set of bonds are ruptured. This process might be repeated multiple times, although one expects fewer of these events as the extension of the polymer is larger because the tension of the chain will increase quadratically with the 1507


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extension. This behavior is in fact observed in elongational flow, and it corresponds to stick−slip dynamics (see Figure 5).

enough compared to the unfolding of the chain, then the chain can unfold and form N bonds and become immobilized. This is a highly controversial area at the moment, yet there are strong indications that the mechanism proceeds by first forming a single or small fraction of bonds in the globular state, and then it unfolds, attaching firmly to the substrate.82 Thus, the polymer approaches the surface in “stealth” mode where it does not experience a lift force, and only when some bonds have been formed and the flow rate is high enough it stretches. The bonds are reversible, so if the flow is weak, only a few of them are formed and broken, rendering the polymer nonpermanently bound to the surface, just as in the case of VWF. This mechanism could potentially be quite useful in coatings, where flow could be used as a trigger to cover a surface. Other systems of strong interest for the general community are polymer−colloid composites because these systems can have desired transport, optical, or mechanical properties.83−85 In blood, such composites are formed at the sites of lesion. The polymer in this case is VWF, and the colloid is not a colloid per se, but a platelet. However, very recent work has shown that it is possible to replace the platelets with actual colloids, and the system keeps on working!6 As in the case of surface adsorption, the formation of these composites is rather counterintuitive because they are formed under strong nonequilibrium conditions and are reversible. This means that upon reducing the flow the composites disperse again. Such a phenomenon was not observed before, and it is quite counterintuitive. Normally one dissolves aggregates as the shear rates are increased, but the plug forms as you elevate flow rates. The origin of such behavior actually has to do with kinetics and not with thermodynamics. In fact, in quiescent conditions the system is happily dispersed. To understand the process, it is important to evaluate what are the important conditions under which such aggregates can form. Such conditions are general and do not apply only to blood. However, we believe Nature has optimized such an out-ofequilibrium assembly process. A set of sufficient conditions are: (i) there exist a polymermediated interaction between the platelets/colloids, (ii) the system is dispersed under quiescent conditions, and (iii) the lifetime of the bonds between polymer and colloids be longer than the average colloid−colloid collision rate as well as the colloid rotation time scale. Both of these time scales are dictated by the shear rate. The first condition relates to the fact that there needs to be a reversible polymer linker between the colloids. If the colloids are attracted to each other without the need of a bridging molecule, one faces diffusion-limited aggregation or reactionlimited aggregation.86−89 Both of these scenarios are not reversible and break upon the application of high flow rates. On the other hand, if one uses a “polymer bridge”, one can link two or more colloids with a bonding energy that scales with the degree of polymerization and can be tuned with the flow rate. To maintain the system from gelating in quiescent conditions, one has to use small concentrations and/or engineer the polymer to prefer itself when no flow is imposed. This is effectively achieved by using collapsed polymers. The second condition is trivial in the sense that it accounts to have reversibility to the dispersed state. The last condition is essentially the key to the aggregation phenomena. What it implies is that a polymer that binds to a colloid has to be bound longer than the time it takes for each colloid to collide with another colloid. This makes sense physically as there will be no

Figure 5. Schematic of the stick−slip unfolding dynamics of selfassociating polymers in elongational flows. The evolution of the stretched length of a globule is plotted. L0 and Lmax correspond to the compact and fully elongated size of the polymer, respectively. The inset shows the relevant flow geometry.

Combining the knowledge of solvophobically collapsed polymers with self-associating polymers, we believe that it is possible to precisely tailor the response of such polymers to shear or elongation as well as other types of deformation.51,52 The combination of both has not been explored yet, but it is expected to yield interesting results because of the competition between thermodynamic and kinetically regulated time scales that can be tuned independently. Also, the rheology of these systems remains essentially virgin. In the case of shear flow, one expects a shear thinning to thickening transition for dilute suspensions of these polymers, opening the door for more control on viscosity engineering of fluids.

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ADHESION OF VWF TO SURFACES AND COLLOIDS An emergent field of research is that of self-healing materials that either can heal themselves53−61 or can fix damaged regions.62,63 Blood performs with incredible accuracy the latter, and presumably the materials formed during the formation of the clot can heal themselves as well. The process of wound healing, however, starts by the adhesion of VWF to the exposed collagen and to platelets. Interestingly, the adhesion of VWF to these surfaces is highly counterintuitive. The reason is because VWF exhibits an increased potential for adhesion at high shear rates, while most common polymers detach from surfaces at high flow rates.64−66 The origin of the latter behavior in planar surfaces can be traced back to the strong lift force that stretched polymers experience near a wall.67−80 Thus, the fact that VWF is able to adhere under strong flowing conditions is intriguing in itself. We currently do not have a complete explanation for the single molecule adhesion to surfaces at elevated shear rates, yet some insights have emerged during the past year. By observing the scaling form of the lift force and the adhesive force, one can start to draw conclusions. The lift force scales with γ̇L4, where L is the stretched length of the polymer along the shearing axis (note that L is always less or equal than the contour length Lmax).81 The adhesion force scales with L. Thus, it is impossible to have the polymer bind to the substrate from the stretch state unless the polymer is not completely weakly stretched, and the adhesion force is large enough so that the prefactor makes adhesion preferable. In the limit in which the polymer is basically unstretched, the lift force is minimal and the polymer can bind, albeit it cannot form the N bonds at once. However, if the lifetime of one of these bonds is long 1508


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formed and then reduce the shear rate and monitor how the number of bonds decreases. As can be seen in Figure 7c, the process is highly reversible and can be switched on and off by raising or lowering the shear rate. The origin of the reversibility is due to stored mechanical and chemical energy. Polymers do not like to be stretched, and even less if they are globular to start with, so once the flow is lowered and there is no bias toward the stretched conformation, then the polymer can relax back to its original state and the aggregate dissolves. The reversibility seems to be maintained even for long polymers, as the relaxation time of the polymers only grows as N and is weakly dependent on the shear rate from the simulation results.93 While chains longer than 100 effective units have not been studied due to computational limitations in the size of the box, one expects to find a point where the chains are long enough so that the relaxation time of the system becomes very large and can be thought as an irreversible aggregation process. There are already indications that such an scenario is possible form simulating chains of up to 80 units.93 Another interesting recent observation is that the relaxation time of the polymers increases with shear rate, meaning that by injecting energy into the system, the system seems to “freeze”,93 reminiscent of a jamming transition. Both collapse and theta-polymers have been studied. In general, one finds that the aggregates formed can be classified as loose aggregates, compact aggregates, and log-rolling aggregates. Above a certain shear rate the aggregates start to break apart, and it might be an interesting way to regulate their size (see Figure 8). One of the most important results in the formation of such aggregates is that they are nearly universal in the sense that a dimensionless parameter allows us to collapse all the aggregation data into one curve. For aggregation in shear, the critical parameter that was mentioned above is the comparison of the collision and rotation time scale to the unbinding of a polymer monomer from the surface of the colloid. The unbinding follows a Bell-like probability, so the bond lifetime will be proportional to τUB ∼ e(EUB−fx)/kT, where EUB is the energy difference from the bound state to the barrier, f is the tension force being applied on the bond, x is the microscopic distance between the bound state and the barrier along the reaction coordinate, and kT is the thermal energy. If the distance to the barrier is very small compared to the size of the colloids and monomers, as is the case in VWF, the tension will not play a major role. The other time scale is the rotational/ collision time scale τrot ∼ 1/γ̇. The ratio between these two time scales determines if one will find an aggregate or not. In Figure 9 we show the effect of changing polymer size and the concentration of colloids on the size of the aggregate as a function of the dimensionless number introduced above. Note that the data collapses into a single curve. Thus, the role of concentration is not so important and can be thought as of second order. A simple calculation assuming no interactions and mean-field conditions would include a term proportional to the concentration in the collision frequency. Diffusion in this strongly driven scenario is irrelevant until one goes to extremely dilute conditions and low flow rates. The collapse of the data exhibits why it is so important to consider such kinetic mechanisms in this problem. These results are the first to show that such a process is possible, and some of them have been corroborated in experiments with reconstituted blood that does not contain platelets, but instead contains spherical silica colloids functionalized with VWF antigen to mimic platelets.6

composite if the linking polymers (on average) are bound to the colloids for much shorter times compared to the collisions between colloids because the probability of forming bridges between colloids will be strongly reduced. In shear, the rate of collisions is determined by the concentration and the shear rate. Once this rate is larger than that of polymer unbinding, an aggregate will form. The rotation of the colloids is also important since it winds the polymers onto its surface, increasing the number of bonds substantially. This process has two interesting outcomes in terms of the aggregates formed. First, it stabilizes the polymer on the surface, so it can last longer to form a bridge once another colloid is encountered. Second, once a bridge has been formed, the rotation serves as reinforcement since it further drives the winding of the polymer onto the colloids. We call this mechanism the bridge-and-stitch mechanism in polymer− colloid aggregation in flow, and it is depicted in Figure 6. Note that such mechanism is maximized in shear flow, and thus one does not expect to see the same mechanism in, for example, pure elongational flow.

Figure 6. The bridge-and-stitch mechanism of polymer-mediated colloid−colloid reinforced interactions. In a first instance, a polymer forms a bond with a colloid. Afterward, a collision between two colloids occurs, and the polymer bridges both colloids by forming a few bonds with each of them. Because of the rotation of the colloids in shear flow, the polymer wraps around them, forms many more bonds, and effectively stitches the colloids.

The aggregation phenomena described above has been analyzed using computer simulations and scaling arguments based on the sufficient conditions needed for aggregation.6 The model utilized is essentially a variation of the RM described above. The colloids are described using the raspberry model, and each of the beads in the surface of the colloids can undergo a binding reaction with a monomer in a polymer (see Figure 7a). The colloids and polymers are modeled in flow using a hybrid molecular dynamics−lattice Boltzmann solver.90−92 At sufficiently high shear rates the system forms compact large aggregates (see Figure 7b). The aggregation is reversible as one can increase the shear rate and monitor the number of bonds 1509


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Figure 7. Reversible polymer−colloid aggregates formed in shear flow. (A) The binding model for the polymers to the colloids. In this case the polymers do not react with themselves, but only with the colloids, represented by the raspberry model. (B) A typical aggregate fromed in shear flow. (C) The number of bonds formed as a function of time as one cycles the shear rate between high and low values. Notice that the system is reversible. In the upper panel we show snapshots of the two different states of the system depending on the value of the shear rate. The polymer chains are collapsed in this case corresponding to a depth of the attractive potential of approximately 2kT. Reproduced with permission from ref 6. Copyright 2013 Nature Publishing Group.

Figure 8. Different types of aggregates as one increases the shear rate. The upper row corresponds to collapsed polymers and the lower row to thetapolymers. The attractive potential between the monomers and the receptor sites on the colloid corresponds to −5kT. The density is 3% by volume of colloids and 0.5% polymer. Reproduced with permission from ref 6. Copyright 2013 Nature Publishing Group.

emerging systems where understanding more deeply these areas can have a great impact: Novel Materials with Potential Self-Healing Properties. In this realm it is interesting to note that by careful tuning of the interactions in the flow-induced aggregates, one can freeze the system. This could be done by a sudden change of pH, oxidation, temperature, etc. A collection of small aggregates can then form a larger material that would have interesting selfhealing properties because it would heal upon being sheared, again a counterintuitive idea. We are still not there, but once newer nonbiological mimics appear such ideas could be tested in a straightforward manner. Tailoring the Mesoscale Properties of the Aggregates. The polymer chains wrap around the colloids in these aggregates, forming multiple bonds and being in a rather stretched conformation depending on the flow conditions. Thus, the mechanical responses of such systems can be tuned by controlling the flow, the chemistry of the bond, and the length of the polymers. Currently there is strong interest in the mechanics of such aggregates, and this system would be

In particular, the reversibility was shown. The universal features are hard to study with blood since it is not trivial to modify the interaction parameters, but other model systems could be used in this respect.

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CONCLUSIONS AND OUTLOOK In this Perspective we have introduced a natural system that has served as inspiration to develop and understand novel polymer systems that could one day mimic some of the properties of blood. While this has been the motivation, many different concepts have emerged during the understanding phase, and such developments can lead to new materials where the connections to blood are not necessary anymore. In particular, we have shown that flow coupled with chemistry in polymer− colloid systems can lead to the formation of aggregates and composites. The formation and characteristics of such composites are critically dependent on the flow conditions and, thus, tunable. While the first simplified systems have been studied, there are multiple avenues of research that could yield important results. Below we will expand on some of the 1510


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simulation techniques. The same applies to experiments. The concepts are also easily translated to general polymer systems, as could be clearly seen from this Perspective. In fact, at no place did we actually describe VWF; instead, general models were developed to understand their behavior and of any other equivalent polymer system. We sincerely hope that in the near future many more developments occur in this area given that the rewards can be enormous.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]. Notes

The authors declare no competing financial interest. Biography Figure 9. Universal behavior of polymer-mediated colloid aggregates. The average fractional number of bonds as a function of the dimensionless ratio between the characteristic time for unbinding and the colloid rotation time scale (see text for details). The conditions under which the data were obtained are shown in the figure. The black points have been reproduced from ref 6.

interesting to analyze given the potential to tailor its mechanical properties at a larger scale. Perhaps more importantly, the wrapping behavior is intimately related to the shape of the colloids because the rotation mechanism is different for different shapes and different concentrations. As a matter of fact, platelets are not spherical; they are oblate spheroids, and such a shape might be important for some biological functions. Extending previous work to address the issue of colloid shape is highly relevant as one could think of making very anisotropic aggregates with distinctive responses along each of their principal axes. If such aggregates are incorporated into for example fibers, they could lead to very interesting reinforcers. Other systems could include mixtures of colloids with different shapes and their self-organization in the aggregate due to polymer-induced attractions and stresses. While this area is speculative, such systems would undoubtedly be of high interest. Controlled Responses to Flow and Stress. Rheological modifiers depend on the response of polymers to particular flow conditions. Polymers of the VWF type offer promise into other ways in which one can control such responses in flow (as described here) and under other conditions.51,52 In particular, we have analyzed mostly systems where confinement effects are not relevant, apart from flat walls. Yet, there are many instances in which such effects could be important and could lead to presumably even more nonintuitive behaviors. Such is the nature of flowing suspensions in confined spaces, especially in the dilute regime, as the one we have addressed here. To perform such computational studies will be challenging, and new multiscale techniques will be necessary given the multiple scales that need to be bridged if one would like to resolve from the full vessel geometry to the polymer effective monomers because this implies resolution from tens of nanometers to hundreds of micrometers. As a final remark, we would like to mention that the understanding of how blood clots and translating this knowledge into controlled systems is just beginning. Thus, for theorists, this area is a beautiful workground since not much has been explained, and there is a lot of open space for creativity in many areas such as models, analytics, and

Alfredo Alexander-Katz received a Ph.D. in (Polymer) Physics from the University of California at Santa Barbara and a B.Sc. in Physics from the Universidad Nacional Autonoma de Mexico. He was an NSF postdoctoral fellow in Munich (Germany) from 2004 to 2006 and a CNRS Postdoctoral Researcher in ESPCI (Paris) from 2006 to 2008. He moved back to the US to start as an assistant professor in the Department of Materials Science and Engineering at the Massachusetts Institute of Technology in 2008. He currently is the Walter Henry Gale Associate Professor of Materials Science and Engineering. His research revolves around fundamentals and applications of soft materials in and out of equilibrium. Prof. Alexander-Katz has received several awards including a NSF CAREER Award and a DOE Early Investigator Award.

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ACKNOWLEDGMENTS I am indebted to the many collaborators and students that have worked and discussed with me during the past 10 years about blood-clotting-related phenomena. In particular, I thank two of my graduate students, Charles Sing and Hsieh Chen, for their relentless drive to uncover some of the secrets behind adhesion and plug formation in flow. They carried most of the work on VWF discussed in this work. I also sincerely thank Matthias Schneider, with whom I have had a wonderful and lasting collaboration on VWF and other phenomena and who ignited our work in this field, asking what I suspect at that time was a “simple” polymer question. Another important person with whom I had the pleasure to work with is Roland Netz, and it was in his lab where we started to explore the polymer physics of VWF while I was in Germany as a postdoc. Roland opened my eyes to new, untouched, yet potentially very important territory in the area of polymer dynamics. Finally, I thank NSF for their kind support through a CAREER Award No. DMR1511


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(26) Springer, T. A. Biology and physics of von Willebrand factor concatamers. J. Thromb. Haemostasis 2011, 9, 130−143. (27) Saariaho, M.; et al. On lyotropic behavior of molecular bottlebrushes: A Monte Carlo computer simulation study. J. Chem. Phys. 1997, 107 (8), 3267−3276. (28) Rathgeber, S.; et al. On the shape of bottle-brush macromolecules: Systematic variation of architectural parameters. J. Chem. Phys. 2005, 122 (12), 124904. (29) Claesson, P. M.; et al. Bottle-brush polymers: Adsorption at surfaces and interactions with surfactants. Adv. Colloid Interface Sci. 2010, 155 (1−2), 50−57. (30) Alexander-Katz, A.; Netz, R.R. Dynamics and instabilities of collapsed polymers in shear flow. Macromolecules 2008, 41 (9), 3363− 3374. (31) Schneider, S. W.; et al. Shear-induced unfolding triggers adhesion of von Willebrand factor fibers. Proc. Natl. Acad. Sci. U. S. A. 2007, 104 (19), 7899−7903. (32) Alexander-Katz, A.; Netz, R. R. Surface-enhanced unfolding of collapsed polymers in shear flow. EPL 2007, 80, 1. (33) Alexander-Katz, A.; et al. Shear-flow-induced unfolding of polymeric globules. Phys. Rev. Lett. 2006, 97, 13. (34) Sing, C. E.; Alexander-Katz, A. Equilibrium structure and dynamics of self-associating single polymers. Macromolecules 2011, 44 (17), 6962−6971. (35) Chen, H.; Alexander-Katz, A. Polymer-based catch-bonds. Biophys. J. 2011, 100 (1), 174−182. (36) Korn, C. B.; Schwarz, U. S. Dynamic states of cells adhering in shear flow: From slipping to rolling. Phys. Rev. E 2008, 77, 4. (37) Bell, G. I. Theoretical models for the specific adhesion of cells to cells or to surfaces. Adv. Appl. Probab. 1980, 12 (3), 566−567. (38) Bell, G. I. Models for specific adhesion of cells to cells. Science 1978, 200 (4342), 618−627. (39) Kim, J.; et al. A mechanically stabilized receptor-ligand flex-bond important in the vasculature. Nature 2010, 466 (7309), 992−U123. (40) Marshall, B. T.; et al. Direct observation of catch bonds involving cell-adhesion molecules. Nature 2003, 423 (6936), 190−193. (41) Sing, C. E.; Alexander-Katz, A. Elongational flow induces the unfolding of von Willebrand factor at physiological flow rates. Biophys. J. 2010, 98 (9), L35−L37. (42) Sing, C. E.; Alexander-Katz, A. Globule-stretch transitions of collapsed polymers in elongational flow fields. Macromolecules 2010, 43 (7), 3532−3541. (43) Sing, C. E.; Alexander-Katz, A. Dynamics of collapsed polymers under the simultaneous influence of elongational and shear flows. J. Chem. Phys. 2011, 135, 1. (44) Degennes, P. G. Coil-stretch transition of dilute flexible polymers under ultrahigh velocity-gradients. J. Chem. Phys. 1974, 60 (12), 5030−5042. (45) Tang, J.; Du, N.; Doyle, P.S. Compression and selfentanglement of single DNA molecules under uniform electric field. Proc. Natl. Acad. Sci. U. S. A. 2011, 108 (39), 16153−16158. (46) Chen, H.; Alexander-Katz, A. Dynamics of polymers in flowing colloidal suspensions. Phys. Rev. Lett. 2011, 107, 12. (47) Sendner, C.; Netz, R.R. Single flexible and semiflexible polymers at high shear: Non-monotonic and non-universal stretching response. Eur. Phys. J. E 2009, 30 (1), 75−81. (48) Alexander-Katz, A.; Wada, H.; Netz, R. R. Internal friction and nonequilibrium unfolding of polymeric globules. Phys. Rev. Lett. 2009, 103, 2. (49) Einert, T. R.; et al. Conformational dynamics and internal friction in homopolymer globules: equilibrium vs. non-equilibrium simulations. Eur. Phys. J. E 2011, 34, 12. (50) Sing, C. E.; et al. Probing structural and dynamical transitions in polymer globules by force. Phys. Rev. E 2011, 83 (4), 040801. (51) Sing, C. E.; Alexander-Katz, A. Force spectroscopy of selfassociating homopolymers. Macromolecules 2012, 45 (16), 6704−6718. (52) Sing, C. E.; Alexander-Katz, A. Designed molecular mechanics using self-associating polymers. Soft Matter 2012, 8 (47), 11871− 11879.

1054671 that has allowed my group to perform the work here presented.

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