Allosteric regulation plays an important role in many biological processes, such as signal transduction, transcriptional regulation, and metabolism. Allostery is rooted in the fundamental physical properties of macromolecular systems, but its underlying mechanisms are still poorly understood. A collection of contributions to a recent interdisciplinary CECAM (Center Européen de Calcul Atomique et Moléculaire) workshop is used hereto provide an overview of the progress and remaining limitations in the understanding of the mechanistic foundations of allostery gained from computational and experimental analyses of real protein systems and model systems. The main conceptual frameworks instrumental in driving the field are discussed. We illustrate the role of these frameworks in illuminating molecular mechanisms and explaining cellular processes, and describe some of their promising practical applications in engineering molecular sensors and informing drug design efforts.

We study theoretically and numerically the microscopic cause of the rigidity of hard sphere glasses near their maximum packing. We show that, after coarse-graining over time, the hard sphere interaction can be described by an effective potential which is exactly logarithmic at the random close packing φc. This allows to define normal modes, and to apply recent results valid for elastic networks: rigidity is a non-local property of the packing geometry, and is characterized by some length scale l * which diverges at φc [1,2]. We compute the scaling of the bulk and shear moduli near φc, and speculate on the possible implications of these results for the glass transition.Hard spheres present a glass phase between φ 0 , where the glass transition occurs and structural relaxation becomes unobservable, and φ c where the pressure p diverges. In this region this system is solid and resists to shear on any measurable time scales. Although a large amount of works focused on the super-cooled liquid, the glass itself received less attention. In particular, there is no undoubted microscopic theory to explain its mechanical properties and its rigidity. In the cage-escape picture [3], the cage formed by the neighboring particles tighten as φ increases, and the typical time for a particle to escape its cage grows and eventually diverges. Nevertheless, Maxwell showed that the stability against collective motions of particles is more demanding than against individual particle displacements: in particular z = d + 1 inter-particle contacts are sufficient to pin one particle in d dimensions, whereas z c = 2d contacts in average are required to guarantee mechanical stability [4]. Thus considering a priori rigidity as a local property may be inappropriate.Recently several works [1,2,5,6,8,7] studied the mechanical properties of weaklyconnected elastic networks with an average contacts number -the coordination numberz close to the critical value z c = 2d, such as those encountered for athermal repulsive shortrange particles above φ c [5,6]. In particular it was shown that (i) these systems present an c EDP Sciences

We derive a microscopic criterion for the stability of hard sphere configurations and we show empirically that this criterion is marginally satisfied in the glass. This observation supports a geometric interpretation for the initial rapid rise in viscosity with packing fraction or previtrification. It also implies that barely stable soft modes characterize the glass structure, whose spatial extension is estimated. We show that both the short-term dynamics and activation processes occur mostly along those soft modes and we study some implications of these observations. This article synthesizes new and previous results [C. Brito and M. Wyart, Europhys. Lett. 76, 149 (2006); C. Brito and M. Wyart, J. Stat. Mech.: Theory Exp. 2007, L08003] in a unified view.

We conduct experiments on two-dimensional packings of colloidal thermosensitive hydrogel particles whose packing fraction can be tuned above the jamming transition by varying the temperature. By measuring displacement correlations between particles, we extract the vibrational properties of a corresponding "shadow" system with the same configuration and interactions, but for which the dynamics of the particles are undamped. The vibrational spectrum and the nature of the modes are very similar to those predicted for zero-temperature idealized sphere models and found in atomic and molecular glasses; there is a boson peak at low frequency that shifts to higher frequency as the system is compressed above the jamming transition.PACS numbers: 63. 63.50 Lm, 82.70 Dd Crystalline solids are all alike in their vibrational properties at low frequencies; every disordered solid is disordered in its own way. Disordered solids nonetheless exhibit common low-frequency vibrational properties that are completely unlike those of crystals, which are dominated by sound modes. Disordered atomic or molecular solids generically exhibit a "boson peak," where many more modes appear than expected for sound. The excess modes of the boson peak are believed to be responsible for the unusual behavior of the heat capacity and thermal conductivity at low-to-intermediate temperatures in disordered solids [2].It has been proposed that a zero-temperature jamming transition may provide a framework for understanding this unexpected commonality [3]. For frictionless, idealized spheres this jamming transition lies at the threshold of mechanical stability, known as the isostatic point [3,4]. As a result of this coincidence, the vibrational behavior of the marginally jammed solid at densities just above the jamming transition is fundamentally different from that of ordinary elastic solids [5][6][7][8]. A new class of lowfrequency vibrational modes arises because the system is at the threshold of mechanical stability [10]; these modes give rise to a divergent boson peak at zero frequency [5]. As the system is compressed beyond the jamming transition, the boson peak shrinks in height and shifts upwards in frequency [5]. Generalizations of the idealized sphere model suggest that the boson peaks of a wide class of disordered solids may arise from proximity to the jamming transition [9][10][11][12]. Moreover, the jamming scenario predicts that systems with larger constituents such as colloids should also have boson peaks.Colloidal glasses offer signal advantages over atomic or molecular disordered solids because colloids can be tracked by video microscopy. Vibrational behavior has been explored in hard-sphere colloids [13] and vibrated granular packings [14], but difficulties with statistics [13] or micro-cracks [14] were encountered. In contrast, we use deformable, thermosensitive hydrogel particles to tune the packing fraction in situ. Our experiments show unambiguously that the commonality in vibrational properties observed in atomic and molecular glas...

Our results provide the basis for a detailed prospective evaluation of autoimmunity and inflammation in the context of PIDs, with a view to accurately assessing these risks and describing the possible effect of medical intervention.

In a recent publication we established an analogy between the free energy of a hard sphere system and the energy of an elastic network [1]. This result enables one to study the free energy landscape of hard spheres, in particular to define normal modes. In this Letter we use these tools to analyze the activated transitions between meta-bassins, both in the aging regime deep in the glass phase and near the glass transition. We observe numerically that structural relaxation occurs mostly along a very small number of nearly-unstable extended modes. This number decays for denser packing and is significantly lowered as the system undergoes the glass transition. This observation supports that structural relaxation and marginal modes share common properties. In particular theoretical results [2,3] show that these modes extend at least on some length scale l * ∼ (φc − φ) −1/2 where φc corresponds to the maximum packing fraction, i.e. the jamming transition. This prediction is consistent with very recent numerical observations of sheared systems near the jamming threshold [4], where a similar exponent is found, and with the commonly observed growth of the rearranging regions with compression near the glass transition. PACS numbers:A colossal effort has been made to characterize the spatial nature of the structural relaxation near the glass transition. Numerical simulations [5] and experiments [6,7] have shown that the dynamics in super-cooled liquids is heterogeneous. Both the string-like [8] and the compact [9] aspects of the particles' displacements have been emphasized. Nevertheless, the cause of such collective motions remains debated [10,11]. To make progress, one would like to relate these motions to other objects. A possible candidate is the excess of low-frequency modes present in all glasses, the so-called boson peak [12]. Because these modes shift in general to lower frequencies as the temperature increases toward the glass transition temperature T g , it has been proposed that they are responsible for the melting of the glass [13,14]. This suggests the use of widely employed tools, such as the low-frequency instantaneous normal modes [15] or the negative directions of saddles of the potential energy landscape [16], to analyze the collective motions causing relaxation. Nevertheless, this approach has the major drawback of being based on energy instead of free energy. As such, it cannot be applied for example to hard spheres or colloids, where structural relaxation is also known to be collective, see e.g. [7]. In this case barriers between meta-stable states are purely entropic. More generally, one expects entropic effects to be important for glasses where hard-core repulsions and non-linearities are not negligible, which is presumably the case in general above T g [17].Recent developments make this analysis possible in hard sphere systems. In [1], we derived an analogy between the free energy of a hard sphere glass and the energy of a weakly-connected network of logarithmic springs. This allows us to define norm...

We theoretically and numerically study the elastic properties of hard-sphere glasses and provide a real-space description of their mechanical stability. In contrast to repulsive particles at zero temperature, we argue that the presence of certain pairs of particles interacting with a small force f soften elastic properties. This softening affects the exponents characterizing elasticity at high pressure, leading to experimentally testable predictions. Denoting P(f ) ∼ f θe , the force distribution of such pairs and ϕ c the packing fraction at which pressure diverges, we predict that (i) the density of states has a low-frequency peak at a scale ω*, rising up to it as D(ω) ∼ ω 2+a , and decaying above ω* as D(ω) ∼ ω −a where a = (1 − θ e )=(3 + θ e ) and ω is the frequency, (ii) shear modulus and mean-squared displacement are inversely proportional with 〈δR 2 〉 ∼ 1=μ ∼ (ϕ c − ϕ) κ , where κ = 2 − 2=(3 + θ e ), and (iii) continuum elasticity breaks down on a scale ℓ c ∼ 1= ffiffiffiffiffi δz p ∼ (ϕ c − ϕ) −b , where b = (1 + θ e )=(6 + 2θ e ) and δz = z − 2d, where z is the coordination and d the spatial dimension. We numerically test (i) and provide data supporting that θ e ≈ 0:41 in our bidisperse system, independently of system preparation in two and three dimensions, leading to κ ≈ 1:41, a ≈ 0:17, and b ≈ 0:21. Our results for the mean-square displacement are consistent with a recent exact replica computation for d = ∞, whereas some observations differ, as rationalized by the present approach.colloids | glass transition | marginal stability | boson peak | jamming T he emergence of rigidity near the glass transition is a fundamental and highly debated topic in condensed matter and is perhaps most surprising in hard-sphere glasses where rigidity is purely entropic in nature. The rapid growth of relaxation time around a packing fraction ϕ g ≈ 0:58 suggests that metastable states have appeared in the free-energy landscape, and that activation above barriers is required for the system to flow (1). This scenario is presumably what mode-coupling theory captures (2, 3) and can be rationalized via density functional theory (4) and via the replica method (5). Recently a real-space description of mechanical stability and elasticity in hard-sphere glasses has been proposed (6, 7), which is most easily tested at large pressure, deep in the glass phase. It is based on two results. First, in elastic networks and athermal packings of soft spheres (8-10), mechanical stability is controlled by the mean number of contacts per particle, or coordination z (as already discussed by Maxwell in ref. 11), and the applied compressive strain e (10). As one may intuitively expect, increasing coordination is stabilizing, whereas increasing pressure at fixed coordination is destabilizing. Second, within a long-lived metastable state the vibrational free energy of a hard-sphere system can be approximated as a sum of local interaction terms between pairs of colliding particles, which are said to be in contact. On a time scale that contains many...

We introduce a numerical scheme to evolve functional elastic materials that can accomplish a specified mechanical task. In this scheme, the number of solutions, their spatial architectures, and the correlations among them can be computed. As an example, we consider an "allosteric" task, which requires the material to respond specifically to a stimulus at a distant active site. We find that functioning materials evolve a less-constrained trumpetshaped region connecting the stimulus and active sites, and that the amplitude of the elastic response varies nonmonotonically along the trumpet. As previously shown for some proteins, we find that correlations appearing during evolution alone are sufficient to identify key aspects of this design. Finally, we show that the success of this architecture stems from the emergence of soft edge modes recently found to appear near the surface of marginally connected materials. Overall, our in silico evolution experiment offers a window to study the relationship between structure, function, and correlations emerging during evolution. disordered materials | proteins | evolution P roteins are long polymers that can fold in a reproducible way and achieve a specific function. Often, the activity of the main functional site depends on the binding of an effector on a distant site (1, 2). Such an allosteric behavior can occur over large distances, such as 20 residues or more (3), and often involves only a sparse subset of residues in the protein (3, 4). Allosteric regulation offers an appealing target for drug design (5), and there is considerable interest in predicting allosteric pathways (6, 7). One central difficulty is that the physical mechanisms allowing such an "action at a distance" remain elusive. In some cases, allostery can be understood as the modulation of a hinge connecting two extended rigid parts of the protein (8, 9), but, often, the displacement field induced by the binding of the effector cannot be described in these terms (4, 10, 11). Another route, statistical coupling analysis (12), considers correlations within sequences of proteins of the same family to infer allosteric pathways (4, 7). The generality of this elegant approach is, however, debated (13).From a physical viewpoint, specific response at a distance is surprising. The structure of proteins is similar to randomly packed spheres (14). Generically, the response of such systems is nonspecific and decays rapidly in space (in a manner similar to a continuum medium) at distances larger than the particle size; this is true, except close to a critical point where the number of constraints coming from strongly interacting particles is just sufficient to match the number of degrees of freedom of the particles (15). There, the elastic response becomes heterogeneous on all scales (16,17). This point is illustrated in Fig. 1A, showing the rapidly decaying response of a random spring network to a stimulus. However, as shown in Fig. 1B (and independently found in ref. 18 using a different algorithm), springs can be move...