We report theoretical and numerical evaluations of the phase diagram for patchy colloidal particles of new generation. We show that the reduction of the number of bonded nearest neighbours offers the possibility of generating liquid states (i.e. states with temperature T lower than the liquidgas critical temperature) with a vanishing occupied packing fraction (φ), a case which can not be realized with spherically interacting particles. Theoretical results suggest that such reduction is accompanied by an increase of the region of stability of the liquid phase in the (T -φ) plane, possibly favoring the establishment of homogeneous disordered materials at small φ, i.e. stable equilibrium gels.The physico-chemical manipulation of colloidal particles is growing at an incredible pace. The large freedom in the control of the inter-particle potential has made it possible to design colloidal particles which significantly extend the possibilities offered by atomic systems [1]. An impressive step further is offered by the newly developed techniques to assemble (and produce with significant yield) colloidal molecules, particles decorated on their surface by a predefined number of attractive sticky spots, i.e. particles with specifically designed shapes and interaction sites [2,3,4,5]. These new particles, thanks to the specificity of the built-in interactions, will be able not only to reproduce molecular systems on the nano and micro scale, but will also show novel collective behaviors. To guide future applications of patchy colloids, to help designing bottom-up strategies in self-assembly [6,7,8] and to tackle the issue of interplay between dynamic arrest and crystallisation -a hot-topic related for example to the possibility of nucleating a colloidal diamond crystal structure for photonic applications [9] -it is crucial to be able to predict the region in the (T -φ) plane in which clustering, phase separation or even gelation is expected.While design and production of patchy colloids is present-day research, unexpectedly theoretical studies of the physical properties of these systems have a longer history, starting in the eighties in the context of the physics of associated liquids [10,11,12,13,14,15]. These studies, in the attempt to pin-down the essential features of association, modelled molecules as hard-core particles with attractive spots on the surface, a realistic description of the recently created patchy colloidal particles. A thermodynamic perturbation theory (TPT) appropriate for these models was introduced by Wertheim [16] to describe association under the hypothesis that a sticky site on a particle cannot bind simultaneously to two (or more) sites on another particle. Such a condition can be naturally implemented in colloids, due to the relative size of the particle as compared to the range of the sticky interaction. These old studies provide a very valuable starting point for addressing the issue of the phase diagram of this new class of colloids, and in particular of the role of the patches number.In this ...

Recently, an increasing experimental effort has been devoted to the synthesis of complex colloidal particles with chemically or physically patterned surfaces and possible specific shapes that are far from spherical. These new colloidal particles with anisotropic interactions are commonly named patchy particles. In this Perspective article, we focus on patchy systems characterized by spherical neutral particles with patchy surfaces. We summarize most of the patchy particle models that have been developed so far and describe how their basic features are connected to the physical systems they are meant to investigate. Patchy models consider particles as hard or soft spheres carrying a finite and small number of attractive sites arranged in precise geometries on the particle's surface. The anisotropy of the interaction and the limited valence in bonding are the salient features determining the collective behavior of such systems. By tuning the number, the interaction parameters and the local arrangements of the patches, it is possible to investigate a wide range of physical phenomena, from different self-assembly processes of proteins, polymers and patchy colloids to the dynamical arrest of gel-like structures. We also draw attention to charged patchy systems: colloidal patchy particles as well as proteins are likely charged, hence the description of the presence of heterogeneously distributed charges on the particle surface is a promising perspective for future investigations.

We numerically study a simple fluid composed of particles having a hard-core repulsion, complemented by two short-ranged attractive (sticky) spots at the particle poles, which provides a simple model for equilibrium polymerization of linear chains. The simplicity of the model allows for a close comparison, with no fitting parameters, between simulations and theoretical predictions based on the Wertheim perturbation theory, a unique framework for the analytic prediction of the properties of self-assembling particle systems in terms of molecular parameter and liquid state correlation functions. This theory has not been subjected to stringent tests against simulation data for ordering across the polymerization transition. We numerically determine many of the thermodynamic properties governing this basic form of self-assembly (energy per particle, order parameter or average fraction of particles in the associated state, average chain length, chain length distribution, average end-to-end distance of the chains, and the static structure factor) and find that predictions of the Wertheim theory accord remarkably well with the simulation results.

We report theoretical and numerical evaluations of the phase diagram for a model of patchy particles. Specifically, we study hard spheres whose surface is decorated by a small number f of identical sites ("sticky spots") interacting via a short-ranged square-well attraction. We theoretically evaluate, solving the Wertheim theory, the location of the critical point and the gas-liquid coexistence line for several values of f and compare them to the results of Gibbs and grand canonical Monte Carlo simulations. We study both ordered and disordered arrangements of the sites on the hard-sphere surface and confirm that patchiness has a strong effect on the phase diagram: the gas-liquid coexistence region in the temperature-density plane is significantly reduced as f decreases. We also theoretically evaluate the locus of specific heat maxima and the percolation line.

Typically, patchy systems are characterized by the formation of a small number of directional, possibly selective, bonds due to the presence of attractive regions on the surface of otherwise repulsive particles. Here, we consider a new type of particles with patterned surfaces and we refer to them as inverse patchy colloids because, in this case, the patches on the repulsive particles repel each other instead of attracting. Further, these patches attract the parts of the colloid that are free of patches. Specifically, we consider heterogeneously charged colloids consisting of negatively charged spherical particles carrying a small number of positively charged patches. Making use of the Debye-H€ uckel theory, we derive the effective interaction potential between a pair of inverse patchy colloids with two patches on opposite poles. We then design a simple coarse-grained model via a mapping with the analytical pair potential. The coarsegrained model quantitatively reproduces the features of its microscopic counterpart, while at the same time being characterized by a much higher degree of computational simplicity. Moreover, the mesoscopic model is generalizable to an arbitrary number of patches.

Background: A systemic immune-inflammation index (SII) based on neutrophil (N), lymphocyte (L), and platelet (P) counts has shown a prognostic impact in several solid tumors. The aim of this study is to evaluate the prognostic role of SII in metastatic castration-resistant prostate cancer (mCRPC) patients treated with abiraterone post docetaxel.Patients and Methods: We retrospectively reviewed consecutive mCRPC patients treated with abiraterone after docetaxel in our Institutions. X-tile 3.6.1 software, cut-off values of SII, neutrophil-to-lymphocyte ratio (NLR) defined as N/L and platelets-to-lymphocyte ratio (PLR) as P/L. Overall survival (OS) and their 95% Confidence Intervals (95% CI) was estimated by the Kaplan-Meier method and compared with the log-rank test. The impact of SII, PLR, and NLR on overall survival (OS) was evaluated by Cox regression analyses and on prostate-specific antigen (PSA) response rates were evaluated by binary logistic regression.Results: A total of 230 mCRPC patients treated abiraterone were included. SII ≥ 535, NLR ≥ 3 and PLR ≥ 210 were considered as elevated levels (high risk groups. The median OS was 17.3 months, 21.8 months in SII < 535 group and 14.7 months in SII ≥ 535 (p < 0.0001). At univariate analysis Eastern Cooperative Oncology Group (ECOG) performance status, previous enzalutamide, visceral metastases, SII, NLR, and PLR predicted OS. In multivariate analysis, ECOG performance status, previous enzalutamide, visceral metastases, SII, and NLR remained significant predictors of OS [hazard ratio (HR) = 5.08, p < 0.0001; HR = 2.12, p = 0.009, HR = 1.77, 95% p = 0.012; HR = 1.80, p = 0.002; and HR = 1.90, p = 0.001, respectively], whereas, PLR showed a borderline ability only (HR = 1.41, p = 0.068).Conclusion: SII and NLR might represent an early and easy prognostic marker in mCRPC patients treated with abiraterone. Further studies are needed to better define their impact and role in these patients.

Under experimental conditions in which the self-association of the adenine phosphates (AP), that is, of adenosine 5'-monophosphate (AMP(2-)) and adenosine 5'-diphosphate (ADP(3-)), is negligible, potentiometric pH titrations were carried out to determine the stabilities of the M(H;AP) and M(AP) complexes where M(2+)=Mg(2+), Ca(2+), Sr(2+), Ba(2+), Mn(2+), Co(2+), Ni(2+), Cu(2+), Zn(2+), or Cd(2+) (25 degrees C; I=0.1 M, NaNO(3)). It is concluded that in the M(H;AMP)(+) species M(2+) is bound at the adenine moiety and in the M(H;ADP) complexes at the diphosphate unit; however, the proton resides in both types of monoprotonated complexes at the phosphate residue. The stabilities of nearly all the M(AMP) and M(ADP)(-) complexes are significantly larger than what is expected for a sole coordination of M(2+) to the phosphate residue. This increased complex stability is attributed, in agreement with previous (1)H NMR shift studies and further information existing in the literature, to the formation of macrochelates of the phosphate-coordinated metal ions with N7 of the adenine residues. On the basis of recent measurements with simple phosphate monoesters and phosphonate ligands (R-MP(2-)) as well as with diphosphate monoesters (R-DP(3-)), where R is a noncoordinating and noninhibiting residue, the increased stabilities of the M(AMP) and M(ADP)(-) complexes due to the M(2+)-N7 interaction could be evaluated and the extent of macrochelate formation calculated. The results show that the formation degrees of the macrochelates for the complexes of the alkaline earth ions are small (about 15 % at the most), whereas for the 3d metal ions as well as for Zn(2+) and Cd(2+) the formation degrees vary between about 15 % (Mn(2+)) and 75 % (Ni(2+)) with values of about 40 and 50 % for Zn(2+) and Cu(2+), respectively. It is interesting to note, taking earlier results for M(ATP)(2-) complexes also into account (ATP(4-)=adenosine 5'-triphosphate), that for a given metal ion in nearly all instances the formation degrees of the macrochelates are within the error limits the same for M(AMP), M(ADP)(-) and M(ATP)(2-) complexes; except for Co(2+) and Ni(2+) it holds M(AMP) > M(ADP)(-) approximately M(ATP)(2-). This result is astonishing if one considers that the absolute stability constants of these complexes, which are determined largely by the affinity of the phosphate residues, can differ by more than two orders of magnitude. The impact and conclusions of these observations for biological systems are shortly lined out.

Self-assembly is the mechanism that controls the formation of well-defined structures from disordered preexisting parts. Despite the importance of self-assembly as a manufacturing method and the increasingly large number of experimental realizations of complex self-assembled nano-aggregates, theoretical predictions are lagging behind. Here, we show that for a nontrivial self-assembly phenomenon, originating branched loopless clusters, it is possible to derive a fully predictive parameter-free theory of equilibrium self-assembly by combining the Wertheim theory for associating liquids with the Flory-Stockmayer approach for chemical gelation.Intermolecular self-assembly is the ability of molecules to form supramolecular assemblies 1 as well as a manufacturing method used to construct aggregate at the nano-or micro-scale, by proper design of the constituent molecules. In the selfassembly bottom-up paradigm, the final (desired) structure is encoded in the shape and properties of the designed building blocks. Realizations of complex self-assembled nano-aggregates [2][3][4] have been guided by intuition and sophisticated experimental techniques. A full comprehension of the self-assembly process requires the ability to predict the structures (and their relative abundance) which will be observed in equilibrium as a function of temperature T and density F, starting from the knowledge of the interparticle interaction potential. Such a request is very much akin to the one that has guided the development of the physics of liquids in the last decades. Differently from the simple liquid case, self-assembly is characterized by a very strong interparticle attraction (significantly larger than the thermal energy k B T) and by the fact that the interaction geometry is far from being spherical. The leading "bonding" interaction may indeed be localized in a specific part of the particle surface (patchy interactions 5 ), it may be active only in the presence of a specific complementary group (lock-and-key interactions, very often encountered in biological self-assembly 6-9 ), or it may be strongly dependent on the particle orientation. 10 The presence of strong and patchy interactions poses significant challenges to a parameter-free description of self-assembly. Only equilibrium chain polymerization, the simplest self-assembly process which takes place when bifunctional particles self-assemble into chains of variable length, can be considered to be sufficiently established. [11][12][13][14][15][16] In this article, we show that for systems with a small average functionality (but larger than two) it is possible to provide a parameter-free full description of the self-assembly process. We study theoretically and numerically one of the simplest but not trivial self-assembly processes, namely, a binary mixture of particles with two and three attractive sites. The presence of three (or more)-functional particles, which act as branching points in the self-assembled clusters, introduces two important phenomena which are missing in equilibr...