Connecting brain and behavior in clinical neuroscience: A network approach

In recent years, there has been an increase in applications of network science in many different fields. In clinical neuroscience and psychopathology, the developments and applications of network science have occurred mostly simultaneously, but without much collaboration between the two fields. The promise of integrating these network applications lies in a united framework to tackle one of the fundamental questions of our time: how to understand the link between brain and behavior. In the current overview, we bridge this gap by introducing conventions in both fields, highlighting similarities, and creating a common language that enables the exploitation of synergies. We provide research examples in autism research, as it accurately represents research lines in both network neuroscience and psychological networks. We integrate brain and behavior not only semantically, but also practically, by showcasing three methodological avenues that allow to combine networks of brain and behavioral data. As such, the current paper offers a stepping stone to further develop multi-modal networks and to integrate brain and behavior

Spinor representation of surfaces and complex stresses on membranes and interfaces

Variational principles are developed within the framework of a spinor representation of the surface geometry to examine the equilibrium properties of a membrane or interface. This is a far-reaching generalization of the Weierstrass-Enneper representation for minimal surfaces, introduced by mathematicians in the nineties, permitting the relaxation of the vanishing mean curvature constraint. In this representation the surface geometry is described by a spinor field, satisfying a two-dimensional Dirac equation, coupled through a potential associated with the mean curvature. As an application, the mesoscopic model for a fluid membrane as a surface described by the Canham-Helfrich energy quadratic in the mean curvature is examined. An explicit construction is provided of the conserved complex-valued stress tensor characterizing this surface.Comment: 17 page

Elastic deformation of a fluid membrane upon colloid binding

When a colloidal particle adheres to a fluid membrane, it induces elastic deformations in the membrane which oppose its own binding. The structural and energetic aspects of this balance are theoretically studied within the framework of a Helfrich Hamiltonian. Based on the full nonlinear shape equations for the membrane profile, a line of continuous binding transitions and a second line of discontinuous envelopment transitions are found, which meet at an unusual triple point. The regime of low tension is studied analytically using a small gradient expansion, while in the limit of large tension scaling arguments are derived which quantify the asymptotic behavior of phase boundary, degree of wrapping, and energy barrier. The maturation of animal viruses by budding is discussed as a biological example of such colloid-membrane interaction events.Comment: 14 pages, 9 figures, REVTeX style, follow-up on cond-mat/021242

Structure of Polyelectrolytes in Poor Solvent

We present simulations on charged polymers in poor solvent. First we investigate in detail the dilute concentration range with and without imposed extension constraints. The resulting necklace polymer conformations are analyzed in detail. We find strong fluctuations in the number of pearls and their sizes leading only to small signatures in the form factor and the force-extension relation. The scaling of the peak in the structure factor with the monomer density shows a pertinent different behavior from good solvent chains.Comment: 7 pages, 5 figures. submitted to EP

Balancing torques in membrane-mediated interactions: Exact results and numerical illustrations

Torques on interfaces can be described by a divergence-free tensor which is fully encoded in the geometry. This tensor consists of two terms, one originating in the couple of the stress, the other capturing an intrinsic contribution due to curvature. In analogy to the description of forces in terms of a stress tensor, the torque on a particle can be expressed as a line integral along any contour surrounding the particle. Interactions between particles mediated by a fluid membrane are studied within this framework. In particular, torque balance places a strong constraint on the shape of the membrane. Symmetric two-particle configurations admit simple analytical expressions which are valid in the fully nonlinear regime; in particular, the problem may be solved exactly in the case of two membrane-bound parallel cylinders. This apparently simple system provides some flavor of the remarkably subtle nonlinear behavior associated with membrane-mediated interactions.Comment: 16 pages, 10 figures, REVTeX4 style. The Gaussian curvature term was included in the membrane Hamiltonian; section II.B was rephrased to smoothen the flow of presentatio

Interface mediated interactions between particles -- a geometrical approach

Particles bound to an interface interact because they deform its shape. The stresses that result are fully encoded in the geometry and described by a divergence-free surface stress tensor. This stress tensor can be used to express the force on a particle as a line integral along any conveniently chosen closed contour that surrounds the particle. The resulting expression is exact (i.e., free of any "smallness" assumptions) and independent of the chosen surface parametrization. Additional surface degrees of freedom, such as vector fields describing lipid tilt, are readily included in this formalism. As an illustration, we derive the exact force for several important surface Hamiltonians in various symmetric two-particle configurations in terms of the midplane geometry; its sign is evident in certain interesting limits. Specializing to the linear regime, where the shape can be analytically determined, these general expressions yield force-distance relations, several of which have originally been derived by using an energy based approach.Comment: 18 pages, 7 figures, REVTeX4 style; final version, as appeared in Phys. Rev. E. Compared to v2 several minor mistakes, as well as one important minus sign in Eqn. (18a) have been cured. Compared to v1, this version is significantly extended: Lipid tilt degrees of freedom for membranes are included in the stress framework, more technical details are given, estimates for the magnitude of forces are mad

Volume terms for charged colloids: a grand-canonical treatment

We present a study of thermodynamic properties of suspensions of charged colloids on the basis of linear Poisson-Boltzmann theory. We calculate the effective Hamiltonian of the colloids by integrating out the ionic degrees of freedom grand-canonically. This procedure not only yields the well-known pairwise screened-Coulomb interaction between the colloids, but also additional volume terms which affect the phase behavior and the thermodynamic properties such as the osmotic pressure. These calculations are greatly facilitated by the grand-canonical character of our treatment of the ions, and allow for relatively fast computations compared to earlier studies in the canonical ensemble. Moreover, the present derivation of the volume terms are relatively simple, make a direct connection with Donnan equilibrium, yield an explicit expression for the effective screening constant, and allow for extensions to include, for instance, nonlinear effects.Comment: 16 pages, 6 figures, published in Phys.Rev.

Effective surface interactions mediated by adhesive particles

In biomimetic and biological systems, interactions between surfaces are often mediated by adhesive molecules, nanoparticles, or colloids dispersed in the surrounding solution. We present here a general, statistical-mechanical model for two surfaces that interact via adhesive particles. The effective, particle-mediated interaction potential of the surfaces is obtained by integrating over the particles' degrees of freedom in the partition function. Interestingly, the effective adhesion energy of the surfaces exhibits a maximum at intermediate particle concentrations, and is considerably smaller both at low and high concentrations. The effective adhesion energy corresponds to a minimum in the interaction potential at surface separations slightly larger than the particle diameter, while a secondary minimum at surface contact reflects depletion interactions. Our results can be generalized to surfaces with specific receptors for solute particles, and have direct implications for the adhesion of biomembranes and for phase transitions in colloidal systems.Comment: 6 pages, 5 figures; to appear in Europhys. Let