Funnels in Energy Landscapes

Local minima and the saddle points separating them in the energy landscape are known to dominate the dynamics of biopolymer folding. Here we introduce a notion of a "folding funnel" that is concisely defined in terms of energy minima and saddle points, while at the same time conforming to a notion of a "folding funnel" as it is discussed in the protein folding literature.Comment: 6 pages, 3 figures, submitted to European Conference on Complex Systems 200

QAA subject benchmark statement architecture : version for consultation December 2019

The Statement is intended to guide lecturers and course leaders in the design of academic courses leading to qualifications in architecture, it will also be useful to those developing other related courses. Higher education providers may need to consider other reference points in addition to this Statement in designing, delivering and reviewing courses. These may include requirements set out by the Architects Registration Board (ARB), the Royal Institute of British Architects (RIBA) and the Institute for Apprenticeships and Technical Education (IfATE). Providers may also need to consider industry or employer expectations. Individual higher education providers will decide how they use this information. The broad subject of architecture is both academic and vocational. The bachelor's award for architecture is the first stage of the typical education of an architect. This is typically either a BSc or a BA degree. The second stage of academic qualification is a master's level degree, typically in the form of a two-year MArch, which is defined as an undergraduate master's award. Architecture qualifications typically require a total of 360 (Credit Accumulation and Transfer Scheme, or CATS) credits at bachelor's level and 240 (CATS) credits within a master's level degree. While this may equate to five years of 120 (CATS) credits each, higher education providers may construct alternatives to enable flexibility in student learning. This Statement seeks to encapsulate the nature of a rich and diverse academic discipline. It is not intended to prescribe a curriculum, but rather describes the broad intellectual territory within which individual higher education providers will locate their courses of study in architecture

Proteinlike behavior of a spin system near the transition between ferromagnet and spin glass

A simple spin system is studied as an analog for proteins. We investigate how the introduction of randomness and frustration into the system effects the designability and stability of ground state configurations. We observe that the spin system exhibits protein-like behavior in the vicinity of the transition between ferromagnet and spin glass. Our results illuminate some guiding principles in protein evolution.Comment: 12 pages, 4 figure

Phase transition and landscape statistics of the number partitioning problem

The phase transition in the number partitioning problem (NPP), i.e., the transition from a region in the space of control parameters in which almost all instances have many solutions to a region in which almost all instances have no solution, is investigated by examining the energy landscape of this classic optimization problem. This is achieved by coding the information about the minimum energy paths connecting pairs of minima into a tree structure, termed a barrier tree, the leaves and internal nodes of which represent, respectively, the minima and the lowest energy saddles connecting those minima. Here we apply several measures of shape (balance and symmetry) as well as of branch lengths (barrier heights) to the barrier trees that result from the landscape of the NPP, aiming at identifying traces of the easy/hard transition. We find that it is not possible to tell the easy regime from the hard one by visual inspection of the trees or by measuring the barrier heights. Only the {\it difficulty} measure, given by the maximum value of the ratio between the barrier height and the energy surplus of local minima, succeeded in detecting traces of the phase transition in the tree. In adddition, we show that the barrier trees associated with the NPP are very similar to random trees, contrasting dramatically with trees associated with the $p$ spin-glass and random energy models. We also examine critically a recent conjecture on the equivalence between the NPP and a truncated random energy model

Energy landscapes, supergraphs, and "folding funnels" in spin systems

Dynamical connectivity graphs, which describe dynamical transition rates between local energy minima of a system, can be displayed against the background of a disconnectivity graph which represents the energy landscape of the system. The resulting supergraph describes both dynamics and statics of the system in a unified coarse-grained sense. We give examples of the supergraphs for several two dimensional spin and protein-related systems. We demonstrate that disordered ferromagnets have supergraphs akin to those of model proteins whereas spin glasses behave like random sequences of aminoacids which fold badly.Comment: REVTeX, 9 pages, two-column, 13 EPS figures include

Geometric and Statistical Properties of the Mean-Field HP Model, the LS Model and Real Protein Sequences

Lattice models, for their coarse-grained nature, are best suited for the study of the ``designability problem'', the phenomenon in which most of the about 16,000 proteins of known structure have their native conformations concentrated in a relatively small number of about 500 topological classes of conformations. Here it is shown that on a lattice the most highly designable simulated protein structures are those that have the largest number of surface-core switchbacks. A combination of physical, mathematical and biological reasons that causes the phenomenon is given. By comparing the most foldable model peptides with protein sequences in the Protein Data Bank, it is shown that whereas different models may yield similar designabilities, predicted foldable peptides will simulate natural proteins only when the model incorporates the correct physics and biology, in this case if the main folding force arises from the differing hydrophobicity of the residues, but does not originate, say, from the steric hindrance effect caused by the differing sizes of the residues.Comment: 12 pages, 10 figure

Smectic blue phases: layered systems with high intrinsic curvature

We report on a construction for smectic blue phases, which have quasi-long range smectic translational order as well as three dimensional crystalline order. Our proposed structures fill space by adding layers on top of a minimal surface, introducing either curvature or edge defects as necessary. We find that for the right range of material parameters, the favorable saddle-splay energy of these structures can stabilize them against uniform layered structures. We also consider the nature of curvature frustration between mean curvature and saddle-splay.Comment: 15 pages, 11 figure

Use of a porous membrane for gas bubble removal in microfluidic channels: physical mechanisms and design criteria

We demonstrate and explain a simple and efficient way to remove gas bubbles from liquid-filled microchannels, by integrating a hydrophobic porous membrane on top of the microchannel. A prototype chip is manufactured in hard, transparent polymer with the ability to completely filter gas plugs out of a segmented flow at rates up to 7.4 microliter/s per mm2 of membrane area. The device involves a bubble generation section and a gas removal section. In the bubble generation section, a T-junction is used to generate a train of gas plugs into a water stream. These gas plugs are then transported towards the gas removal section, where they slide along a hydrophobic membrane until complete removal. The system has been successfully modeled and four necessary operating criteria have been determined to achieve a complete separation of the gas from the liquid. The first criterion is that the bubble length needs to be larger than the channel diameter. The second criterion is that the gas plug should stay on the membrane for a time sufficient to transport all the gas through the membrane. The third criterion is that the gas plug travel speed should be lower than a critical value: otherwise a stable liquid film between the bubble and the membrane prevents mass transfer. The fourth criterion is that the pressure difference across the membrane should not be larger than the Laplace pressure to prevent water from leaking through the membrane