Complexity of evolutionary equilibria in static fitness landscapes

A fitness landscape is a genetic space -- with two genotypes adjacent if they differ in a single locus -- and a fitness function. Evolutionary dynamics produce a flow on this landscape from lower fitness to higher; reaching equilibrium only if a local fitness peak is found. I use computational complexity to question the common assumption that evolution on static fitness landscapes can quickly reach a local fitness peak. I do this by showing that the popular NK model of rugged fitness landscapes is PLS-complete for K >= 2; the reduction from Weighted 2SAT is a bijection on adaptive walks, so there are NK fitness landscapes where every adaptive path from some vertices is of exponential length. Alternatively -- under the standard complexity theoretic assumption that there are problems in PLS not solvable in polynomial time -- this means that there are no evolutionary dynamics (known, or to be discovered, and not necessarily following adaptive paths) that can converge to a local fitness peak on all NK landscapes with K = 2. Applying results from the analysis of simplex algorithms, I show that there exist single-peaked landscapes with no reciprocal sign epistasis where the expected length of an adaptive path following strong selection weak mutation dynamics is $e^{O(n^{1/3})}$ even though an adaptive path to the optimum of length less than n is available from every vertex. The technical results are written to be accessible to mathematical biologists without a computer science background, and the biological literature is summarized for the convenience of non-biologists with the aim to open a constructive dialogue between the two disciplines.Comment: 14 pages, 3 figure

Edge effects in game theoretic dynamics of spatially structured tumours

Background: Analysing tumour architecture for metastatic potential usually focuses on phenotypic differences due to cellular morphology or specific genetic mutations, but often ignore the cell's position within the heterogeneous substructure. Similar disregard for local neighborhood structure is common in mathematical models. Methods: We view the dynamics of disease progression as an evolutionary game between cellular phenotypes. A typical assumption in this modeling paradigm is that the probability of a given phenotypic strategy interacting with another depends exclusively on the abundance of those strategies without regard local heterogeneities. We address this limitation by using the Ohtsuki-Nowak transform to introduce spatial structure to the go vs. grow game. Results: We show that spatial structure can promote the invasive (go) strategy. By considering the change in neighbourhood size at a static boundary -- such as a blood-vessel, organ capsule, or basement membrane -- we show an edge effect that allows a tumour without invasive phenotypes in the bulk to have a polyclonal boundary with invasive cells. We present an example of this promotion of invasive (EMT positive) cells in a metastatic colony of prostate adenocarcinoma in bone marrow. Interpretation: Pathologic analyses that do not distinguish between cells in the bulk and cells at a static edge of a tumour can underestimate the number of invasive cells. We expect our approach to extend to other evolutionary game models where interaction neighborhoods change at fixed system boundaries.Comment: 14 pages, 3 figures; restructured abstract, added histology to fig. 1, added fig. 3, discussion of EMT introduced and cancer biology expande

Measuring as a new mode of inquiry that bridges evolutionary game theory and cancer biology

We show that as game theory was transferred from mathematical oncology to experimental cancer biology, a new mode of inquiry was created. Modelling was replaced by measuring. The game measured by a game assay can serve as a bridge that allows knowledge to flow backwards from target (cancer research) to source (game theory). Our finding suggests that the conformist and creative (Houkes & Zwart, 2019) types of transfer need to be augmented. We conclude by introducing the expansive and transformative types to get a four-tier typology of knowledge transfer

Dirac fermions and flat bands in the ideal kagome metal FeSn.

A kagome lattice of 3d transition metal ions is a versatile platform for correlated topological phases hosting symmetry-protected electronic excitations and magnetic ground states. However, the paradigmatic states of the idealized two-dimensional kagome lattice-Dirac fermions and flat bands-have not been simultaneously observed. Here, we use angle-resolved photoemission spectroscopy and de Haas-van Alphen quantum oscillations to reveal coexisting surface and bulk Dirac fermions as well as flat bands in the antiferromagnetic kagome metal FeSn, which has spatially decoupled kagome planes. Our band structure calculations and matrix element simulations demonstrate that the bulk Dirac bands arise from in-plane localized Fe-3d orbitals, and evidence that the coexisting Dirac surface state realizes a rare example of fully spin-polarized two-dimensional Dirac fermions due to spin-layer locking in FeSn. The prospect to harness these prototypical excitations in a kagome lattice is a frontier of great promise at the confluence of topology, magnetism and strongly correlated physics

Vortex core switching by coherent excitation with single in-plane magnetic field pulses

The bistability of the core magnetization of nano-scaled magnets with a magnetic vortex configuration has great potential for data storage applications. To exploit this, reliable switching between the two possible states is needed. Time resolved x-ray microscopy was used to study the response of the vortex core to excitation pulses at sub-ns timescales and image the vortex core switching. A reliable switching process by coherent excitation with leading and trailing edges of in-plane magnetic field pulses was found and compared with micromagnetic simulations.Comment: 4 pages, 3 figure

Charge density waves in cuprate superconductors beyond the critical doping

The unconventional normal-state properties of the cuprates are often discussed in terms of emergent electronic order that onsets below a putative critical doping of xc = 0.19. Charge-density wave (CDW) correlations represent one such order; however, experimental evidence for such order generally spans a limited range of doping that falls short of the critical value xc, leading to questions regarding its essential relevance. Here, we use x-ray diffraction to demonstrate that CDW correlations in La2-xSrxCuO4 persist up to a doping of at least x = 0.21. The correlations show strong changes through the superconducting transition, but no obvious discontinuity through xc = 0.19, despite changes in Fermi surface topology and electronic transport at this doping. These results demonstrate the interaction between CDWs and superconductivity even in overdoped cuprates and prompt a reconsideration of the role of CDW correlations in the high-temperature cuprate phase diagram.Comment: 8 pages + 5 pages of supplemental material; accepted in npj Quantum Material

Molecular simulation studies of cyanine-based chromonic mesogens: spontaneous symmetry breaking to form chiral aggregates and the formation of a novel lamellar structure

All‐atom molecular dynamics simulations are performed on two chromonic mesogens in aqueous solution: 5,5′‐dimethoxy‐bis‐(3,3′‐di‐sulphopropyl)‐thiacyanine triethylammonium salt (Dye A) and 5,5′‐dichloro‐bis‐(3,3′‐di‐sulphopropyl)‐thiacyanine triethylammonuim salt (Dye B). Simulations demonstrate the formation of self‐assembled chromonic aggregates with an interlayer distance of ≈0.35 nm, with neighboring molecules showing a predominantly head‐to‐tail antiparallel stacking arrangement to minimize electrostatic repulsion between hydrophilic groups. Strong overlap of the aromatic rings occurs within the self‐assembled columns, characteristic of H‐aggregation in aqueous solution. At low concentrations, aggregates of Dye A form chiral columns, despite the presence of strictly achiral species. Chirality arises out of the minimization of steric repulsion between methoxy groups, which would otherwise disrupt the stacking of aromatic molecular cores. At higher concentrations, simulations suggest the interaction of short columns leads to the formation of an achiral‐layered structure in which hydrophobic aromatic regions of the molecule are sandwiched between two layers of hydrophilic groups. This novel lamellar structure is suggested as a likely candidate for the structure of a J‐aggregate. The latter is known to exhibit intense red‐shifted absorption peaks in solution but their structure has not yet been characterized. Self‐organization of such structures provides a route to the formation of “smectic” chromonic mesophases