A Family of Fitness Landscapes Modeled through Gene Regulatory Networks

Fitness landscapes are a powerful metaphor for understanding the evolution of biological systems. These landscapes describe how genotypes are connected to each other through mutation and related through fitness. Empirical studies of fitness landscapes have increasingly revealed conserved topographical features across diverse taxa, e.g., the accessibility of genotypes and “ruggedness”. As a result, theoretical studies are needed to investigate how evolution proceeds on fitness landscapes with such conserved features. Here, we develop and study a model of evolution on fitness landscapes using the lens of Gene Regulatory Networks (GRNs), where the regulatory products are computed from multiple genes and collectively treated as phenotypes. With the assumption that regulation is a binary process, we prove the existence of empirically observed, topographical features such as accessibility and connectivity. We further show that these results hold across arbitrary fitness functions and that a trade-off between accessibility and ruggedness need not exist. Then, using graph theory and a coarse-graining approach, we deduce a mesoscopic structure underlying GRN fitness landscapes where the information necessary to predict a population’s evolutionary trajectory is retained with minimal complexity. Using this coarse-graining, we develop a bottom-up algorithm to construct such mesoscopic backbones, which does not require computing the genotype network and is therefore far more efficient than brute-force approaches. Altogether, this work provides mathematical results of high-dimensional fitness landscapes and a path toward connecting theory to empirical studies.     

Exploring the origins of the power-law properties of energy landscapes: An egg-box model

Multidimensional potential energy landscapes (PELs) have a Gaussian distribution for the energies of the minima, but at the same time the distribution of the hyperareas for the basins of attraction surrounding the minima follows a power-law. To explore how both these features can simultaneously be true, we introduce an “egg-box” model. In these model landscapes, the Gaussian energy distribution is used as a starting point and we examine whether a power-law basin area distribution can arise as a natural consequence through the swallowing up of higher-energy minima by larger low-energy basins when the variance of this Gaussian is increased sufficiently. Although the basin area distribution is substantially broadened by this process, it is insufficient to generate power-laws, highlighting the role played by the inhomogeneous distribution of basins in configuration space for actual PELs.     

Generative Art with Swarm Landscapes

We present a generative swarm art project that creates 3D animations by running a Particle Swarm Optimization algorithm over synthetic landscapes produced by an objective function. Different kinds of functions are explored, including mathematical expressions, Perlin noise-based terrain, and several image-based procedures. A method for displaying the particle swarm exploring the search space in aesthetically pleasing ways is described. Several experiments are detailed and analyzed and a number of interesting visual artifacts are highlighted.     

Quasispecies distribution of Eigen model

We have studied sharp peak landscapes of the Eigen model from a new perspective about how the quasispecies are distributed in the sequence space. To analyse the distribution more carefully, we bring in two tools. One tool is the variance of Hamming distance of the sequences at a given generation. It not only offers us a different avenue for accurately locating the error threshold and illustrates how the configuration of the distribution varies with copying fidelity $q$ in the sequence space, but also divides the copying fidelity into three distinct regimes. The other tool is the similarity network of a certain Hamming distance $d_{0}$, by which we can gain a visual and in-depth result about how the sequences are distributed. We find that there are several local similarity optima around the centre (global similarity optimum) in the distribution of the sequences reproduced near the threshold. Furthermore, it is interesting that the distribution of clustering coefficient $C(k)$ follows lognormal distribution and the curve of clustering coefficient $C$ of the network versus $d_{0}$ appears to be linear near the threshold.     

Molecular Basis of the Dynamic Strength of the Sialyl Lewis X—Selectin Interaction

The selectins are Ca²⁺‐dependent cell adhesion molecules that facilitate the initial attachment of leukocytes to the vascular endothelium by binding to a carbohydrate moiety as exemplified by the tetrasaccharide, sialyl Lewis X (sLeX). An important property of the selectin‐sLeX interaction is its ability to withstand the hydrodynamic force of the blood flow. Herein, we used single‐molecule dynamic force spectroscopy (DFS) to identify the molecular determinants within sLeX that give rise to the dynamic properties of the selectin/sLeX interaction. Our atomic force microscopy (AFM) measurements revealed that the unbinding of the selectin/sLeX complexes involves overcoming at least two activation barriers. The inner barrier, which determines the dynamic response of the complex at high forces, is governed by the interaction between the Fuc residue of sLeX and a Ca²⁺ ion chelated to the lectin domain of the selectin molecule, whereas the outer activation barrier can be attributed to interactions involving the sialic acid residue of sLeX. Due to their steep inner activation barriers, the selectin‐sLeX complexes are less sensitive to high pulling forces. Hence, besides its contribution to the bond energy, the Ca²⁺ ion also grants the selectin–sLeX complexes a tensile strength that is crucial for the selectin‐mediated rolling of leukocytes.     

A conformational analysis method for understanding the energy landscapes of clusters.

A newly developed unbiased structural optimization method, named dynamic lattice searching (DLS), is proposed as an approach for conformational analysis of atomic/molecular clusters and used in understanding the energy landscape of large clusters. The structures of clusters are described in terms of the number of basic tetrahedron (BT) units they contain. We found that the hit numbers of different structural motifs in DLS runs is proportional to the number of BTs. A parameter T(max) is defined to limit the maximal number of atoms moved in a structural transition. Results show that T(max) is a key parameter for modulating the efficiency of the DLS method and has a great influence on the hit number of different motifs in DLS runs. Finally, the effect of potential range on the conformational distribution of the (Morse)(98) cluster is also discussed with different potential-range parameters.     

Autocorrelation measures for the quadratic assignment problem

In this article we provide an exact expression for computing the autocorrelation coefficient ξ and the autocorrelation length ? of any arbitrary instance of the Quadratic Assignment Problem (QAP) in polynomial time using its elementary landscape decomposition. We also provide empirical evidence of the autocorrelation length conjecture in QAP and compute the parameters ξ and ? for the 137 instances of the QAPLIB. Our goal is to better characterize the difficulty of this important class of problems to ease the future definition of new optimization methods. Also, the advance that this represents helps to consolidate QAP as an interesting and now better understood problem.     

Local Rules and Fitness Landscapes: A Catastrophe Model

This paper examines the imposition of local rules in five mail delivery centres of Australia Post. Local rules are patterns of behaviour used by subunits of an organization to optimise their payoff. These local rules may ultimately benefit the total organization. Fitness landscapes are used to examine the emergence of local rules in this workplace. This research examined the relationship between the time taken to sort the mail and the volume of this mail. Work rates show a clear catastrophe shift; that is, work rates suddenly drop when the volume of mail exceeds a certain level, as Postal Delivery Officers apply local rules to maximise gains inherent in the pay structures. Such behaviour is close to that predicted by Kauffman (1995) in computer simulations of lattices and may be indicative of the application of local rules in organizations. The implications of the use of local rules are that behaviour in social systems may be dictated by systemic and emergent processes which are outside immediate management control. A further implication is that organizations may be structured to a significant extent by such local rules.     

Spin-glass energy landscape

We consider a nearest-neighbor-interaction ±J Ising spin glass in a square lattice. Inspired by natural evolution, we design a dynamic rule that includesselection, randomness, andmultibranch exploration. Following this rule, we succeed in walking along the space of states between local energy maxima and minima alternately. During the walk, we store various information about the spin states corresponding to these minima and maxima for later statistical analysis. In particular, we plot a histogram displaying how many times each minimum (or maximum) energy is visited as a function of the corresponding density value. Through finite-size scaling analysis, we conclude that a nonvanishing fraction of bonds remains unsatisfied (satisfied) at these energy minimum (maximum) states in the thermodynamic limit. This fraction measures the degree of unavoidable frustration of the system. Also in this limit, the width of these histograms vanishes, meaning that almost all metastable states occur at the same energy density value, with no dispersion.