Transferable measurements of heredity in models of the origins of life

We propose a metric which can be used to compute the amount of heritable variation enabled by a given dynamical system. A distribution of selection pressures is used such that each pressure selects a particular fixed point via competitive exclusion in order to determine the corresponding distribution of potential fixed points in the population dynamics. This metric accurately detects the number of species present in artificially prepared test systems, and furthermore can correctly determine the number of heritable sets in clustered transition matrix models in which there are no clearly defined genomes. Finally, we apply our metric to the GARD model and show that it accurately reproduces prior measurements of the model's heritability.Comment: 12 pages, 7 figure

A Strategy for Origins of Life Research

Aworkshop was held August 26–28, 2015, by the Earth- Life Science Institute (ELSI) Origins Network (EON, see Appendix I) at the Tokyo Institute of Technology. This meeting gathered a diverse group of around 40 scholars researching the origins of life (OoL) from various perspectives with the intent to find common ground, identify key questions and investigations for progress, and guide EON by suggesting a roadmap of activities. Specific challenges that the attendees were encouraged to address included the following: What key questions, ideas, and investigations should the OoL research community address in the near and long term? How can this community better organize itself and prioritize its efforts? What roles can particular subfields play, and what can ELSI and EON do to facilitate research progress? (See also Appendix II.) The present document is a product of that workshop; a white paper that serves as a record of the discussion that took place and a guide and stimulus to the solution of the most urgent and important issues in the study of the OoL. This paper is not intended to be comprehensive or a balanced representation of the opinions of the entire OoL research community. It is intended to present a number of important position statements that contain many aspirational goals and suggestions as to how progress can be made in understanding the OoL. The key role played in the field by current societies and recurring meetings over the past many decades is fully acknowledged, including the International Society for the Study of the Origin of Life (ISSOL) and its official journal Origins of Life and Evolution of Biospheres, as well as the International Society for Artificial Life (ISAL)

Accelerating the Finite-Element Method for Reaction-Diffusion Simulations on GPUs with CUDA

DNA nanotechnology offers a fine control over biochemistry by programming chemical reactions in DNA templates. Coupled to microfluidics, it has enabled DNA-based reaction-diffusion microsystems with advanced spatio-temporal dynamics such as traveling waves. The Finite Element Method (FEM) is a standard tool to simulate the physics of such systems where boundary conditions play a crucial role. However, a fine discretization in time and space is required for complex geometries (like sharp corners) and highly nonlinear chemistry. Graphical Processing Units (GPUs) are increasingly used to speed up scientific computing, but their application to accelerate simulations of reaction-diffusion in DNA nanotechnology has been little investigated. Here we study reaction-diffusion equations (a DNA-based predator-prey system) in a tortuous geometry (a maze), which was shown experimentally to generate subtle geometric effects. We solve the partial differential equations on a GPU, demonstrating a speedup of ∼100 over the same resolution on a 20 cores CPU

Hereditable states as a function of vesicle size.

<p>In the GARD paper, the authors observed the trend that as the vesicle size <i>N</i>_max was increased, the number of heritable states decreased [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140663#pone.0140663.ref008" target="_blank">8</a>]. We show that our algorithm can detect this trend successfully by plotting the average number of heritable states measured as a function of <i>N</i>_max, for simulations of 24 different <i>β</i> matrices, with the number of lipid types <i>N</i>_<i>G</i> = 100 in each case. The points are slightly offset horizontally for clarity, but all are measured at the same values of <i>N</i>_max: 24, 50, 100, 200, 500. Error bars indicating a confidence interval of one standard deviation in the measurement over 24 simulations are shown. The black hexagons show the average number of distinct compotypes <i>N</i>_<i>C</i> detected in simulations in [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140663#pone.0140663.ref008" target="_blank">8</a>] using the same <i>N</i>_<i>G</i>.</p

Confidence regions for detecting different numbers of heritable states.

<p>Upper: detection confidence regions (50% error) for the easy case (<i>m</i> = 0.05, <i>f</i>₁ = 0.5, uniform distribution of species). In this case the algorithm is mostly data-limited, accurately detecting at most a number of species roughly equal to 0.25<i>N</i>_<i>P</i>. Lower: detection confidence regions for a harder case (<i>m</i> = 0.05, <i>f</i>₁ = 0.05, heterogeneous distribution of species). In this regime the algorithm is feature-limited —more features are needed to detect more species.</p

Eigenvalue plot corresponding to transition matrices with different numbers of clusters.

<p>When the number of clusters is small, there is a clearly-defined gap between eigenvalues corresponding to cluster identity and eigenvalues corresponding to the fluctuations. As the number of clusters increases, the gap closes and it becomes more difficult to detect the structure of the population. Inset: Number of clusters detected by the algorithm versus actual number of clusters.</p

Convergence of the measured number of heritable states as the number of data points is increased.

<p>This shows the effect of regularization and of the choice of <i>α</i> on the convergence pattern in this particular test case. The parameters for these data are <i>f</i>₁ = 0.05, <i>m</i> = 0.2, <i>N</i>_<i>S</i> = 40.</p

Flow diagram of GARD dynamics in heritable-state space.

<p>This figure shows the average time-dependent behavior of the system state for a particular choice of the <b><i>β</i></b> matrix and a distribution of selection pressures, projected onto the first two PCA eigenvectors. The thickness of the streamlines indicates the magnitude of the vectors in the underlying averaged vector field. As the mean vector field is the result of averaging a number of random walks, this can be thought of as the strength of the local bias. The underlying greyscale intensity shows the logarithm of the probability density for the system state being found at that location.</p

Transition matrix network structure.

<p>Example structure of the transition matrix with 100 nodes, <i>N</i>_<i>L</i> = 20, and <i>N</i>_<i>C</i> = 3 visualized as a network. The darkness of edges is proportional to the probability of a transition along that edge. Even though there are more between-cluster links than within-cluster links, within-cluster links are a factor of 1000 more likely to be followed than between-cluster links, meaning that overall a random walker tends to stay within its current cluster.</p