SNP Analysis of Single-Cell RNA Sequencing Data
Paola Castro, Wendy Lee and Nader Pourmand

Breast cancer has the highest incidence in women. For this reason it is an important problem to address. Cancer treatments are not always successful. The problem with current cancer treatments might be that a tumor is treated as an entity. However, as it is shown in this study each cell in a tumor might be different, even if the cell is from the same tissue. In the present study, cells from the the MDA-MD-231 cancer cell line were treated with Taxol. Taxol kills cell by inhibiting mitosis. Taxol inhibits mitosis by targeting microtubule polymerization. Microtubule polymerization is required for formation of the mitotic spindle. However, some cells survive Taxol treatment. The fact that some cells die from Taxol treatment but others don’t is a clue that each cell is different. The data provided in this study shows, through Single Nucleotide Polymorphism analysis, that some cells survive Taxol treatment and some don’t because not every cell is affected the same by Taxol treatment.

A Novel Model for DNA Packaging Simulations
Brian Cruz

We present a new model for DNA packaging simulations in bacteriophages that includes the effect of the packaging motor. We simulate the motor using a kinetic Monte Carlo algorithm that feeds the DNA into the virus and couple it with a dynamics simulation of the DNA. The model of the DNA takes into account the effect of local torsional stress on the conformation of the chain—as well as the effect of stretching and bending stresses.

Modelling the Evolution of Genetic Instability During Tumour Progression
Ruchira S. Datta, Alice Gutteridge, Charles Swanton, Carlo C. Maley, Trevor A. Graham

The role of genetic instability in driving carcinogenesis remains controversial. Genetic instability should accelerate carcinogenesis by increasing the rate of advantageous driver mutations, however, genetic instability can also potentially retard tumour growth by increasing the rate of deleterious mutation. As such, it is unclear whether genetically unstable clones would tend to be more selectively advantageous than their genetically stable counterparts within a growing tumour. Here we show the circumstances where genetic instability evolves during tumour progression towards cancer.

We employ a Wright-Fisher type model that describes the evolution of tumour sub-clones. Clones can acquire both advantageous and deleterious mutations, and mutator mutations that increase a cell’s intrinsic mutation rate.

Within the model, cancers evolve with a mutator phenotype when driver mutations bestow only moderate increases in fitness: very strong or weak selection for driver mutations suppresses the evolution of a mutator phenotype. Genetic instability occurs secondarily to selectively advantageous driver mutations. Deleterious mutations have relatively little effect on the evolution of genetic instability unless selection for additional driver mutations is very weak or if deleterious mutations are very common.

Our model provides a framework for studying the evolution of genetic instability in tumour progression. Our analysis highlights the central role of selection in shaping patterns of mutation in carcinogenesis.

DNA Unknotting on the Cubic Lattice — Modeling the Enzymatic Action of Type II Topoisomerases
Kevin He, Reuben Brasher, Thomas Schuster, Mariel Vazquez

In nature, circular DNA molecules often become knotted or linked. DNA knots and links can impact vital cellular processes such as replication and transcription. Type II topoisomerases are enzymes that remove these undesirable topological forms using strand passage. The high unknotting and unlinking efficiency of the enzyme suggests preferential targeting of certain sites on the DNA molecule. To better understand this enzymatic action, we model circular DNA as a self-avoiding polygon in the simple cubic lattice and use Monte-Carlo methods to sample polygons of each knot type. We use a novel, knot-centric approach to simulate strand passage, allowing us to search for and target specific local topological features in our model. We find that preferential targeting of clasped juxtapositions in our model increases one-step unknotting probabilities in twist knots and leads to faster unknotting, compared to performing strand passage “at random”. The extent of unknotting varies with the knot type. We highlight geometrical features that seem more conducive to unknotting.

Application of Compressed Sensing to Network Reconstruction
Graham Heimberg, Matthew Thomson, Hana El-Samad

Quantitative models of cellular signaling networks are necessary for predictive understanding of cellular networks.  Feasible, generalizable and unbiased machine learning methods for deriving dynamical systems models from gene expression data have yet to be developed because in current techniques the number of measurements scales poorly with the size of the network.  Here, we address this problem by applying a recently developed signal processing technique called compressed sensing (CS) to biological network reconstruction. CS prescribes an efficient procedure to sample gene expression profiles in a way that minimizes redundancies between measurements. This allows us to infer the structure of linearized biological networks with fewer measurements than traditional methods.  We demonstrate that if a biological network has S non-zero interaction edges out of n^2 possible interactions between n proteins, then we can reconstruct the network connectivity coefficient on the order of 2S*log(n) measurements, provided that these measurement form a diverse set of uncorrelated, or incoherent, expression profiles. We discuss how to practically obtain such measurements.

Analysis of SMRT Sequence Data in R
Robert M. Horton, Oliver M. Bannard, Jason G. Cyster

Single-Molecule Real-Time (SMRT, or ”PacBio”) sequencing is a new technology for high-throughput DNA sequence determination. It provides exceptionally long read-length and the ability to read from individual molecular templates, but it is prone to miscounting errors. Here we present a preliminary evaluation of this technology for mutation detection as a way to ascertain a history of germinal center (GC) reactions in B cells.

Quantitative Analysis of Hi-C Data: Understanding the Folding of Human Chromatin
Reyka Jayasinghe, Bradley McAuley, Rob Scharein, Mariel Vasquez, Javier Arsuaga

Determining the 3D structure of chromatin is key for understanding a number of biological processes including long range chromatin interactions, gene regulation and chromosome aberration formation. Novel experimental methods such as Chromatin Conformation Capture (CCC) or its extension Hi-C are proving to be extremely valuable in determining this structure. Based on these assays Lieberman-Aiden and colleagues (Lieberman-Aiden et. al. 2009) showed that the 3D structure of the chromatin cannot be an equilibrium globule (i.e. a random walk) but instead they proposed chromatin should resemble a crumpled or fractal globule  (Grossberg et al 1996). In this model chromatin is space filling, globular, largely unknotted and self-similar. These properties clearly distinguish the fractal and equilibrium globule but these are somehow to extremes of chromatin organization. Here we propose an algorithm (based on the well known BFACF algorithm for self-avoiding walks) to analyze these properties separately in their relation to experimental data.  We show that our algorithm generates space filling curves, can reproduce the data experimental data presented by (Lieberman-Aiden et. al. 2009) and allows us to quantify the contribution of globularity and knottedness to the structure of the genome.

Finding the Minimum Step Number of Knots Confined to a 1-Slab in the Simple Cubic Lattice
Michael Jun, Koya Shimokawa , Mariel Vazquez

Knots can be found in DNA and proteins and provide clues for topological analysis of their structures. Key parameters to consider in such studies are the minimum number of monomers required to construct a knot and the volume confinement in which the constructions take place. We here consider the minimum length (minimum step number) needed to form a knot in the simple cubic lattice confined between two parallel planes (or by a slab). The minimum step number of a trefoil in a 1-slab has been determined analytically in Ishihara et al. (2011) to be 26. In this paper the authors proposed the Minimum Step Number (MSN) Algorithm to address this problem. Though a very systematic approach, the MSN Algorithm becomes very complicated and expensive when extended to larger knots. In Ishihara et al., 2011, upper bounds for the minimal step number were proposed for all knots with 10 and less crossings by using a Monte Carlo based approach. We here propose a computational exhaustive enumeration program, that would allow to confirm, or improve some of the numerical estimates where the MSN algorithm becomes intractable. We confirm that the minimum step number of a trefoil in the 1-slab is indeed 26. We aim to generalize this to 4 and 5-crossing knots.

Tipping the Balance Between Adhesion and Myosin Contraction Drives Spontaneous Motility Initiation and Turning in Keratocytes as Revealed by Modeling and Experiment
Kun-Chun Lee, Erin L. Barnhart, Greg M. Allen, Julie A. Theriot, Alex Mogilner 

Fish keratocytes spontaneously break symmetry and become motile in the absence of known external cues. It is known that motility initiates at the prospective rear of the cell where centripetal actin flow increases prior to the symmetry break, but what causes this flow increase and whether respective trigger is biochemical or mechanical is not clear. We applied our published model of continuum mechanics of viscous contractile actin network with free boundary to test two simple mechanical pathways of the initial asymmetric flow increase: spatial bias of myosin toward the prospective rear, or weakening of adhesion there. Both scenarios predicted the accelerated actin flow at the rear, but gave opposite predictions about traction force distributions.  Experimental measurements showed that the traction forces are attenuated at the rear prior to motility, so the experiment supports the adhesion weakening as the symmetry break trigger.  Simulations of the model showed, however, that such transient adhesion change does not support stable motility.  We therefore propose a model in which the adhesion strength depends on the actin flow rate or myosin strength such that adhesions slip at high flow or contraction. Simulations of this model with stochastic self-organizing acto-myosin dynamics coupled with mechanosensitive adhesion reproduced the data and made additional predictions on dependence of frequency of the motility initiation on overall adhesiveness of the substrate and localized application of drags that were tested experimentally and confirmed.  Our model showed the coupling can further trigger left-right asymmetry in the traction forces.  The asymmetric force causes model cells to turn toward the side with higher traction forces similar to the measured traction forces in turning keratocytes.  We propose therefore that the mechanical adhesion-contraction switch underlies the motile polarization and cell turning in simple keratocyte cells, though additional biochemical mechanisms can complement this switch.

Towards Robotics-Inspired, Automated and Flexible Model-Building Method for Medium to Low Resolution Crystallographic Data
Dimitar V. Pachov, Buu-Minh Ta, Henry van den Bedem, Keith Hodgson

High quality atomic crystallographic models can be gateway to understanding functional mechanisms of biomolecules. Unfortunately, conformational dynamics and multiple substates underlie biological activity and when in the crystal, often lead to ambiguous and/or low resolution electron density maps that are difficult to interpret. Existing refinement algorithms rely on manual intervention, rigid body fits, or restraints derived from related, high resolution atomic models.

We extend the kino-geometric sampling (KGS), a novel algorithm developed by the Prof. Latombe’s group (Stanford), that samples the folded landscape of a protein by representing it as a kinematic linkage of rigid groups of atoms (rigid bodies, links) and rotatable bonds (joints), to automatically generate structural models that best fit observed electron density maps. KGS deforms a complex network of kinematic cycles without breaking the covalent and favorable hydrogen bonds defining these interdependent cycles. We apply a minimization protocol to locally guide model search and validate flexible fits with large radius of convergence. Particularly, we start the refinement by selecting the rigid body that best fits the electron density and gradually add and minimize successive groups of rigid bodies.

Tests on synthetic data (PDB 2LAO) have shown a promising domain movement exceeding 4.5A of radius of convergence. We further apply our methodology to refine an unsolved low-resolution molecular replacement data set of the Aminotransferase protein system and identify local heterogeneity.

Simulating Direct Recombination Using Lattice Methods
Reuben Brasher, Kai Ishihara, Maasaki Yoshida, Koya Shimokawa, Mariel Vazquez

The operation of direct recombination on two linked circular DNA plasmid with one recombination site will produce a single knotted dimer. On a single knotted dimer, the operation will produce two linked plasmids. In either case, the topological complexity can decrease from the operation, only in steps. The possible steps in the pathway from complicated link to unlinked and unknotted forms are known precisely only for relatively simple links. This study applies Monte Carlo methods to identify the probabilities for the pathway from the (-2,6) torus link through to two unlinked unkotted components.

Optimal Signal Transmission
Gabriele Scheler, Johann Schumann

We propose a model of parameter learning for signal transduction, where the objective function is defined by signal transmission efficiency. This is a novel approach compared to the usual technique of adjusting parameters only on the basis of experimental data. We apply this to learn kinetic rates as a form of evolutionary learning, and find parameters which satisfy the objective. These may be intersected with parameter sets generated from experimental time-series data to further constrain a signal transduction model. The resulting model is self-regulating, i.e. perturbations in protein concentrations or changes in extracellular signaling will automatically lead to adaptation. We systematically perturb protein concentrations and observe the response of the system. We find fits with common observations of compensatory or co-regulation of protein expression levels in cellular systems (e.g. PDE3, AC5). In a novel experiment, we alter the distribution of extracellular signaling, and observe adaptation based on optimizing signal transmission. Self-regulating systems may be predictive of unwanted drug interference effects, since they aim to mimic complex cellular adaptation in a unified way.

Multiscale Natural Moves Refine Macromolecules Using Single-Particle Electron Microscopy Projection Images
Junjie Zhang, Peter Minary, Michael Levitt

The method presented here refines molecular conformations directly against projections of single particles measured by electron microscopy. By optimizing the orientation of the projection at the same time as the conformation, the method is well-suited to two-dimensional class averages from cryoelectron microscopy. Such direct use of two-dimensional images circumvents the need for a three-dimensional density map, which may be difficult to reconstruct from projections due to structural heterogeneity or preferred orientations of the sample on the grid. Our refinement protocol exploits Natural Move Monte Carlo to model a macromolecule as a small number of segments connected by flexible loops, on multiple scales. After tests on artificial data from lysozyme, we applied the method to the Methonococcus maripaludis chaperonin. We successfully refined its conformation from a closed-state initial model to an open-state final model using just one class-averaged projection. We also used Natural Moves to iteratively refine against heterogeneous projection images of Methonococcus maripaludis chaperonin in a mix of open and closed states. Our results suggest a general method for electron microscopy refinement specially suited to macromolecules with significant conformational flexibility. The algorithm is available in the program Methodologies for Optimization and Sampling In Computational Studies.

Quantitative Analysis of Combinatorial Regulation in Unfolded Protein Responses Using an Automated Flow Cytometry System
Ignacio Zuleta, Hana El-Samad, Hao Li

Cells respond to environmental cues using a variety of transient mechanisms. In many situations, the phenotypic response is dominated by the need to reprogram the transcription of biomass components to specialize to life in new environments. Gene expression measurements using mRNA quantification techniques are usually opaque with respect to both dynamics and distribution across a cell population. Here we describe a quantitative high throughput approach that aims at addressing both issues by leveraging novel automated flow cytometry stimulus-response experiments. We built a novel high throughput flow cytometry setup that is capable of growing 96 cultures in real time while collecting single cell parameters. Using this technology we can measure instantaneous cell growth simultaneously with single-cell fluorescence, which in turn enables us to estimate instantaneous gene expression. We then show that detailed measurement of gene expression using a library of single-integration promoter fusion during protein folding stress sheds light onto the simultaneous regulation of stress-responsive gene promoter activity and growth rate. To do so, we built 44 Reporter strains containing transcriptional reporters for stress-responsive genes that are known to be targets of the heat-shock response (HSR) and the unfolded-protein response (UPR). Additionally, synthetic reporters containing the binding sites for one transcriptional regulator of the canonical pathways were used to estimate transcription factor activity. Using the measured transcriptional rates for all the promoters and the inferred factor activities, we tested whether the contribution to the log(expression) from each transcription factor is linearly proportional to the copy number of the corresponding binding motif. We also test whether the contributions of different regulatory factors to the expression of a given promoter are additive. We found that while HSF and MSN2/4 regulate expression linearly with respect to the number of binding sites, the pattern for other factors is more complex. We discuss some of the implications of these patterns, like the possibility of context-sensitive repressive activity of activators, and suggest follow-up experiments using promoter mutations to confirm this hypothesis.