Optimizing information flow in small genetic networks. I

In order to survive, reproduce and (in multicellular organisms) differentiate, cells must control the concentrations of the myriad different proteins that are encoded in the genome. The precision of this control is limited by the inevitable randomness of individual molecular events. Here we explore how cells can maximize their control power in the presence of these physical limits; formally, we solve the theoretical problem of maximizing the information transferred from inputs to outputs when the number of available molecules is held fixed. We start with the simplest version of the problem, in which a single transcription factor protein controls the readout of one or more genes by binding to DNA. We further simplify by assuming that this regulatory network operates in steady state, that the noise is small relative to the available dynamic range, and that the target genes do not interact. Even in this simple limit, we find a surprisingly rich set of optimal solutions. Importantly, for each locally optimal regulatory network, all parameters are determined once the physical constraints on the number of available molecules are specified. Although we are solving an over--simplified version of the problem facing real cells, we see parallels between the structure of these optimal solutions and the behavior of actual genetic regulatory networks. Subsequent papers will discuss more complete versions of the problem

Models of RNA Interaction from Experimental Datasets: Framework of Resilience

Resilience is a network property of systems responding under stress, which for biomedicine correlates to chronic or acute insults. Current need exists for models and algorithms to study whole transcriptome differences between tissues and disease states to understand resilience. Goal of this effort is to interpret cellular transcription in a dynamic system biology framework of RNA molecules forming an information structure with regulatory properties acting on individual transcripts. We develop and evaluate a bioinformatics framework based on information theory that utilizes RNA expression data to create a whole transcriptome model of interaction that could lead to the discovery of new biological control mechanisms. This addresses a fundamental question as to why transcription yields such a small fraction of protein products. We focus on a transformative concept that individual transcripts collectively form an “information cloud” of sequence words, which for some genes may have significant regulatory impact. Extending the concept of cis‐ and trans‐regulation, we propose to search for RNAs that are modulated by interactions with the transcriptome cloud and calling such examples nebula regulation. This framework has implications as a paradigm change for RNA regulation and provides a deeper understanding of nucleotide sequence structure and ‐omic language meaning

Dynamic load balancing for the distributed mining of molecular structures

In molecular biology, it is often desirable to find common properties in large numbers of drug candidates. One family of methods stems from the data mining community, where algorithms to find frequent graphs have received increasing attention over the past years. However, the computational complexity of the underlying problem and the large amount of data to be explored essentially render sequential algorithms useless. In this paper, we present a distributed approach to the frequent subgraph mining problem to discover interesting patterns in molecular compounds. This problem is characterized by a highly irregular search tree, whereby no reliable workload prediction is available. We describe the three main aspects of the proposed distributed algorithm, namely, a dynamic partitioning of the search space, a distribution process based on a peer-to-peer communication framework, and a novel receiverinitiated load balancing algorithm. The effectiveness of the distributed method has been evaluated on the well-known National Cancer Institute’s HIV-screening data set, where we were able to show close-to linear speedup in a network of workstations. The proposed approach also allows for dynamic resource aggregation in a non dedicated computational environment. These features make it suitable for large-scale, multi-domain, heterogeneous environments, such as computational grids

Theoretical Design and Analysis of Multivolume Digital Assays with Wide Dynamic Range Validated Experimentally with Microfluidic Digital PCR

This paper presents a protocol using theoretical methods and free software to design and analyze multivolume digital PCR (MV digital PCR) devices; the theory and software are also applicable to design and analysis of dilution series in digital PCR. MV digital PCR minimizes the total number of wells required for “digital” (single molecule) measurements while maintaining high dynamic range and high resolution. In some examples, multivolume designs with fewer than 200 total wells are predicted to provide dynamic range with 5-fold resolution similar to that of single-volume designs requiring 12 000 wells. Mathematical techniques were utilized and expanded to maximize the information obtained from each experiment and to quantify performance of devices and were experimentally validated using the SlipChip platform. MV digital PCR was demonstrated to perform reliably, and results from wells of different volumes agreed with one another. No artifacts due to different surface-to-volume ratios were observed, and single molecule amplification in volumes ranging from 1 to 125 nL was self-consistent. The device presented here was designed to meet the testing requirements for measuring clinically relevant levels of HIV viral load at the point-of-care (in plasma, 1 000 000 molecules/mL), and the predicted resolution and dynamic range was experimentally validated using a control sequence of DNA. This approach simplifies digital PCR experiments, saves space, and thus enables multiplexing using separate areas for each sample on one chip, and facilitates the development of new high-performance diagnostic tools for resource-limited applications. The theory and software presented here are general and are applicable to designing and analyzing other digital analytical platforms including digital immunoassays and digital bacterial analysis. It is not limited to SlipChip and could also be useful for the design of systems on platforms including valve-based and droplet-based platforms. In a separate publication by Shen et al. (J. Am. Chem. Soc., 2011, DOI: 10.1021/ja2060116), this approach is used to design and test digital RT-PCR devices for quantifying RNA

Information capacity of genetic regulatory elements

Changes in a cell's external or internal conditions are usually reflected in the concentrations of the relevant transcription factors. These proteins in turn modulate the expression levels of the genes under their control and sometimes need to perform non-trivial computations that integrate several inputs and affect multiple genes. At the same time, the activities of the regulated genes would fluctuate even if the inputs were held fixed, as a consequence of the intrinsic noise in the system, and such noise must fundamentally limit the reliability of any genetic computation. Here we use information theory to formalize the notion of information transmission in simple genetic regulatory elements in the presence of physically realistic noise sources. The dependence of this "channel capacity" on noise parameters, cooperativity and cost of making signaling molecules is explored systematically. We find that, at least in principle, capacities higher than one bit should be achievable and that consequently genetic regulation is not limited the use of binary, or "on-off", components.Comment: 17 pages, 9 figure

Dynamic Combinatorial Libraries: From Exploring Molecular Recognition to Systems Chemistry

Dynamic combinatorial chemistry (DCC) is a subset of combinatorial chemistry where the library members interconvert continuously by exchanging building blocks with each other. Dynamic combinatorial libraries (DCLs) are powerful tools for discovering the unexpected and have given rise to many fascinating molecules, ranging from interlocked structures to self-replicators. Furthermore, dynamic combinatorial molecular networks can produce emergent properties at systems level, which provide exciting new opportunities in systems chemistry. In this perspective we will highlight some new methodologies in this field and analyze selected examples of DCLs that are under thermodynamic control, leading to synthetic receptors, catalytic systems, and complex self-assembled supramolecular architectures. Also reviewed are extensions of the principles of DCC to systems that are not at equilibrium and may therefore harbor richer functional behavior. Examples include self-replication and molecular machines.

Thermodynamics of Information Processing Based on Enzyme Kinetics: an Exactly Solvable Model of Information Pump

Motivated by the recent proposed models of the information engine [D. Mandal and C. Jarzynski, Proc. Natl. Acad. Sci. 109, 11641 (2012)] and the information refrigerator [D. Mandal, H. T. Quan, and C. Jarzynski, Phys. Rev. Lett. 111, 030602 (2013)], we propose a minimal model of the information pump and the information eraser based on enzyme kinetics. This device can either pump molecules against the chemical potential gradient by consuming the information encoded in the bit stream or (partially) erase the information encoded in the bit stream by consuming the Gibbs free energy. The dynamics of this model is solved exactly, and the "phase diagram" of the operation regimes is determined. The efficiency and the power of the information machine is analyzed. The validity of the second law of thermodynamics within our model is clarified. Our model offers a simple paradigm for the investigating of the thermodynamics of information processing involving the chemical potential in small systems

High performance subgraph mining in molecular compounds

Structured data represented in the form of graphs arises in several fields of the science and the growing amount of available data makes distributed graph mining techniques particularly relevant. In this paper, we present a distributed approach to the frequent subgraph mining problem to discover interesting patterns in molecular compounds. The problem is characterized by a highly irregular search tree, whereby no reliable workload prediction is available. We describe the three main aspects of the proposed distributed algorithm, namely a dynamic partitioning of the search space, a distribution process based on a peer-to-peer communication framework, and a novel receiver-initiated, load balancing algorithm. The effectiveness of the distributed method has been evaluated on the well-known National Cancer Institute’s HIV-screening dataset, where the approach attains close-to linear speedup in a network of workstations

Entanglement Measures for Single- and Multi-Reference Correlation Effects

Electron correlation effects are essential for an accurate ab initio description of molecules. A quantitative a priori knowledge of the single- or multi-reference nature of electronic structures as well as of the dominant contributions to the correlation energy can facilitate the decision regarding the optimum quantum chemical method of choice. We propose concepts from quantum information theory as orbital entanglement measures that allow us to evaluate the single- and multi-reference character of any molecular structure in a given orbital basis set. By studying these measures we can detect possible artifacts of small active spaces.Comment: 14 pages, 4 figure

Real-Time Propagation TDDFT and Density Analysis for Exciton Couplings Calculations in Large Systems

Photo-active systems are characterized by their capacity of absorbing light energy and transforming it. Usually, more than one chromophore is involved in the light absorption and excitation transport processes in complex systems. Linear-Response Time-Dependent Density Functional (LR-TDDFT) is commonly used to identify excitation energies and transition properties by solving well-known Casida's equation for single molecules. However, this methodology is not useful in practice when dealing with multichromophore systems. In this work, we extend our local density decomposition method that enables to disentangle individual contributions into the absorption spectrum to computation of exciton dynamic properties, such as exciton coupling parameters. We derive an analytical expression for the transition density from Real-Time Propagation TDDFT (P-TDDFT) based on Linear Response theorems. We demonstrate the validity of our method to determine transition dipole moments, transition densities and exciton coupling for systems of increasing complexity. We start from the isolated benzaldehyde molecule, perform a distance analysis for $\pi$-stacked dimers and finally map the exciton coupling for a 14 benzaldehyde cluster.Comment: 32 pages, 8 figures; added references in introductions, typos fixe