Thermodynamic Analysis of Interacting Nucleic Acid Strands

Motivated by the analysis of natural and engineered DNA and RNA systems, we present the first algorithm for calculating the partition function of an unpseudoknotted complex of multiple interacting nucleic acid strands. This dynamic program is based on a rigorous extension of secondary structure models to the multistranded case, addressing representation and distinguishability issues that do not arise for single-stranded structures. We then derive the form of the partition function for a fixed volume containing a dilute solution of nucleic acid complexes. This expression can be evaluated explicitly for small numbers of strands, allowing the calculation of the equilibrium population distribution for each species of complex. Alternatively, for large systems (e.g., a test tube), we show that the unique complex concentrations corresponding to thermodynamic equilibrium can be obtained by solving a convex programming problem. Partition function and concentration information can then be used to calculate equilibrium base-pairing observables. The underlying physics and mathematical formulation of these problems lead to an interesting blend of approaches, including ideas from graph theory, group theory, dynamic programming, combinatorics, convex optimization, and Lagrange duality

Random Coding Bounds for DNA Codes Based on Fibonacci Ensembles of DNA Sequences

We consider DNA codes based on the concept of a weighted 2-stem similarity measure which reflects the ”hybridization potential” of two DNA sequences. A random coding bound on the rate of DNA codes with respect to a thermodynamic motivated similarity measure is proved. Ensembles of DNA strands whose sequence composition is restricted in a manner similar to the restrictions in binary Fibonacci sequences are introduced to obtain the bound

PseudoBase++: an extension of PseudoBase for easy searching, formatting and visualization of pseudoknots

Pseudoknots have been recognized to be an important type of RNA secondary structures responsible for many biological functions. PseudoBase, a widely used database of pseudoknot secondary structures developed at Leiden University, contains over 250 records of pseudoknots obtained in the past 25 years through crystallography, NMR, mutational experiments and sequence comparisons. To promptly address the growing analysis requests of the researchers on RNA structures and bring together information from multiple sources across the Internet to a single platform, we designed and implemented PseudoBase++, an extension of PseudoBase for easy searching, formatting and visualization of pseudoknots. PseudoBase++ (http://pseudobaseplusplus.utep.edu) maps the PseudoBase dataset into a searchable relational database including additional functionalities such as pseudoknot type. PseudoBase++ links each pseudoknot in PseudoBase to the GenBank record of the corresponding nucleotide sequence and allows scientists to automatically visualize RNA secondary structures with PseudoViewer. It also includes the capabilities of fine-grained reference searching and collecting new pseudoknot information

Conceptual Design of RNA-RNA Interaction Based Devices

AbstractA key goal of synthetic biology is to use biological molecules to create novel biological systems. Due to their role as transmitters in such systems, RNA molecules have gained much attention from synthetic biologists to design and construct novel RNA molecules with desirable functions and properties. In recent decades, the design of RNAs, however, has been limited to RNA architecture with primitive functions: aptamer and catalysis. To expand the paradigm of RNA-based design, we herein propose a conceptual design of RNA-RNA interaction based systems, considering domain-based structures of RNAs, as well as thermodynamic properties of RNA molecules and their interactions. Two evaluation scores, namely structural score (SS) and affinity score (AS), are used as criteria for selection of proper RNA sets. We employ this concept to design various RNA sets, each of which contains three RNA strands that altogether function like a comparator device. With these criteria, we show that four out of forty RNA sets would behave like a biological comparator since they have appropriate structure (SS=1) and proper interaction order (AS>1). The proposed scores are proven to be proper criteria for selection of RNA sets with required functions. This preliminary design offers an opportunity for synthetic biologists to expand the design of RNA sequence from a single strand to multiple strands that would behave in the same manner as enzymatic reactions

Theory on the mechanism of DNA renaturation: Stochastic nucleation and zipping

Renaturation of complementary single strands of DNA is one of the important processes that requires better understanding in the view of molecular biology and biological physics. Here we develop a stochastic dynamical model on the DNA renaturation. According to our model there are at least three steps in the renaturation process viz. incorrect-contact formation, correct-contact formation and nucleation, and zipping. Most of the earlier two-state models combined nucleation with incorrect-contact formation step. In our model we suggest that it is considerably meaningful when we combine the nucleation with the zipping since nucleation is the initial step of zipping and the nucleated and zipping molecules are indistinguishable. Incorrect-contact formation step is a pure three-dimensional diffusion controlled collision process. Whereas nucleation involves several rounds of one-dimensional slithering dynamics of one single strand of DNA on the other complementary strand in the process of searching for the correct-contact and then initiate nucleation. Upon nucleation, the stochastic zipping follows to generate a fully renatured double stranded DNA. It seems that the square-root dependency of the overall renaturation rate constant on the length of reacting single strands originates mainly from the geometric constraints in the diffusion controlled incorrect-contact formation step. Further the inverse scaling of the renaturation rate on the viscosity of the reaction medium also originates from the incorrect-contact formation step. On the other hand the inverse scaling of the renaturation rate with the sequence complexity originates from the stochastic zipping which involves several rounds of crossing over the free-energy barrier at microscopic levels.Comment: 17 pages, 2 figure

Programmable in situ amplification for multiplexed imaging of mRNA expression

In situ hybridization methods enable the mapping of mRNA expression within intact biological samples. With current approaches, it is challenging to simultaneously map multiple target mRNAs within whole-mount vertebrate embryos, representing a significant limitation in attempting to study interacting regulatory elements in systems most relevant to human development and disease. Here, we report a multiplexed fluorescent in situ hybridization method based on orthogonal amplification with hybridization chain reactions (HCR). With this approach, RNA probes complementary to mRNA targets trigger chain reactions in which fluorophore-labeled RNA hairpins self-assemble into tethered fluorescent amplification polymers. The programmability and sequence specificity of these amplification cascades enable multiple HCR amplifiers to operate orthogonally at the same time in the same sample. Robust performance is achieved when imaging five target mRNAs simultaneously in fixed whole-mount and sectioned zebrafish embryos. HCR amplifiers exhibit deep sample penetration, high signal-to-background ratios and sharp signal localization

Design of insulating devices for in vitro synthetic circuits

This paper describes a synthetic in vitro genetic circuit programmed to work as an insulating device. This circuit is composed of nucleic acids, which can be designed to interact according to user defined rules, and of few proteins that perform catalytic functions. A model of the circuit is derived from first principle biochemical laws. This model is shown to exhibit time-scale separation that makes its output insensitive to downstream time varying loads. Simulation results show the circuit effectiveness and represent the starting point for future experimental testing of the device

Structure Aware Smart Encoding and Decoding of Information in DNA

Our increasingly information driven world is growing the demand for new storage technologies. Current estimates place the total storage demands exceeding the supply of usable silicon by 2040 [1]. DNA is an attractive technology due to its incredible density, almost negligible energy requirements, and data retention measured in centuries [1]. DNA does, however, come with new challenges. It is an organic compound with complex internal interactions which complicate the design and synthesis of DNA sequences for the purpose of data storage. In this work we demonstrate a new encoding-decoding process that accounts for some of the challenges in encoding and decoding, including issues arising from the secondary structure of the sequence, repeated nucleotides, unwanted subsequences, as well as GC content, vital for ensuring stable sequences. This is accomplished by using a graph representation of the possible encoding space that captures the relevant constraints, combined with a search algorithm that identifies the optimal encoding for the given input data accounting for these constraints. A benefit of our approach is that by leveraging the constraints on the encoding process, the decoding algorithm is able to correct single point errors without the aid of error correction codes; this is something no current competing solution can accomplish