Evolution of Protein Molecules

THE JOURNAL OF BIOLOGICAL CHEMISTRY: The Biochemical Behavior of LeadL I. Influence of Calcium, Phosphorus, and Vitamin D on Lead in Blood and Bone

To construct sophisticated biochemical circuits from scratch, one needs to understand how simple the building blocks can be and how robustly such circuits can scale up. Using a simple DNA reaction mechanism based on a reversible strand displacement process, we experimentally demonstrated several digital logic circuits, culminating in a four-bit square-root circuit that comprises 130 DNA strands. These multilayer circuits include thresholding and catalysis within every logical operation to perform digital signal restoration, which enables fast and reliable function in large circuits with roughly constant switching time and linear signal propagation delays. The design naturally incorporates other crucial elements for large-scale circuitry, such as general debugging tools, parallel circuit preparation, and an abstraction hierarchy supported by an automated circuit compiler.

http://science.sciencemag.org/content/sci/332/6034/1196.full.pdf

Scaling Up Digital Circuit Computation with DNA Strand Displacement Cascades

A number of different approaches have been described to identify proteins from tandem mass spectrometry (MS/MS) data. The most common approaches rely on the available databases to match experimental MS/MS data. These methods suffer from several drawbacks and cannot be used for the identification of proteins from unknown genomes. In this communication, we describe a new de novo sequencing software package, PEAKS, to extract amino acid sequence information without the use of databases. PEAKS uses a new model and a new algorithm to efficiently compute the best peptide sequences whose fragment ions can best interpret the peaks in the MS/MS spectrum. The output of the software gives amino acid sequences with confidence scores for the entire sequences, as well as an additional novel positional scoring scheme for portions of the sequences. The performance of PEAKS is compared with Lutefisk, a well-known de novo sequencing software, using quadrupole-time-of-flight (Q-TOF) data obtained for several tryptic peptides from standard proteins.

/pdf/peaks-powerful-software-for-peptide-de-novo-sequencing-by-1htzy7q8mi.pdf

PEAKS: powerful software for peptide de novo sequencing by tandem mass spectrometry

The impressive capabilities of the mammalian brain—ranging from perception, pattern recognition and memory formation to decision making and motor activity control—have inspired their re-creation in a wide range of artificial intelligence systems for applications such as face recognition, anomaly detection, medical diagnosis and robotic vehicle control Yet before neuron-based brains evolved, complex biomolecular circuits provided individual cells with the ‘intelligent’ behaviour required for survival However, the study of how molecules can ‘think’ has not produced an equal variety of computational models and applications of artificial chemical systems Although biomolecular systems have been hypothesized to carry out neural-network-like computations in vivo and the synthesis of artificial chemical analogues has been proposed theoretically, experimental work has so far fallen short of fully implementing even a single neuron Here, building on the richness of DNA computing and strand displacement circuitry, we show how molecular systems can exhibit autonomous brain-like behaviours Using a simple DNA gate architecture that allows experimental scale-up of multilayer digital circuits, we systematically transform arbitrary linear threshold circuits (an artificial neural network model) into DNA strand displacement cascades that function as small neural networks Our approach even allows us to implement a Hopfield associative memory with four fully connected artificial neurons that, after training in silico, remembers four single-stranded DNA patterns and recalls the most similar one when presented with an incomplete pattern Our results suggest that DNA strand displacement cascades could be used to endow autonomous chemical systems with the capability of recognizing patterns of molecular events, making decisions and responding to the environment

/pdf/neural-network-computation-with-dna-strand-displacement-2m7egtgffn.pdf

Neural network computation with DNA strand displacement cascades

The double digest problem is a common NP-hard approach to constructing physical maps of DNA sequences. This paper presents a new approach called the enhanced double digest problem. Although this new problem is also NP-hard, it can be solved in linear time in certain theoretically interesting cases.

The Enhanced Double Digest Problem for DNA Physical Mapping

We consider the problem of efficiently designing sets (codes) of equal-length DNA strings (words) that satisfy certain combinatorial constraints. This problem has numerous motivations including DNA computing and DNA self-assembly. Previous work has extended results from coding theory to obtain bounds on code size for new biologically motivated constraints and has applied heuristic local search and genetic algorithm techniques for code design. This paper proposes a natural optimization formulation of the DNA code design problem in which the goal is to design n strings that satisfy a given set of constraints while minimizing the length of the strings. For multiple sets of constraints, we provide high-probability algorithms that run in time polynomial in n and any given constraint parameters, and output strings of length within a constant factor of the optimal. To the best of our knowledge, this work is the first to consider this type of optimization problem in the context of DNA code design.

Randomized fast design of short DNA words

Consider a truck running along a road. It picks up a load Li at point βi and delivers it at αi, carrying at most one load at a time. The speed on the various parts of the road in one direction is given by f(x) and that in the other direction is given by g(x). Minimizing the total time spent to deliver loads L1,...,Ln is equivalent to solving the Traveling Salesman Problem (TSP) where the cities correspond to the loads Li with coordinates (αi, βi) and the distance from Li to Lj is given by $\int^{\beta_j}_{\alpha_i} f(x)dx$ if βj ≥ αi and by $\int^{\alpha_i}_{\beta_j} g(x)dx$ if βj < αi. This case of TSP is polynomially solvable with significant real-world applications.

Gilmore and Gomory obtained a polynomial time solution for this TSP [6]. However, the bottleneck version of the problem (BTSP) was left open. Recently, Vairaktarakis showed that BTSP with this distance metric is NP-complete [10].

We provide an approximation algorithm for this BTSP by exploiting the underlying geometry in a novel fashion. This also allows for an alternate analysis of Gilmore and Gomory's polynomial time algorithm for the TSP. We achieve an approximation ratio of (2+γ) where $\gamma \geq \frac{f(x)}{g(x)} \geq \frac{1}{\gamma} \; \forall x$. Note that when f(x)=g(x), the approximation ratio is 3.

/pdf/an-approximation-algorithm-for-a-bottleneck-traveling-1g622omlql.pdf

An approximation algorithm for a bottleneck traveling salesman problem

Let G be a plane graph of n nodes, m edges, f faces, and no self-loop. G need not be connected or simple (i.e., free of multiple edges). We give three sets of coding schemes for G which all take O(m+n) time for encoding and decoding. Our schemes employ new properties of canonical orderings for planar graphs and new techniques of processing strings of multiple types of parentheses. 
For applications that need to determine in O(1) time the adjacency of two nodes and the degree of a node, we use 2m+(5+1/k)n + o(m+n) bits for any constant k > 0 while the best previous bound by Munro and Raman is 2m+8n + o(m+n). If G is triconnected or triangulated, our bit count decreases to 2m+3n + o(m+n) or 2m+2n + o(m+n), respectively. If G is simple, our bit count is (5/3)m+(5+1/k)n + o(n) for any constant k > 0. Thus, if a simple G is also triconnected or triangulated, then 2m+2n + o(n) or 2m+n + o(n) bits suffice, respectively. 
If only adjacency queries are supported, the bit counts for a general G and a simple G become 2m+(14/3)n + o(m+n) and (4/3)m+5n + o(n), respectively. 
If we only need to reconstruct G from its code, a simple and triconnected G uses roughly 2.38m + O(1) bits while the best previous bound by He, Kao, and Lu is 2.84m.

Compact Encodings of Planar Graphs via Canonical Orderings and Multiple Parentheses

We present two graph compression schemes for solving problems on dense graphs and complement graphs They compress a graph or its complement graph into two kinds of succinct representations based on adjacency intervals and adjacency integers, respectively These two schemes complement each other for different ranges of density Using these schemes, we develop optimal or near optimal algorithms for fundamental graph problems In contrast to previous graph compression schemes, ours are simple and efficient for practical applications

Ming-Yang Kao

Papers

The Enhanced Double Digest Problem for DNA Physical Mapping

Randomized fast design of short DNA words

An approximation algorithm for a bottleneck traveling salesman problem

Compact Encodings of Planar Graphs via Canonical Orderings and Multiple Parentheses

Simple and Efficient Graph Compression Schemes for Dense and Complement Graphs