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

This paper proposes novel lattice algorithms to compute tail conditional expectation. To improve the naive approach, we develop tilting, trinomial, and extrapolation algorithms together with some syntheses of these algorithms. Furthermore, we introduce fractional‐step lattices to prevent interpolation error in the extrapolation algorithms. A key finding is that combining the techniques of tilting lattice, extrapolation and fractional steps substantially increases speed and accuracy. We demostrate the efficiency and accuracy of these algorithms with numerical results.

Fast Accurate Algorithms for Tail Conditional Expectation

Searching for a goal is a central and extensively studied problem in computer science. In classical searching problems, the cost of a search function is simply the number of queries made to an oracle that knows the position of the goal. In many robotics problems, as well as in problems from other areas, we want to charge a cost proportional to the distance between queries (e.g., the time required to travel between two query points). With this cost function in mind, the abstract problem known as the w-lane cow-path problem was designed. There are known optimal deterministic algorithms for the cow-path problem; we give the first randomized algorithm in this paper. We show that our algorithm is optimal for two paths (w = 2) and give evidence that it is optimal for larger values of w. Subsequent to the preliminary version of this paper, Kao et al. (in “Proceedings, 5th ACM–SIAM Symposium on Discrete Algorithm," pp. 372-381, 1994) have shown that our algorithm is indeed optimal for all w ≥ 2. Our randomized algorithm gives expected performance that is almost twice as good as is possible with a deterministic algorithm. For the performance of our algorithm, we also derive the asymptotic growth with respect to w—despite similar complexity results for related problems, it appears that this growth has never been analyzed.

/pdf/reprinted-with-permission-no-further-reproduction-is-4v7mbp0axb.pdf

***Reprinted with permission. No further reproduction is authorized without written permission from Elsevier. This version of the document is not the version of record. Figures and/or pictures may be missing from this format of the document.***

This study considers all the possible actions a borrower may have, i.e., to default, to prepay, and to maintain the mortgage, during mortgage horizon. Then, we provide an effective and accurate pricing formula, which not only considers the effect that default might affect the mortgage value, but also more accurately explores the impact due to prepayment risk. In our model, we define prepayment value of the mortgage as the amount of outstanding principle. In contrast, previous literature defines prepayment value as a constant proportion of maintaining value of the mortgage. Finally, based on closed-form pricing formula, we analyze the yield, duration and convexity of risky mortgage loan, providing a better framework for risk management.

Closed-form mortgage pricing formula with outstanding principal as prepayment value

Let G be an embedded planar undirected graph that has n vertices, m edges, and f faces but has no self-loop or multiple edge. If G is triangulated, we can encode it using {4/3}m-1 bits, improving on the best previous bound of about 1.53m bits. In case exponential time is acceptable, roughly 1.08m bits have been known to suffice. If G is triconnected, we use at most (2.5+2\log{3})\min\{n,f\}-7 bits, which is at most 2.835m bits and smaller than the best previous bound of 3m bits. Both of our schemes take O(n) time for encoding and decoding.

Linear-Time Succinct Encodings of Planar Graphs via Canonical Orderings

Given a planar graph G and a sequence C_1,...,C_q, where each C_i is a family of vertex subsets of G, we wish to find a plane embedding of G, if any exists, such that for each i in {1,...,q}, there is a face F_i in the embedding whose boundary contains at least one vertex from each set in C_i. This problem has applications to the recovery of topological information from geographical data and the design of constrained layouts in VLSI. Let I be the input size, i.e., the total number of vertices and edges in G and the families C_i, counting multiplicity. We show that this problem is NP-complete in general. We also show that it is solvable in O(I log I) time for the special case where for each input family C_i, each set in C_i induces a connected subgraph of the input graph G. Note that the classical problem of simply finding a planar embedding is a further special case of this case with q=0. Therefore, the processing of the additional constraints C_1,...,C_q only incurs a logarithmic factor of overhead.

Ming-Yang Kao

Papers

Fast Accurate Algorithms for Tail Conditional Expectation

Reprinted with permission. No further reproduction is authorized without written permission from Elsevier. This version of the document is not the version of record. Figures and/or pictures may be missing from this format of the document.

Closed-form mortgage pricing formula with outstanding principal as prepayment value

Linear-Time Succinct Encodings of Planar Graphs via Canonical Orderings

Common-Face Embeddings of Planar Graphs