Eugen Czeizler

DNA rendering of polyhedral meshes at the nanoscale

It was suggested more than thirty years ago that Watson–Crick base pairing might be used for the rational design of nanometre-scale structures from nucleic acids. Since then, and especially since the introduction of the origami technique, DNA nanotechnology has enabled increasingly more complex structures. But although general approaches for creating DNA origami polygonal meshes and design software are available, there are still important constraints arising from DNA geometry and sense/antisense pairing, necessitating some manual adjustment during the design process. Here we present a general method of folding arbitrary polygonal digital meshes in DNA that readily produces structures that would be very difficult to realize using previous approaches. The design process is highly automated, using a routeing algorithm based on graph theory and a relaxation simulation that traces scaffold strands through the target structures. Moreover, unlike conventional origami designs built from close-packed helices, our structures have a more open conformation with one helix per edge and are therefore stable under the ionic conditions usually used in biological assays.

An Extension of the Lyndon Schützenberger Result to Pseudoperiodic Words

One of the particularities of information encoded as DNA strands is that a string u contains basically the same information as its Watson-Crick complement, denoted here as ?(u). Thus, any expression consisting of repetitions of u and ?(u) can be considered in some sense periodic. In this paper we give a generalization of Lyndon and Schutzenbergers classical result about equations of the form u l = v n w m , to cases where both sides involve repetitions of words as well as their complements. Our main results show that, for such extended equations, if l ? 5, n, m ? 3, then all three words involved can be expressed in terms of a common word t and its complement ?(t). Moreover, if l ? 5, then n = m = 3 is an optimal bound. We also obtain a complete characterization of all possible overlaps between two expressions that involve only some word u and its complement ?(u).

Synthesizing Minimal Tile Sets for Complex Patterns in the Framework of Patterned DNA Self-Assembly

Ma and Lombardi (2009) introduce and study the Pattern self-Assembly Tile set Synthesis (PATS) problem. In particular they show that the optimization version of the PATS problem is NP-hard. However, their NP-hardness proof turns out to be incorrect. Our main result is to give a correct NP-hardness proof via a reduction from the 3SAT. By definition, the PATS problem assumes that the assembly of a pattern starts always from an “L”-shaped seed structure, fixing the borders of the pattern. In this context, we study the assembly complexity of various pattern families and we show how to construct families of patterns which require a non-constant number of tiles to be assembled.

A tight linear bound on the neighborhood of inverse cellular automata

Reversible cellular automata (RCA) are models of massively parallel computation that preserve information. They consist of an array of identical finite state machines that change their states synchronously according to a local update rule. By selecting the update rule properly the system has been made information preserving, which means that any computation process can be traced back step-by-step using an inverse automaton. We investigate the maximum range in the array that a cell may need to see in order to determine its previous state. We provide a tight upper bound on this inverse neighborhood size in the one-dimensional case: we prove that in a RCA with n states the inverse neighborhood is not wider than n–1, when the neighborhood in the forward direction consists of two consecutive cells. Examples are known where range n–1 is needed, so the bound is tight. If the forward neighborhood consists of m consecutive cells then the same technique provides the upper bound nm−1–1 for the inverse direction.

On the size of the inverse neighborhoods for one-dimensional reversible cellular automata

In this paper we investigate the possible neighborhood size of the inverse automaton of some types of one-dimensional reversible cellular automata. Considering only the case when the local function is a size two map, we give a quadratic upper bound for the neighborhood size of the inverse automaton. We show that this bound can be lowered in some particular cases, and give an algorithm for computing these better bounds.

Synthesizing small and reliable tile sets for patterned DNA self-assembly

We consider the problem of finding, for a given 2D pattern of colored tiles, a minimal set of tile types self-assembling to this pattern in the abstract Tile Assembly Model of Winfree (1998). This Patterned self-Assembly Tile set Synthesis (PATS) problem was first introduced by Ma and Lombardi (2008), and subsequently studied by Goos and Orponen (2011), who presented an exhaustive partition-search branch-and-bound algorithm (briefly PS-BB) for it. However, finding the true minimal tile sets is very time consuming, and PS-BB is not well-suited for finding small but not necessarily minimal solutions. In this paper, we modify the basic partition-search framework by using a heuristic to optimize the order in which the algorithm traverses its search space. We find that by running several parallel instances of the modified algorithm PS-H, the search time for small tile sets can be shortened considerably. We also introduce a method for computing the reliability of a tile set, i.e. the probability of its error-free self-assembly to the target tiling, based on Winfrees analysis of the kinetic Tile Assembly Model (1998). We present data on the reliability of tile sets found by the algorithms and find that also here PS-H constitutes a significant improvement over PS-BB.

On the power of parallel communicating Watson-Crick automata systems

Parallel communicating Watson-Crick automata systems were introduced in [E. Czeizler, E. Czeizler, Parallel communicating Watson-Crick automata systems, in: Z. Esik, Z. Fulop (Eds.), Proc. Automata and Formal Languages, Dobogoko, Hungary, 2005, pp. 83-96] as possible models of DNA computations. This combination of Watson-Crick automata and parallel communicating systems comes as a natural extension due to the new developments in DNA manipulation techniques. It is already known, see [D. Kuske, P. Weigel, The Role of the Complementarity Relation in Watson-Crick Automata and Sticker Systems, DLT 2004, Lecture Notes in Computer Science, Vol. 3340, Auckland, New Zealand, 2004, pp. 272-283], that for Watson-Crick finite automata, the complementarity relation plays no active role. However, this is not the case when considering parallel communicating Watson-Crick automata systems. In this paper we prove that non-injective complementarity relations increase the accepting power of these systems. We also prove that although Watson-Crick automata are equivalent to two-head finite automata, this equivalence is not preserved when comparing parallel communicating Watson-Crick automata systems and multi-head finite automata.

Controlling Directed Protein Interaction Networks in Cancer

Control theory is a well-established approach in network science, with applications in bio-medicine and cancer research. We build on recent results for structural controllability of directed networks, which identifies a set of driver nodes able to control an a-priori defined part of the network. We develop a novel and efficient approach for the (targeted) structural controllability of cancer networks and demonstrate it for the analysis of breast, pancreatic, and ovarian cancer. We build in each case a protein-protein interaction network and focus on the survivability-essential proteins specific to each cancer type. We show that these essential proteins are efficiently controllable from a relatively small computable set of driver nodes. Moreover, we adjust the method to find the driver nodes among FDA-approved drug-target nodes. We find that, while many of the drugs acting on the driver nodes are part of known cancer therapies, some of them are not used for the cancer types analyzed here; some drug-target driver nodes identified by our algorithms are not known to be used in any cancer therapy. Overall we show that a better understanding of the control dynamics of cancer through computational modelling can pave the way for new efficient therapeutic approaches and personalized medicine.

The Phosphorylation of the Heat Shock Factor as a Modulator for the Heat Shock Response

The heat shock response is a well-conserved defence mechanism against the accumulation of misfolded proteins due to prolonged elevated heat. The cell responds to heat shock by raising the levels of heat shock proteins (hsp), which are responsible for chaperoning protein refolding. The synthesis ofhspis highly regulated at the transcription level by specific heat shock (transcription) factors (hsf). One of the regulation mechanisms is the phosphorylation ofhsfs. Experimental evidence shows a connection between the hyper-phosphorylation ofhsfs and the transactivation of thehsp-encoding genes. In this paper, we incorporate several (de)phosphorylation pathways into an existing well-validated computational model of the heat shock response. We analyze the quantitative control of each of these pathways over the entire process. For each of these pathways we create detailed computational models which we subject to parameter estimation in order to fit them to existing experimental data. In particular, we find conclusive evidence supporting only one of the analyzed pathways. Also, we corroborate our results with a set of computational models of a more reduced size.

Self-activating P Systems

Until now, the solving of NP complete problems in polynomial time in the framework of P systems was accomplished by the use of three different techniques: the duplication of membranes, the creation of membranes, and the replication of strings. In this paper we introduce a new type of P systems which comes with a new technique of approaching this class of problems. In the initial configuration of these P systems we have an arbitrarily large number of unactivated base-membranes, which, in a polynomial time, are activated in an exponential number. Using these type of systems we solve the SAT problem in a linear time, with respect to the number of variables and clauses.