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Eugen Czeizler

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Enrico Formenti

University of Nice

Benjamin Steinberg

Yale University

Jean-charles Delvenne

Centre National de la Recherche Scientifique / French National Centre for Scientific Research

Carnegie Mellon University

Trent University

François Blanchard

Ievgen Bondarenko

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Papers by Eugen Czeizler

On testing the equality of soc systems

In this paper we study three classes of nite automata satisfying the properties that every bi- in... more In this paper we study three classes of nite automata satisfying the properties that every bi- innite word is the label of at most one, at least one and exactly one bi-innite path. In particular, we investigate the algorithmic complexity of testing if a given nite automaton has one of these properties. Also, when restricted to the rst class above,

Yield Optimization Strategies for (DNA) Staged Tile Assembly Systems

Lecture Notes in Computer Science, 2013

Synthesizing Small and Reliable Tile Sets for Patterned DNA Self-assembly

Lecture Notes in Computer Science, 2011

We consider the problem of finding, for a given 2D pattern of coloured tiles, a minimal set of ti... more We consider the problem of finding, for a given 2D pattern of coloured tiles, a minimal set of tile types self-assembling to this pattern in the abstract Tile Assembly Model of . This Patterned self-Assembly Tile set Synthesis (PATS) problem was first introduced by Ma and Lombardi (2008), and subsequently studied by Göös 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 the algorithm PS-BB is not well-suited for finding small but not necessarily minimal solutions. In this paper, we modify the basic partitionsearch framework by using a heuristic to optimize the order in which the algorithm traverses its search space. We find that by running several parallel executions of the modified algorithm PS-H, the search time for small tile sets can be shortened considerably. Additionally, we suggest a new approach, answer set programmin (ASP), to solving the PATS problem. We also introduce a method for computing the reliability of a given tile set, i.e. the probability of its error-free self-assembly to the desired target tiling, based on Winfree's analysis of the kinetic Tile Assembly Model (1998). We present empirical data on the reliability of tile sets found by the PS-BB and PS-H algorithms and find that also here the PS-H algorithm constitutes a significant improvement over the earlier PS-BB algorithm.

Control Strategies for the Regulation of the Eukaryotic Heat Shock Response

by Eugen Czeizler, Ion Petre, and Ralph-johan Back

Elevated temperatures cause proteins in living cells to misfold. They start forming larger and la... more Elevated temperatures cause proteins in living cells to misfold. They start forming larger and larger aggregates that can eventually lead to the cell’s death. The heat shock response is an evolutionary well conserved cellular response to massive protein misfolding and it is driven by the need to keep the level of misfolded proteins under control. We consider in this paper

A Tight Linear Bound on the Neighborhood of Inverse Cellular Automata

Lecture Notes in Computer Science, 2005

Reversible cellular automata (RCA) are models of massively parallel computation that preserve inf... more 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 n m−1 − 1 for the inverse direction.

Nano Architectures for Carbon Nanotube Circuits: Design, Analysis, and Experimental Attempts Extended Abstract

On the synchronization delay of local automata

On testing the equality of sofic systems

A design framework for carbon nanotube circuits affixed on DNA origami tiles

Quantitative Refinement of Reaction Models

by Eugen Czeizler, Ion Petre, and Bogdan Iancu

ABSTRACT One approach to modelling complex biological systems is to start from an abstract repres... more ABSTRACT One approach to modelling complex biological systems is to start from an abstract representation of the biological process and then to incorporate more details regarding its reactions or reactants through an iterative refinement process. The refinement should be done so as to ensure the preservation of the numerical properties of the model, such as its numerical fit and validation. Such approaches are well established in software engineering: starting from a formal specification of the system, one refines it step-by-step towards an implementation that is guaranteed to satisfy a number of logical properties. We introduce here the concepts of (quantitative) data refinement and process refinement of a biomolecular, reaction-based model. We choose as a case study a recently proposed model for the heat shock response and refine it to include some details of its acetylation-induced control. Although the refinement process produces a substantial increase in the number of kinetic parameters and variables, the methodology we propose preserves all the numerical properties of the model with a minimal computational effort.

A tight linear bound on the synchronization delay of bijective automata

Theoretical Computer Science, 2007

Reversible cellular automata (RCA) are models of massively parallel computation that preserve inf... more Reversible cellular automata (RCA) are models of massively parallel computation that preserve information. We generalize these systems by introducing the class of ωω bijective finite automata. It consists of those finite automata where for any bi-infinite word there exists a unique path labelled by that word. These systems are strictly included in the class of local automata. Although the synchronization delay of an n-state local automaton is known to be Θ(n 2 ) in the worst case, we prove that in the case of ωω bijective finite automata the synchronization delay is at most n − 1. Based on this we prove that for a one-dimensional n-state RCA where the neighborhood consists of m consecutive cells, the neighbourhood of the inverse automaton consists of at most n m−1 − (m − 1) cells. Similar bounds are obtained also in [E. Czeizler, J. Kari, A tight linear bound on the neighborhood of inverse cellular automata, in: Proceedings of ICALP 2005, in: LNCS, vol. 3580, 2005, pp. 410-420] but here the result comes as a direct consequence of the more general result. We also construct examples of RCA with large inverse neighbourhoods proving that the upper bounds provided here are the best possible in the case m = 2.

Unambiguous Automata

Mathematics in Computer Science, 2008

We give a new presentation of two results concerning synchronized automata. The first one gives a... more We give a new presentation of two results concerning synchronized automata. The first one gives a linear bound on the synchronization delay of complete local automata. The second one gives a cubic bound for the minimal length of a synchronizing pair in a complete synchronized unambiguous automaton. The proofs are based on results on unambiguous monoids of relations. . 68Q45;20M35;94A45;68R15.

Quantitative Analysis of the Self-Assembly Strategies of Intermediate Filaments from Tetrameric Vimentin

by Ion Petre and Eugen Czeizler

IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2000

In vitro assembly of intermediate filaments from tetrameric vimentin consists of a very rapid pha... more In vitro assembly of intermediate filaments from tetrameric vimentin consists of a very rapid phase of tetramers laterally associating into unit-length filaments and a slow phase of filament elongation. We focus in this paper on a systematic quantitative investigation of two molecular models for filament assembly, recently proposed in (Kirmse et al. mathematical modeling, model fitting, and model validation. We analyze the quantitative contribution of each filament elongation strategy: with tetramers, with unit-length filaments, with longer filaments, or combinations thereof. In each case, we discuss the numerical fitting of the model with respect to one set of data, and its separate validation with respect to a second, different set of data. We introduce a high-resolution model for vimentin filament self-assembly, able to capture the detailed dynamics of filaments of arbitrary length. This provides much more predictive power for the model, in comparison to previous models where only the mean length of all filaments in the solution could be analyzed. We show how kinetic observations on low-resolution models can be extrapolated to the high-resolution model and used for lowering its complexity.

Quantitative Model Refinement as a Solution to the Combinatorial Size Explosion of Biomodels

by Eugen Czeizler, Ion Petre, and Bogdan Iancu

Electronic Notes in Theoretical Computer Science, 2012

Building a large system through a systematic, step-by-step refinement of an initial abstract spec... more Building a large system through a systematic, step-by-step refinement of an initial abstract specification is a well established technique in software engineering, not yet much explored in systems biology. In the case of systems biology, one starts from an abstract, high-level model of a biological system and aims to add more and more details about its reactants and/or reactions, through a number of consecutive refinement steps. The refinement should be done in a quantitatively correct way, so that (some of) the numerical properties of the model (such as the experimental fit and validation) are preserved. In this study, we focus on the data-refinement mechanism where the aim is to increase the level of details of some of the reactants of a given model. That is, we analyse the case when a model is refined by substituting a given species by several types of subspecies. We show in this paper how the refined model can be systematically obtained from the original one. As a case study for this methodology we choose a recently introduced model for the eukaryotic heat shock response, . We refine this model by including details about the acetylation of the heat shock factors and its influence on the heat shock response. The refined model has a significantly higher number of kinetic parameters and variables. However, we show that our methodology allows us to preserve the experimental fit/validation of the model with minimal computational effort.

On the synchronization delay of complete local automata

Search methods for tile sets in patterned DNA self-assembly

ABSTRACT The Pattern self-Assembly Tile set Synthesis (PATS) problem, which arises in the theory ... more ABSTRACT The Pattern self-Assembly Tile set Synthesis (PATS) problem, which arises in the theory of structured DNA self-assembly, is to determine a set of coloured tiles that, starting from a bordering seed structure, self-assembles to a given rectangular colour pattern. The task of finding minimum-size tile sets is known to be NP-hard. We explore several complete and incomplete search techniques for finding minimal, or at least small, tile sets and also assess the reliability of the solutions obtained according to the kinetic Tile Assembly Model.

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

by Eugen Czeizler, Ion Petre, and Vladimir Rogojin

IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2000

The heat shock response is a well-conserved defence mechanism against the accumulation of misfold... more 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 of hsp is highly regulated at the transcription level by specific heat shock (transcription) factors (hsf). One of the regulation mechanisms is the phosphorylation of hsf&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s. Experimental evidence shows a connection between the hyper-phosphorylation of hsfs and the transactivation of the hsp-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.

On testing the equality of soc systems

In this paper we study three classes of nite automata satisfying the properties that every bi- in... more In this paper we study three classes of nite automata satisfying the properties that every bi- innite word is the label of at most one, at least one and exactly one bi-innite path. In particular, we investigate the algorithmic complexity of testing if a given nite automaton has one of these properties. Also, when restricted to the rst class above,

Yield Optimization Strategies for (DNA) Staged Tile Assembly Systems

Lecture Notes in Computer Science, 2013

Synthesizing Small and Reliable Tile Sets for Patterned DNA Self-assembly

Lecture Notes in Computer Science, 2011

We consider the problem of finding, for a given 2D pattern of coloured tiles, a minimal set of ti... more We consider the problem of finding, for a given 2D pattern of coloured tiles, a minimal set of tile types self-assembling to this pattern in the abstract Tile Assembly Model of . This Patterned self-Assembly Tile set Synthesis (PATS) problem was first introduced by Ma and Lombardi (2008), and subsequently studied by Göös 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 the algorithm PS-BB is not well-suited for finding small but not necessarily minimal solutions. In this paper, we modify the basic partitionsearch framework by using a heuristic to optimize the order in which the algorithm traverses its search space. We find that by running several parallel executions of the modified algorithm PS-H, the search time for small tile sets can be shortened considerably. Additionally, we suggest a new approach, answer set programmin (ASP), to solving the PATS problem. We also introduce a method for computing the reliability of a given tile set, i.e. the probability of its error-free self-assembly to the desired target tiling, based on Winfree's analysis of the kinetic Tile Assembly Model (1998). We present empirical data on the reliability of tile sets found by the PS-BB and PS-H algorithms and find that also here the PS-H algorithm constitutes a significant improvement over the earlier PS-BB algorithm.

Control Strategies for the Regulation of the Eukaryotic Heat Shock Response

by Eugen Czeizler, Ion Petre, and Ralph-johan Back

Elevated temperatures cause proteins in living cells to misfold. They start forming larger and la... more Elevated temperatures cause proteins in living cells to misfold. They start forming larger and larger aggregates that can eventually lead to the cell’s death. The heat shock response is an evolutionary well conserved cellular response to massive protein misfolding and it is driven by the need to keep the level of misfolded proteins under control. We consider in this paper

A Tight Linear Bound on the Neighborhood of Inverse Cellular Automata

Lecture Notes in Computer Science, 2005

Reversible cellular automata (RCA) are models of massively parallel computation that preserve inf... more 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 n m−1 − 1 for the inverse direction.

Nano Architectures for Carbon Nanotube Circuits: Design, Analysis, and Experimental Attempts Extended Abstract

On the synchronization delay of local automata

On testing the equality of sofic systems

A design framework for carbon nanotube circuits affixed on DNA origami tiles

Quantitative Refinement of Reaction Models

by Eugen Czeizler, Ion Petre, and Bogdan Iancu

ABSTRACT One approach to modelling complex biological systems is to start from an abstract repres... more ABSTRACT One approach to modelling complex biological systems is to start from an abstract representation of the biological process and then to incorporate more details regarding its reactions or reactants through an iterative refinement process. The refinement should be done so as to ensure the preservation of the numerical properties of the model, such as its numerical fit and validation. Such approaches are well established in software engineering: starting from a formal specification of the system, one refines it step-by-step towards an implementation that is guaranteed to satisfy a number of logical properties. We introduce here the concepts of (quantitative) data refinement and process refinement of a biomolecular, reaction-based model. We choose as a case study a recently proposed model for the heat shock response and refine it to include some details of its acetylation-induced control. Although the refinement process produces a substantial increase in the number of kinetic parameters and variables, the methodology we propose preserves all the numerical properties of the model with a minimal computational effort.

A tight linear bound on the synchronization delay of bijective automata

Theoretical Computer Science, 2007

Reversible cellular automata (RCA) are models of massively parallel computation that preserve inf... more Reversible cellular automata (RCA) are models of massively parallel computation that preserve information. We generalize these systems by introducing the class of ωω bijective finite automata. It consists of those finite automata where for any bi-infinite word there exists a unique path labelled by that word. These systems are strictly included in the class of local automata. Although the synchronization delay of an n-state local automaton is known to be Θ(n 2 ) in the worst case, we prove that in the case of ωω bijective finite automata the synchronization delay is at most n − 1. Based on this we prove that for a one-dimensional n-state RCA where the neighborhood consists of m consecutive cells, the neighbourhood of the inverse automaton consists of at most n m−1 − (m − 1) cells. Similar bounds are obtained also in [E. Czeizler, J. Kari, A tight linear bound on the neighborhood of inverse cellular automata, in: Proceedings of ICALP 2005, in: LNCS, vol. 3580, 2005, pp. 410-420] but here the result comes as a direct consequence of the more general result. We also construct examples of RCA with large inverse neighbourhoods proving that the upper bounds provided here are the best possible in the case m = 2.

Unambiguous Automata

Mathematics in Computer Science, 2008

We give a new presentation of two results concerning synchronized automata. The first one gives a... more We give a new presentation of two results concerning synchronized automata. The first one gives a linear bound on the synchronization delay of complete local automata. The second one gives a cubic bound for the minimal length of a synchronizing pair in a complete synchronized unambiguous automaton. The proofs are based on results on unambiguous monoids of relations. . 68Q45;20M35;94A45;68R15.

Quantitative Analysis of the Self-Assembly Strategies of Intermediate Filaments from Tetrameric Vimentin

by Ion Petre and Eugen Czeizler

IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2000

In vitro assembly of intermediate filaments from tetrameric vimentin consists of a very rapid pha... more In vitro assembly of intermediate filaments from tetrameric vimentin consists of a very rapid phase of tetramers laterally associating into unit-length filaments and a slow phase of filament elongation. We focus in this paper on a systematic quantitative investigation of two molecular models for filament assembly, recently proposed in (Kirmse et al. mathematical modeling, model fitting, and model validation. We analyze the quantitative contribution of each filament elongation strategy: with tetramers, with unit-length filaments, with longer filaments, or combinations thereof. In each case, we discuss the numerical fitting of the model with respect to one set of data, and its separate validation with respect to a second, different set of data. We introduce a high-resolution model for vimentin filament self-assembly, able to capture the detailed dynamics of filaments of arbitrary length. This provides much more predictive power for the model, in comparison to previous models where only the mean length of all filaments in the solution could be analyzed. We show how kinetic observations on low-resolution models can be extrapolated to the high-resolution model and used for lowering its complexity.

Quantitative Model Refinement as a Solution to the Combinatorial Size Explosion of Biomodels

by Eugen Czeizler, Ion Petre, and Bogdan Iancu

Electronic Notes in Theoretical Computer Science, 2012

Building a large system through a systematic, step-by-step refinement of an initial abstract spec... more Building a large system through a systematic, step-by-step refinement of an initial abstract specification is a well established technique in software engineering, not yet much explored in systems biology. In the case of systems biology, one starts from an abstract, high-level model of a biological system and aims to add more and more details about its reactants and/or reactions, through a number of consecutive refinement steps. The refinement should be done in a quantitatively correct way, so that (some of) the numerical properties of the model (such as the experimental fit and validation) are preserved. In this study, we focus on the data-refinement mechanism where the aim is to increase the level of details of some of the reactants of a given model. That is, we analyse the case when a model is refined by substituting a given species by several types of subspecies. We show in this paper how the refined model can be systematically obtained from the original one. As a case study for this methodology we choose a recently introduced model for the eukaryotic heat shock response, . We refine this model by including details about the acetylation of the heat shock factors and its influence on the heat shock response. The refined model has a significantly higher number of kinetic parameters and variables. However, we show that our methodology allows us to preserve the experimental fit/validation of the model with minimal computational effort.

On the synchronization delay of complete local automata

Search methods for tile sets in patterned DNA self-assembly

ABSTRACT The Pattern self-Assembly Tile set Synthesis (PATS) problem, which arises in the theory ... more ABSTRACT The Pattern self-Assembly Tile set Synthesis (PATS) problem, which arises in the theory of structured DNA self-assembly, is to determine a set of coloured tiles that, starting from a bordering seed structure, self-assembles to a given rectangular colour pattern. The task of finding minimum-size tile sets is known to be NP-hard. We explore several complete and incomplete search techniques for finding minimal, or at least small, tile sets and also assess the reliability of the solutions obtained according to the kinetic Tile Assembly Model.

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

by Eugen Czeizler, Ion Petre, and Vladimir Rogojin

IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2000

The heat shock response is a well-conserved defence mechanism against the accumulation of misfold... more 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 of hsp is highly regulated at the transcription level by specific heat shock (transcription) factors (hsf). One of the regulation mechanisms is the phosphorylation of hsf&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s. Experimental evidence shows a connection between the hyper-phosphorylation of hsfs and the transactivation of the hsp-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.