1,525 research outputs found
Computational Complexity of Atomic Chemical Reaction Networks
Informally, a chemical reaction network is "atomic" if each reaction may be
interpreted as the rearrangement of indivisible units of matter. There are
several reasonable definitions formalizing this idea. We investigate the
computational complexity of deciding whether a given network is atomic
according to each of these definitions.
Our first definition, primitive atomic, which requires each reaction to
preserve the total number of atoms, is to shown to be equivalent to mass
conservation. Since it is known that it can be decided in polynomial time
whether a given chemical reaction network is mass-conserving, the equivalence
gives an efficient algorithm to decide primitive atomicity.
Another definition, subset atomic, further requires that all atoms are
species. We show that deciding whether a given network is subset atomic is in
, and the problem "is a network subset atomic with respect to a
given atom set" is strongly -.
A third definition, reachably atomic, studied by Adleman, Gopalkrishnan et
al., further requires that each species has a sequence of reactions splitting
it into its constituent atoms. We show that there is a to decide whether a given network is reachably atomic, improving
upon the result of Adleman et al. that the problem is . We
show that the reachability problem for reachably atomic networks is
-.
Finally, we demonstrate equivalence relationships between our definitions and
some special cases of another existing definition of atomicity due to Gnacadja
Programmability of Chemical Reaction Networks
Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri Nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior
Synthesizing and tuning chemical reaction networks with specified behaviours
We consider how to generate chemical reaction networks (CRNs) from functional
specifications. We propose a two-stage approach that combines synthesis by
satisfiability modulo theories and Markov chain Monte Carlo based optimisation.
First, we identify candidate CRNs that have the possibility to produce correct
computations for a given finite set of inputs. We then optimise the reaction
rates of each CRN using a combination of stochastic search techniques applied
to the chemical master equation, simultaneously improving the of correct
behaviour and ruling out spurious solutions. In addition, we use techniques
from continuous time Markov chain theory to study the expected termination time
for each CRN. We illustrate our approach by identifying CRNs for majority
decision-making and division computation, which includes the identification of
both known and unknown networks.Comment: 17 pages, 6 figures, appeared the proceedings of the 21st conference
on DNA Computing and Molecular Programming, 201
Viability, Invariance and Reachability for Controlled Piecewise Deterministic Markov Processes Associated to Gene Networks
We aim at characterizing viability, invariance and some reachability
properties of controlled piecewise deterministic Markov processes (PDMPs).
Using analytical methods from the theory of viscosity solutions, we establish
criteria for viability and invariance in terms of the first order normal cone.
We also investigate reachability of arbitrary open sets. The method is based on
viscosity techniques and duality for some associated linearized problem. The
theoretical results are applied to general On/Off systems, Cook's model for
haploinssuficiency, and a stochastic model for bacteriophage lambda.Comment: submitte
BioDiVinE: A Framework for Parallel Analysis of Biological Models
In this paper a novel tool BioDiVinEfor parallel analysis of biological
models is presented. The tool allows analysis of biological models specified in
terms of a set of chemical reactions. Chemical reactions are transformed into a
system of multi-affine differential equations. BioDiVinE employs techniques for
finite discrete abstraction of the continuous state space. At that level,
parallel analysis algorithms based on model checking are provided. In the
paper, the key tool features are described and their application is
demonstrated by means of a case study
Reachability in Restricted Chemical Reaction Networks
The popularity of molecular computation has given rise to several models of
abstraction, one of the more recent ones being Chemical Reaction Networks
(CRNs). These are equivalent to other popular computational models, such as
Vector Addition Systems and Petri-Nets, and restricted versions are equivalent
to Population Protocols. This paper continues the work on core reachability
questions related to Chemical Reaction Networks; given two configurations, can
one reach the other according to the system's rules? With no restrictions,
reachability was recently shown to be Ackermann-complete, this resolving a
decades-old problem.
Here, we fully characterize monotone reachability problems based on various
restrictions such as the rule size, the number of rules that may create a
species (k-source) or consume a species (k-consuming), the volume, and whether
the rules have an acyclic production order (feed-forward). We show
PSPACE-completeness of reachability with only bimolecular reactions with
two-source and two-consuming rules. This proves hardness of reachability in
Population Protocols, which was unknown. Further, this shows reachability in
CRNs is PSPACE-complete with size-2 rules, which was previously only known with
size-5 rules. This is achieved using techniques within the motion planning
framework.
We provide many important results for feed-forward CRNs where rules are
single-source or single-consuming. We show that reachability is solvable in
polynomial time if the system does not contain special void or autogenesis
rules. We then fully characterize all systems of this type and show that if you
allow void/autogenesis rules, or have more than one source and one consuming,
the problems become NP-complete. Finally, we show several interesting special
cases of CRNs based on these restrictions or slight relaxations and note future
significant open questions related to this taxonomy.Comment: This research was supported in part by National Science Foundation
Grant CCF-181760
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