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Liposome Logic
James SmaldonComputer Science
University of [email protected]
Natalio KrasnogorComputer Science
University of [email protected]
Cameron AlexanderPharmacy
University of Nottinghamcameron.alexander@
nottingham.ac.uk
Marian GheorgheComputer Science
The University of [email protected]
ABSTRACTVLSI research, in its continuous push toward further minia-turisation, is seeking to break through the limitations ofcurrent circuit manufacture techniques by moving towardsbiomimetic methodologies that rely on self-assembly, self-organisation and evodevo-like processes. On the other hand,Systems and Synthetic biology’s quest to achieve ever moredetailed (multi)cell models are relying more and more onconcepts derived from computer science and engineering suchas the use of logic gates, clocks and pulse generator analogsto describe a cell’s decision making behavior. This paperis situated at the crossroad of these two enterprises. Thatis, a novel method of non-conventional computation basedon the encapsulation of simple gene regulatory-like networkswithin liposomes is described. Three transcription Booleanlogic gates were encapsulated and simulated within lipo-somes self-assembled from DMPC (dimyristoylphosphatidyl-choline) amphiphiles using an implementation of DissipativeParticle Dynamics (DPD) created with the NVIDIA CUDAframework, and modified to include a simple collision chem-istry in a stochastic environment. The response times ofthe AND, OR and NOT gates were shown to be positivelyeffected by the encapsulation within the liposome inner vol-ume.
Categories and Subject DescriptorsI.6.8 [Computing Methodologies]: SIMULATION ANDMODELING—Types of Simulation; F.0 [Theory of Com-
putation]: GENERAL; J.J.3 [Computer Applications]:LIFE AND MEDICAL SCIENCES—Biology and Genetics
General TermsDesign, Experimentation, Theory
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KeywordsBiomolecular Computing, Synthetic Biology, Systems Biol-ogy, Dissipative Particle Dynamics, CUDA, GPU Comput-ing, Liposome
1. INTRODUCTIONIn living cells, complex behaviour is achieved by an exquisite
tuning of biological regulatory networks (BRN), such as ge-netic, signaling and metabolic networks. In turn, these BRNare orchestrated within a (complex) membrane and medi-ated by a plethora of organelles. Certain BRN motifs[2],patterns of gene regulation which occur far more frequentlywithin natural cell genomes than in randomly generatedregulatory networks, have been identified and these motifsproduce functionality such as oscillation, feed forward andfeed back loops and simple Boolean logic. The combina-tion of these motifs can produce complex decision makingbehaviours in cells, such as chemotaxis towards an exter-nal signal molecule (e.g. glucose in e-coli bacteria), quorumsensing, etc.
Research in top-down synthetic biology has attempted toharness the power of gene and signaling networks for com-putation. By altering the genetic code that specifies thebehaviour of these regulatory networks through a clever re-engineering of gene circuits it is possible to to implementsimple Boolean logic gates for non-conventional computa-tion[11, 22]. In this way the biological entity (typically abacterium) becomes the computer “wet ware” that is pro-grammed through suitable alterations to its BRN as to im-plement a specific type of behaviour. Although some stan-dardised parts for engineering synthetic biology entities arebecoming more common (e.g. iGEM registry of standardparts), computational tasks such as logic circuits remainquite foreign to the natural biology of the species[3] andhence a challenge to implement. That is, unexpected diffi-culties arise when attempting to make computational alter-ations[21] because our understanding of the processes occur-ring within the bacterial volume is not yet complete hence,except in the simplest of cases, disruption of the computa-tional logic by the bug’s primordial circuits, which attemptto maintain themselves against interference, is almost in-evitable.
Computation is also possible through a precise manipu-lation of DNA molecules in bulk solution and the Adlemanexperiment[1], in which a 7 node Hamiltonian path problem
was represented and solved entirely with DNA molecules invitro, was of great interest in the field of non-conventionalcomputation. For the first time it was shown that not onlywas the implementation of a DNA based computer feasi-ble in the lab with standard equipment and techniques, butalso that the resulting implementation could exploit themassive parallelism and self-assembly properties afforded bybiomolecules.
In this work, we describe and illustrate a proof of con-cept model of simple computational entities, that could com-bine the beneficial features of both of these approaches. Atthe core of these entities are gene transcriptional systemsencapsulated within self-assembled vesicles (in this case li-posomes), spherical membranes which provide a selectivelypermeable barrier around a surrounded volume of fluid. Thisapproach is similar in some aspects to membrane comput-ing[18], in which computation can take place by applying re-action rules to chemicals within encapsulated volumes, andin [23] we employed a hybrid DPD-membrane computingtechnique to simulate diffusion in vesicles. In contrast withthe most common, top-down, approach to synthetic biologic,we advocate a bottom-up approach with engineered compo-nents of manageable complexity. The aim is to avoid manyof the difficulties that arise when attempting to modify ahighly complex system (e.g. a living cell). To avoid thiscomplexity trap, we build our computational device fromscratch utilising any biochemical or chemical system thatmay be relevant in solving a computational problem. Thatis, our aim is to chart a route for a vesicles-based computerthat jettisons the billion year evolutionary baggage of bacte-ria and, instead, mimics their key critical components thatcould make a vesicle computer possible: a simple membraneand a simple regulatory-like circuit. That is, the “legacysystem” that is present in current top-down synthetic biol-ogy projects is discarded in favor of a bottom-up approachin which the complexity of every single component is known(and characterised) in advance.
This paper presents a rigorous computational simulationas a proof of concept for our approach. Our model is spec-ified and simulated in a full 3D particle simulation usingDissipative Particle Dynamics (DPD). DPD simulations inthe fields of artificial life and synthetic biology have includedstudies of micellar catalysis[7] and the life cycle of a mini-mal protocell inspired by the “Los Alamos” bug[5]. DPDhas become an established tool for mesoscale modelling ofmembrane and liposome dynamics[19, 6, 9].
Three logic gates, AND, OR and NOT (based on the tran-scriptional logic reported by Silva-Rocha and de Lorenzo[21])were implemented within liposomes and simulated with DPD.The behaviour of the logic gates compared with control ex-periments in which the reactions and particle types are notencapsulated within a liposome is investigated as to ascer-tain whether the synergy between bottom-up protomem-branes and simple gene circuits produce better logic gates.
2. METHODSSimulation and modelling techniques have been applied in
synthetic biology to create, analyse and prototype modelsof protocell computation[5]. Typically the simulation meth-ods used are ODEs or stochastic simulation techniques suchas versions of Gillespie’s Stochastic Simulation Algorithm(SSA), modified to permit the inclusion of membrane en-capsulation and different regions[17]. These algorithms are
well suited to the simulation of the stochastic environment ofa cell or vesicle inner volume where the number of moleculesof a chemical species may be very small, and the reactiondynamics very noisy, but dynamics such as protocell divisionmust be included explicitly in the model.
To simulate the liposomes, we use an NVIDIA CUDAbased implementation of DPD, with modifications to sup-port simple chemical reactions. As DPD involves the simu-lation of the dynamics of a particles composing a volume offluid, and calculation of the dynamics involves the numericalintegration of the equations of motion, rather than stochas-tic approaches such as the SSA in which the simulation isdriven by the reactions, properties such as self-assembly, dif-fusion and dynamics which are reliant on the locality (mi-cellar catalysis[7] for example) are included implicitly.
The benefit of the proposed system over other stochasticmodelling techniques is that the dynamics of the compart-ment encapsulating the computation are emergent, due tothe repeated application of simple rules rather than beingspecified in the model explicitly. Once the initial state of thesystem is specified, the complex behaviour of the system isa consequence of the application of simple force calculationsand reactions. Clearly, the tradeoff for this added detail isthat the amount of processing time required for the simula-tion is drastically increased, however recent developments ingraphics processing unit (GPU) technology has meant thatsuch simulations are becoming more feasible, and the extralevel of detail provided is more important in synthetic bi-ology where there may not be an experimental data set tocompare the modelling results against.
2.1 Liposome Logic Modelling FrameworkThe logic gate experiments described below were designed
and implemented using a self-developed toolkit of programscreated for the design, specification and creation of liposomesimulations within DPD. The toolkit is composed of a DPDsimulation program which takes as input a configuration filedescribing the required parameters for the simulation, andproduces a binary data file containing data from the simu-lation. The code has been implemented to run within theNVIDIA CUDA framework and allows simulation of poly-mers and simple model chemical reactions based on the ex-tensions to the method first proposed by Fellermann et al[5].Outputted data from the simulations can then be viewedwithin a 3D OpenGL based viewer application, which en-ables automated analysis, extraction and storage of (pre-viously simulated) self-assembled objects (vesicles, bilayersetc). The extracted objects can then be read, modified andrecombined to produce a new initial state for a DPD simu-lation which represents the required liposome design. Thusit is possible to create a combinatorial library of simulatedobjects, which in turn could be used to bootstrap new simu-lations employing those objects without the need to reinvestCPU effort on them. A more detailed description of thisframework and the CUDA implementation will be providedin a later publication. Figure 1 shows a work flow diagramof the simulation process just described.
2.2 Dissipative Particle DynamicsThe core of the protocell modelling toolkit is the Dissi-
pative Particle Dynamics (DPD) method, first proposed byHoogerbrugge and Koelmann[10]. DPD simulation involvesthe integration of the equations of motion for a set of “beads”
Figure 1: Work Flow Diagram of the protocell simulationprocess
or particles representing several molecules of a particularchemical species. The approach is similar in implementationto molecular dynamics (MD) modeling techniques, exceptin MD each entity in the system might represent an atomand the potentials acting between elements are a model ofinter-atomic interaction, such as the Lennard-Jones poten-tial, whereas in DPD the entities represent a group of atomsor molecules and so the interactions between elements are amesoscopic (i.e. coarser) approximation of the net result ofthose dynamics over longer timescales. The DPD methodwas initially proposed as an empirical simulation techniquefor fluid dynamics, and was given a theoretical basis in sta-tistical mechanics by Espanol and Warren[4], and later aphysical basis for the parameterisation of the system wasproduced by Groot and Warren[9]. DPD has proved to be avery useful tool for membrane dynamics simulations of sys-tems which would be too large to simulate in MD, such asvesicle formation (see figure 2), fusion and fission[20].
The interactions between particles in DPD take into con-sideration three forces that act between each pair of parti-cles within a predefined force interaction radius (which typi-cally defines the unit length in the simulation). These forcesare the conservative force (F C), the dissipative force(F D)and the random force(F R). The random and dissipativeforces maintain the temperature in the system by introduc-ing and removing energy respectively, and the conservativeforce drives the dynamics of the system by producing a pa-rameterised repulsion between particles.
The conservative force acting between a pair of particlesi and j is defined as follows:
FCij = α(1 − |rij |
rc
) (1)
Where α is the conservative force strength parameters, whichis typically defined as a symmetric matrix where each ele-ment is the strength of the repulsion between two particlesof the given types, and is related to the immiscibility of thesubstances (e.g. water and oil would have a higher α pa-rameter than water and water), |rij | is the distance fromparticle j to particle i and rc is the force interaction radius.
The dissipative force acting between a pair of particles i
and j is defined as follows:
FDij = −γw
D(rij)(rij · vij)rij (2)
Where γ is the maximum dissipative force parameter, wD(rij)is the dissipative force weighting function described below,rij is the unit vector pointing from particle j to particle i
and vij is a vector that is the difference between the velocityof particle j and the velocity of particle i.
(a) The initial state (b) Micelle formation
(c) Bowl shaped mem-brane
(d) Fully formed vesicle
Figure 2: Formation of a vesicle within a DPD Simula-tion (the hydrophilic head section of the DMPC polymeris red, the hydrophobic tails green, solvent not shown). Ini-tially the amphiphiles are distributed randomly in the space(2a), as the hydrophobic tail chains are pushed together,micelles form, and the micelles accumulate to form a largebilayer(2b), which curls first into a bowl shape (2c) finallyforming the spherical vesicle shape(2d)
The random force acting between a pair of particles i andj is defined as follows:
FRij =
σwR(rij)θij
√3rij√
dt(3)
Where σ is the maximum random force parameters, wR(rij)is the random force weighting function described below, θij
is a random variable with unit variance, zero mean and nomemory between time-steps of particle pairs. The
√3 term
appears in the force equation to alter the range of the ran-dom numbers (which were drawn from a uniform distribu-tion) to match that of the Gaussian distribution[9].
In order to ensure the correct temperature in the simula-tion, the γ and σ force parameters should be set in accor-dance with the following relation [4]:
σ2 = 2γkBT (4)
where kBT is the required temperature, (see [9] for an expla-nation of the coupling between the random and dissipativeforces).
Spring forces can be introduced between particles to sim-ulate polymer chains, these are defined as follows:
FSij = k(rij − r0) (5)
where k is the bond strength parameter, and r0 is the pre-ferred bond length. preferred angles between two bonds canbe included with a harmonic 3-body potential[13]
Uθ =1
2kθ(θ − θ0)
2 (6)
Where kθ is the angle force strength parameter, θ is theangle between the two bonds and θ0 is the preferred angle.
The total force acting between a pair of particles is thenthe summation of the three forces:
Fij = FCij + F
Dij + F
Rij (7)
with the additional polymer bond forces applying if theparticle is assigned to a polymer:
Fpolymerparticlesij = Fij + F
Sij + F
Uijk (8)
where F Uijk is the harmonic angle force (Eq. 6) and k is
the third particle involved in the three-body constraint forcecalculation.
In all of our simulations, the σ and γ parameters wereset to 3.0 and 4.5 respectively, producing a system temper-ature of kBT = 1.0. The equations of motion are then in-tegrated to evolve the state of the system. Several differentintegration schemes exist, and we choose the velocity Verletintegration scheme which requires an additional parameterλ (see [15] for details) which is set to 0.65. The time-steplength is set to dt = 0.05 in all of the following simulations.The conservative force parameters for the components of thelogic gates are shown in the section 2.3.
A simple form of chemical reactions were added to theDPD method in order to enable simulations of the biochem-ical logic gates. The implementation of chemical reactionswithin DPD follow the scheme proposed by Fellermann etal[5]. For each reaction that can occur in the system, the im-plementation enables the specification of reactants with twoinputs and two outputs, and a rate parameter ω which canbe altered to modify the probability of two particles reactingif they are within the reaction radius rcr . In our simulationswe have set it to be equivalent to the force interaction radiusmentioned previously. The method by which reactions occuris as follows: if two particles which can react are within rcr
distance of each other, a pseudo random number in the in-terval [0,1] is generated. If this random number is less thanωdt then the reaction takes place, and the types of the twoparticles are modified to reflect the output of the reaction.This is a slight modification from the reactions proposed byFellermann, where the probability of a reaction occurring isdependent on distance. Some reactions require only a singleinput and produce several outputs, in these cases, the reac-tion can be included in the simulation by adding a “dummy”input/output, of the bulk solvent type. In this way, the totalnumber of particles in the system is always constant, thusmaintaining the correct number density etc. For example,a model of an enzyme complexation/decomplexation mightbe specified as follows:
enzyme + substrate → complex
complex → enzyme + substrate
complex → enzyme + product
and could be altered in the following manner to enable mod-elling within the DPD framework, in which the number ofinputs specified in the reaction should be the same as thenumber of outputs to ensure the maintenance of correct den-sity in the simulation.
enzyme + substrate → complex + solvent
complex + solvent → enzyme + substrate
complex + solvent → enzyme + product
To speed up our DPD code as to make the simulation ofliposome logic feasible, we ported our algorithm to an NvidiaGeforce 8800 GTX GPU by utilising the Nvidia CUDA gen-eral purpose GPU (GPGPU) programming toolkit[16]. Mod-ern GPUs contain 100s of independent processors, and op-erate at a very high level of data parallelism. In CUDA,this parallelism can be harnessed for general purpose com-puting by specifying thread “kernels” in the C programminglanguage, each processor then executes many threads, eachwith the instruction set specified in the kernel, but perform-ing the instructions on different data (achieving single in-struction multiple data (SIMD) style parallelism).
Pseudo random numbers required for the random forcecalculations in DPD were generated by each thread usinga simple linear congruential algorithm specified by GeorgeMarsaglia, in order to reduce the possibility that correla-tions will occur, safe-prime seed numbers for each PRNGwere created following the process specified by Steven Grat-ton[8]. CUDA based DPD results were validated againstour serial version of the code obtaining almost identical re-sults (variations are due to nondeterminism and stochas-ticity). The CUDA implementation was approximately 40times faster than the serial version running on modern hard-ware. The CUDA DPD implementation will be described indetail elsewhere.
2.3 Modelling RegulationThe logic gates which we use as a case study (see Fig-
ure 3 for implementation within the simulated liposomes arebased on the transcriptional regulation of genes that occursin prokaryotic cells. For example, the expression of a genestarts with the binding of an RNA polymerase enzyme to thepromoter of the gene sequence. The gene is then transcribedinto messenger RNA which is translated by a ribosome intoa protein. The expression of the gene can be regulated bythe presence or absence of a repressor which binds to thepromoter, if the repressor is bound to the promoter thenthe polymerase cannot transcribe the gene sequence. Webase our logic gates on those listed in work by Silva-Rochaand Lorenzo[21], in which the logic gate behaviour is a re-sult of different types of regulation that can effect the rateof transcription of a gene. For example, if a signal moleculewere to change the conformation of a repressor protein suchthat it was then able to bind to the promoter region of thegene (thus blocking transcription) then the transcription ofthe gene could be considered as being similar to a logicalNOT gate, the output (protein expression) of the system,occurs only when the input (signal molecule) is not present.
Models of three different types of logic gates were created,an AND gate, an OR gate and a NOT gate. The modelswere intended to be general and qualitative, similar in styleto those used by Magnasco to show the Turing universal-ity of chemical reactions[14]. The logic gates were based onthe behaviour of biological protein expression in prokary-otes, but without using rates measured from any specificbiological system. Thus, in principle at least, they could beimplemented through a bottom-up synthetic biology route.
The model NOT gate is based on the deactivation of a
(a) AND gate (b) OR gate
(c) NOT gate
Figure 3: The gene interactions representing the three logicgates: rectangles represent activators/repressors. Arrowsshow the binding of the activator or repressor to the genepromoter (green for activation, red for repression). Curvedarrows show the enabling of the activator/repressor by thegiven signal molecule.
Type S T HSig
X,Y
Act
X,Y
Repr
X
Gene
X,Y
XY
Output
S 78 104 78 78 78 78 78 78T 104 78 104 78 104 104 104 78H 78 104 78 78 78 78 78 78Sig
X,Y78 78 104 78 78 78 78 78
Act
X,Y78 104 78 78 78 78 78 78
Repr
X78 104 78 78 78 78 78 78
Gene
X,Y
XY
78 104 78 78 78 78 78 78
Output 78 78 78 78 78 78 78 78
Table 1: The conservative force α parameter for the encap-sulated AND gate simulations. S, T and H are the solvent,DMPC tail and DMPC head types respectively.
repressor protein which is competing to bind to the gene.When the repressor is bound to the gene, no transcriptioncan occur. The presence of the X signal molecule changesthe conformation of the repressor protein such that it can nolonger bind to the gene, allowing transcription to occur. TheNOT gate is modelled in DPD with the following reactions:
sigX + ReprX(inactive)0.1−−→ ReprX + solvent
gene + ReprX0.1−−→ geneX + solvent
geneX + solvent0.01−−→ gene + ReprX(inactive)
gene + solvent0.1−−→ gene + output
The model AND gate is based on a gene that requirestwo activator proteins to bind to the promoter region beforetranscription can occur. The activator proteins are enabledby two signal molecules, X and Y respectively and once en-abled are able to bond to the gene. Transcription can beginonly when both activators are bound to the gene. For the
DPD model gates, the mechanism by which the transcrip-tion and translation occurs is not included, and is replacedwith a single reaction. The AND gate is modelled in DPDwith the following reactions:
sigX + actX(inactive)0.1−−→ actX + solvent
sigY + actY (inactive)0.1−−→ actY + solvent
gene + actX0.1−−→ geneX + solvent
gene + actY0.1−−→ geneY + solvent
geneX + actY0.1−−→ geneXY + solvent
geneY + actX0.1−−→ geneXY + solvent
geneX + solvent0.01−−→ gene + actX(inactive)
geneY + solvent0.01−−→ gene + actY (inactive)
geneXY + solvent0.01−−→ geneX + actY (inactive)
geneXY + solvent0.01−−→ geneY + actX(inactive)
geneXY + solvent0.1−−→ geneXY + output
The model OR gate is the same as the model AND gate,except that transcription can occur when either one of thetwo activators is bound to the gene. The OR gate is mod-elled in DPD with the following reactions:
sigX + actX(inactive)0.1−−→ actX + solvent
sigY + actY (inactive)0.1−−→ actY + solvent
gene + actX0.1−−→ geneX + solvent
gene + actY0.1−−→ geneY + solvent
geneX + solvent0.01−−→ gene + actX(inactive)
geneY + solvent0.01−−→ gene + actY (inactive)
geneX + solvent0.1−−→ geneX + output
geneY + solvent0.1−−→ geneY + output
Table 1 shows the conservative force parameter matrix forall simulations, the large maximum repulsion value (104.00)between the particles representing the lipid of the mem-branes and the genes and activators ensure that particlesof these types are held within the liposome inner volume,as they cannot diffuse across the membrane. An α valueof 78.00 gives the types the same immiscibility as water atroom temperature.
The rates for the DPD reactions were not based on anyparticular observation or parameter set, but were insteadchosen to ensure that the reactions would occur within thetime scale of the simulation. DPD simulations typically donot simulate more than a second of real time, clearly far lessthan the amount of time for the transcription and transla-tion reactions to occur in biology, where the time taken toexpress a protein ranges from minutes to hours. However,the work in this paper is intended as a proof of principle forthe inclusion of logic gates within vesicles, and that doingso has a beneficial effect on the dynamics of such systems.Thus in vivo time scales do not translate to our system.That is, as we are following a non biological implementationfor liposome logic we are interested in the structure of the
gene circuits for the AND, NOT and OR gates rather thenon a cell biology specific modelisation. Moreover, we use thewords ’gene’ and ’gene circuits’ in the sense of (1) an objectthat encodes information, but that it does not have to bea nucleic acid based information store, (2) converts that in-formation into an output, but again for a vesicle computerthis does not have to be the familiar RNA → protein route,etc. The logical operation is the conversion of the informa-tion into an output requiring an energy input and yieldingan output. With this in mind, we define “fast“ and “slow“reactions with the reaction constant ω set to 0.1 and 0.01respectively. Reactions between signal molecules and ac-tivators/repressors, the binding of activators/repressors togenes and the production of the output protein were “fast“and the decomplexation of activators/repressors from geneswas “slow”.
2.4 Creating the Liposomes and Simulation ofInitial Conditions
The transcriptional logic gate reactions were simulatedin two situations, firstly with all particles moving freely inbulk solution (control experiment), and secondly with thegene and activator particles encapsulated within the innervolume of the liposome. In order to create the initial condi-tions, liposomes were extracted from the output of a DPDsimulation and the types of the particles in the inner vol-ume were altered to produce the required promoter/geneconcentrations within the liposome. By running simulationsin bulk and within-liposome we can assess the impact ofthe protomembrane in encapsulating complex behavior. Itis important to note that, in the absence of either temporalor chemical specificity-derived compartmentalization (whichare extremely difficult to achieve in vitro), the most realisticroute for obtaining complex circuits depends on embeddinglogic circuits within liposomes as proposed here.
The liposomes were created by randomly placing modelDMPC phospholipid polymers based on coarse parametersfrom Kranenberg et al[12] into a volume of 503rc with anumber density ρ = 3.0 such that 18% of the total num-ber of particles (375000) in the simulation volume composedthe polymers, creating 5192 polymers in total. The bondstrength for the bonds in the DMPC polymer was set to100kBT and the preferred bond length was set to 0.7. An-gle forces were added to the tail chains with strength 6kbT
and preferred angle π radians. The point where the two tailgroups join the head group also had an angle force imposedon it with strength 3kbT and preferred angle of π
2radians.
The system was then evolved for 10000 DPD time units(with a time step length of dt = 0.05), and liposomes werefound to have self-assembled at around τ = 6250. The vesi-cle formation simulation took less than 8 hours using theCUDA implementation of the DPD software running on anNvidia 8800 GTX graphics card.
The initial states for the logic gate experiments were cre-ated by loading the particles and polymers of a pre-computedliposome into a new simulation space, and modifying thetypes of solvent particles encapsulated within the inner vol-ume such that the required gene/promoter types were encap-sulated. The inner volume of the liposome contained 13884solvent particles. Table 2 shows how many particles of eachtype were placed within the liposome inner volume.
The initial state was then loaded into the software, andafter an equilibration period of 50 time units, in which no
Type ANDCount
ORCount
NOTcount
Solvent 12490 12490 13184activator X (inactive) 694 694 694activator Y (inactive) 694 694 0
gene 5 5 5
Table 2: The count of each particle type placed within the in-ner volume when initialising the liposome for the logic gatesexperiments.
reactions were allowed to occur, the system was evolved for1000 DPD time units, and the number of particles of eachtype was counted at the end of each time unit, in orderto record the dynamics of the system. As to account forthe stochastic nature of the dynamics, each simulation wasperformed three times, and each run took 37 minutes inCUDA. This process was repeated for each set of inputs tothe logic gate, in order to observe the dynamics of the systemin response to the presence or absence of the different signalinputs.
3. RESULTSThe following figures show the time series of the number
of particles (for each particle type) for each logic gate forboth the control and the within-liposome experiments. Fig-ure 4 shows the results for the control and vesicle AND gateexperiments respectively. The figures show that the creationof the output gene occurs very infrequently in the control ex-periments, and in fact only a single output protein is createdin all three runs. This is in contrast with the results from theruns where the AND gate is encapsulated within the vesicle,where on average 275 output proteins were produced bythe end of each run, due to the maintenance of the regionof high activator and gene concentration within the vesiclevolume. Figure 4 also illustrates the correct functioning ofthe AND logic gate, as the output protein is only producedwhen both input signals are present. The graphs in figure5 show that the OR gate reactions occurred at a faster ratethan the AND gate reactions, most likely because the path-way from signal to output protein involves only two reactions(as opposed to three in the case of the AND gate) in orderto generate proteins. The OR gate reactions functioned cor-rectly in terms of modelling the OR logic gate in the vesicleand control experiment as the output protein was producedwhen either or both of the inputs was present, in both thecontrol and vesicle experiments, the number of output par-ticles produced was greater when both input signals werepresent, as both activators are enabled and could react withthe gene rather than only one for the single input cases. Forthe NOT logic gate, the graphs in figure 6 show that whenthe X signal molecule is present, the number of output pro-teins present at the end of the simulation is reduced due tothe binding of the signal molecule to the repressor, whichprohibits production of the output molecule. However theproduction of the output protein is not inhibited entirely, asthe the repressor can decomplex from the gene. The effectof the encapsulation of the NOT gate is to increase the like-lihood that the repressor and gene can come into contactand form a complex, therefore the overall expression rate ofthe protein is, as expected, lowered.
Y = 0 Y = 1
X=
0X
=1
Figure 4: AND Gate Results
Y = 0 Y = 1
X=
0X
=1
Figure 5: OR Gate Results
X = 0 X = 1
Figure 6: NOT Gate Results
4. DISCUSSIONThree simple logic gates were implemented and the effects
of encapsulation on their dynamics was investigated using anew method based on DPD simulations. The results showedthat by constraining the gene transcription/translation mole-cules within the liposome, the response time of the gate (i.e.the time for the gate to produce an output after a change ofinput) was reduced drastically by ensuring a high concentra-tion of activators/repressors within the liposome inner vol-ume. This ensures that the activator and gene are in closeproximity, so the activator does not have to diffuse very farto collide with the gene after being activated by a signalmolecule. Clearly, simple logic gates are not useful in isola-tion, and so a key area of further research is to investigatemethods by which the liposome gates could be combinedinto more complex functionality, several possibilities springto mind: One liposome logic gate could be nested within an-other, with the inputs and outputs of the liposomes coupledtogether, or the gates could be held together by moleculartethering to ensure the output of one gate is not dispersedbefore reaching the next gate. By synthesizing simple pro-tocell like structures containing selected biochemistries, amuch wider range of bio and standard chemistries are avail-able as building blocks for computation, and are less likelyto suffer from incompatibilities with complex biological sys-tems in a heterogeneous environment. With regard to syn-thetic biology, combination of these structures in relationto existing biomolecular machinary could allow the modulardesign and specification of artificial life from the bottom up.
Our simulations have indicated that it may be possible tocreate liposome logic systems, however to validate these sim-ulations an attempt should be made to construct the lipo-some logic systems in the laboratory. Work by Neureux andLibchaber has shown that encapsulating plasmids and cell-free extract to enable gene expression within a liposome in-ner core is achievable, and gene sequences for logic gates canbe found in the MIT registry of standard biological parts.
5. ACKNOWLEDGMENTSEPSRC grants EP/017215/1 and EP/D021847/1, and BB-
SRC grant BB/F01855X/1.
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