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Abstract. We report here the design and implementation in vivo of a gene circuit that can count up to 4. In essence, it uses two toggle switches, each storing 1 bit, to keep track of the 4 states. The design of the counter is highly modular, with the hope that it can be included as a unit in larger circuits, and also combined with further counter instances to keep track of a much larger number of states, up to (2^(n+1)) with n units. To facilitate further developments and integration to other projects, the counter is available in form of BioBricks. Among many exciting applications, the availability of a counter enables the execution of sequential instructions, and paves the way for the execution of artifical programs inside living cells.

Introduction

The past few years have seen the emergence of the field of synthetic biology, in which functional units are designed and built into cells to generate a particular behaviour, and ultimately to better understand Life's mechanisms. Previous efforts include the creation of gene circuits that generate oscillating behaviour (Elowitz00), toggle switch functionality (Atkinson03), artificial cell-cell communication (Bulter04) or pattern-forming behaviour (Basu2005). The present document describes the design and realization of a gene circuit that counts to 4.

Design of the Counter

The counter is a genetic circuit that has 1 input and 4 outputs. It uses the input signal to switch from one of the four output to the next. When the input signal is high, either output 1 or 3 is active, when it is low, output 2 or 4 is active. Thus, output 1 and 3 alternatively keep track of high input signal, while output 2 and 4 alternatively keep track of low input signals.

As depicted above, the counter is made of two parts, serially linked:

• the "Input" module, which splits the input into two opposite signals.
• the "NOR" module, which uses these two signals to sequencially switch through the outputs 1, 2, 3 and 4.

Note that all interfaces have flows described in Polymerase Per Second (PoPS), is explained in details on the [http://partsregistry.org/cgi/htdocs/AbstractionHierarchy/index.cgi abstraction hierarchy] of the MIT Registry of Parts. For instance, the input can be of any nature as long as an adequate promoter is available (e.g. heat-shock using a sigma32 promoter, IPTG using a LacI promoter, AHL using quorum sensing promoters...)

Input Module

The input module splits the input into two opposite signals. It is best described through its system boundaries. One of the outputs should be high and the other low when S is high and vice versa when S is low:

To achieve such behaviour, we use the λ-system, with IPTG as inductor. It is relatively easy to handle/debug, and does not restrict the module from being extended to work with other types of inputs. More importantly, it is already available as a BioBrick (Registry package 7.05) in its unidirectional flavour (In nature, the λ-system is bidirectional, with Pr on one DNA strand and Prm on the other, overlapping). The following picture shows the gene circuit of the input module in details:

cI is a dimer and regulates the activity of the two promoter regions, Pr and Prm, on the λ-system. Pr is constitutively active and is repressed when cI binds to the two operator regions it overlaps with (OR1, OR2). Conversly, Prm has low basal activity, and is activated by cI. Since the two promoters are regulated by the same protein-operator interactions, repression and activation is expected to be symmetrical (as very desirable proprety, see results from simulation below). For more details, please consult the page Input-module.

NOR Module

The "NOR" module uses two inputs to sequencially switch through its outputs 1, 2, 3 and 4. To achieve such behaviour, we use four interconnected "NOR" gates. In essence, a NOR gate is a component that has two inputs and one output, where the output is only high if *none* of the input is high. Concretly, a NOR gate can be implemented through a promoter with high basal activity that is repressed by two effectors. In the particular case, our NOR gates have three inputs (or effectors), none of which must be active for the gene to be expressed.

The following diagram (which should be redrawn using better tools than ASCII art) shows how the four NOR gates are interconnected:

            R3 R2         R4 R1                           R4 R3         R1 R2    
             | |           | |                             | |           | |                               
     /|____  | |           | |  ____|\             /|____  | |           | |  ____|\                        
 ___/  R1  |_=_=___     ___=_=_| R3   \___     ___/  R2  |_=_=___     ___=_=_| R4   \___
    \  ____|     =       =     |____  /           \  ____|     =       =     |____  /     
     \|          |       |          |/             \|          |       |          |/        
                 \       /                                     \       /                   
                  \     /                                       \     /               

                  input 2                                       input 1

The design is highly symmetrical. We have 4 genes producing 4 repressor proteins R1, R2, R3 and R4. The production of each protein is repressed by 3 specific repressors, the two "following" repressors as well as either input 1 (for R2 and R4) or input 2 (for R1 and R3). By design of the input module, input 1 and input 2 have opposite activity, meaning that either R1/R3 or R2/R4 is active. Furthermore, since R1/R3 (respectively R2/R4) are repressing each other, only one of the two is active. Therefore, in a stable situation, only 1 of the 4 repressor proteins is expressed.

Let us assume that R1 is being expressed. Input 2 must then be low, and therefore input 1 high. This situation is stable and remains until there is a change in the inputs. Now, if input 1 decreases, and input 2 increases, the expression of R1 will come to a halt. Since input 1 is now low, either R2 or R4 will be expressed. At this stage, R1 is still present in relatively high concentration and by repressing R4, tips the balance in favor of R2, leading to a new stable state in which only R2 is expressed.

Note that electrical engineers call such a device a "J-K flip flop". It can also be seen as a combination of two toggle switches (Atkinson03), each being able to store one bit.

Simulation

Implementation

Results and Discussion

Applications and Perspecitves