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Hysteresis in a synthetic mammalian gene network

Kramer, B.P. and Fussenegger, M. 2005. Hysteresis in a synthetic mammalian gene network. Proc. Natl. Acad. Sci. 102: 9517-9522.


In 2005, the lab of Martin Fussenegger (at the Federal Institute of Technology in Zurich, Switzerland) published a paper on the construction a hysteretic switch in mammalian cells. This research can be viewed as an extension of the toggle switch that was constructed in the lab of J.J. Collins 5 years earlier. While the toggle switch construct was able to respond to two separate inputs in different ways, the hysteretic system can respond to a single input in different ways depending on the history of the cell. Using an autoregulatory positive feedback design, this system is a step in the direction of constructing a permanent memory circuit, which will be the topic of the next example paper. This work is also significant because of the use of a mammalian cell chassis, in which it is substantially more complicated to implement a genetic network than it is in E. coli.

What is Hysteresis?

Figure 1: A graphical depiction of hysteresis.

"A system with hysteresis exhibits path-dependence, or 'rate-independent memory'. Consider a deterministic system with no hysteresis and no dynamics. In that case, we can predict the output of the system at some instant in time, given only the input to the system at that instant. If the system has hysteresis, then this is not the case; we can't predict the output without looking at the history of the input. In order to predict the output, we must look at the path that the input followed before it reached its current value. A system with hysteresis has memory" (Wikipedia).

In Figure 1 on the right, hysteresis in demonstrated graphically. The arrows indicate the direction of movement from one state to another. For a system that exists in the low output state initially (red line), a relatively high level of input is required to induce a change to a high system output. For a system that exists in the high state initially (blue line), a relatively low level of input is required to induce a change to a low system output. In other words, more extreme amounts of input are required to move out of a state than are required to move into a state (meaning that the system resists a change of state). Linebreak.png

Specific Biological Design

Figure 2 below shows the specific biological design that was used to construct a hysteretic gene network in mammalian cells. The system uses a type of autoregulatory positive feedback whereby an activator gene is downstream of its promoter, but in this case the activator is in competition for promoter binding with a repressor molecule. The activator molecule in this design is a fusion of the tetR gene and the VP16 transactivation domain. This protein binds to the tetO7 operator region of the hybrid promoter (PhCMVmin) and increases the promoter's affinity for RNA Polymerase, thus increasing promoter activity. The reporter gene in this design is secreted alkaline phosphatase (SEAP), a protein whose levels inside the cell can be easily measured without cell lysis. The SEAP gene is also downstream of the hybrid promoter (PhCMVmin) and is, therefore, transcribed at the same rate as the transactivator gene. On a separate plasmid, the E-KRAB repressor gene lies downstream of a constitutive (always on) promoter, PSV40. This repressor binds to the ETR8 operator region of the hybrid promoter (PhCMVmin) and blocks binding of RNA Polymerase to the promoter. The antibiotic erythromycin (EM) is able to bind to the E-KRAB repressor and prevent it from binding to the promoter. With no input of EM in the system, repressor binding will out-compete activator binding, and transcription downstream of the hybrid promoter will be blocked. As the concentration of EM in the system is increased, more promoter activity occurs and the system is able to toggle into the "SEAP on" state. In this state, an overabundance of activator in the system allows autoregulatory positive feedback to win out over repression from E-KRAB. Because of the competitive nature of promoter binding, the system resists a change in its stable steady state (whether that be from on to off or off to on) and, therefore, demonstrates hysteresis. This effectively means that a higher concentration of EM is required to change the system from off to on than is required to remain in the on state. Likewise, a lower concentration of EM is required to change the system from on to off than is required to remain in the off state.

Figure 2: Biological design of a hysteretic switch in mammalian cells.

Mathematical Modeling

Again, the mathematical modeling behind this biological design will not be discussed in detail, as the mathematical modeling section of this wiki paper has covered most of the principles behind the modeling of memory circuits already. In short, a differential equation was derived that described the rate of SEAP production in terms of activator concentration and EM concentration. The degradation rate of the activator, the promoter strength, and the dissociation constant for EM binding to the repressor were all determined/estimated based on experimental data. Cooperativity of both the activator and the repressor was set equal to 2. By inputting these constants into the differential equation for the rate of SEAP production and setting it equal to 0, the concentration of EM required to move between states could be calculated for a given initial concentration of activator in the system. This revealed hysteresis. The concentration of EM required to move from the on to the off state was calculated to be approximately 500 ng/mL. Depending on the basal expression of the activator in the off state, the concentration of EM required to move from the off to the on state was shown to vary, however, for normal levels of basal expression, this EM concentration was estimated to be >800 ng/mL. Once again, cooperativity of binding was required to achieve bistability in the system. This mathematical model also utilized experimentally determined constants to predict the input and output values of the system. These mathematical predictions could then be compared to experimental results (see Figure 3 below).


Figure 3: Experimental results of the hysteretic switch in mammalian cells.

Figure 3, on the right, demonstrates to functionality of the hysteretic switch. Panel A shows the behavior of two different cell populations. One population was cultivated in EM for three days to turn SEAP production on [+EM (ON to OFF)]. The other population was cultivated without EM in order to set the SEAP expression to the off state [-EM (OFF to ON)]. The populations were then exposed to different concentrations of EM for 48 hours, at which point the level of SEAP expression was measured. Populations that began in the off state required >1000 ng/mL to be turned on, while populations that began in the on state required <500 ng/mL to be turned off. Simulations produced by the mathematical model are also shown to demonstrate the accuracy of the model, although the simulation curves have been normalized to the expression data. Note the similarities between Figure 1A and Figure 3, each of which demonstrates hysteresis.

Panel B demonstrates the ability of the populations to toggle between the on and off states multiple times. Cell populations were initialized to the on state (solid line), through 3 days of exposure to EM, and the off state (dotted line), through lack of exposure to EM for 3 days. The environments were then reversed for three days and then reversed again for another three days. As can be seen in the figure, SEAP concentrations move between the on and the off states as expected. It can also be observed that a decrease in the on-state SEAP expression occurs over time. However, this trend is not explained in the paper. Linebreak.png


The hysteretic system described in this paper was one of the earliest attempts to construct a memory network in a mammalian cell. As the authors state, this paper showed that "network design principles evolved in E. coli also function in a mammalian cell. Such genericness among gene control circuitries increases hope for successful therapeutic interventions in future gene therapy and tissue engineering" (Kramer, 2005). In other words, if gene circuits such as this one can be tested in simple systems and moved into more complex ones, then the prospect of one day having the ability to control such things as human cell differentiation is not as far off as might be expected. This technology has vast implications for all sort of medical treatments.

In addition to successfully engineering and modeling a gene network in mammalian cells, this work also demonstrates the design of a hysteretic memory system which could have applications in many types of more complex synthetic devices. In the next paper, a similar network will be discussed that confers permanent memory.