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We want to build biological memory and logic devices, implement them in systems.
To achieve this, we need well understood and characterized memory devices that perform well with respect to the below defined requirements.
The bits (or memory switches) that underlie a biological counter must be:
Memory device design
The flippee, a recombinase-driven bit, is a memory device. Preliminary experiments show this works:
Modeling and experiment to characterize devices
The problem is that we cannot easily measure each step in the process of flipping individually. We only have bulk measurement of GFP expression at some after induction. This limited data provides insufficient basis to build a predictive model. Furthermore, individual events - such as recombination- are hard to measure. In vitro assay may be feasible but don’t capture holistic complexity.
Experiments that allow us to interrogate and learn about each process individually provide data about the stability and speed of switching.
we can capture in a model for flippee performance. This flippee will serve as the basis for models use to optimize the system architecture.
Modeling requires data to which we can fit a mathematical representation of the system. Fitting model to data allows us to define parameters that give the model predicative capability. This means that the model describes the behavior of the flippee within a defined domain of possible input parameters; of particular interest are trigger pulse length and flipper (intergrase and excisionase) expression dynamics. This predictive capability will be useful when examining possible counter architectures. To build a descriptive model, we need data related to the timescale of various processes that compose flipping.
With this in mind, we can build sub-systems and independently test them. The dynamics for these sub-processes along with bulk data about flipping may be sufficient to back-calculate the dynamics of difficult to measure processes, such as recombination. At the very least, measurement of these sub-systems should give us a feel for the general timescale of the steps in the flipping process. In order to do this, we simply need to know the design of Jerome's flippe and then design genetically normalized sub-systems. This may involve detailed study of the design and method used in prior work with flouresnce and stroboscopic imaging to visualize binding Choi et al.
* What are the steps and what is the relative timescale for each step?
* How leaky is the flipper promoter?
* How much leakiness can we tolerate before flipping occurs?
What we want to model?
1. Biological memory and logic devices
2. Systems that implement these devices
Scope of other modeling efforts
Models have been used to inform design the of genetic networks that encode certain dynamical behaviors. Parameter values lump many biological processes together and represent high-level functions such as "synthesis rate of a repressor" or "cooperativity" / "strength" of binding. Collins (Toggle Switch, 2000) and Elowitz (Repressilator, 2000) use models to gain a qualitative understanding of the parameter values necessary to achieve bi-stability or oscillation. For example, the models help them conclude things such as synthesis rate for two repressors must be high and strong binding is needed to get the desired dynamical behavior. This qualitative understanding aids in selection of parts. This process can be generally described as shown below left. Other models seek to describe the dynamics of a mechanism, such as the kinetics of Cre and Flp recombination (Ringrose, 1998). This process involves construction of a cartoon mechanism with associated differential equations and experimental work to gather data about the system to which the model can be fitted. The model captures and integrates diverse data and, with parameters gathered from empirical study, is (hopefully) predictive across a domain of possible inputs.
What kind of models do we need?
As mentioned above we want a model to help us collate diverse data about the performance of our system within a single framework. We want a model that describes accurately and with predictive power how the Flippee performs across an input domain of signal frequency / lengts, and across the space of Xis/Int expression and decay. With a strong descriptive flip-flop model, we want to find an architecture for connecting flippees together that meets our counter requirements and exhibits robust counting across a range of input parameters (or perturbations).
What kind of measurements do we need?
Conventional tools to interrogate biological systems often have three features: 1) study an ensemble of molecules or cells with (observed) deterministic and reproducible temporal behavior. 2) kinetics of enzymatic processes under non-equilibrium non-steady-state conditions. 3) Experiments on isolated molecules, outside of their holistic context. In vivo molecules are often at low copy number and process take place under non-equilibrium steady-state conditions; many cellular enzymatic reactions such as transcription, translation, and replication occur with a constant supply of free energy and substrates.
These and other factors drive stochastic behavior - a particular time trace for one cell’s behavior is not reproducible and cannot be synchronized with that of another cell - that must be recognized when approaching biological modeling efforts. Single-molecule measurements may provide a way to get much better data for modelers, such as population distributions rather than bulk averages of molecular properties and study of single molecule behaviors in the physiological context, which reflects holistic complexity.
Exhaustive step in flipee mechanism for modeling
Inducer IPTG diffuse into a cell
Induction and mRNA synthesis for integrase
Translation of integrase
Extensive mechanism posed by Ringrose, 1998 (for Cre, Flp).
Extensive mechanism posed by Ringrose, 1998 for Cre, Flp