Endy:Notebook/Computational modeling

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Context
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.

Requirements
The bits (or memory switches) that underlie a biological counter must be:
 * Bi-stable: holds state, minimal leakiness
 * Controllable: a state change that is
 * Fast: short time between I/O
 * Specific: minimal cross talk

Memory device design
The flippee, a recombinase-driven bit, is a memory device. Preliminary experiments show this works:


 * Need to add more details on the design here.
 * Need to ass data that describes how well it works.
 * Timescale
 * Leakiness

Goals

 * We want a design that optimally meets our requirements :
 * Maximize speed
 * Minimize leakiness
 * Maximize specificity


 * We want models that predict behavior to :
 * Inform design of system architecture
 * What are the requirements for bit interconnection?

Approach

 * Determine rate limiting step in the process
 * Gather data that can be incorporated ...

Problem


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.

Approach
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.

Need
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.

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Solution


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.

Current knowledge

 * Right now in the OFF state, the system still flips
 * PCR data?
 * Not quantitative
 * Doesn't tell us the fraction
 * GFP data?
 * Can resolve single cell

Questions
'''
 * What is the time distribution for flipping across a population of cells?'''
 * If we know the flipping time distribution across a population of cells, then what:
 * Can go from population-level data about time of flipping to P distribution for flipping
 * Probability distribution then can slip into mathematical framework and allow us to evaluate flipping
 * Time between signal in and out is "all we care about."

* What are the steps and what is the relative timescale for each step?
 * Additional data to fit to a dynamic model for flipping.
 * This should help in the design of the flippee to increase its speed.

* How leaky is the flipper promoter?
 * Can leaky expression reach the flipee.
 * If in the weakest case you get binding, then there's no way to tightly control the system.

* How much leakiness can we tolerate before flipping occurs?
 * Promoter/RBS combinations


 * Decouple effects of promoter from effects of recombinase




 * Jerome's design :
 * Integrase generator
 * Inducible promoter, RBS, terminator
 * Flipee plasmid
 * Sequence
 * Promoter
 * GFP


 * To test time between flipper induction and binding, we need:
 * Flipper fused with pholorphre that we can visualize when bond
 * Fusion design :
 * N and C terminal fusion
 * Length of linker


 * Strength: if too high, can't see localization but if too low, then can't see anything.
 * Leaky expression may produce a signal
 * Expression itself is leaky for LacI
 * T. Ham regulation system?


 * Fusion construction :
 * PCR with linker
 * Precedent
 * Has anyone done this before?

What we want to model?

 * Summary of and application for biological memory & logic systems

1. Biological memory and logic devices

 * Introduce Flippee
 * Introduce analogous electronic device : flip-flop
 * Show prior work : iGem 2004

2. Systems that implement these devices

 * Introduce electronic counter applications
 * Introduce analogous electronic counter : asynchronous & synchronous architectures

Design questions

 * How does flip speed change with respect to pulse length and pulse frequency?
 * How does flip speed change with respect to int and xis expression /degradation levels?

Modeling objectives

 * Find optimal design for flipee
 * Consider all steps in flippee mechanism
 * Highlight data needed to understand dynamics of each step
 * Integrate diverse data into model
 * Iterate until model predicts behavior with respect to :
 * Pulse length
 * Int/Xis expression levels


 * Investigate different counter architectures
 * Pulse length, Int/Xis expression levels represent interconnects between bits within the counter
 * With predictive model for each bit, evaluate robustness of counting with respect to changes in these interconnection parameters for (asynchronous / synchronous) architectures

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.

Inducer IPTG diffuse into a cell



 * Mechanism and notes
 * IPTG diffuses across E.coli cell membrane and cytosol and binds to lacI
 * Diffusion rate of IPTG across cell membrane
 * Diffusion rate of IPTG in cytosol
 * IPTG-lacI binding rate
 * Number of lacI in a single cell


 * Prior study:
 * Modeled by Collins et al.


 * Mathematical representation
 * Cellular consumption: d[iptg]/dt=-c[iptg]
 * Decay following suspension in new media: d[iptg]/dt=-d[iptg]


 * Unknown parameters
 * c, d


 * Experimental tools to get data
 * Most groups fit GFP data to model and find parameters
 * Check on what Ari / Collins did ...
 * Choi bio-physics review provides many single molecule methods

Induction and mRNA synthesis for integrase



 * Mechanism and notes
 * lacI-IPTG leaves the promoter
 * lacI-IPTG has much lower affinity toward Lac operator than lacI and likely to dissociate
 * Dissociation rate of lacI-IPTG from the lac operon
 * Number


 * Prior study
 * Collins, Elowitz, Alon, etc.


 * Mathematical representation
 * Basal synthesis rate without induction: s0
 * Synthesis rate when induced (Hill function with coefficient 1): sT*[iptg]/([iptg]+k)
 * Exponential decay rate on mRNA: -D[mRNA]


 * Unknown parameters
 * s0, sT, K, hill coefficient, D


 * Experimental tools to get data
 * Most groups fit GFP data to model and find parameters
 * Check on what Ari / Collins did ...
 * Choi bio-physics review provides many single molecule methods

Translation of integrase



 * Mechanism and notes
 * List...


 * Prior study
 * Collins, Elowitz, Alon, etc.


 * Mathematical representation
 * Translation rate of protein, k * [mRNA],
 * Exponential protein decay : d * [protein]


 * Unknown parameters
 * d, k


 * Experimental tools to get data
 * Most groups fit GFP data to model and find parameters
 * Check on what Ari / Collins did ...
 * Choi bio-physics review provides many single molecule methods

Integrase search



 * Mechanism and notes
 * 3D and 1D?


 * Prior study
 * Choi bio-physics review ...


 * Mathematical representation


 * Unknown parameters


 * Experimental tools to get data
 * See Choi stroboscopic imaging for LacI ...

Integrase binding


Extensive mechanism posed by Ringrose, 1998 (for Cre, Flp).


 * Mathematical representation : Detailed


 * Unknown parameters : Many


 * Experimental tools to get data : See Choi stroboscopic imaging for LacI and Ringrose uses gel mobility shift (in vitro)

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Recombination


Extensive mechanism posed by Ringrose, 1998 for Cre, Flp


 * Mathematical representation : Detailed


 * Unknown parameters : Many


 * Experimental tools to get data
 * See Choi stroboscopic imaging for LacI
 * Ton's ideas on binding site displacement
 * Re-capituate binding site at one corner of the flipping DNA
 * Ringrose uses in vitro recombination assays

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