Module Locking in Biochemical Synthesis Brian Fett and Marc D. Riedel Electrical and Computer Engineering University of Minnesota Brian’s Automated Modular Biochemical Instantiator (BAMBI)

students at the University of Minnesota Brian FettAdam SheaWeikang Qian Matt Cook Institute of Neuroinformatics, ETH Zürich Tim Mullins Senior Technical Staff Member, HPC Life Sciences Applications, IBM Systems and Technology Group Acknowledgements

“Minnesota Farmer” Most of the cells in his body are not his own! Most of the cells in his body are not even human! Most of the DNA in his body is alien! Who is this guy? Acknowledgements

“Minnesota Farmer” 100 trillion bacterial cells of at least 500 different types inhabit his body. Who is this guy? He’s a human-bacteria hybrid: vs. only 1 trillion human cells of 210 different types. [like all of us]

“Minnesota Farmer” Who is this guy?What’s in his gut? 100 trillion bacterial cells of at least 500 different types inhabit his body. He’s a human-bacteria hybrid: vs. only 1 trillion human cells of 210 different types. [like all of us]

About 3 pounds of bacteria! What’s in his gut? “E. coli, a self-replicating object only a thousandth of a millimeter in size, can swim 35 diameters a second, taste simple chemicals in its environment, and decide whether life is getting better or worse.” – Howard C. Berg

“Stimulus, response! Stimulus response! Don’t you ever think!” We should put these critters to work…

Synthetic Biology Positioned as an engineering discipline. –“Novel functionality through design”. – Repositories of standardized parts. Driven by experimental expertise in particular domains of biology. – Gene-regulation, signaling, metabolism, protein structures …

Building Bridges "Think of how engineers build bridges. They design quantitative models to help them understand what sorts of pressure and weight the bridge can withstand, and then use these equations to improve the actual physical model. [In our work on memory in yeast cells] we really did the same thing.” – Pam Silver, Harvard 2007 Quantitative modeling. Mathematical analysis. Incremental and iterative design changes. Engineering Design

Synthetic Biology Cellulosic ethanol (Nancy Ho, Purdue, ’04) Anti-malarial drugs (Jay Keasling, UC Berkeley, ‘06) Tumor detection (Chris Voigt, UCSF ‘06) Feats of synthetic bio-engineering: Strategy: apply experimental expertise; formulate ad-hoc designs; perform extensive simulations.

From ad hoc to Systematic… Claude E. Shannon 1916 –2001 “A Mathematical Theory of Communication,” Bell System Technical Journal, Basis of information theory, coding theory and all communication systems. Basis of all digital computation. “A Symbolic Analysis of Relay and Switching Circuits,” M.S. Thesis, MIT, 1937

inputsoutputs Design is driven by the input/output specification. CAD tools are not part of the design process; they are the design process. Building Digital Circuits digital circuit...

[computational] Synthetic Biology [computational] Analysis “There are known ‘knowns’; and there are unknown ‘unknowns’; but today I’ll speak of the known ‘unknowns’.” – Donald Rumsfeld, 2004 Biological Process Molecular Inputs Molecular Products Known Unknown Known / Unknown Unknown Given

Artificial Life US Patent (pending): “The present invention relates to a minimal set of protein-coding genes which provides the information required for replication of a free-living organism in a rich bacterial culture medium.” – J. Craig Venter Institute Going from reading genetic codes to write them.

Artificial Life Going from reading genetic codes to write them. Moderator: “Some people have accused you of playing God.” J. Craig Venter: “Oh no, we’re not playing.

Biochemistry in a Nutshell DNA: string of n nucleotides ( n ≈ 10 9 )... ACCGTTGAATGACG... Nucleotides: Amino acid: coded by a sequence of 3 nucleotides. Proteins: produced from a sequence of m amino acids (m ≈ 10 3 ).

Logic Gates: how digital values are computed. Biochemical Reactions: how types of molecules combine. “XOR” gate Basic Mechanisms + + 2a2a b c

Biochemical Reactions cell speciescount Discrete chemical kinetics; spatial homogeneity.

Biochemical Reactions slow medium fast Relative rates or (reaction propensities): Discrete chemical kinetics; spatial homogeneity.

Design a system that computes output quantities as functions of input quantities. Synthesizing Biological Computation Biochemical Reactions givenobtain Quantities of Different Types M N independent for us to design specified

Start with no amount of types b and c. Example: Exponentiation Start with M of type m. Produce of type n. M 2 Use working types a, b, c. Start with any non-zero amount of types a and n. nana   fast 2 med a obtain 1 of n bm slow cbn b  2 v.fast b nc med. obtain of n M 2

Functional Dependencies Logarithm Linear Raising-to-a-Power Exponentiation

Biochemical Reactions computationinputsoutputs Molecular Triggers Molecular Products Synthesizing Biological Computation

How can we control the quantity of molecular product at the populational level? Biological Computation at the Populational Level

product trigger Engineer a probabilistic response in each cell. with Prob. 0.3 product with Prob. 0.7 Synthesizing Stochasticity

Obtain a fractional response. Biological Computation at the Populational Level

The probability that a given reaction is the next to fire is proportional to: Its rate. The quantities of its reactants. See D. Gillespie, “Stochastic Chemical Kinetics”, Stochastic Kinetics k1k1 k2k2 k3k3

Jargon vs.Terminology “Now this end is called the thagomizer, after the late Thag Simmons.”

Design a system that produces a probability distribution on the production of output types as a function of input quantities. Synthesizing Stochasticity Biochemical Reactions givenobtain Quantities of Different Types Probability Distribution on Different Types independent for us to design specified

Design a system that produces a probability distribution on the production of output types as a function of input quantities. Synthesizing Stochasticity cell A with Prob. 0.3 B with Prob. 0.2 C with Prob. 0.5

Synthesizing Stochasticity cell Generalization: engineer a probability distribution on logical combinations of different outcomes. A and B with Prob. 0.3 B and C with Prob. 0.7 Further: program probability distribution with (relative) quantity of input compounds. X Y Design a system that produces a probability distribution on the production of output types as a function of input quantities.

Generalization: engineer a probability distribution with a functional dependence on input quantities. Synthesizing Stochasticity Stochastic Module x y m n e

Synthesizing Stochasticity Structure computation to obtain initial choice probabilistically. Then amplify this choice and inhibit other choices. Method is: Precise. Robust. Programmable. Strategy: With “locking”, produces designs that are independent of rates.

Timing slow medium fast Synthesis schemes dependent on relative reaction rates.

Composition Rate separation increases with composition/modularity Module 2... Module 1 slow 1 fast 1 slow 2 fast 2 fast 1 slow 2 < ?

Timing then Mario Luigi Biochemical rules are inherently parallel. Sequentialize? Step 1: Step 2:

Module Locking slow fast Sequentialize computation with only two rates: “ fast ” and “ slow ”.

Module Locking Sequentialize computation with only two rates: “ fast ” and “ slow ”.

A Comparison of the Accuracy of the Locked and Unlocked Versions of Three Modules: Multiplication, Exponentiation, and Logarithm. Unlocked Locked “Accuracy”:

Locking the Linear Stochastic Module

CAD Tool Library of biochemical models. Designated input and output types. Specific quantities (or ranges) of input types. Target functional dependencies. Target probability distribution. Brian’s Automated Modular Biochemical Instantiator (BAMBI) Given: Outputs: Reactions/parameters implementing specification. Detailed measures of accuracy and robustness. Targets can be nearly any analytic function or data set.

Computational Infrastructure Implementing a “front-end” database of biochemical models in Structured Query Language (SQL) from online repositories: BioBricks, SBML.org, … Implementing “back-end” number crunching algorithms for analysis and synthesis on a high performance computing platform. IBM System Z MainframeIBM’s Blue Gene/L

Discussion Synthesize a design for a precise, robust, programmable probability distribution on outcomes – for arbitrary types and reactions. Computational Synthetic Biology vis-a-vis Technology-Independent Logic Synthesis Implement design by selecting specific types and reactions – say from “toolkit”. Experimental Design vis-a-vis Technology Mapping in Circuit Design

circuit computationinputsoutputs Probability Distributions on Boolean output streams Stochastic Logic Probability Distributions on Boolean input streams DAC 08, “The Synthesis of Robust Polynomial Arithmetic with Stochastic Logic”

circuit inputsoutputs 0,1,1,0,1,0,1,1,0,1,… 1,0,0,0,1,0,0,0,0,0,… p 1 = Prob(one) p 2 = Prob(one) Stochastic Logic Consider a probabilistic interpretation:

circuit inputsoutputs Consider a probabilistic interpretation: Stochastic Logic

circuit p 1 = Prob(one) p 2 = Prob(one) parallel bit streams Consider a probabilistic interpretation: Stochastic Logic inputsoutputs

circuit parallel bit streams Consider a probabilistic interpretation: Stochastic Logic p 1 = Prob(one) p 2 = Prob(one)

A real value x in [ 0, 1 ] is encoded as a stream of bits X. For each bit, the probability that it is one is: P( X=1 ) = x. Probabilistic Bundles x X

Communicating Ideas