Model and analysis of cell population density estimation via Quorum Sensing Nicolò Michelusi Purdue University https://engineering.purdue.edu/~michelus/ michelus@purdue.edu Nafplio, Communications Theory Workshop May 18, 2016 1
Molecular bio-nano communication networks 2 q Advances in bio-nano technology and biology Ø bio-inspired nano-devices, biological nanosensors, prosthetic devices q Biomedical, industrial, environmental applications q Comm. networks & protocols at nanometer length scales Molecular nanonetwork with 2 nodes Ø Actuation, coordination, Source : http://www.ece.gatech.edu/research/labs/bwn/monaco/ chemotaxis, etc.
Molecular bio-nano communication networks 3 Diffusion Transmitter Receiver q Electromagnetic comm. Channel unfeasible q Communication via molecular diffusion q Most recent literature: [Nakano&al.’13],[Akyildiz&al.’08], [Mian&Rose,’11],[Eckford,’07], [Einolghozati&al.’13],[Kadloor&al.’12], [Arjmandi&al.’13]… q Capacity achieving schemes? Molecular nanonetwork with 2 nodes Source : http://www.ece.gatech.edu/research/labs/bwn/monaco/ Ø Any simpler scheme?
What is Quorum Sensing? 4 q Quorum sensing in bacteria: Ø Gene expression = f( cell density ) Ø How does it work? AutoInducers (AI) produced 1. AI concentration = f( cell density ) 2. AI reception activates gene 3. expression Ø Regulates biofilm formation, virulence, diseases, antibiotic resistance, etc.
What is Quorum Sensing? 5 q Light emission very demanding , should be done only when population size is large enough q Symbiotic relationship Ø The squid provides nutrients to V.Fischeri to grow Ø V.Fischeri provides light to hide from predators Ø Every morning, the squid gets Hawaiian bobtail squid rid of 95% of bacteria, & the process repeats
Motivation 6 q Quorum Sensing enables coordination among large populations of cells q Coordinate mechanism in future nanonetworks q Goals: Ø Develop a model of Quorum Sensing Ø Necessary conditions for QS to function Ø Analysis of QS dynamics & cell population density estimation
Towards a model of QS 7 q “ Ingredients ” of QS Microbial community ( e.g. , Vibrio Fischeri ) 1. Autoinducers ( AI ) 2. v Produced by each cell and released in the extracellular environment Transmission Receptors ( R ) 3. v They bind to AIs within each cell to form complexes Complexes ( C ) 4. Reception v 1 AI bound to 1 R Synthases ( S ) 5. v “machines” that produce AI s DNA binding sites 6. Actuation v C activates DNA transcription (produce more S,R ) v Costly gene expression
Towards a model of QS 8 q “ Ingredients ” of QS Microbial community ( e.g. , Vibrio Fischeri ) 1. Autoinducers ( AI ) 2. v Produced by each cell and released in the extracellular environment Receptors ( R ) 3. v They bind to AIs within each cell to form complexes Complexes ( C ) 4. Reception v 1 AI bound to 1 R Synthases ( S ) 5. v “machines” that produce AI s DNA binding sites 6. Actuation v C activates DNA transcription (produce more S,R ) v Costly gene expression
Towards a model of QS 9 q “ Ingredients ” of QS Microbial community ( e.g. , Vibrio Fischeri ) 1. Autoinducers ( AI ) 2. v Produced by each cell and released in the extracellular environment Receptors ( R ) 3. v They bind to AIs within each cell to form complexes Complexes ( C ) 4. v 1 AI bound to 1 R Synthases ( S ) 5. v “machines” that produce AI s DNA binding sites 6. Actuation v C activates DNA transcription (produce more S,R ) v Costly gene expression
Towards a model of QS 10 q “ Ingredients ” of QS Microbial community ( e.g. , Vibrio Fischeri ) 1. Autoinducers ( AI ) 2. v Produced by each cell and released in the extracellular environment Receptors ( R ) 3. v They bind to AIs within each cell to form complexes Complexes ( C ) 4. v 1 AI bound to 1 R Synthases ( S ) 5. v “machines” that produce AI s DNA binding sites 6. v C activates DNA transcription (produce more S,R ) v Costly gene expression
Model of each cell 11 R i (t) receptors S i (t) synthases ✏ C, 1 ✏ C, 2 ✏ C, 3 Sites 1 2 3 q Synthases & Receptors produced at low basal rate
Model of each cell 12 A i (t) AIs (inside) R i (t) receptors S i (t) synthases β Sites 1 2 3 q Synthases produce AIs inside cell
Model of each cell 13 A ext (t) Ais (outside) A i (t) AIs (inside) R i (t) receptors S i (t) synthases C i (t) complexes β Sites 1 2 3 q Transmission : AI diffusion across cell membrane (in/out)
Model of each cell 14 A ext (t) Ais (outside) A i (t) AIs (inside) R i (t) receptors γ S i (t) synthases C i (t) complexes β Sites 1 2 3 q Reception : Complex formation
Model of each cell 15 A ext (t) Ais (outside) A i (t) AIs (inside) R i (t) receptors γ S i (t) synthases C i (t) complexes Gene expression β ✏ C, 1 ✏ C, 2 ✏ C, 3 Sites 1 2 3 q Actuation : DNA binding à gene expression
Queuing model of QS 16 C 1 ( t ) ✏ 1 C 1 ( t ) ✏ 2 q Each cell modeled by R 1 (t) S 1 (t) A 1 (t) R 2 (t) S 2 (t) A 2 (t) queues C 1 (t) C 2 (t) COMPLEXES RECEPTOR SYNTHASE q Cell population N(t) AI QUEUE QUEUE QUEUE QUEUE S 1 ( t ) β Ø Increases with cell A ext (t) growth R 1 ( t ) A ( t ) γ S 4 (t) R 4 (t) A 4 (t) q Huge complexity! AUTOINDUCER QUEUE C 4 (t) S 3 (t) R 3 (t) A 3 (t) q Cells coupled via AI C 3 (t) queue A ( t ) δ ( N ( t )) AI leakage
Simulations 17 100 q Simulation tools based on Open system, time series 90 Open system, QS activation time queuing model Autoinducers concentration [nM] 80 Closed system, time series [Michelusi&al.2015] Closed system, QS activation time 70 60 Experimental 50 activation OPEN SYSTEM: cells grow in 40 time open space & closely packed 30 (no boundaries à leakage of AI) 20 CLOSED SYSTEM: cells grow in 10 finite box & sparse 0 (boundaries à no leakage) 0 2 4 6 8 10 TIME [hours]
Simulations 18 q Higher density in open system Ø > AI concentration 11 10 Cell density [cells per mL] Ø Faster activation time 10 10 OPEN SYSTEM: cells grow in 9 10 open space & closely packed (no boundaries à leakage of AI) Open system, time series 8 10 Open system, QS activation time CLOSED SYSTEM: cells grow in Closed system, time series finite box & sparse Closed system, QS activation time (boundaries à no leakage) 7 10 0 2 4 6 8 10 TIME [hours]
Simplified model 19 More comprehensive model Simplified model + + DNA AIs generate more AIs
Simplified model 20 q Internal AIs for each cell (local state) & external AIs Ø A i (t): local AI Ø AI diffusion in-out proportional to AI A 1 (t) A 2 (t) concentration, λα α i ( t ) = A i ( t ) Local: λα 1 ( t ) λα 2 ( t ) λα ext ( t ) V c A ext (t) λα ext ( t ) A ext ( t ) Ext: α ext ( t ) = V − NV c A 4 (t) EXTERNAL AUTOINDUCER Ø AI synthesis QUEUE λα 4 ( t ) proportional to local A 3 (t) λα ext ( t ) λα ext ( t ) AI availability λα 3 ( t ) ρ S, 0 + ρ S A i ( t )
Simplified model 21 q Local AI A i (t): Ø Diffusion out-in: Augments w.r. λα ext ( t ) Ø Diffusion in-out: Diminishes w.r. λα i ( t ) A 1 (t) Ø Synthesis: Augments w.r. ρ S, 0 + ρ S A i ( t ) Ø AI & complex deg.: Diminishes w.r. µ D A i ( t ) q External AI A ext (t): Ø Diffusion out-in: Diminishes w.r. N λα ext ( t ) N Ø Diffusion in-out: Augments w.r. α i ( t ) λ X i =1 Ø AI degradation: Diminishes w.r. µ D,ext A ext ( t ) q Cells coupled through external AI q Local AI captures local state and cell fluctuations
Analysis of expected AI evolution 22 q State is ( α ext ( t ) , α 1 ( t ) , α 2 ( t ) , . . . , α N ( t )) q We want to compute & α cell ( t ) = E [ α i ( t )] ¯ α ext ( t ) = E [ α ext ( t )] ¯ (note: is the same for all cells) α cell ( t ) ¯ characterizes cell sensitivity to population density α cell ( t ) ¯ q q Asymptotic analysis with fixed β = N/V V → ∞ ¯ ¯ � � � d 0 α ext ( t ) α ext ( t ) = W + ρ S, 0 α i ( t ) ¯ α i ( t ) ¯ d t V c det( W − s I ) = 0 s (+) , s ( − ) q Study eigenvalues of W : 0s of ,
Analysis of expected AI evolution 23 q Average response: 8 X (+) � s (+) t α ext ( t ) ¯ ext exp + C ext ' > < X (+) s (+) t � > α cell ( t ) ¯ cell exp + C cell : ' q Response driven by largest eigenvalue, s (+) ( ρ ) s (+) ( ρ ) > 0 : exponentialincrease , positive feedback loop Ø s (+) ( ρ ) = 0 : linear increase, positive feedback loop Ø s (+) ( ρ ) < 0 : exponential decay , steady state regime Ø
Desirable properties of QS 24 q In the limit , response should decay , s (+) (0) < 0 β → 0 ρ S < λ + µ D V c AI synthesis rate AI diffusion AI degradation Ø Why? Positive feedback loop only for β ≥ β th Ø Intuition : if synthesis > diffusion + degradation, local AI grows unbounded, not informative!
Desirable properties of QS 25 d s (+) ( β ) q Response should be stronger for larger , > 0 β d β µ D − µ D,ext < ρ S < λ + µ D V c AI internal AI external AI synthesis rate degradation degradation Ø Why? QS activity should increase for larger population size Ø Intuition : if internal degradation too intense, diffusion to the external environment is negligible
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