Simulating ribosome biogenesis in replicating whole cells

Simulating ribosome biogenesis in replicating whole cells Tyler Earnest / PI: Zan Luthey-Schulten (UIUC) NCSA Blue Waters Symposium for Petascale Science and Beyond: June 15, 2016

Multi-scale modeling in biology Timestep: femtoseconds picoseconds microseconds Molecules to macromolecular assemblies Whole cells and colonies

Multi-scale modeling in biology

Whole-cell modeling with Lattice Microbes

Whole-cell modeling with Lattice Microbes Discretize to lattice

Whole-cell modeling with Lattice Microbes Discretize to lattice Probability of the state of the cell: Reaction-diffusion master equation dp (x,t) dt = VX v RX r a r (x v )P (x v,t) + a r (x v S r )P (x v S r,t) + VX ±î,ĵ,ˆk X NX d x v P (x,t) v + d (x v+ + 1)P (x + 1 v+ 1 v,t)

Whole-cell modeling with Lattice Microbes Discretize to lattice 0 Probability of the state of the cell: dp (x,t) dt x(t) = B @ x 1,1,1 (t) Reaction-diffusion master equation x nx,n y,n z (t) 1 x 1,1,2 (t). x (t) 1,1,nz VX... RX = a r (x v )P (x v,t)... v r x + a r (x v S r )P (x v S r,t) 1,ny,n (t) z... VX ±î,ĵ,ˆk X NX +... d x v P (x,t) v... + d C (x A v+ + 1)P (x + 1 v+ 1 v,t)

Whole-cell modeling with Lattice Microbes Discretize to lattice 0 Probability of the state of the cell: dp (x,t) dt x(t) = B @ x 1,1,1 (t) x 1,1,2 (t). 0 1 x (t) x 1,1,nz 1 (t) VX... RX x 2 (t) = a r (x x i,j,k v )P(t) (x = v,t) B... C... @ A v r x (t) x + a r (x v S r )P (x v S r,t) 1,ny,n (t) nsp z... VX ±î,ĵ,ˆk X NX +... d x v P (x,t) v... + d C (x A v+ + 1)P (x + 1 v+ 1 v,t) Reaction-diffusion master equation x nx,n y,n z (t) 1

Whole-cell modeling with Lattice Microbes Designed for CUDA Roberts et al. J. Comput. Chem. 2013

Whole-cell modeling with Lattice Microbes Designed for CUDA Multiple levels of parallelism GPGPU Roberts et al. IPDPS 2009 Multi-GPU Hallock et al. Parallel Comput. 2014 MPI (w.i.p.) Roberts et al. J. Comput. Chem. 2013

Ribosome biogenesis in Escherichia coli Protein synthesis Large subunit (LSU) Small subunit (SSU)

Ribosome biogenesis in Escherichia coli Protein synthesis Large subunit (LSU) 1/4 of the cellular dry mass Small subunit (SSU)

Ribosome biogenesis in Escherichia coli Protein synthesis Large subunit (LSU) 1/4 of the cellular dry mass Requires understanding and modeling of Gene regulation Transcription Translation Small subunit (SSU)

Complexity of SSU assembly 16S rrna + 20 r-protein 30S small subunit

Complexity of SSU assembly 16S rrna + 20 r-protein 30S small subunit 2 20 (10 6 ) intermediate species; 20! (10 18 ) reactions; 20! (10 18 ) parameters

Kinetic model of small subunit assembly 5ʹ Central 3ʹ us17 us4 bs20 us8 us15 us7 Primary bs16 bs6:bs18 us9 us13 us19 Secondary Reactions us11 us10 us14 us12 us5 bs21 Tertiary us3 us2 Rates

Kinetic model of small subunit assembly 5ʹ Central 3ʹ us17 us4 bs20 us8 us15 us7 Primary Reactions bs16 bs6:bs18 us9 us13 us19 Secondary us11 us10 us14 us5 bs21 us12 Held,, Nomura. JBC (1974) Rates us3 us2 Tertiary

Kinetic model of small subunit assembly 5ʹ Central 3ʹ us17 us4 bs20 us8 us15 us7 Primary bs16 bs6:bs18 us9 us13 us19 Secondary Reactions us11 us10 us14 us12 us5 bs21 Tertiary us3 us2 Rates Mulder,, Williamson Science (2010)

Kinetic model of small subunit assembly 5ʹ Central 3ʹ us17 us4 bs20 us8 us15 us7 Primary bs16 bs6:bs18 us9 us13 us19 Secondary Reactions us11 us10 us14 us12 us5 bs21 Tertiary us3 us2 Rates

Reactions involved in ribosome biogenesis Assembly Transcription: rrna Transcription: mrna Reaction Sx + Ii Ii+1 DNA DNA + rrna DNA DNA + mrna Data source Kinetic model (Earnest 2015), Pulse/ chase (Mulder 2010) Chosen to achieve 6000 ribosomes prior to cell division (Roberts 2011) Chosen to ensure even abundance, and < 50% excess Degradation mrna Microarray (Selinger 2003) Translation 30S + mrna + 50S 30S + mrna + 50S + n Protein 10 a.a/sec; transcript length from genome Diffusion Xi(x) Xi(x+δj) Single particle diffusion (Sanamrad 2014), Estimations (Kalwarczyk 2012)

Cell division and DNA replication

Measure cell cycle parameters Escherichia coli K-12 MG1655 lac - 120 minute doubling time Earnest,, Kuhlman, ZLS Biopolymers (2016) Accepted

Measure cell cycle parameters Escherichia coli K-12 MG1655 lac - 120 minute doubling time Construct 14 strains fluorescently labeling a different locus in the genome Earnest,, Kuhlman, ZLS Biopolymers (2016) Accepted

Measure cell cycle parameters Escherichia coli K-12 MG1655 lac - 120 minute doubling time Construct 14 strains fluorescently labeling a different locus in the genome Measure cell lengths and count fluorescent foci Earnest,, Kuhlman, ZLS Biopolymers (2016) Accepted

Measure cell cycle parameters (7000 cells) Escherichia coli K-12 MG1655 lac - 120 minute doubling time Construct 14 strains fluorescently labeling a different locus in the genome Measure cell lengths and count fluorescent foci P (`,n gene; ) = 8 < P (`,n gene; ) = : 8 < µ, length at d µ, length at division µ, time to begin replication : duration of replication 9 = µ, time to be ; duration of rep Fit to probabilistic model to get cell cycle parameters and mean cell size at division Earnest,, Kuhlman, ZLS Biopolymers (2016) Accepted

Measure cell cycle parameters (7000 cells) Escherichia coli K-12 MG1655 lac - 120 minute doubling time Parameter Description Value Construct 14 strains fluorescently labeling a different locus in the genome 8 σlen0 SD length at division 0.744 ± 0.024 µm < µ, length at division P (`,n gene; ) = P = µ, time to begin replication µtrep Mean replication initation time 42.2 : : ± 3.0 min duration of replication Measure cell lengths and count fluorescent foci σtrep SD replication initation time 22.1 ± 1.9 min Fit to probabilistic Trep model Replication to get cell duration 42.2 ± 5.0 min cycle parameters and mean cell size at division µlen0 Mean length at division 4.772 ± 0.021 µm 8 < µ, length at d 9 = µ, time to be ; duration of rep Earnest,, Kuhlman, ZLS Biopolymers (2016) Accepted

Cell geometry Earnest,, Kuhlman, ZLS Biopolymers (2016) Accepted 8 Expt. cell widths P(w)/µm 1 6 4 2 0 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 w/µm

Cell geometry Earnest,, Kuhlman, ZLS Biopolymers (2016) Accepted 8 Expt. cell widths P(w)/µm 1 6 4 2 0 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 w/µm Roberts,, Baumeister, ZLS. PLoS Comput. Biol. (2011)

Cell geometry Earnest,, Kuhlman, ZLS Biopolymers (2016) Accepted

Results 1.5 Volume/fl 1.0 0.5 0.0 0.5 1.0 1.5 2.0 t/hr Earnest,, Kuhlman, ZLS Biopolymers (2016) Accepted

Results 7 10 3 Ribosome abundance 7 6 14 6 14 Copy number 5 4 3 2 12 10 8 rrna operons Concentration/10 6 M 5 4 3 2 12 10 8 rrna operons 1 1 0.5 1.0 1.5 2.0 t/hr Earnest,, Kuhlman, ZLS Biopolymers (2016) Accepted 0.5 1.0 1.5 2.0 t/hr

Results 9 10 4 Total protein abundance 90 8 18 80 18 Copy number 7 6 5 4 3 16 14 12 10 r-protein operons Concentration/10 6 M 70 60 50 40 30 16 14 12 10 r-protein operons 2 0.5 1.0 1.5 2.0 t/hr Earnest,, Kuhlman, ZLS Biopolymers (2016) Accepted 20 0.5 1.0 1.5 2.0 t/hr

Results z/µm 2 1 0 1 2 z 10 5 2.25 All r-protein 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 x 0.00 3 9 15 21 27 33 40 46 52 58 64 70 77 83 89 95 101 107 114 120 10 3 Copy number over y t/min Earnest,, Kuhlman, ZLS Biopolymers (2016) Accepted

Results 0.00 10 3 z/µm 2 1 0 1 2 Translating ribosomes z x 3 9 15 21 27 33 40 46 52 58 64 70 77 83 89 95 101 107 114 120 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 Copy number over y t/min Earnest,, Kuhlman, ZLS Biopolymers (2016) Accepted

Results 12.0 z/µm 2 1 0 1 2 z All 30S intermediates 1.5 x 0.0 3 9 15 21 27 33 40 46 52 58 64 70 77 83 89 95 101 107 114 120 10.5 9.0 7.5 6.0 4.5 3.0 Copy number over y t/min Earnest,, Kuhlman, ZLS Biopolymers (2016) Accepted

Benchmarks: Lattice Microbes v2.3a Reaction/diffusion/growth New reaction kernel: Hallock & ZLS. HiCOMB 2016

Outlook E. coli whole-cell model Regulation of ribosomal gene expression Explicit treatment of DNA Metabolism

Outlook E. coli whole-cell model Regulation of ribosomal gene expression Explicit treatment of DNA Metabolism Lattice Microbes Multi-scale modeling: high concentration and/or fast diffusion rates MPI: Eukaryotic cells, bacterial colonies, tissues (BW necessary!) IPython/Jupyter notebook environment

Acknowledgements Zan Tom Kuhlman Mike Hallock Joe Peterson John Cole Luthey-Schulten Lattice Microbes: http://goo.gl/akksyg