Quantum Self-assembly in Artificial Minimal Living Cells
dotVilnius University (Institute of theoretical Physics and Astronomy)

quantumAbstract: The natural and artificial living cells and their substructures are self-assembling due to electron correlation interactions among biological and water molecules which leads to appearing the attraction dispersion forces and hydrogen bonds. Dispersion forces  are weak intermolecular forces that arise from the attractive force between quantum multipoles. A hydrogen bond is a special type of quantum attractive interaction that exists between an electronegative atom and a hydrogen atom bonded to another electronegative atom and this hydrogen atom exists in two quantum states. The best method to simulate these dispersion forces and hydrogen bonds is to perform quantum mechanical non-local density functional potential calculations of artificial minimal living cells consisiting of around 1000 atoms. The cell systems studied are based on peptide nucleic acid and are 3.0 - 4.2 nm in diameter. The electron tunneling and associated light absorption of most intense transitions as calculated by the time dependent density functional theory method differs from spectrosopic experiments by only 0.2 - 0.3 nm, which are within the value of experimental errors. This agreement implies that the quantum mechanically self-assembled structure of artificial minimal living cells very closely approximate the realistic one.

Working paper (pdf)           Programming source code


Quantum mechanical self-assembly of squarine based micelle (last 48 points of total energy minimization procedure)

Related links:
Molecular quantum computing cloud

Related references:
- A. Tamulis, V. Tamulis, A. Graja, "Quantum mechanical modeling of self-assembly and photo-induced electron transfer in PNA based artificial living organisms", Journal of Nanoscience and Nanotechnology, Vol. 6, 965-973 (2006)
 - J. Tamuliene and A. Tamulis, "Quantum mechanical investigations of self-assembled system consisting of peptide nucleic acid, sensitizer, and lipid precursor molecules", Lithuanian Journal of Physics, Vol. 45(3), 167-174 (2005)
 - J. Tamuliene and M. L. Balevicius, "Search for sensitizer to peptide nucleic acid sequence with adenine and guanine bases", Viva Origino, vol. 34, 112-115 (2006)
 - A Tamuls and V. Tamulis, H. Ziock, S. Rasmussen, "Influence of water and fatty acid molecules on quantum photoinduced electron tunnelling in photosynthetic systems of PNA based self-assembled protocells, in book: "Multiscale simulation methods for materials", eds. R. Ross and S. Mohanty, John Wiley & Sons, Inc., New Jersei, 2007, in press

Self-replicating nanocells
dotComplex Systems Lab (UPF)

Abstract: Coarse-grained simulations of spatially organized chemical reactions can be used to gain detailed insight into growth and replicationsmall processes of protocells on a single cell level. Here, we extend the coarse-grained particle-based method of dissipative particle dynamics (DPD) by a stochastic process that allows for simulating chemical reactions.
We use a simplified representation of amphiphilic molecules as hydrophilic head particles connected to hydrophobic chain particles by an elastic bond. The model allows us to study the self-assembly of micellar structures and surfactant coated oil droplets which can serve as containers for protocells. In this information-free scenario, the surfactant is thought to catalyze the transformation of energy rich precursor molecules into additional surfactants. This minimal metabolism enables the protocells to grow in aggregate size. Using the spatially resolved simulation method, it can be observed how the growing aggregate undergoes a shape change to compensate the changing precursor to surfactant ratio, when passing a threshold, the elongated aggregate becomes unstable and finally divides into two daughter cells. The spatial resolution of the model allows to observe the replication process which follows an exponential growth law over several generations.

Working paper (pdf)

Related links:
UPF website

Related references:
- Pascale Angelica Bachmann, Pier Luigi Luisi, and Jacques Lang.  Autocatalytic self-replicating micelles as models for prebiotic structures. Nature, 357:57–59, 1992.
- P. V. Coveney, A. N. Emerton, and B. M. Boghosian. Simulation of self-reproducing micelles using a lattice-gas automaton. J. Amer. Chem. Soc., 118:10719–10724, 1996.
- Harold Fellermann and Ricard V. Solé. Self-replicating nanocells: an information-free, physically embodied scenario. Phil. Soc. Roy. Trans. B, 2007, DOI: 10.1098/rstb.2007.2072, in press

Life-cycle of the Los Alamos Bug
dotLos Alamos National Laboratory (LANL) and Complex Systems Lab (UPF)
Harold Fellermann, Steen Rasmussen, Hans-Joachim Ziock, Ricard V. Solé
Abstract:  This project extends the simulations of the self-replicating nanocells toward a system that posesses not only container and metabolism, but also inheritable genetic information (the so-called "Los Alamos Bug"). To orchestrate the collective growth and replication of these three components, container, metabolism, and genome are functionally coupled. This work focusses on (i) the self-replication of the genetic biopolymer, (ii) the emergence of a molecular fitness function from first principles, (iii) the functional coupling of container, metabolism and genome, and (iv) crutial steps in the life cycle of the Los Alamos Bug. It provides thefoundations for the first integrated spatially resolved computer simulationof a whole protocellular life-cycle.

Working paper (pdf)                   Programming source code

Related links:
New Scientist article
Protolife manuscript

Related references:
- S. Rasmussen, L. Chen, M. Nilsson, and S. Abe. Bridging nonliving and living matter. Artificial Life, 9:269–316, 2003.
- T. Rocheleau, S. Rasmussen, P. E. Nielson, M. N. Jacobi, and H. Ziock. Emergence of protocellular growth laws. Phil. Trans. R. Soc. B, 2006. in press.

Molecular Dynamics (MD) studies of lipid-water systems and their interaction with short information molecules
dotLos Alamos National Laboratory (LANL)

lipAbstract: We have used molecular dynamics simulations to study the self-assembly and stability of fatty acid and phosphor lipid assemblies (membranes and micelles) and their interactions with small peptide nucleic acid (PNA) molecules. Classical MD computer simulation is a powerful and suitable method for modeling the phenomena at the molecular level provided that quantum effects can be neglected and sufficient computational resources are available. This approach allows calculation the molecular system time evolution by considering forces (electrostatic, dispersion, and chemical bonds) acting on individual atoms and numerically solving Newton’s equations of motion over short time steps, based on the system’s potential function [Flores and Moss, 1990]. Most of the parameters for our systems have already been obtained from ab initio quantum chemistry computations or vibrational spectroscopy and are available in the standard MD packages such as CHARMM [Brooks et al., 1983]. Those that are not directly available can be approximated using the existing parameters for similar chemical structures. This is the case for the peptide nucleic acid (PNA) that we have used in our simulations as the information molecule [Weronski et al., 2007]. This lab-created analogue of DNA, in which the nucleic bases (adenine, guanine, thymine and cytosine) are attached to a pseudo-peptide backbone, is much less hydrophilic than the natural DNA nucleic acids and therefore is expected either in direct form or with modified backbones to be able to adsorb at the surfactant-water interface, which is a necessary condition for an appropriately coupled gene and container replication process for the Los Alamos Bug [Rasmussen et al., 2004]

At neutral pH, without any salt, and in a constant pressure and temperature ensemble, two similar PNA molecules (6-mers) with the same nucleic base sequence and different terminal groups are investigated at the interface between water and a 1-palmitoyl-2-leoylphosphatidylcholine lipid bilayer [Weronski et al., 2007]. The results of our simulations suggest that at low ionic strength of the solution, both PNA molecules adsorb at the lipid-water interface. In the case where the PNA molecule has charged terminal groups, the main driving force of adsorption is the electrostatic attraction between the charged groups of PNA and the lipid heads. The main driving force of adsorption of the PNA molecule with neutral terminal groups is the hydrophobic interaction of the nonpolar groups. Our simulations suggest that the system free energy change associated with PNA adsorption at the lipid-water interface is on the order of several tens of kT per PNA molecule in both cases. See movie 1.

In order to design the minimal self-replicating nanomachine we need to understand not only the process of surfactant self-assembling but also to know under which conditions the assembly can split into two smaller micelles [Weronski et al., 2008]. MD provides a direct insight into the micellar system at the atomic level and therefore allows better understanding of the physics of this system. In our simulations, we studied a system composed of a number of the protonated decanoic acid molecules as well as the decanoate anions and sodium cations in water at the constant pressure. We adjusted the ratio of the protonated and deprotonated surfactant molecules to indirectly simulate the system at different pH values. We also used sodium cations and chlorium anions to verify the effect of solution ionic strength on micelle aggregation. See movie 2.

Related links:


Related references:

- Brooks, B.R.; Bruccoleri, R.E.; Olafson, B.D.; States, D.J.; Swaminathan, S.; Karpus, M. CHARMM: a Program for Macromolecular Energy, Minimization, and Dynamics Calculations. J Comput Chem 1983, 4, 187.
- Flores, T.P.; Moss, D.S. Simulating the Dynamics of Macromolecules. In: Molecular Dynamics. Applications in Molecular Biology; Goodfellow, J.M., Ed.; CRC Press Inc.: Boca Raton, FL, 1990.

- Rasmussen, S.; Chen, L.; Deamer, D.; Krakauer, D.C.; Packard, N.H.; Stadler, P.F.; Bedau, M.A. Transitions from Nonliving to Living Matter. Science 2004, 303, 963.
Weronski P., Jiang Y., and Rasmussen S., Molecular Dynamics Study of Small PNA Molecules in Lipid-Water System, Biophysical Journal, Volume 92 May 2007, 3081–3091
- Weronski P., Jiang Y., and Rasmussen, S. "Application of Molecular dynamics computer simulations in the design of a minimal self-replicating molecular machine", Complexity, vol. 13, pp. 10-17, 2008
- Weronski P.
, Jiang Y., and Rasmussen S., Molecular Dynamics Study of Small PNA Molecules in Lipid-Water System, Biophysical Journal, Volume 92 May 2007, 3081–3091
Weronski P., Jiang Y., and Rasmussen, S. "Application of Molecular dynamics computer simulations in the design of a minimal self-replicating molecular
machine", Complexity, vol. 13, pp. 10-17, 2008

see Movie 1

Related links:
ALGOR website
The guide to computing literature

Related references:
- Schroer, J.P., and K. Lindgren (2006). Simulation of higher-order self-assembly. Proceedings of ECCS06.
- Lindgren, K., J. Nyström, J.P. Schroer (2007). Prototype simulation package for physically self-assembling units. PACE report for Deliverable D13.
- Witten, T., & L. Sander (1981). Diffusion-limited aggregation, a kinetic critical ph

Reaction Linetics (RK) coupling of gene and container replication: Emergence of protocellular growth laws
dotLos Alamos National Laboratory (LANL)


Template-directed replication is known to obey a parabolic growth law due to product inhibition (Sievers & Von Kiedrowski, 1994 Nature 369, 221; Lee et al., 1996 Nature 382, 525; Varga & Szathmary, 1997, Bull. Math. Biol. 59, 1145). We investigate a template-directed replication with a coupled template catalyzed lipid aggregate production as a model of a minimal protocell and show analytically that the autocatalytic template–container feedback ensures balanced exponential replication kinetics; both the genes and the container grow exponentially with the same exponent. The parabolic gene replication does not limit the protocellular growth, and a detailed stoichiometric control of the individual protocell components is not necessary to ensure a balanced gene–container growth as conjectured by various authors (Ganti, 2004, Chemoton theory). Our analysis also suggests that the exponential growth of most modern biological systems emerges from the inherent spatial quality of the container replication process as we show analytically how the internal gene and metabolic kinetics determine the cell population’s generation time and not the growth law (Burdett & Kirkwood, 1983, J. Theor. Biol. 103, 11–20; Novak et al., 1998, Biophys. Chem. 72, 185–200; Tyson et al., 2003, Curr. Opin. Cell Biol. 15, 221–231). Previous extensive replication reaction kinetic studies have mainly focused on template replication and have not included a coupling to metabolic container dynamics (Stadler et al., 2000,Bull. Math. Biol. 62, 1061–1086; Stadler & Stadler, 2003, Adv. Comp. Syst. 6, 47). The reported results extend these investigations. Finally, the coordinated exponential gene–container growth law stemming from catalysis is an encouraging circumstance for the many experimental groups currently engaged in assembling self-replicating minimal artificial cells (Szostak et al., 2001, Nature 409, 387–390; Pohorille & Deamer, 2002, Trends Biotech. 20 123–128; Rasmussen et al., 2004, Science 303, 963–965; Szathmary, 2005, Nature 433, 469–470; Luisi et al., 2006, Naturwissenschaften 93, 1–13).

The main results from this work from this work are summarized here: The template catalyses the lipid production while the lipid aggregate makes possible (catalyses) the template replication. Because the local template concentration is kept approximately constant due to the aggregate growth the template replicates exponentially. The generation (doubling) time is given by , where all parameters in principle are experimentally observable quantities (for details see Roucheleau et al., 2007).

Working paper (pdf)

Related links:

Springer Verlag JMB

Related references:

- Brooks, B.R.; Bruccoleri, R.E.; Olafson, B.D.; States, D.J.; Swaminathan, S.; Karpus, M. CHARMM: a Program for Macromolecular Energy, Minimization, and Dynamics Calculations. J Comput Chem 1983, 4, 187.
- Flores, T.P.; Moss, D.S. Simulating the Dynamics of Macromolecules. In: Molecular Dynamics. Applications in Molecular Biology; Goodfellow, J.M., Ed.; CRC Press Inc.: Boca Raton, FL, 1990.

- Rasmussen, S.; Chen, L.; Deamer, D.; Krakauer, D.C.; Packard, N.H.; Stadler, P.F.; Bedau, M.A. Transitions from Nonliving to Living Matter. Science 2004, 303, 963.

Metabolic photo-fragmentation reaction kinetics (RK) for a minimal protocell
dotLos Alamos National Laboratory (LANL)

Metabolic photo-fragmentation reaction kinetics (RK) for a minimal protocell: Rate limiting factors, efficiency, and implications for evolution


A key requirement of an autonomous self-replicating molecular machine, a protocell, is the ability to digest resources and turn them into building blocks. Thus a protocell needs a set of metabolic processes fueled by external free energy in the form of available chemical redox potential or light. We introduce and investigate a minimal photo-driven metabolic system, which is based on photofragmentation of resource molecules catalyzed by genetic molecules. We represent and analyze the full metabolic set of reaction kinetic equations and, through a set of approximations, simplify the reaction kinetics such that analytical expressions can be obtained for the building block production. The analytical approximations are compared to the full equation set and to corresponding experimental results to the extent they are available. It should be noted, however, that the proposed metabolic system has not been experimentally implemented, so this investigation is conducted to obtain a deeper understanding of its dynamics and perhaps to anticipate its limitations. We demonstrate that this type of minimal photo-driven metabolic scheme is typically rate limited by the front-end photoexcitation process while its yield is determined by the genetic catalysis. We further predict how gene catalyzed metabolic reactions can only undergo evolutionary selection for certain combinations of the involved reaction rates due to their intricate interactions. We finally discuss how the expected range of metabolic rates likely impacts other key protocellular processes such as container growth and division as well as gene replication.

Working paper (pdf)                  Programming source code

Related links:
BioInfoBank Library

Related references:

- Flores, T.P.; Moss, D.S. Simulating the Dynamics of Macromolecules. In: Molecular Dynamics. Applications in Molecular Biology; Goodfellow, J.M., Ed.; CRC Press Inc.: Boca Raton, FL, 1990.

- Rasmussen, S.; Chen, L.; Deamer, D.; Krakauer, D.C.; Packard, N.H.; Stadler, P.F.; Bedau, M.A. Transitions from Nonliving to Living Matter. Science 2004, 303, 963.
- Chad Knutson,
Gil Benko, Tristan Rocheleau, Fouzi Mououk, Jerzy Maselko, Liaohai Chen, Andrew P. Shreve and Steen Rasmussen, Artificial Life, 14 (2008) 189-201.

Multipole Reactive DPD with Applications to Vesicular Protocells
dotBioMIP Research Group (Ruhr-University-Bochum)

Abstract: Dissipative particle dynamics provides a momentum conserving extension to Brownian Dynamics allowing Langevin type mesoscale simulation with proper preservation of the hydrodynamic limit. Hydrodynamic effects already play an important role at molecular scales, and their proper treatment is important to attain the correct scaling properties in multiscale simulations. While DPD operates with point particles with central forces (which may be "covalently" linked to form more complex entities) it turns out to be more efficient to allow the interacting entities to have at least an orientation given by a dipole (or higher order multipolar). The dipole vector can be viewed as the surface normal, so that surface self-assembling particles can be characterized in direct relation to the structures they form. In fact mprDPD particles can form a rich variety of amphiphile structures such as micelles, vesicles, multilaminar sheets and nanotubes. Another important extension of DPD which we employ is to use density dependent interactions. Multipolar reaction DPD further extends traditional DPD by adding stochastic reaction kinetics to the particles, allowing it to function as a structural extension to stochastic reaction diffusion modelling, and a mesoscale alternative to reactive molecular dynamics.

Working paper (pdf)            Programming source code

Related links:
Self-assembled structures in reaction networks
Lipid world: molecular dynamics
Chemical System Evolution
GSA - Genetic Self-assembly

Related references:
- Hoogerbrugge PJ, Koelman, JMVA (1992) Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. Europhys. Lett. 19: 155.
- Espanol P, Warren P (1995) Statistical mechanics of Dissipative Particle Dynamics. Europhys. Lett. 30: 191.
- Groot, RD Warren PD (1997) Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation. J. Chem. Phys. 107: 4423.
- Warren PB (1998) Dissipative particle dynamics. Curr. Op. Colloid. Sci. 3: 620.
- Vattulainen I, Karttunen M, Besold G, Polson JM (2002) Integration schemes for dissipative particle dynamics simulations: From softly interacting systems towards hybrid models. J. Chem. Phys. 116: 3967.
- Pagonabarraga I and Frenkel D (2001) Dissipative Particle Dynamics for Ineracting Systems. J. Chem. Phys. 115: 5015-5026.
- Espanol P. (1998) Fluid particle model. Phys Rev E 57, 2930-2948.
- De Fabritiis G., Coveney P.V., Flekkoy E.G. (2002) Multiscale dissipative particle dynamics. Phil Trans R Soc Lond A 360: 317-331.
- Rudolf M. Füchslin, Harold Fellermann, Anders Eriksson and Hans-Joachim Ziock, Coarse-graining and Scaling in Dissipative Particle Dynamics, http://arxiv.org/abs/cond-mat/0703682

Evolving inductive generalization via genetic self-assembly
dotBioMIP Research Group (Ruhr-University-Bochum)sa

Abstract: Genetic self-assembly is a technique for building complex systems by self-assembly from a small set of genetically encoded types of components. One particularly important case is circuit design, and here we have completed the full evolution of complex circuits from scratch, focusing primarily on the example of digital multipiers.
Genetic encoding of self-assembling components greatly enhances the evolution of complex systems and provides an efficient platform for inductive generalization, i.e. the inductive derivation of a solution to a problem with a potentially infinite number of instances from a limited set of test examples. We exemplify this in simulations by evolving scalable circuitry for several problems. One of them, digital multiplication, has been intensively studied in recent years, where hitherto the evolutionary design of only specific small multipliers was achieved. The fact that this and other problems can be solved in full generality employing self-assembly sheds light on the evolutionary role of self-assembly in biology and is of relevance for the design of complex systems in nano- and bionanotechnology.

Working paper (pdf)          Programming source code

Related links:
Self-assembled structures in reaction networks
GSA - Genetic Self-assembly

Related references:
- Weberndorfer, G., Hofacker, I. L., and Stadler, P. F. On the evolution of primitive genetic codes. Origins of life and evolution of the biosphere 33, 491-514 (2003).
- von Kiedrowski, G. A self-replicating hexadeoxynucleotide.
Angew. Chem. Int. Edit. 25, 932-935 (1986).
- Rebek, J. Synthetic replicators and extrabiotic chemistry.
Chem. Ind. London 5, 171-174 (1992).
- Lehn, J.M. Toward complex matter: supramolecular chemistry and self-organization.
P. Natl. Acad. Sci. USA 99, 4763-4768 (2002).
- Carbone, A., & Seeman, N. C. Circuits and programmable self-assembling DNA structures.
P. Natl. Acad. Sci. USA 99, 12577-12582 (2002).
- Syms, R.R.A., Yeatman, E.M., Bright, V.M. & Whitesides, J. M. Surface tension-powered self-assembly of microstructures - The state of the art.
J. Microelectro-mechanical Systems 12, 387-417 (2003).
- Terfort, A. & Whitesides, G.M. Self-assembly of an operating electrical circuit based on shape complementarity and the hydrophobic effect.
Adv. Mater. 10, 470-+ (1998).
- DeHon, A., Lincoln, P., Savage, P.E. Stochastic assembly of sublithographic nanoscale interfaces.
IEEE T. Nanotechnol 2, 165-174 (2003).
- J.F. Miller, D. Job, V.K. Vassilev. Principles in the Evolutionary Design of Digital Circuits--Part I.
J. Genetic Programming and Evolutionary Machines, 1, 7-35 (2000).
- Torresen, J. Evolving multiplier circuits by training sets and training vector partitioning.
Lect. Notes in Comp. Sci. 2606, 228-237 (2003).
- Hillis, W.D. Co-evolving parasites improve simulated evolution as an optimization procedure.
Physica D 42, 228-234 (1990).
- Bryant, R. E. On the complexity of VLSI implementations and graph representations of boolean functions with applications to integer multiplication.
IEEE Transactions on computers 40, 205-213 (1991).
- McCaskill, J. S. A stochastic theory of macromolecular evolution.
Biol. Cybern. 50, 63-73 (1984). Michel ,F., Westhof, E. Visualizing the logic behind RNA self-assembly. Science 273, 1676-1677 (1996).

Rigid body mechanic simulations
dotComplex Systems Group (Chalmers University of Technology)pasted

Abstract: The model used here is based on the Diffusion Limited Aggregation (DLA) model introduced by Witten and Sanders (1981), extended with a mechanistic simulation to drive the system towards an equilibrium state. Each model step consists of two parts: first the DLA step in which new particles are attached to the aggregate and second the simulation of the internal dynamics of the aggregate. In this model, particles are not considered to be of the same type (unlike the standard DLA model), but to be of different types that are distinguished by their surface features. The different particle types get concentrations assigned at the beginning of a simulation which determine the probabilities for generating the different particle types, when they are inserted. The particles are modeled as hard spheres with a diameter Dp and with circular patches on the surface, called binding sites, through which the particles can bind to each other. A binding site has three properties: the position p on the surface of a particle, the opening angle a, and a set of other binding sites S to which it can bind.

Working paper (pdf)          Programming source code

Related links:
ALGOR website
The guide to computing literature

Related references:
- Schroer, J.P., and K. Lindgren (2006). Simulation of higher-order self-assembly. Proceedings of ECCS06.
- Lindgren, K., J. Nyström, J.P. Schroer (2007). Prototype simulation package for physically self-assembling units. PACE report for Deliverable D13.
- Witten, T., & L. Sander (1981). Diffusion-limited aggregation, a kinetic critical phenomenon, Phys. Rev. Lett. 47, 1400.

Evolutionary self-organization of amphiphilic systems (Evoself)
dotJohn S. McCaskill, Norman H. Packard, Steen Rasmussen, Mark A. Bedau
Abstract: Evolving self-assembling physico-chemical systems provide a key to exploiting life-like properties of collective information processing via molecular structures. The EvoSelf simulation platform is based on the spin lattice model abstraction of complex fluids for describing their dynamic structural self-assembly. This framework has been very successful in accounting for the equilibrium phase diagrams of amphiphile systems.
The EvoSelf platform extends the homogeneous physical lattice models by
1. allowing local interactions to be modulated by the presence of combinatorial chemicals exhibiting hydrophobic, hydrophilic or amphiphilic properties.
2. introducing a coupled reactive dynamics of these combinatorial chemicals, allowing in principle an open-ended evolutionary dynamics of molecular species
The initial Widom-based version of the platform was developed by J. McCaskill, N.H. Packard, S.Rasmussen and M.A. Bedau [1]. Subsequently extended versions of the platform have been developed by J.S.McCaskill to address explicit amphiphile states and combinatorial recognition in amphiphile self-assembly.

The evoself model consists of 

  • a lattice model of a multiphase system such as a  ternary oil-water amphiphile system
  • a population of spatially distributed combinatorial molecules modulating amphiphile thermodynamics
  • spin lattice dynamics of (heterogeneous) multiphase system
  • thermodynamically consistent diffusion of combinatorial molecules biased by energetics
  • reactions of combinatorial amphiphiles (e.g. chemical self-replication)
  • evolution induced by these reactions having variant combinatorial byproducts

Working paper (pdf)           Programming source code

Related links:

Related references:
- McCaskill, JS, Packard, NH, Rasmussen, S and Bedau, MA "Evolutionary self-organization in complex fluids" Phil Trans B (2007) 362(1486) 1763-1779.

Algorithmic Self-assembly
dotBioMIP Research Group (Ruhr-University-Bochum)
Abstract: It is an old dream of computer- scientists to evolve software and abandon the time-consuming error-prone man-made development of complex software-systems. Exactly this problem is predominant in the creation of artificial cells. We believe that complex entities like artificial cells have to be evolved, at least partly. Getting this evolution under control and open it for programmability is a major motivation in this study. Other questions behind this work are robustness of evolving entities, the origin of replication and of course evolvability. It is apparent that nature has created a marvelous system of evolving creatures and we, as one product out of these fantastic achievements, have no idea how nature solved this problem. All our computer-models more or less immediately stagnate or evolve into simple boring system dynamics. We should not mix complex appearance with complex organization. For example, fractals do have intricate graphical representations but are extremely simple to produce. Many phenomena of natural numbers combined with appropriate procedures yield very intricating pictures and seemingly pretend telling us something about evolution. The presented system of evolving micro-controllers gives insights in how information-processing in artificial cells should be orchestrated and how this information-processing could be made robust against external or internal perturbations.

Working paper (pdf)        Programming source code     A simple example with images and data-files     A complex example (ca. 80MB)

Related links:
Chemical System Evolution
EvoCPU-algorithm self-assembly

Related references:
 - C. Adami and C. T. Brown. Evolutionary learning in the 2d artificial life system  "Avida". In R. Brooks and P. Maes, editors, Artificial Life IV, pages 377-381. MIT Press, Cambridge, MA, 1994.
- S. Altmeyer and J. S. McCaskill. Error threshold for spatially resolved evolution in the quasispecies model. Phys. Rev. Lett., 86:5819-5822, 2001.
- G. J. Bauer, J. S. McCaskill, and H. Otten. Traveling waves of in vitro evolving RNA. Proc. Natl. Acad. Sci. USA, 86:7937-7941, 1989.
- E. R. Berlekamp, J. H. Conway, and R. K. Guy. Winning Ways for Your Mathematical Plays. Academic Press, New York, 1982.
- M. C. Boerlijst and P. Hogeweg. Spiral wave structure in pre-biotic evolution: Hypercycles stable against parasites. Physica D, 48:17-28, 1991.
- P. Dittrich, J. Ziegler, and W. Banzhaf. Artificial chemistries - a review. Artif. Life, 7:225-275, 2001.
- R. Ehricht, T. Ellinger, and J. S. McCaskill. Cooperative amplification of templates by crosshybridisation (CATCH). Eur. J. Biochem., 243:356-364, 1997.
- M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Z. Naturwissenschaften, 58:465-523, 1971.
- W. Fontana. Algorithmic chemistry: A model for functional self-organization. In C. G. Langton, editor, Artificial Life II, pages 159-202. Addison-Wesley, Reading, Massachusetts, 1991.
- R. Füchslin, T. Maeke, U. Tangen, and J. S. McCaskill. Evolving inductive generalization via genetic self-assembly. Adv. in Compl. Systems, 9:1-29, 2005.
- J. H. Holland. Studies of the spontaneous emergence of self-replicating systems using cellular automata and formal grammars. In A. Lindenmayer and G. Rozenberg, editors, Automata, Languages, Development, pages 385-404. North Holland Publishing Company, Amsterdam, 1976.
- S. A. Kauffman. Autocatalytic sets of proteins. J. Theor. Biol., 119:1-24, 1986.
- J. S. McCaskill. Polymer Chemistry on Tape: A Computational Model for Emergent Genetics. Max-Planck-Society, Göttingen, Germany, 1988. Report.
- J. S. McCaskill, S. Altmeyer, and R. M. Füchslin. The stochastic evolution of catalysts in spatially resolved molecular systems. J. Biol. Chem., 382:1343-1363, 2001.
- A. N. Pargellis. The spontaneous generation of digital "Life". Physica D, 91:86-96, 1996.
- S. Rasmussen, J. A. Bailey, J. M. Boncella, L. Chen, G. Collis, S. Colgate, M. S. DeClue, H. Fellermann, G. Goranovic, Y. Jiang, C. Knutson, P.-A. Monnard, F. Mouwouk, P. Nielsen, A. Sen, A. Shreve, A. Tamulis, B. Travis, P. Weronski, J. Zhang, X. Zhou, H. Ziock, and W. H. Woodruff. "assembly of a minimal protocell". In "Bridging Nonliving and Living Matter", volume 2038, "MIT Cambridge", 2007. In press.
- D. Sievers and G. von Kiedrowski. Self replication of complementary nucleotide-based oligomers. Nature, 369:221-224, 1994.
- U. Tangen. From evolving software towards models of dynamically self-assembling processing systems. In J. Jost, F. Reed-Tsochas, and P. Schuster, editors, "Proceedings of ECCS 2006", pages 50, p85.pdf. "ECSS, Paris", 2006. URL http://complexsystems.lri.fr/FinalReview/FILES/PDF/p85.pdf.
- J. von Neumann. Theory of Self-Reproducing Automata. Burks, A. W. University of Illinois Press, Urbana, 1966.
- B. Wlotzka and J. S. McCaskill. A molecular predator and its prey: Coupled isothermal amplification of nucleic acids. Chem. & Biology, 4:25-33, 1997.
- D. Y. Zhang, A. J. Turberfield, B. Yurke, and E. Winfree. Engineering entropy-driven reactions and networks catalyzed by DNA. Science, 318:1121-1125, 2007.

Omega Machine
dotBioMIP Research Group (Ruhr-University-Bochum)omega

Abstract: The omega machine is a programmable microfluidic control environment that can "see" the state of the chemical system and adjust a combinatorially complex set of control signals appropriately. It differs from the control center of a chemical plant both in the degree of monitoring and control, with significant combinatorial complexity, and in that the spatial control elements and spatially resolved sensors are on the same microscopic scale as the individual cells formed by the system. This qualitative jump in integration allows one to smoothly transfer functionality and information between the chemical system and the computerized control system: specific information in the control system can be associated with individual cells. The omega machine incudes the concepts of microscale complementation and in its strongest form also electronic genomes. Instead of presenting software the user-manual and a short tutorial is given.

ng_biopro-user-manual (pdf)              Tutorial

Related links:
The Omega Machine BioMIP

Related references:
- S. Chemnitz, U. Tangen, P.F. Wagler, T. Maeke and J.S. McCaskill »Electronically programmable membranes for improved biomolecule handling in micro-compartments on-chip« Chemical Engineering Journal, 2008, 135S, 276-279
- C.-Y. Lin, L.-M. Fu, K.-H. Lee, R.-J. Yang and G.-B. Lee. "Novel surface modification methods and surface property analysis for separation of DNA biomolecules using capillary electrophoresis" in micro-TAS, pp. 1081-1084, Squaw Valley, California USA, 2003.U.
- Tangen, P.F. Wagler, S. Chemnitz, G. Goranovic, T. Maeke, J. S. McCaskill CompPlexUs Vol. 3, No.1-3, 2006, 48-57. 
- M. G. Pollack, R. B. Fair and A. D. Shenderov, "Electrowetting-based actuation of liquid droplets for microfluidic applications", Applied Physics Letters, vol. 77, pp. 1725-1726, 2000
- T. Thorsen, S. Maerkl and S. Quake, "Microfluidic large-scale integration", Science, vol. 298, pp. 580-584, 2002
- E. Verpoorte and N. F. De Rooij, "Microfluidics meets MEMS", Proceedings of the IEEE, vol. 91, pp. 930-953, 2003
- F. Su and K. Chakrabarty, "Unified high-level synthesis and module placement for defect-tolerant microfluidic biochips", Proc. IEEE/ACM Design Automation Conference, pp. 825-830, 2005
- K. Chakrabarty and J. Zeng, "Design automation for microfluidics-based biochips", ACM Journal on Emerging Technologies in Computing Systems, vol. 1, pp. 186-223, December 2005
- C. Priest, S. Herminghaus, and R. Seemann, "Generation of Monodisperse Gel Emulsions in a Microfluidic Device", Appl. Phys. Lett. (88), 2006 

Mesoscopic Simulations of Metabolism-vesicle Growth
dotComplex Systems Lab (UPF)

finiteAbstract: We have also extended previous work on metabolism-vesicle growth and replication dynamics under a mesoscopic approximation. In two previous papers (Macia and Sole, 2007a, 2007b) we explored the problem of the necessary conditions required for desestabilizing a closed vesicle under the presence of a minimal metabolic set of reactions. By using such models (including Turing instabilities) we showed that a feasible mechanism of membrane growth and destabilization took place as a result of a new class of dynamical instability in two dimensions. Over the last year we have extended this mesoscopic framework to a three-dimensional setting. In order to do so we have used a Finite Element approach, where space is triangulated and our previous edges in 2D representing pieces of the 1D membrane) have now been replaced by surfaces. We have been able to obtain self-replicating 3D cells using a simple, enzyme-catalyzed reaction set (as the one used in Macia-Solé model "Protocell self-reproduction in a spatially explicit metabolism-vesicle system" J. Macia and R. V. Sole, J. Theor. Biol. 245(3), 400-410 (2007). Current work involves developing both a mean field approximation to this 3D setting as well as a parameter exploration of the numerical simulation model.

Working paper (pdf)            Programming source code

Related links:
Biophysics Journal: mesoscopic simulations
Mesoscopic simulations of lipid bilayers

Related references:
 - Macià, J. and Solé, R. Protocell self-reproduction in a spatially explicit metabolism-vesicle system. J. Theor. Biol. 245(3), 400-410 (2007)

Hypercycle Dynamics: Stochastic Cellular Automata
dotComplex Systems Lab (UPF)

Abstract: Mounting theoretical and experimental evidence indicates that the success of molecular replicators is strongly tied to the local nature of their interactions. Local dispersal in a given spatial domain, particularly on surfaces, might strongly enhance the growth and selection of fit molecules and their resistance to parasites. In this work the spatial dynamics of a simple hypercycle model consisting of two molecular species is analyzed. In order to characterize it, both mean field models and stochastic, spatially explicit approaches are considered. The mean field approach predicts the presence of a saddle-node bifurcation separating a phase involving stable hypercycles from extinction, consistently with spatially explicit models, where an absorbing first-order phase transition is shown to exist and diffusion is explicitly introduced. The saddle-node bifurcation is shown to leave a ghost in the phase plane. A metapopulation-based model is also developed in order to account for the observed phases when both diffusion and reaction are considered. The role of information and diffusion as well as the relevance of these phases and the underlying spatial structures are discussed, and their potential implications for the evolution of early replicators are outlined.

Working paper (pdf)            Programming source code


CAmodel        CA2
Spatiotemporal dynamics for the symmetric two-membered hypercycle. (Left) First member
(right) second member. Each cell can be empty (white) or occupied (black) by the first, the second, or both replicators. 

Related links:
Complex Systems Lab Hypercycles website

Related references:
- E
igen, M. and Schuster, P. (1979) The Hypercycle. A Pinciple of Natural Self-Organization. Springer-Verlag
- Bernd-Olaf Küppers (1985) Molecular Theory of Evolution. Outline of a Physico-Chemical Theory of the Origin of Life
- D. H. Lee, K. Severin, and M. Reza Ghadiri. Autocatalytic networks: the transition from molecular self-replication to molecular ecosystems. Curr. Opin. Chem. Biol., 1:491-496, 1997
- B.M.R Stadler and P. F. Stadler. Molecular Replicator Dynamics, Advances in Complex Systems 6: 47-77 2003
- Sardanyés, J., and Solé, R. V. Bifurcations and phase transitions in spatially-extended two-member hypercycles. J. Theor. Biol. 243(4), 468-482 (2006)

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Vesicle Fusion and Nanoparticle-Membrane Interactions
dotDepartment of Micro and Nanotechnology (Technical University of Denmark)


Abstract: cells maintain strict control over the integrity of their plasma membrane so
 as to ensure a stable internal
environment for their many functions. But material has to be brought in and waste removed in order for the cell to live and grow. The processes of membrane fusion, vesicle budding, endo- and exocytosis, among others, all transport material between the cell's exterior and interior or between various internal compartments. Although membrane fusion is controlled by proteins in vivo, simplified model systems of lipid vesicles can also be made to fuse in vitro, and computer simulations have been used recently to explore the various molecular rearrangements that take place during fusion. An important clinical application of artificial fusion is the controlled delivery of a drug into a cell's cytoplasm. Designing so-called drug delivery vehicles so as to optimize their entry into a cell, and still maintain their stability on the journey to the cell through the circulatory system, is a challenge. The vehicle must remain intact long enough to reach its target, but still be readily degradable on arrival so as to release its drug payload. Various types of vehicle are being investigated, ranging from lipid vesicles and polymer vesicles to layered shells or nanoparticles.

Here are some movies taken from Dissipative Particle Dynamics (DPD) simulations of vesicle fusion and nanoparticles translocating across a membrane. Although these models are highly simplified, they demonstrate that coarse-grained simulation techniques, such as DPD, can capture the material properties of complex fluids and nanoparticles on the length and time scales needed to explore the behaviour of drug delivery vehicles and, potentially, endocytosis.


Working paper (pdf)           Programming source code

Related links:

Julian Shillcock's Homepage
Julian Shillcock

Related references:
- Dissipative Particle Dynamics: bridging the gap between atomistic and mesoscopic simulations. R. D. Groot and P. B. Warren, J. Chem. Phys. 107, 4423 (1997).
- Tension-induced fusion of bilayer membranes and vesicles. J. C. Shillcock and R. Lipowsky, Nature Materials 4, 225 (2005).
- The computational route from bilayer membranes to vesicle fusion (invited review).Visualizing soft matter: mesoscopic simulations of membranes, vesicles and nanoparticles.J. C. Shillcock and R. Lipowsky, Biophys. Rev. and Lett. 2:33-55 (2007).
- Insight or illusion? seeing inside the cell with mesoscopic simulations.J. C. Shillcock, HFSP Journal 2(1):1-6 (2008).
- Tension-induced vesicle fusion: pathways and pore dynamics.L. Gao, R. Lipowsky and J. C. Shillcock, Soft Matter 4:1208-1214 (2008).

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Simulation Package for Physically Self-assembling Units
dotComplex Systems Group (Chalmers University of Technology)
Abstract: This software package is used for simulations on Cellular Potts Model (CPM). The Potts model is based on statistical mechanics, like the well-known Ising model. The CPM is a discrete, lattice based model where each lattice site has two properties given by a type description and which cell belongs to, respectively. Based on these two properties a Hamiltonian is constructed, where the energy of the cells is gathered. Using this Hamiltonian, a Monte Carlo scheme is generally set up to evolve the system of cells forward in time.

Working paper (pdf)           Programming source code

Related links:
Potts model
Cellular Potts Model

Related references:
- Whitesides, G., and Boncheva, M. PNAS 99, 4769 (2002)
- Savill, N. J., and Hogeweg, P. Journal of theoretical Biology 184, 229 (1997)
- Maree, A., Panfilov, A. V., and Hogeweg, P. Journal of Theoretical Biology 199, 297 (1999)
- Maree, A. and Hogeweg, P. PNAS 98, 3879 (2001)
- Chiruvolu, S., Walker, S., Israelachvili, F., Schmitt, J., Leckband, D., and Zasadzinski, J. Science 264 (2003)

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Monte Carlo Simulations of Amphiphiles
dotComplex Systems Lab (UPF)Monte

Abstract: In the framework of micellar self-assembly processes, we have studied the stability and self-aggregation capabilities of a family of lipid molecules characterized by different shapes. For this objective, we have employed a mesoscale approach by developing a Monte Carlo application algorithm (Metropolis Monte Carlo). The application used three types of molecules: water, amphiphiles and oil-like molecules. Two types of amphiphiles are used: ellipsoidal  (Johnston et al. 2002, Phys. Rev. E 65, 051706) and pear-shaped (Barmes et al. 2003, Phys. Rev. E 68, 021708).  In both cases and dependent on the characteristic shape of the amphiphiles, an adapted Gay-Berne type of interaction potential (Gay&Berne 1981, J. Chem. Phys. 74, 3316) was employed.   The Gay-Berne potential models the anisotropic interaction between two amphiphiles considered as ellipsoids.  The extension to pear-shaped molecules of  Barmes et al. (2003) consists in a class of models denoted as parametrized hard Gaussian overlap, models that provide an analytical form of the shape parameter. More precisely, the shape parameter for the pear-type molecules is based on an approximated Bezier-curves geometry easily suitable for Monte Carlo simulations.     Moreover, we have incorporated chemical reactions  (Fellermann&Solé 2007, Phil. Trans. R. Soc. B 362, 1803) by considering the transformation of precursors into surfactants in reactions catalyzed by existent surfactants.

Working paper (pdf)           Programming source code


Monte Carlo simulations of a growing lipidic bilayer from elipsoidal precursors

Related links:
Biophysics Journal: Monte Carlo simulations
The Journal of Chemical Physics: Lipid Membranes and Monte Carlo Simulations

Related references:
- J. D. Gunton, M. San Miguel, and P. S. Sahni, Phase Transitions and Critical Phenomena, edited byC. Domb and J. L. Lebowitz (Academic, London, 1983), Vol. 8
- A. C. Balazs, V. V. Ginzburg, F. Qiu, G. Peng, and D. Jasnow, J. Phys. Chem. B 104, 3411 (2000).
- M. Dijkstra, R. van Roij, and R. Evans, Phys. Rev. E 59, 5744 (1999). [MEDLINE]
- G. Pastore, R. Santin, S. Taraphder, and F. Colonna, J. Chem. Phys. 122, 181104 (2005). [ISI] [MEDLINE]
- E. Díaz-Herrera, G. Ramírez-Santiago, and J. A. Moreno-Razo, Phys. Rev. E 68, 061204 (2003). [ISI]
- K. Simons and E. Ikonen, Nature (London) 387, 569 (1997). [MEDLINE]
- R. G. W. Anderson and K. Jacobson, Science 296, 1821 (2002). [MEDLINE]
- K. Simons and D. Toomre, Mol. Cell. Biol. 1, 31 (2000).
- A. D. Douglass and R. D. Vale, Cell 121, 937 (2005). [MEDLINE] [ChemPort]
- S. Mayor and M. Rao, Traffic (Oxford, U. K.) 5, 231 (2004). [MEDLINE]
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Simulations of Minimal Protocell Self-replication
dotComplex Systems Lab (UPF)self-replic

Abstract: The reproduction of a living cell requires a repeatable set of chemical events to be properly coordinated. Such events define a replication cycle, coupling the growth and shape change of the cell membrane with internal metabolic reactions. Although the logic of such process is determined by potentially simple physico-chemical laws, the modeling of a full, self-maintained cell cycle is not trivial. Here we present a novel approach to the problem which makes use of so called symmetry breaking instabilities as the engine of cell growth and division. It is shown that the process occurs as a consequence of the breaking of spatial symmetry and provides a reliable mechanism of vesicle growth and reproduction. Our model opens the possibility of a synthetic protocell lacking information but displaying self-reproduction under a very simple set of chemical reactions.

Working paper (pdf)            Programming source code

Related links:
OCCAM: Osmo-Controled Cell-division Active Mechanism

Related references:
- Bozic, B. Svetina, S. 2004. A relationship between membrane properties forms the basis of a selectivity mechanism for vesicle self-reproduction. Eur. Biophys. J., 33: 565-571
- Discher, D. E., and Eisenberg, A. 2002. Polymer vesicles. Science 297, 967-973
- Luisi, P. L. 2002. Towrd the engineering of minimal living cells. Anat. Record 268, 208-214
- Szostack W., Bartel, D. P. and Luisi, P. L. 2001. Synthesizing life. Nature 409, 387-390
Chemoton Model: Software Simulation Tools
dotComplex Systems Lab (UPF)

Abstract: The Chemoton model was introduced by Gánti in 1971 (see review Gánti 2002) as a fundamental unit model of living systems. It consists in three functionally dependent autocatalytic subsystems: the metabolic chemical network, the template polimerization and the membrane subsystem enclosing them all. The correct functioning of the chemoton lies in the precise stoichiometric coupling of these three subunits. It ensures that both the surface and the inner components evolve into doubling their initial value, leading to the subsequent division into two identical chemotons. Besides the detail introductory papers of Gánti, only a few studies of this model exist in the literature, presenting however contradictory conclusions. The present study aims toward a thorough survey of the chemoton's characteristics, such as replication period or optimal template length, in the parameters' space. Additionally, a comparative study between deterministic approach and the stochastic one is performed.

Working paper (pdf)            Programming source code

Related links:
Complex Systems Lab Chemoton website

Related references:
- T. Csendes (1984) A simulation study on the chemoton Kybernetes, 13 (2): 79.
- C. Fernando and Di E.A., Paolo. The Chemoton: A model for the origin of long RNA templates. Proceedings of the Ninth International Conference on the Simulation and Synthesis of Living Systems, ALIFE'9 Boston, September 12th-15th, MIT Press 2004
- T. Gánti (2002) On the early evolution of biological periodicity. Cell. Biol. Int. , 26 (8): 729
- T. Gánti.The principles of life. Oxford University Press 2003.
- D. Gillespie. A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions. J.Comp. Phys., 22: 403, 1976
- D. Gillespie. Exact Stochastic Simulation of Coupled Chemical Reactions. J. Phys. Chem., 81: 2340, 1977

Simulations of Victim-exploiter Replicator Dynamics
dotComplex Systems Lab (UPF)spat

Abstract: Sochastic cellular automata models are used to simulate molecular host-parasite dynamics between self-replicating bit strings with simple genetic mechanisms of recognition/interaction. Outstanding implemented processes are molecular decay, diffusion and self-replication processes submitted to errors (mutation). Here, hosts have self-replicating activity and they can replicate under parasites spatial absence. On the other hand, parasites also self-replicate but they need a spatial meeting with hosts in order to eliminate them and successfully replicate. Both populations are also left to molecular decay. With these state-transition rules, we investigate victim-exploiter spatiotemporal dynamics in neutral hypercubes where extinctions and coevolutionary cycling are found. Such dynamical outputs are the result of a race for survival through the configurations space.

Working paper (pdf)            Programming source code

Related links:
SETH: Spatiotemporal Evolution Through Hypercubes

Related references:
- Breyer, J., Ackermann, J. and McCaskill, J. (1998) Evolving reaction-diffusion ecosystems with self-assembling structures in thin films. Artificial Lifeybernetes, 479, 25-40
- Dieckmann, U., Marrow, P. & Law, R. (1995) Evolutionary cycling in predator-prey interactions: Population dynamics and the red queen. J theor Biol 176, 91-102
- Ikegami, T., and Kaneko, K. (1992) Evolution of host-parasitoid network through homeochaotic dynamics. Chaos 2, 397-207
- Stadler, B. M. R. and Stadler, P. F. (2002) Molecular replicator dynamics. Adv. Complex Systems

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Demonstration of Multi-level Selection in an Artificial Chemistry

dotaLife Lab, RINCE, Dublin City Universitydcu

Abstract: The first experiment is an implementation of an Artificial Replicator Chemistry, vaguely similar to an RNA world. Molecules consist of digital bit-strings and are implemented as agents in a Multi-Agent Simulation. All molecules are capable of (error-prone) replication on the condition that the reaction is catalysed by an appropriate enzyme. The replicator molecules themselves act as the enzymes. The simulation is instantiated with 1000 instances of a randomly chosen molecule. The simulation proceeds by selecting two molecules at random, one to act as substrate, and one to act as an enzyme. If the enzyme's digital bit-string is a substring of the substrates bit-string, a (possibly mutated) copy of the substrate is created and added to the population, replacing another randomly selected molecule. This experiment shows progressive displacement of shorter molecules by longer ones, leading to an increase in mutation rate (since mutation is a per-copied-bit quantity) and a corresponding reduction in reaction rate. The next experiment sets up an Agent-Based protocell population. The protocells are abstract containers, each of which contains an instance of the above described replicator world, with one difference: we no longer replace a molecule with a newly created one, the new one is just added to the protocell. Now, when the protocell reaches a certain pre-determined size, it undergoes binary fission and randomly distributes the replicating molecules between the two daughter cells. Since we fix the population size at the protocell level, when we undergo a binary fission, we must replace an entire protocell, randomly selected, with one of the new ones.

Working paper (pdf)          Programming source code

Related links:
The DCU ALife Lab

Related references:
- Dawkins, R. (1976) The Selfish Gene. Oxford: Oxford University Press
- Dittrich, P., Ziegler, J., and Banzhaf, W. (2001) Artificial Chemistries - A review. Artificial Life, 7(3) 225-75
- Maynard Smith, J. and Szathmáry, E. (1997) The Major Transitions in Evolution. Oxford Press
Szathmáry, E. and Maynard Smith, J. (1997) From Replicators to Reproducers: the First Major Transitions Leading to Life. J. theor. Biol, 187 555-571

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Simulation of  Self-replicating Spots
dotComplex Systems Lab (UPF)division

Abstract: Among reaction-diffusion systems showing Turing patterns, the diffusive Gray-Scott model [Pearson, J.~A., 1993, Science 261, 189] stands out by showing self-replicating patterns (spots), which makes it the ideal simple model for developmental research. A first study of the influence of noise in the Gray-Scott model was performed by Lesmes et al. [2003 Phys. Rev. Lett. 91, 238301] concluding that there exits an optimal noise intensity for which spot multiplication is maximal. Here we show in details the transition from non-spotlike to spotlike pattern, with the identification of a wide range of noise intensities instead of an optimal value for which this transition occurs. Additional studies also reveal that noise produces a shift and a shrinkage of the regions of spatial patterns in the phase diagram, without introducing qualitative changes to the diagram.

Working paper (pdf)            Programming source code

Related links:
Complex Systems Lab Self-replicating spots website

Related references:
- Lee K.J., McCormick W.D., Ouyang, Q. ,Swinney, H.L., Pattern formation by interacting chemical fronts, Science, 251:192, 1993
- Lee,K.J., McCormick, W.D., Swinney, H.L., Pearson, J.E., Experimental observation of self-replicating spots in a reaction-diffusion system, Nature, 369:215, 1994

- Lesmes F, Hochberg D, Moran F, et al., Noise-controlled self-replicating patterns, Phys. Rev. Lett. 91 (23): Art. No. 238301 DEC 5 2003
- Gray P., Scott S.K.,Sustained oscillations and other exotic patterns in isothermal reactions, J.Phys.Chem., 89:25, 1985  
- Koch A.J., Meinhardt H., Biological pattern-formation - from basic mechanisms to coplex structures, Rev.Modern Physics, 66 (4): 1481, 1994
- Mazin, W. , Rasmussen, K.E., Mosekilde, E., Borckmans,P., Dewel, G., Pattern formation in the bistable Gray-Scott model, Mathematics and Computers in Simulation, 40:371, 1996
- Nishiura, Y., Ueyama, D., A skeleton structure of self-replicating dynamics, Physica D, 130(48):73, 1999
- Pearson, J.E., Complex patterns in a simple system, Science 261:189,1993

Simulation Software of Molecular Quasispecies: the Error Threshold
dotComplex Systems Lab (UPF)polio

Abstract: The molecular quasispecies theory initially developed and formalized by Manfred Eigen and Peter Schuster (Eigen and Schuster 1979) is an excellent theoretical framework to analyze RNA virus dynamics. These viruses show a huge adaptability to changing environments because of their high mutability during replication. Viral genomes form the so-called molecular quasispecies, which are represented by a set of sequences forming a cloud of mutants with extremely heterogeneous genotypes. The quasispecies structure actually provides to this set of sequences with extremely large capacities to face changes in the environment, sometimes helping to avoid the immune system action. RNA virus actually mutate near the critical region of the so-called error catastrophe. By means of mean field models and in silico simulations with bit strings used to simulate the viral strands, we have shown that the so-called informational error catastrophe can also be achieved through replication thresholds.

Working paper (pdf)            Programming source code

Related links:
Complex Systems Lab VIRUS dynamics website
Plant virus diversity and evolution group (Santiago Elena)
Genetic variability of RNA virus

Related references:
- Eigen, M. and Schuster, P. The Hypercycle. A principle of Natural Self-organization Springer-Verlag, 1979
- Domingo, E. (Ed) (2005) Virus entry into error catastrophe as a new antiviral strategy. Virus Research 107(2), 115-228
- Crotty, S., Cameron, C. E., Andino, R. (2001) RNA virus error catastrophe: direct molecular test by using ribavirin Proc. Natl Acad. Sci. USA 98, 6895-6900
- Solé, R. V., Goodwin, B. C. (2001) Signs of life: How compexity pervades biology. Basic Books, Perseus, New York

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Catalysis by Self-assembled Structures in Reaction Networks

dotProtoLife SRL; European Center for Living Technology; Reed College (Portland)

Abstract: We introduce a new variant of dissipative particle dynamics (DPD) models that includes the possibility of dynamically forming and breaking strong bonds. The emergent reaction kinetics may then interact with self-assembly processes. We observe that self-assembled amphiphilic aggregations such as micelles have a catalytic effect on chemical reaction networks, changing both equilibrium concentrations and reaction rates. These simulation results are in accordance with experimental results on the so-called "concentration effect".

Working paper (pdf)            Programming source code

Related links:
Dissipative Particle Dynamics (DPD)
Biphysics and softmatter (DPD)

Related references:
- Farmer, : D., Kauffman, S. A., and Packard, N. H. Autocatalytic replication of polymers. Physica D 22 Vol. 50 (1986)
- Groot R. and Warren, P. Dissipative particle dynamics: bridging the gap between atomistic and mesoscopic simulations. J. Chem. Phys. Vol.107 4423-4435 (1997)
- Kauffman, S. A. Autocatalytic sets of proteins J. theor. Biol. 119 1-24 (1986)
- Mallik, K., Jewrajka, S., Pradhan, N., Pal, T. Micelle-catalysed redox reaction. Current Science 80, 1408-1412
- Schilling, C. H., and Palsson, B. O. The underlying pathway structure of biochemical reaction networks Proc. Natl. Acad. Science 95, 4193-4198

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Lipid World: Molecular Dynamics Simulation Tool

dotComplex Systems Lab (UPF)fission

Abstract: We study the formation and evolution of lipid aggregates like micelles and vesicles which had been involved in the process of emergence of life in prebiotic conditions. A molecular dynamics approach is used to simulate the motion of individual particles with high physical accuracy. The aim of our work is to explore the role of a variety of physical parameters as noise or friction, on the dynamics of lipid aggregates. Furthermore, our simulations allow to study auto- and cross-catalytic reactions between lipids that might have been important in the early stages of life.

Working paper (pdf)            Programming source code

We start simulations with a small micelle that is charged with some catalyst and exposed to a solution of
While time passes, precursors diffuse into the micelle and are transformed into new
lipids and catalysts leading to micelle growth.
When reaching a certain threshold size, micelles may become
unstable and finally split. One of our aims is to study the impact of
the underlying physics on this micelle division.

Related links:
Complex Systems Lab LIPID WORLD website

Related references:
- Aravanis, A. M., J. L. Pyle, and R. W. Tsien. 2003. Single synaptic vesicles fusing transiently and successively without loss of identity. Nature. 423:643–647. [PubMed].
- Berger, O., O. Edholm, and F. Jahnig. 1997. Molecular dynamics simulations of a fluid bilayer of dipalmitoylphosphatidylcholine at full hydration, constant pressure, and constant temperature. Biophys. J. 72:2002–2013. [PubMed].
- Blume, A. 1979. Comparative study of the phase transitions of phospholipid bilayers and monolayers. Biochim. Biophys. Acta. 557:32–44. [PubMed].
- Boden, N., S. A. Jones, and F. Sixl. 1991. On the use of deuterium nuclear magnetic resonance as a probe of chain packing in lipid bilayers. Biochemistry. 30:2146–2155. [PubMed].
- Brown, M. F., A. A. Ribeiro, and G. D. Williams. 1983. New view of lipid bilayer dynamics from 2H and 13C NMR relaxation time measurements. Proc. Natl. Acad. Sci. USA. 80:4325–4329. [PubMed].
- Colman, P. M., and M. C. Lawrence. 2003. The structural biology of type I viral membrane fusion. Nat. Rev. Mol. Cell Biol. 4:309–319. [PubMed].
- Darden, T., D. York, and L. Pedersen. 1993. Particle mesh Ewald—an n·log(n) method for Ewald sums in large systems. J. Chem. Phys. 98:10089–10092.
- De Loof, H., S. C. Harvey, J. P. Segrest, and R. W. Pastor. 1991. Mean field stochastic boundary molecular dynamics simulation of a phospholipid in a membrane. Biochemistry. 30:2099–2113. [PubMed].
- Douliez, J. P., A. Leonard, and E. J. Dufourc. 1995. Restatement of order parameters in biomembranes: calculation of C-C bond order parameters from C-D quadrupolar splittings. Biophys. J. 68:1727–1739. [PubMed].
- Egberts, E., S. J. Marrink, and H. J. C. Berendsen. 1994. Molecular dynamics simulation of a phospholipid membrane. Eur. Biophys. J. 22:423–436. [PubMed].

ALICE Software Package: Artificial Lipids Interactions
dotComplex Systems Lab (UPF)comb

Abstract: We explore in silico, toy models of dynamics and evolution of protocellular aggregates with a lipid matrix. Instead of considering a realistic, molecular dynamics approach to membrane formation, we use simple rules of interactions among molecules based on a minimal physics. The aim of this work is to use the formation of aggregates as a platform to explore evolutionary processes, the formation of compositional genomes and particularly the study of the impact of fluctuations on protocell dynamics and adaptation.

Working paper (pdf)            Programming source code

                                                SIMULATION SEQUENCE DISPLAY

Related links:
Complex Systems Lab ALICE website
PNAS (Artificial cells)
Lipid simulations

Related references:

- Shelley, J. C.; Shelley, M. Curr. Opin. Colloid Interface Sc. 2000, 5, 101. [ChemPort] [CrossRef]
- Müller, M.; Katsov, K.; Schick, M. J. Pol. Sci. B 2003, 41, 1441. [CrossRef]
- Smit, B.; Hilbers, P. A. J.; Esselink, K.; Rupert, L. A. M.; Van Os, N. M.; Schlijper, A. G. Nature 1990, 348, 624. [ChemPort] [CrossRef]
- Smit, B.; Esselink, K.; Hilbers, P. A. J.; Van Os, N. M.; Rupert, L. A. M.; Szleifer, I. Langmuir 1993, 9, 9. [ChemPort]-
- Palmer, B. J.; Liu, J. Langmuir 1996, 12, 746.[Full text - ACS] [ChemPort]
- Goetz, R.; Lipowsky, R. J. Chem. Phys. 1998, 108, 7397. [ChemPort] [CrossRef]
- Den Otter, W. K.; Briels, W. J. J. Chem. Phys. 2003, 118, 4712. [CrossRef-]
- Von Gottberg, F. K.; Smith, K. A.; Hatton, T. A. J. Chem. Phys. 1997, 106, 9850. [CrossRef]
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