Spatially resolved simulations of membrane reactions and dynamics: multipolar reaction DPD.

Biophysical chemistry of mesoscale systems and quantitative modeling in systems biology now require a simulation methodology unifying chemical reaction kinetics with essential collective physics. This will enable the study of the collective dynamics of complex chemical and structural systems in a spatially resolved manner with a combinatorially complex variety of different system constituents. In order to allow a direct link-up with experimental data (e.g. high-throughput fluorescence images) the simulations must be constructed locally, i.e. mesoscale phenomena have to emerge from local composition and interactions that can be extracted from experimental data. Under suitable conditions, the simulation of such local interactions must lead to processes such as vesicle budding, transport of membrane-bounded compartments and protein sorting, all of which result from a sophisticated interplay between chemical and mechanical processes and require the link-up of different length scales. In this work, we show that introducing multipolar interactions between particles in dissipative particle dynamics (DPD) leads to extended membrane structures emerging in a self-organized manner and exhibiting the necessary mechanical stability for transport, correct scaling behavior, and membrane fluidity so as to provide a two-dimensional self-organizing dynamic reaction environment for kinetic studies in the context of cell biology.

The stochastic evolution of catalysts in spatially resolved molecular systems.

A fully stochastic chemical modelling technique is derived which describes the influence of spatial separation and discrete population size on the evolutionary stability of coupled amplification in biopolymers. The model is analytically tractable for an infinite-dimensional space (simplex geometry), which also provides insight into evolution in normal Euclidean space. The results are compared with stochastic simulations describing the co-evolution of combinatorial families of molecular sequences both in the simplex geometry and in lower (one, two and three) space dimensions. They demonstrate analytically the generic limits which exploitation place on co-evolving multi-component amplification systems. In particular, there is an optimal diffusion (or migration) coefficient for cooperative amplification and minimal and maximal threshold values for stable cooperation. Over a bounded range of diffusion rates, the model also exhibits stable limit cycles. Furthermore, the co-operatively coupled system has a maximum tolerable error rate at intermediate rates of diffusion. A tractable model is thereby established which demonstrates that spatial effects can stabilize catalytic biological information. The analytic behaviour in infinite-dimensional simplex space is seen to provide a reasonable guide to the spatial dependence of the error threshold in physical space. Nanoscale possibilities for the evolution of catalysis on the basis of the model are outlined. We denote the modelling technique by PRESS, Probability Reduced Evolution of Spatially-discrete Species.

Evolutionary self-organization of cell-free genetic coding.

Genetic encoding provides a generic construction scheme for biomolecular functions. This paper addresses the key problem of coevolution and exploitation of the multiple components necessary to implement a replicable genetic encoding scheme. Extending earlier results on multicomponent replication, the necessity of spatial structure for the evolutionary stabilization of the genetic coding system is established. An individual-based stochastic model of interacting molecules in three-dimensional space is presented that allows the evolution of genetic coding to be analyzed explicitly. A massively parallel configurable computer (NGEN) is used to implement the model, on the time scale of millions of generations, directly in electronic hardware. The spatial correlations between components of the genetic coding system are analyzed and found to be essential for evolutionary stability.

Error threshold for spatially resolved evolution in the quasispecies model.

The error threshold for quasispecies in 1, 2, 3, and infinity dimensions is investigated by stochastic simulation and analytically. The results show a monotonic decrease in the maximal sustainable error probability with decreasing diffusion coefficient, independently of the spatial dimension. It is thereby established that physical interactions between sequences are necessary in order for spatial effects to enhance the stabilization of biological information. The analytically tractable behavior in an infinity-dimensional (simplex) space provides a good guide to the spatial dependence of the error threshold in lower dimensional Euclidean space.

Optically programming DNA computing in microflow reactors.

The programmability and the integration of biochemical processing protocols are addressed for DNA computing using photochemical and microsystem techniques. A magnetically switchable selective transfer module (STM) is presented which implements the basic sequence-specific DNA filtering operation under constant flow. Secondly, a single steady flow system of STMs is presented which solves an arbitrary instance of the maximal clique problem of given maximum size N. Values of N up to about 100 should be achievable with current lithographic techniques. The specific problem is encoded in an initial labeling pattern of each module with one of 2N DNA oligonucleotides, identical for all instances of maximal clique. Thirdly, a method for optically programming the DNA labeling process via photochemical lithography is proposed, allowing different problem instances to be specified. No hydrodynamic switching of flows is required during operation -- the STMs are synchronously clocked by an external magnet. An experimental implementation of this architecture is under construction and will be reported elsewhere.

End-specific covalent photo-dependent immobilisation of synthetic DNA to paramagnetic beads.

A novel approach for light-dependent covalent immobilisation of synthetic DNA oligomers to amino-coated paramagnetic beads is described. A hetero-bifunctional photo-reactive cross-linking chemical, 4-nitrophenyl 3-diazopyruvate, is applied to attach 5' amino-modified DNA to both silica and polystyrene paramagnetic beads. The coupling yields are comparable with similar methods in which no photo-reactive chemicals are used. The immobilised DNA on the polystyrene and silica beads was used efficiently in hybridisation experiments. An extension of this approach to light-directed immobilisation of specific DNA to beads, located at different positions in micro-flow reactors, opens up a range of integrated applications to complex diagnostics, evolutionary biotechnology and novel areas such as DNA computing.

Open problems in artificial life.

This article lists fourteen open problems in artificial life, each of which is a grand challenge requiring a major advance on a fundamental issue for its solution. Each problem is briefly explained, and, where deemed helpful, some promising paths to its solution are indicated.

Complex patterns predicted in an in vitro experimental model system for the evolution of molecular cooperation.

An isothermal biochemical in vitro amplification system with two trans-cooperatively coupled amplifying DNA molecules was investigated homogeneously using a hierarchy of kinetic models and as a simplified reaction-diffusion system. In our model of this recently developed experimental system, no reaction mechanism higher than second order occurs, yet numerical simulations show a variety of complex spatiotemporal patterns which arise in response to finite amplitude perturbations in a flow reactor. In a certain domain of the kinetic parameters the system shows self-replicating spots. These spots can stabilize the cooperative amplification in such evolving systems against emerging parasites. The results are of high relevance for experimental studies on these functional in vitro ecosystems in spatially resolved microstructured reactors.

In vitro evolution of molecular cooperation in CATCH, a cooperatively coupled amplification system.

BACKGROUND: One of the key issues in the investigation of evolution is how complex systems evolved from simple chemical replicators. Theoretical work proposed several models in which complex replicating systems are kinetically stabilized. The development of powerful isothermal amplification technique allows complex nucleic acid based evolving in vitro systems to be set up, which may then serve to verify experimentally current theories of evolution. Recently such a system based on the 3SR (self-sustained sequence replication) reaction has been established to investigate the evolution of cooperation: the trans-cooperatively coupled CATCH (cooperative amplification by cross hybridization). RESULTS: Over four rounds of serial transfer, the cooperatively coupled two species CATCH system evolved into a more complex cooperative four species system, which then was overgrown by CATCH-derived RNA-Z-like hairpin species. In contrast to the classical RNA-Z species, these molecules have complementary loop sequences and self-amplify using a dual mechanism that includes concentration-dependent phases of noncooperative and cooperative amplification. CONCLUSIONS: The evolution of a cooperative system, under conditions that were alternately unfavorable and favorable for cooperative amplification, led to a system showing facultative cooperation. This principle of facultative cooperation preserves the complexity of the system investigated and could have general implications for the evolution and stabilization of cooperation under oscillating reaction conditions.

Spatially resolved in vitro molecular ecology.

Sensitive CCD-based fluorescence detection has made spatially resolved studies of evolving cell-free molecular systems possible. In recent years our attention has focussed on making the transition to open and interacting spatially-resolved amplification systems using silicon microreactor technology and on providing a hardware platform for individual based simulation of such systems. Significant progress has been achieved in this direction. Open microflow reactors have been realized in zero (well-mixed), one and two dimensions with volumes small enough to allow long-time studies with limited biochemical materials. The primer directed 3SR reaction (amplifying DNA and RNA) has been used as a basis for constructing interacting model systems with both predator-prey and cooperative amplification character. Theoretical work has demonstrated the need for individual based modeling of such systems: a significant fraction of the population consists of distinct sequence polymers in any case. A massively parallel processor-configurable computer NGEN has been designed and constructed which allows the high speed simulation in hardware of relatively large populations of locally interacting individual strings of chosen length (e.g. up to 2000*2000 for 64 bases), in addition to its application as an evolvable hardware machine. Simulations show self-replicating spots to stabilize the cooperative amplification in evolving systems (a mechanism proposed by the author in 1994). Both oscillatory kinetics and pattern formation are expected in the experimental model systems under investigation which profoundly affect the course of evolution. Such in vitro model systems serve both to test current theories of cooperative evolution and provide clues for optimisation strategies in molecular biotechnology.

Cooperative amplification of templates by cross-hybridization (CATCH).

In vitro amplification systems not only serve as a tool for the processing of DNA, but have also provided important model systems for the investigation of fundamental issues in evolutionary optimization. In this work we present a coupled amplification system based on the self-sustained sequence replication (3SR), also known as nucleic acid sequence-based amplification (NASBA), which allows the experimental investigation of evolving molecular cooperation. The 3SR reaction is an isothermal method of nucleic acid amplification and an alternative to PCR. A target nucleic acid sequence can be amplified exponentially in vitro using two enzymes: reverse transcriptase (RT) and a DNA-dependent RNA polymerase (RNAP). A system has been constructed in which amplification of two molecular species is cooperatively coupled. These species are single-stranded (ss)DNA templates (D1 and D2) of lengths 58 and 68 nucleotides, respectively. Coupling occurs when D1 and D2 anneal to each other via a complementary region (DB and DB') situated at the 3' end of each template. RT elongates the hybridized templates producing a double-stranded (ds)DNA of 106 base pairs (bp). This double strand contains two promoters, which are situated on either side of, and directly adjacent to DB, and which are oriented towards each other. These promoters specify two RNA transcripts encompassing, respectively, the D1 and D2 portion of the dsDNA. After hybridization of two primers (P1 and P2) to the transcripts (R1 and R2) and reverse transcription, the ss templates D1 and D2 are regenerated. Amplification cycles of D1 and D2 are coupled cooperatively via the common dsDNA intermediate. Under optimized batch conditions the system shows the expected growth phases: exponential, linear and saturation phase. The enzymes of the 3SR cycle tend to misincorporate nucleotides and to produce abortive products. In future experiments, we intend to use the system for studies of evolutionary processes in spatially distributed systems where new strategies for optimization at the molecular level are possible.

A molecular predator and its prey: coupled isothermal amplification of nucleic acids.

BACKGROUND: A novel approach to the study of in vitro evolution is provided by the investigation of continuous, functionally coupled, amplifying systems. To date, in vitro evolution experiments have focused on issues of mutation and selection. Our work contributes to the new field of in vitro molecular ecology studies in which detailed information about the relationship between sequence changes and molecular interactions is obtained. Predator-prey systems are interesting in this context both in terms of evolutionary limits and in terms of the potential kinetic properties of oscillation and spatial pattern formation. Such molecular predator-prey models can be extended to a further negative-interaction mode, viral-host molecular evolution. RESULTS: A simple, nonfunctional predator-prey system based on the self-sustained sequence replication reaction is proposed. Coupling within the system is achieved using the single-stranded DNA intermediate of one cycle, the prey cycle, as primer for the second one, the predator cycle. Hybridization by complementary base pairing is the second order reaction step underlying the predation. Single steps of the whole reaction system have been investigated by radiolabeling. Each isolated subsystem operates according to the proposed reaction scheme, and evidence for an efficient coupling of both subsystems according to the proposed mechanism was found. CONCLUSIONS: Simple, interacting model systems based on nucleic acids can be designed and constructed for the study of coevolution. The results of studies such as the one described here will provide a basis for the construction of coupled systems of ribozymes, from which point the engineering of catalytic units for applications in biotechnology is feasible.

Monitoring the amplification of CATCH, a 3SR based cooperatively coupled isothermal amplification system, by fluorimetric methods.

Three different types of fluorescence detection methods were employed to monitor amplification of a previously established isothermal cooperatively coupled amplification system as it can serve as a tool for the investigation of fundamental issues in evolutionary optimization. By using 5'IRD-41 fluorescent labeled primers, the intercalating dye TOPRO-1 and a 5'fluorescin/3'DABCYL 4-(4-dimethylamino-phenylazo)benzoic acid labeled ss 24 nt DNA, evolving molecular cooperation is accessible, sequence specifically as well as non-sequence-specifically without using radioactivity.

Template-directed and template-free RNA synthesis by Q beta replicase.

In the absence of extraneously added templates, Q beta replicase produces different RNA species after long lag times spontaneously in vitro. The sequences of the spontaneous products are short (30 to 45 nucleotides) and bear little sequence relation to one another and no detectable sequence homology to Q beta virus RNA or to the host. Their replication rates are much lower than those of optimized products. Incubation without template in long closed capillaries produces after long lag times many separate RNA growth foci with heterogeneous kinetics. The template-free reaction is strongly dependent on the conditions: lowering the enzyme or the triphosphate concentrations abolishes the template-free RNA synthesis without affecting the template-dependent synthesis. An explanation of the emerging RNA species in template-free reactions by residual RNA contaminants in the incubation mixture is very unlikely in the light of the experimental evidence; however, the experimental evidence is fully compatible with a de novo mechanism (which may include instruction by non-replicatable oligonucleotides).

Images of evolution: origin of spontaneous RNA replication waves.

Self-replicating molecules set up traveling concentration waves that propagate in an aqueous enzyme solution. The velocity of each wave provides an accurate (+/- 0.1%) noninvasive measure of fitness for the RNA species currently growing in its front. Evolution may be followed from changes in the front velocity, and these differ from wave to wave. Thousands of controlled evolution reactions in traveling waves have been monitored in parallel to obtain quantitative images of the stochastic process of natural selection. An RNA polymerase (RNA-dependent RNA nucleotidyltransferase, EC 2.7.7.6), extracted from bacteria infected by the Q beta RNA virus, catalyzes the replication. The traveling waves that arise spontaneously without added RNA provide a model system for major evolutionary change.

RNA multi-structure landscapes. A study based on temperature dependent partition functions.

Statistical properties of RNA folding landscapes obtained by the partition function algorithm (McCaskill 1990) are investigated in detail. The pair correlation of free energies as a function of the Hamming distance is used as a measure for the ruggedness of the landscape. The calculation of the partition function contains information about the entire ensemble of secondary structures as a function of temperature and opens the door to all quantities of thermodynamic interest, in contrast with the conventional minimal free energy approach. A metric distance of structure ensembles is introduced and pair correlations at the level of the structures themselves are computed. Just as with landscapes based on most stable secondary structure prediction, the landscapes defined on the full biophysical GCAU alphabet are much smoother than the landscapes restricted to pure GC sequences and the correlation lengths are almost constant fractions of the chain lengths. Correlation functions for multi-structure landscape exhibit an increased correlation length, especially near the melting temperature. However, the main effect on evolution is rather an effective increase in sampling for finite populations where each sequence explores multiple structures.

Replication of viruses in a growing plaque: a reaction-diffusion model.

An understanding of the viral replication process commonly referred to as "plaque growth" is developed in the context of a reaction-diffusion model. The interactions among three components: the virus, the healthy host, and the infected host are represented using rates of viral adsorption and desorption to the cell surface, replication and release by host lysis, and diffusion. The solution to the full model reveals a maximum in the dependence of the velocity of viral propagation on its equilibrium adsorption constant, suggesting that conditions can be chosen where viruses which adsorb poorly to their hosts will replicate faster in plaques than those which adsorb well. Analytic expressions for the propagation velocity as a function of the kinetic and diffusion parameters are presented for the limiting cases of equilibrated adsorption, slow adsorption, fast adsorption, and large virus yields. Hindered diffusion at high host concentrations must be included for quantitative agreement with experimental data.

The equilibrium partition function and base pair binding probabilities for RNA secondary structure.

A novel application of dynamic programming to the folding problem for RNA enables one to calculate the full equilibrium partition function for secondary structure and the probabilities of various substructures. In particular, both the partition function and the probabilities of all base pairs are computed by a recursive scheme of polynomial order N3 in the sequence length N. The temperature dependence of the partition function gives information about melting behavior for the secondary structure. The pair binding probabilities, the computation of which depends on the partition function, are visually summarized in a "box matrix" display and this provides a useful tool for examining the full ensemble of probable alternative equilibrium structures. The calculation of this ensemble representation allows a proper application and assessment of the predictive power of the secondary structure method, and yields important information on alternatives and intermediates in addition to local information about base pair opening and slippage. The results are illustrated for representative tRNA, 5S RNA, and self-replicating and self-splicing RNA molecules, and allow a direct comparison with enzymatic structure probes. The effect of changes in the thermodynamic parameters on the equilibrium ensemble provides a further sensitivity check to the predictions.

Traveling waves of in vitro evolving RNA.

Populations of short self-replicating RNA variants have been confined to one side of a reaction-diffusion traveling wave front propagating along thin capillary tubes containing the Q beta viral enzyme. The propagation speed is accurately measurable with a magnitude of about 1 micron/sec, and the wave persists for hundreds of generations (of duration less than 1 min). Evolution of RNA occurs in the wavefront, as established by front velocity changes and gel electrophoresis of samples drawn from along the capillary. The high population numbers (approximately equal to 10(11], their well-characterized biochemistry, their short generation time, and the constant conditions make the system ideal for evolution experiments. Growth is monitored continuously by excitation of an added RNA-sensitive fluorescent dye, ethidium bromide. An analytic expression for the front velocity is derived for the multicomponent kinetic scheme that reduces, for a high RNA-enzyme binding constant, to the Fisher form v = 2 square root of kappa D, where D is the diffusion constant of the complex and kappa is the low-concentration overall replication rate coefficient. The latter is confirmed as the selective value-determining parameter by numerical solution of a two-species system.