Field of the invention

Biomolecular motors have been optimized by evolution to efficiently transport cargo ion the nanoscale for billions of years. This makes them very useful for nanotechnological applications. Some of these applications - such as biocomputation (1 ) - require a massive amount of filaments to be provided on-demand.

The invention provides a system and method for the multiplication of molecular-motor- propelled agents comprising a molecular-motor-propelled agent, at least one agent for stabilizing the molecular-motor-propelled agents, molecular motors, and monomers of the molecular-motor-propelled agents, wherein the number of the molecular-motor-propelled- agents increases exponentially by splitting them while they are transported on a surface of molecular motors; and the average length of the molecular-motor-propelled agents is kept substantially constant by growing said molecular-motor-propelled agents.

Background of the Invention

For nanotechnological applications of biomolecular motors, it is often necessary to provide a large amount of cytoskeletal filaments (actin filaments or microtubules). In many cases, it can be advantageous or even necessary to create the filaments on the fly while the device is running rather than assemble and add them during device fabrication.

Many different types of bio-nanotechnological devices such as diagnostic devices, detectors, simulators or computation devices have been conceived. For example, it was recently demonstrated that actin filaments and microtubules can solve mathematical problems by exploring a network of nanometer-sized channels (1 ). This is particularly interesting for solving combinatorial problems (including so called NP-complete problems), a class of problems that is difficult for conventional electronic computers to solve because the number of calculation operations necessary to solve these problems increases exponentially with problem size. In order to solve this problem more efficiently than conventional electronic computers,, it is necessary for the filaments to multiply exponentially while they traverse the network. Currently, cytoskeletal filaments are being grown separately and added to the motors in a stablilized form that cannot grow but do often shrink or break (2). All filaments needed for the device to work have to be added before the device performs its task. Also, a considerable margin needs to be added to account for shrinkage or breaking of the filaments. Thus the amount of filaments cannot flexibly adapt to the task at hand. This is especially critical in devices, where a large number of filaments is needed and where the entrance is small compared to the working area of the device.

Summary of the invention

In order to overcome the disadvantages of the prior art, the invention provides a new method to exponentially multiply cytoskeletal filaments for nanotechnological applications. In particular, cytoskeletal filaments are being multiplied while they are moving through the nanotechnological device. Thus, their number can flexibly adapt to the available area as needed.

The invention provides a system and method for multiplication of the filaments. In a preferred embodiment, the system and method of the invention provide a combination of monomers added for filament growth with conditions that cause filaments to split. This leads to an exponential increase in filament number while the average length of individual filaments stays substantially constant. This exponential growth can be achieved in an artificial environment such as a nanotechnological device. Furthermore this exponential growth can be achieved while the filaments are being propelled by molecular motors.

Two alternatives for multiplication of filaments are provided according to the invention:

Alternative 1 All-in-one multiplication: By adding monomers to a solution, filaments self- assemble and grow while they are being transported through the device by biomolecular motors. In addition to the monomers, an agent, such as an enzyme is added, that splits the filaments. The concentrations of the monomers and the enzyme are optimized such that the average length of the filaments stays substantially constant over time while their number increases exponentially. The choice and concentration of the enzyme is optimized such that filaments grow normally without significant defects.

Alternative 2 Two-step multiplication: In the first step, a growing solution is added to the device that contains monomers for filament growth. In a second step, a splitting solution with buffer conditions or enzymes that facilitate breaking of the filaments is flushed through the device. These two steps are repeated and the monomer concentration and/or the incubation time are adjusted such that the number of filaments doubles every flush cycle, while their average length stays substantially constant. Thus, the filaments are being multiplied while they are transported by molecular motors through the device.

Brief description of the drawings

Figure 1 shows a conceptual drawing of the invention. Cytoskeletal filaments are grown from monomers. The grown filaments are split enzymatically or by appropriate buffer conditions. The combination of these two processes leads to an exponential increase in filament number.

Figure 2 shows a diagram displaying the length distribution of microtubules within one microscopic field of view (size 82x82 urn ² ) after certain time points of the multiplication process. The control shows the distribution in a neighbouring channel without addition of the multiplication solution.

Figure 3 shows a cross-section (20) through a channel of the device (10) typical for use of microtubules as the molecular-motor-propelled agents, comprising a Si (silicium) layer (21 ), Si0 ₂ (silicium oxide) layers (22), an Au (gold) layer (23), Ti (titanium) layers (24), motor proteins (25) and PEG (26).

Figure 4 shows a cross-section (30) through a channel of the device (10) typical for use of actin filaments as the molecular-motor-propelled agents, comprising a Si0 ₂ layer (31 ); a poly(methyl methacrylate) (PMMA) layer (32); a trimethylchlorosilane (TMCS) layer (33) and myosin motor proteins (34).

Figure 5A illustrates schematically a computation network for the Subset Sum Problem

S = {2, 5, 9}.

Figures 5B and 5C present the solving of the Subset Sum Problem S = {2, 5, 9} by using actin filaments as molecular-motor-propelled agents (left column) and microtubules (right column). Figure 5B shows the experimental results obtained from 2251 actin filaments (total experiment time: 26 min) and Figure 5C shows the experimental results obtained from 179 microtubules (total experiment time: 180 min). Error bars represent the counting error (Vn). Detailed description of the invention

The present invention provides a system for the multiplication of molecular-motor-propelled agents comprising

- a molecular-motor-propelled agent,

- at least one agent for stabilizing the molecular-motor-propelled agents,

- molecular motors, and

- monomers of the molecular-motor-propelled agents,

wherein

the number of the molecular-motor-propelled-agents increases exponentially while they are transported on a surface of molecular motors; and

the average length of the molecular-motor-propelled agents is kept substantially constant by growing and splitting said molecular-motor-propelled agents.

In a further embodiment, the present invention comprises a method for exponential multiplication of the number of molecular-motor-propelled agents, said method comprising the addition of a filament growth solution and a splitting solution or a combined filament growth and splitting solution to a system, comprising

- a molecular-motor-propelled agent,

- at least one agent for stabilizing the molecular-motor-propelled agents,

- molecular motors, and

- monomers of the molecular-motor-propelled agents,

wherein

the number of the molecular-motor-propelled-agents increases exponentially while they are transported on a surface of molecular motors; and

the average length of the molecular-motor-propelled agents is kept substantially constant by growing and splitting said molecular-motor-propelled agents. Generally, the average length of the molecular-motor-propelled agents is suitably greater than 0.02 μηι, more suitably in the range of 0.1 to 200 μηι, preferably in the range of 0.2 to 20 μηι or 0.3 to 10 μηι. More preferably, the average length of the molecular-motor-propelled agents is in the range of 0.3 to 9 μηι, 0.3 to 8 μηι, 0.3 to 7 μηι or 0.3 to 6 μηι. Most preferably, the average length of the molecular-motor-propelled agents is in the range of 0.5 to 5 μηι.

Particular ranges for the average length of the molecular-motor-propelled agents apply to actin filaments and microtubules.

The average length of actin filaments as the molecular-motor-propelled agents is suitably greater than 20 nm, preferably in the range of 0.2 to 50 μηι, more preferably in the range of 0.4 to 5 μηι. Most preferably, the average length of actin filaments as the molecular-motor- propelled agents is at 0.5-2 μηι.

The average length of microtubules as the molecular-motor-propelled agents is suitably greater than 20 nm, more suitably in the range 0.3 to 200 μηι, preferably in the range of 0.4 to 20 μηι, more preferably in the range of 0.5 to 5 μηι. Most preferably, the average length of microtubules as the molecular-motor-propelled agents is in the range of 0.5 to 2 μηι.

In a further preferred embodiment, the minimum length of the molecular-motor-propelled agents is 0.05 μηι, 0.1 μηι or 0.5 μηι because shorter filaments would move unpredictably and thus give erroneous solutions.

Keeping the average length of the molecular-motor-propelled agents substantially constant means that a starting amount of the molecular-motor-propelled agents is added to the system or when performing the method according to the invention. Suitably, at least one filament is added as the starting amount of the molecular-motor-propelled agent used in the system or method of the invention. The starting amount of the molecular-motor-propelled agents is more suitably in the range of 1 to 10 ¹⁷ filaments, preferably in the range of 1 to 10 ¹⁰ filaments, more preferably in the range of 1 to 100.000 filaments, and most preferably in the range of 1 to 1000 filaments of said molecular-motor-propelled agents. These starting filaments of said molecular- motor-propelled agents are then allowed to grow. Growing of said molecular-motor-propelled agents is achieved by increasing the length of filaments, such as of actin filaments or microtubules, by continuous addition of their respective monomers to the filaments, suitably by self-assembly. The so growing molecular-motor-propelled agents are continuously split by a splitting agent in order to exponentially increase their number while keeping the average length of said molecular-motor-propelled agents in the preferred ranges as described above.

Suitably, the molecular-motor-propelled agents in the system and method of the invention are filaments. Preferably, said molecular-motor-propelled agents are selected from microtubules and actin filaments. Most preferably, the molecular-motor-propelled agents are microtubules. In another most preferred embodiment, the molecular-motor-propelled agents are actin filaments.

Microtubules are a component of the cytoskeleton and are found in eukaryotic cells. Microtubules are tubular polymers made up of dimers of alpha and beta tubulin. They can grow as long as 200 μηι and are highly dynamic. The outer diameter of a microtubule is about 24 nm while the inner diameter is about 12 nm.

Microtubules provide platforms for intracellular transport and are involved in a variety of cellular processes, including the movement of secretory vesicles, organelles, and intracellular macromolecular assemblies.

When microtubules are used as the molecular-motor-propelled agents in the system and method of the invention, the molecular motors in said system are suitably selected from proteins from the kinesin family and/or the dynein family. Preferably, according to the invention, the molecular motor in said system is a kinesin. More preferably, the molecular motor in said system is a kinesin of the kinesin families 1 -12 or 14-15.

A kinesin is a protein belonging to a class of motor proteins found in eukaryotic cells. Kinesins move along microtubule filaments, and are powered by the hydrolysis of adenosine triphosphate (ATP). Kinesin moves cargo inside cells away from the nucleus along microtubules.

Dynein is a motor protein in cells, which converts the chemical energy contained in ATP into the mechanical energy of movement. Dynein transports various cellular cargo towards the minus-end of the microtubule, which is usually oriented towards the cell center, i.e. towards the cell nucleus.

When actin filaments are used as the molecular-motor-propelled agents in the system and method of the invention, the molecular motors in said system are suitably selected from proteins of the myosin family, preferably from myosin-l, myosin II or myosin XI.

Myosins comprise a family of ATP-dependent motor proteins, which play a role in muscle contraction and in a wide range of other motility processes in eukaryotes. They are responsible for actin-based motility. Most myosin molecules are composed of a head, neck, and tail domain, wherein the head domain binds the filamentous actin, and uses ATP hydrolysis to generate force and to walk along the actin filament, the neck domain acts as a linker and as a lever arm for transducing force generated by the catalytic motor domain and the tail domain generally mediates interaction with cargo molecules and/or other myosin subunits. The tail domain may also play a role in regulating motor activity.

Myosin I, a ubiquitous cellular protein, which operates as monomer e.g. in vesicle transport. It has a step size of 10 nm.

Myosin II is responsible for producing muscle contraction in muscle cells.

Myosin XI can be found in plants such as Chara where it is responsible for producing cytoplasmic streaming

In a particular embodiment of the invention, the number of the molecular-motor-propelled- agents increases exponentially while the agents are transported on a surface of molecular motors. To achieve this, said molecular-motor-propelled-agents are split.

The splitting can for example be performed using mechanical forces or biological agents.

When the splitting is performed using mechanical forces, techniques like sonication, laser cutting, laser ablation, or vortexing can be used.

Preferably, the splitting is performed using biological agents. More preferably, the splitting is by an agent selected from a salt, ATP, an enzyme, or actin fragmenting myosin molecules. When the molecular-motor-propelled agents used in the system of the invention are actin filaments, the splitting agent is preferably a severing enzyme selected from the actin-binding proteins gelsolin or cofilin.

Cofilin belongs to a family of actin-binding proteins which disassembles actin filaments. Three highly conserved and highly identical genes belonging to this family have been found in humans: CFL1 , coding for cofilin 1 (other tissues than muscle, or n-cofilin), CFL2, coding for cofilin 2 (in muscle tissue: m-cofilin), and ADF (actin depolymerizing factor).

Accordingly, when the molecular-motor-propelled agents used in the system of the invention are actin filaments, the splitting agent is preferably a severing enzyme selected from cofilin 1 , cofilin 2 and ADF.

Gelsolin is an actin-binding protein that is a key regulator of actin filament assembly and disassembly. Gelsolin is located intracellularly (in cytosol and mitochondria) and extracellularly in blood plasma. Thus, in a further most preferred embodiment, when the molecular-motor-propelled agents used in the system of the invention are actin filaments, the splitting agent is preferably gelsolin. Alternatively, a low salt solution with low magnesium concentration or localized areas with non- muscular myosin may achieve actin filament splitting

When the molecular-motor-propelled agents used in the system of the invention are microtubules, the splitting agent is preferably a severing enzyme. More preferably, said severing enzyme is selected from spastin or katanin. Most preferably, said severing enzyme is spastin. Even most preferably, said severing enzyme is katanin.

Spastin and katanin are ATPases and function as a microtubule-severing enzyme. Both enzymes contain a 60 kDa ATPase subunit, which requires ATP and the presence of microtubules for activation.

In a further particular embodiment of the system of the invention, the average length of the molecular-motor-propelled agents is kept substantially constant by regrowing said molecular- motor-propelled agents after splitting. To achieve this, monomers of the molecular-motor- propelled agents are included into the system of invention.

When microtubules are used as the molecular-motor-propelled agents in the system of the invention, the monomers provided in said system are tubulin monomers, in particular alpha and beta tubulin monomers, most suitably a 1 :1 mixture of alpha and beta tubulin monomers.

When actin filaments are used as the molecular-motor-propelled agents in the system of the invention, the monomers provided in said system are suitably G-actin monomers.

In the method the invention, a filament growth solution and a splitting solution or a combined filament growth and splitting solution may be added.

In a further embodiment, the system and method of the invention comprise an agent for stabilization of the molecular-motor-propelled agents.

When the molecular-motor-propelled agents are actin filaments, the filament growth solution preferably comprises G-actin monomers, and an agent for stabilization of the actin filaments. More preferably, the filament growth solution comprises G-actin monomers.

The concentration of G-actin monomers, in the growing solution is suitably in the range of 1 fM to 1 mM, more suitably in the range of 1 nM to 10 μΜ, preferably in the range of 10 nM to 750 nM, most preferably in the range of 20 nM to 500 nM. When the molecular-motor-propelled agents are actin filaments, the agent for stabilization of the actin filaments in the system and method of the invention is preferably phalloidin, more preferably fluorescent phalloidin.

Phalloidin belongs to a class of toxins called phallotoxins, which are found in the death cap of the fungus Amanita phalloides. It functions by binding and stabilizing filamentous actin (F-actin) and effectively prevents the depolymerization of actin filaments. Due to their tight and selective binding to F-actin, derivatives of phalloidin containing fluorescent tags are used widely in microscopy to visualize F-actin in biomedical research.

The concentration of the stabilizing agent, phalloidin or fluorescent phalloidin, in the growing solution is suitably in the range of 1 fM to 1 mM, more suitably in the range of 1 nM to 20 μΜ, preferably in the range of 1 nM to 1 .5 μΜ, most preferably in the range of 2 nM to 1 μΜ.

In the system and method of the invention, G-actin monomers and the agent for stabilizing the molecular-motor-propelled agents may be added simultaneously or pulse-wise. Preferably, G- actin monomers and phalloidin are added simultaneously. Even preferably, G-actin monomers and phalloidin are added pulse-wise.

In a preferred embodiment, the splitting solution of the method of the invention comprises a severing enzyme selected from cofilin 1 , cofilin 2, gelsolin or ADF and/or a low-salt and/or a low-[ATP] solution.

The concentration of severing proteins, such as cofilin 1 , cofilin 2, gelsolin or ADF, in the splitting solution is suitably in the range of 1 fM to 1 mM, more suitably in the range of 1 nM to 2 μΜ, preferably in the range of 5 nM to 1 .5 μΜ, most preferably in the range of 10 nM to 500 nM.

The concentration of the severing protein gelsolin in the splitting solution is suitably in the range of 1 fM to 1 mM, more suitably in the range of 1 pM to 1 μΜ, preferably in the range of 2 pM to 500 nM, most preferably in the range of 5 pM to 200 nM.

Low-[ATP] concentration means an ATP concentration <1 mM, preferably, <0.6 mM, more preferably <0.3 mM, most preferably <0.1 mM.

The low-salt solution contains suitably low concentrations of salts such as KCI or NaCI and low concentrations of MgCI ₂ . Low concentrations of salts such as KCI or NaCI means concentrations of these salts <80 mM, more preferably <60 mM, most preferably <40 mM.

Low concentration of MgCl2 means concentrations of MgCl2 <10 mM, preferably, <5 mM, more preferably <2 mM, most preferably <1 mM. More preferably, the splitting solution comprises the severing enzyme gelsolin. Even more preferably, the splitting solution comprises the severing enzyme cofilin 1 and/or cofilin 2. Most preferably, the splitting solution comprises the severing enzyme ADF. Even most preferably the splitting solution facilitates the breaking of actin filaments by modification of the salt concentration or ATP concentration.

In order to achieve the splitting of the actin filaments, a severin enzyme is added and/or the salt concentration is changed from 70 mM to a low-salt solution within the ranges as described above and/or the ATP concentration is changed from 1 mM to a low ATP concentration within the ranges as described above.

The concentration of severing enzyme is suitably titrated (within the concentration ranges given above) to the actin filament density to achieve actin filament lengths in the desired range of 0.5 to 2 μπι.

The concentration of ATP, salt and magnesium chloride is suitably adjusted (within the concentration ranges given above) to achieve actin filament lengths in the desired range of 1 ίο 2 μηι.

In a further preferred embodiment of the method of the invention, the molecular-motor- propelled agents are microtubules and the combined filament growth and splitting solution comprises tubulin monomers, in particular alpha and beta tubulin monomers, most suitably a 1 :1 mixture of alpha and beta tubulin monomers; an agent for stabilization of the microtubules, a severing enzyme and ATP.

The agent for stabilization of the microtubules is suitably selected from a GTP analog, paclitaxel and/or kip2p. Preferably, the agent for stabilization of the microtubules is a GTP analog. Even preferably, the agent for stabilization of the microtubules is a non-hydrolysable or slowly-hydrolysable GTP analog. Even more preferably, the agent for stabilization of the microtubules is paclitaxel. Most preferably, the agent for stabilization of the microtubules is kip2p.

Kip2p is a kinesin-related protein, which stabilizes microtubules and is required as part of the dynein-mediated pathway in nuclear migration in eukaryotic cells.

The severing enzyme is in the splitting solution is preferably selected from spastin and katanin. More preferably, the severing enzyme comprised in the splitting solution is spastin. Even more preferably, the severing enzyme comprised in the splitting solution is katanin.

In a preferred embodiment, the splitting solution facilitates the breaking of the microtubules by modification of the spastin or katanin concentration or the ATP concentration. Most preferably, the cutting frequency of spastin is adjusted by variation of the concentration of spastin or of ATP.

The ATP concentration in the splitting solution for splitting microtubules is suitably in the range of 1 nM to 1 M, more suitably in the range of 0.005 mM to 50 mM, preferably in the range of 0.05 to 5 mM, more preferably in the range of 0.08 to 3 mM, most preferably in the range of 0.1 to 2 mM. Even most preferably, the ATP concentration used in the splitting solution for microtubules is 1 mM.

The concentration of severing enzyme, such as spastin or katanin, in the splitting solution is suitably in the range of 1 fM to 1 mM, more suitably in the range of 1 nM to 1 μΜ, preferably in the range of 10 nM to 750 nM, most preferably in the range of 20 nM to 500 nM, even most preferably in the range of 40 nM to 250 nM.

The concentration of severing enzyme is suitably titrated (within the concentration ranges given above) to the microtubule density to achieve microtubule lengths in the desired range of 0.5 to 2 μπι.

The method of the invention can be described in general ways as follows:

All-in-one multiplication: One possibility to multiplicate cytoskeletal filaments, while being transported on a surface by biomolecular motors, is to add monomers and severing enzymes simultaneously.

In the first step, a so-called 'gliding motility assay' is set up, which is commonly used for biophysical and nanotechnological assays. Thereby, a solution comprising motor proteins as well as a solution comprising the molecular-motor-propelled agents is flushed into a channel of the device (10). Each solution is incubated for, e.g. 1 to 10 minutes, preferably 2 to 8 minutes, more preferably 3 to 7 minutes, most preferably 5 minutes in order to let the proteins adsorb to the surface.

In the next step, after imaging the gliding molecular-motor-propelled agents, the multiplication solution is added to the channel. This solution suitably comprises monomers of the molecular- motor-propelled agents, GTP and/or ATP, an agent for stabilizing the elongated molecular- motor-propelled agents, a severing enzyme as well as oxygen scavenging agents. The device is then heated to a temperature in the range of 25 °C to 37 ^< Ό, e.g. by a peltier element. The process of elongation of the molecular-motor-propelled agents is now starting. The cutting frequency of the severing enzyme can be adjusted by varying the concentration of the enzyme itself or of ATP and/or GTP. Two-step multiplication: Another possibility to multiplicate cytoskeletal filaments, while being transported on a surface by biomolecular motors, is to add a filament growth solution and a splitting solution in an alternating manner.

Filament growth in a gliding assay is achieved by adding monomers of the molecular-motor- propelled agents into the assay solution. In order to stabilize the filaments a stabilizing agent needs to be added to the solution. This can be done either i) simultaneously with filament elongation, i.e. by adding the stabilizing agent at the same time as monomers of the molecular- motor-propelled agents or ii) by pulse-wise addition of monomers of the molecular-motor- propelled agents and the stabilizing agent in sequence, e.g. with 10 min incubation of the monomers of the molecular-motor-propelled agents followed by 2-5 min incubation with the stabilizing agent, followed by 10 min incubation with monomers of the molecular-motor- propelled agents etc.

In both cases, a buffer solution with salt or ATP conditions that facilitate breaking of the actin filaments is flushed through the device after elongation. These two and three steps, respectively, are repeated and the monomer concentration/incubation time are adjusted such that the number of filaments doubles every flush cycle, while their average length stays substantially constant.

For certain applications it may be necessary (for example to prevent errors in the calculation result of a biocomputation network) to ensure that filaments can grow but no new filaments are formed (so called seeding) at random. In that case, it is necessary to carefully tune the concentration of monomers and stabilizing agent such that the monomer concentration remains below the critical concentration necessary for seed formation.

For both tubulin and actin there exists a critical concentration (~10 μΜ for tubulin and -250 nM for actin, see references 3 and 4) below which existing filaments are elongated but no new filaments are being formed. This is analogous to a crystallization process where without a seed, no crystallization takes place but when a small seeding crystal is added, the seed will grow into a large crystal. Thus by keeping the concentration of tubulin and actin below the respective critical concentrations, it can be ensured, that existing filaments can grow but no new filaments can be formed.

Accordingly, the invention provides a system and method, wherein the concentration of tubulin and actin in the respective filament growth solution is kept below the respective critical concentrations, so that existing filaments can elongate but no or only negligible amounts of new filaments are formed. Examples of the invention

Example 1 : All-in-one multiplication of microtubules

One possibility to multiplicate cytoskeletal filaments, while being transported on a surface by biomolecular motors, is to add monomers and severing enzymes simultaneously. This process is described below for microtubules in detail.

In the first step, a so-called 'gliding motility assay' was set up, which is commonly used for biophysical and nanotechnological assays. Thereby, a 0.5 mg/ml casein, a 2 μg ml kinesin-1 as well as a 100 nM microtubule solution (all in the buffer BRB80, pH=6.9) were flushed consecutively into a channel of the device. Each solution was incubated for 5 minutes in order to let the proteins adsorb to the surface.

In the next step, after imaging the gliding microtubules, the multiplication solution was added to the channel. This solution contained (in BRB80): 1 .6 μΜ tubulin, 1 mM GTP, 1 mM ATP, 4 mM MgCI ₂ , 10 μΜ paclitaxel, 40 nM spastin as well as oxygen scavenging agents. The device was heated to 28°C by a peltier element. Alternatively a solution with 5 μΜ tubulin, 1 mM GTP, 2 mM ATP, 75 nM kip2p, 40 nM spastin and oxygen scavenging agents was used, in which the kinesin-like protein kip2p stabilized the elongated microtubules (instead of paclitaxel) and slightly increased the growth rate without increasing the nucleation of new microtubules. The cutting frequency of spastin can be adjusted by varying the concentration of the enzyme itself or of ATP.

The diagram below displays the length distribution of microtubules within one microscopic field of view (size 82x82 μηι ² ) after certain time points of the multiplication process. The control shows the distribution in a neighboring channel without addition of the multiplication solution.

Example 2: Two-step multiplication of actin filaments

One possibility to multiplicate cytoskeletal filaments, while being transported on a surface by biomolecular motors, is to add a "filament growth" solution and a "splitting" solution in an alternating manner. This process is described below for actin filaments in detail.

Filament growth in a gliding assay is achieved by adding G-actin monomers into the assay solution at G-actin concentrations in the range 0.1 -1 μΜ to minimize formation of newly nucleated actin filaments (F-actin). In order to stabilize the filaments and fluorescence label them, a fluorescent phalloidin, e.g. rhodamine-phalloidin or Alexa-488 phalloidin needs to be added to the solution. This can be done either 1 . simultaneously with filament elongation, i.e. by adding fluorescent phalloidin at the same time as G-actin or 2. by pulse-wise addition of G- actin and fluorescent phalloidin in sequence, e.g. with 10 min incubation of G-actin followed by 2-5 min incubation with fluorescent phalloidin, followed by 10 min incubation with G-actin etc.

If fluorescent phalloidin and G-actin are added simultaneously (alternative 1 ), it will appreciably increase the risk for nucleation of new filaments because phalloidin lowers the critical G-actin concentration for new F-actin formation. However, importantly, the newly nucleated actin filaments are initially so small that, if they form on a motility assay surface, they will rapidly detach in the presence of ATP due to the non-processive nature of fast myosin II from muscle, i.e. with short fractional time spent by the myosin in actin binding states. Furthermore, with myosin driven actin motility only in nanometer-sized channels, filaments newly nucleated in solution are unlikely to enter the channels.

With pulse-wise sequential addition (alternative 2) of G-actin at (0.1 -1 μΜ concentration) for filament elongation and fluorescent phalloidin for stabilization and fluorescence labelling, the risk for formation of newly nucleated filaments is appreciably reduced. The filaments will elongate in the absence of phalloidin, keeping a high critical G-actin concentration for formation of new filaments. Phalloidin is added in a separate pulse.

In both cases, a buffer solution with salt or ATP conditions that facilitate breaking of the actin filaments is flushed through the device after elongation. These two and three steps, respectively, are repeated and the monomer concentration/incubation time are adjusted such that the number of filaments doubles every flush cycle, while their average length stays constant.

Example 3: Computation of the Subset Sum Problem using actin and microtubule filaments

A potential application of exponentially multiplying cytoskeletal filaments is the solving of combinatorial mathematical problems with network based biocomputation. Combinatorial problems include important practical problems such as network routing, chip layout verification and protein folding. These problems are particularly hard to solve with conventional, serially operating computers, because they require the computation of an exponentially growing number of potential solutions and therefore the computation time required by a conventional computer to solve these problems grows exponentially with problem size. In contrast, in a network based biocomputer, each cytoskeletal filament computes one solution and therefore not the computation time but the required number of filaments grows exponentially. As an example that demonstrates operational functionality, the bio-computation system is applied to a benchmark classical NP-complete problem, the Subset Sum Problem. This problem asks whether, given a set S = {si , s ₂ , ...SN} of N integers, there exists a subset of S whose elements sum to a target sum, T. More formally, the question is whether there is a solution T =∑ _{= 1} WjSj where w _t e {0,1), for any given T from 0 to ∑ ₌₁ Sj . To find all possible subset sums by exploring all possible subsets requires the testing of 2 ^N different combinations, which - even for modest values of N - is impractical on electronic computers because of exponentially- increasing time requirements.

The network encoding the Subset Sum Problem is designed in a way that molecular-motor- propelled agents are guided uni-directionally downwards by the channels in vertical or diagonal directions Figure 5A illustrates schematically a computation network for the Subset Sum Problem S = {2, 5, 9}. The molecular-motor-propelled-agents enter the network from the top-left corner. Filled circles represent split-junctions where it is equally probable that molecular-motor-propelled agents continue along their straight path or turn. Empty circles represent pass-junctions where molecular-motor-propelled agents continue along their straight path. Moving diagonally down at a split-junction corresponds to adding that integer (number 2 and 9 for the marked path). The actual value of the integer potentially added at a split-junction is determined by the number of rows of junctions until the next split-junction. The exit numbers correspond to the target sum T (potential solutions) represented by each exit; correct results for this particular set S = {2, 5, 9} are labeled with bold numbers.

Figure 5B and 5C presents the solving of the Subset Sum Problem S = {2, 5, 9} by using actin filaments as molecular-motor-propelled agents (Fig. 5B) and microtubules (Fig. 5C). In particular, cytoskeletal filaments (actin filaments and microtubules), which are propelled by molecular motors (myosin II and kinesin-1 , respectively) along a surface in so-called gliding motility assays (6, 7) were used. Both kinds of cytoskeletal filaments have small diameters (approx. 1 0 nm for actin filaments and approx. 25 nm for microtubules) and move at high speeds (5-1 0 μηη s-1 for actin filaments driven by myosin II and approx. 0.5-1 μηη s- 1 for microtubules driven by kinesin-1 ). The filaments are guided uni-directionally (8, 9) along lithographically defined channels (Figures 3 and 4) that are functionalized with molecular motors and whose roofs are open to supply the motors with biochemical fuel (adenosine-5'-triphosphate, ATP) by diffusion from the surrounding buffer fluid (10, 1 1 ), allowing for a distributed energy supply. To ensure the lateral confinement of the cytoskeletal filaments, the width of the channels was set to below 200 nm and 250 nm, for actin filaments and microtubules, respectively. Figure 5B shows the experimental results obtained from 2251 actin filaments (total experiment time: 26 min) and Figure 5C shows the experimental results obtained from 179 microtubules (total experiment time: 180 min). Error bars represent the counting error (Vn). Total experiment time refers to the time required for the given number of agents to enter and traverse the network. It must be noted that the overall performance of the microtubule device was slightly inferior to the actin device due to a fabrication-based obstruction in a channel leading to exit 1 1 (see Fig. 5A) (causing a lower number of filaments reaching this exit) and a number of filaments landing at random points of the network in the channels where they were transported with high probability by the processive kinesin motors (increasing the number of filaments reaching the wrong exits). Both problems can be remedied by avoidance of fabrication errors and microfluidic focusing of the filaments in solution to the landing zones, respectively. In Figure 5B and 5C, shaded bars represent correct results.

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