5. The cell level The cell level involves phenomena occurring within the cell on the size scale up to the µm (or even tens of µm) and on the typical timescale of msec-sec. The time scale here cited is only indicative: in the reality the cell physiology can occur on a much larger timescale, including hours or days. However, he we will consider mainly the processes included in the field of the “molecular biology”, i.e. interactions between molecules, their diffusion through the cell compartments and subsequent modification of the cell compartments. On the experimental point of view, all of these heavily rely on the (G)FP technology, that was already introduced in Section 3. On the theoretical point of view, this level is much less studied than the other levels and there are a few techniques that can interpret the experimental data. 5.1 (G)FP based visualization techniques The principles of visualization of proteins in living cells with fluorescence microscopy was already introduced in Section 3: the protein to be monitored is tagged with a fluorescent protein of the family of (G)FPs. The tagging is done at the DNA level: the (G)FP genes are integrated into the cell genome into specific locations, so that the living cell express the fluorescent tagged protein instead of the bare protein. The tagged proteins and their motion can then be visualized within the cell with the (confocal)fluorescence microscopy techniques reported in Section 3. Technique Scheme Visualization Fluorescent Labeling The protein to be monitored is labeled with a (G)FP and visualized with fluorescence microscopy techniques. Multi-color labeling is possible using different FPs to tag different proteins

Co-localization When two different proteins localizing in the same cell compartment are tagged with FPs of two different colors, if FRET does not occur, the detected emission will be the sum of the two (green + red = yellow)

FRET (Fluorescence Resonant Energy Transfer) In similar conditions as those of co-localization, if the two proteins interact and FRET occurs only the emission of the acceptor will be detected

FRAP (Fluorescence Recovery After Photobleaching) An area with tagged proteins is photobleached and the fluorescence recovery is measured. Recovery occurs by diffusion of unbleached proteins from adjacent areas

FLIP (Fluorescence loss in Photobleaching) Similar to FRAP, but the bleaching is made repeatedly with pulsed radiation and the loss of fluorescence in a region out of the bleaching region is measured

FLAP (Fluorescence Localization After Photobleaching) The protein is tagged with two FPs, one is bleached, the signal from the second can be used to follow the tagged protein after photobleaching

PA (Photo Activation) The proteins to be monitored are tagged with proteins initially dark or completely photobleached. Then an area is photo-activated (or re-activated) and the diffusion is followed

PC (Photo Conversion) The proteins are tagged with photoconvertible (changing color upon irradiation) FPs. A restricted area is potoconverted and diffusion observed

FISHC (Fluorescence in situ hybridization) A DNA short sequence complementary to the seq to be analyzed is labeled Afted denaturation, it will hybridize with the part of DNA of interest and indicate its location

Table 5.1 The main (G)FP based visualization techniques Apparently, no change in the cell physiology occurs as a consequence of proteins tagging: the GFP are rather inert proteins, although their size might change a little the diffusion constants of the tagged protein, if its size is comparable. The main (G)FP based visualization techniques are reported in Table 5.1, with a schematic explanation and illustrations[1-4]. Apart for the already described FRET, all the others techniques are based on some specific photodynamic properties of the FPs: photobleaching (FRAP, FLIP, FLAP), photo (re)activation, i.e. the properties of some FPs to enhance or recover their

fluorescence after bleaching for illumination at specific wavelengths (PA) or to change color (PC). The measured properties are generally the diffusion constants within or across the cell compartments. A great amount of information can be obtained. The cell structures can be clearly visualized. Interactions among proteins within cells can be detected and the proteins motions and diffusion as a consequence of stimuli can be monitored. In principle, the resolution limit of these techniques is the single protein (~nm). However there are many practical problems that have prevented reaching this limit up to now. The (G)FP fluorescence is very weak, and groups of at least 10-100 proteins are necessary to be visible. Additionally, on the millisecond(microsecond) timescale the fluorescence of the FPs is not continuous, but displays irregular blind periods. This phenomenon is called blinking (flickering) and is thought to be due to the temporary transition to metastable dark states that have not been identified, yet. An hypothesis for blinking involves the zwitterionic state of the chromophore (see Sec 2), while flickering might to involve a neutral state of the chromophore different from A and from the photoswitching dark state. A “state of the art” scheme of the (G)FP states is reported in Fig 5.1, but it should be kept in mind that many of these states are still hypothetical.

Fig 5.1 A possible scheme for the (G)FP states. A, I and B are commonly accepted, while the interpretation/structure of all the others is only hypothetical. Z is sometimes indicated as the state responsible for blinking, and A’ might be involved in flickering. 5.2 Theory: the first order dynamics scheme for the GFP states The kinetic of the transition between the states can be described by a system of first order equations

dx1/dt=k11x1+k12x2+…+k1nxn . . . dxn/dt=kn1x1+kn2x2+…+knnxn where xi are the population of the states and the k are combinations of the kinetic constants. The system can be written in matrix form as dX/dt=K X and the solution can be found diagonalizing

the K matrix: the eigenvector XI will evolve with a first order dynamics

XI(t)=XI,0 exp(-KI t) where KI is the corresponding eigenvalue. This simple theory will be illustrated by a couple of examples.

1. The equilibrium between A and B states. Referring to Fig. 5.2, the thermal equilibrium between A and B state is described by the system

dnA/dt= - nA kAB + nB kBA dnB/dt= +nA kAB – nB kBA If the population are initially out of equilibrium, the equilibrium is reached exponentially with a

time constant 1/(kAB+kBA). The ratio between equilbrium populations is nA/nB=kBA/kAB.

(a)

(b)

Fig 5.2 (a) The scheme of the equilibrium between states A and B in GFPs (b) The time evolution of the populations and of the spectrum. In the model kAB=10-3ns-1 kBA=10-1ns-1 2. The photoswitching (photobleaching and reactivation) In this case the dark state C enters the scheme. The system of equations is

dnA/dt = -(KAB+kA) nA + kBA nB + kAt nAt dnB/dt = +kAB nA – kBA nB dnAt/dt= +kA nA - kAt nAt where KAB=kAB+kA*B*. Photobleaching is obtained by excitation on A, thus one has kA*B*>KBA, KAB kA>kAt. Re-activation is obtained by exciting on C, thus one has kA*B*<<kAB kAt>kA. Using these relationships between kinetic constans one has the behavior described in Fig 5.3. If the system was initially at the thermal equilibrium, when excited on A, one has a very fast depopulation of A in favor of B, followed by a depopulation of B and A in favor of C. When the

excitation is stopped, the equilibrium between A and B is recovered, but their population is very small, while the population of C is increased. Starting from this situation, if one excites on At, the population of C decrease in favor of A and B. The starting situation is recovered when the excitation is stopped and the thermal equilibrium between A and B is recovered. Knowing the spectral characteristic of each single state, the time behavior of the spectra can be predicted (see Fig. 5.3). This behavior was experimentally observed in a mutant of GFP[5].

(a)

(b)

Fig 5.3 (a) The scheme of the GFP photodynamics when the dark state of the photoswitch is added (b) time evolution of the states population and of the spectra. This methodology can help interpreting experimental results or verifying hypotheses on the connections between the states.

Fig 5.4 The simulation of a FRET experiment in a endoplasmic reticulum, according to the methodology of ref [7].

5.3 Theory: simulation of the diffusion among cell compartments The methodology of the first order diffusional dynamics can be applied to the diffusion of proteins among cell compartments. In this case the state is replaced by the cell compartment, the population of the state is replaced by the population of the compartment, and the kinetic constants are replaced by the transverse diffusional constants. At variance with the state model,

in this case the geometry of the system must be included, so that the diffusion constant is a position dependent tensor. The method was tested on a FRET experiment (see Fig. 5.4) and fairly well reproduce the experimental data. References [1] Biophysical chemistry Cantor, Schimmel (2001) Freeman Ed [2] Green Fluorescent Protein Chalfie, Kain (1998) Wiley-Liss [3] Green Fluorescent Proteins and their applications to cell biology and bioelectronics V Tozzini, V Pellegrini, F Beltram in Handbook of organic photochemistry and photobiology, W. M. Horsphool and F. Lenci, Eds., CRC, Washington DC, chapter 139 (2004) [4] Nano-Sized Optical ``Devices'' for Applications in Proteomics and Biomolecular Electronics: Engineered Green Fluorescent Proteins R Bizzarri, R Nifosí, P Pingue, V Tozzini, F Beltram in Functional Nanomaterials KE Geckeler and E Rosenberg Eds, Chapter 2 (2006) [5] Photoreversible dark state in a tristable Green Fluorescent Protein variant R Nifosí, A Ferrari, C Arcangeli, V Tozzini, V Pellegrini and F Beltram J Phys Chem B 107, 1679-1684 (2003) [6] Simulations of (An)Isotropic Diffusion on Curved Biological Surfaces I F Sbalzarini, A Hayer, A Helenius, P Koumoutsakos Biophys J 90 878–885 (2006)