## Info

Where K is the equilibrium constant in the absence of the force. The crucial point is that an external force will couple to a structural change if the structural change is associated with a length change in the direction of the force. If the change in length of a molecule is 4 nm, then a force of 1 pN will change the free energy by 4 pN.nm kT, the unit of thermal energy where k is Boltzmanns constant and T is absolute temperate. According to equation (3), this will lead to an e-fold change in...

## Keq

The Law of Mass Action was used in the last step. If we insert the measured value of the equilibrium constant (for the non-specific interaction) and our estimated value for DNA , we find that F is of the order of 10 2 (the nonspecific equilibrium constant Keq is measured in the absence of lactose so we are assuming here that lactose binding does not affect the non-specific interaction). That is an interesting result Induced lac repressors in E.Coli still live most of the time on DNA even though...

## [AK0expAHkBT Pc l [AK0expAHkBT1

Where K0 is the prefactor of Van't Hoff's law of the temperature dependence of the equilibrium constant K K0 exp AH kBT . Therefore the degree of crosslinking (expressed by Z) can be changed reversibly by variation of the temperature around 20 C. As shown in Figure 11b the viscoelastic moduli change in a characteristic way with Z (or T). The loss modulus G(Z) (expressed in terms of the loss angle tan G G') exhibits a broad band whereas G'(Z) starts to increase sharply by to two orders of...

## Sm a28

Show that the solution is deterministic f(x) 1 or f (x) 0 , so that if the goal is to be correct as often as possible you shouldn't hesitate to make a crisp assignment even at values of x where you aren't sure ( ). c. Consider the case where P (x) are Gaussian distributions with the same variance but different means. Evaluate the minimum error probability (formally) and give asymptotic results for large and small differences in mean. How large do we need to make this signal to be guaranteed...

## [iDNA ka J

This is just the Law of Mass Action so the right hand side must equal the equilibrium constant Because the on and off rates do not depend on concentration, this relation must hold also away from thermal equilibrium That means that we only need to determine one of the two rates, the other rate follows from equation (2.15). In vitro experiments on repressor-DNA solutions (containing the operator sequence) report that for the lac repressor ka is of order 1010 under standard conditions. Using this...

## Estt B Jdxdxcy c332

Where the last limit is at high contrasts. As promised by the lack of a phase transition, this starts as a quadratic function of contrast just like the correlator, but saturates as the ratio of temporal and spatial derivatives. Note that if C(x,t) C(x + vt), then this ratio recovers the velocity v exactly. This simple ratio computation is not optimal in general because real movies have dynamics other than rigid motion and real detectors have noise, but there is a limit in which it must be the...

## The Physics Of Listeria Propulsion

Listeria is a pathogenic bacterium, which can be dangerous for immune deficient individuals. It can be found almost everywhere, in particular in food such as soft cheese and smoked salmon. After ingestion, it is able to penetrate in the cellular system where it moves from cell to cell and divides on average every twenty minutes. The reason why it can move from cell to cell is that it develops a comet-like tail (Fig. 1), which pushes the bacterium forward and deforms the plasma membrane until it...

## Micron feeder channels

A view of the input channel which brings a confined stream of liquid into the array. The input channel is 6 microns wide. Fig. 6. A view of the input channel which brings a confined stream of liquid into the array. The input channel is 6 microns wide. unique reservoir which contains a the material to be transported across the array, in our case DNA molecules. Figure 6 taken 1 4 of the way down the side of the array shows the special channel, hydrodynamically isolated from Fig. 7. An...

## IpredT T St St St T510

In the same way that the entropy of a gas at fixed density is proportional to the volume, the entropy of a time series (asymptotically) is proportional to its duration, so that limTS(T) T Sq entropy is an extensive quantity. But from equation (5.10) any extensive component of the entropy cancels in the computation of the predictive information predictability is a deviation from extensivity. If we write then equation (5.10) tells us that the predictive information is related only to the...

## Dm

Time-resolved FTIR spectra and kinetic analysis. a) Time-resolved ab-sorbance spectra taken along the observation channel. Time-resolved spectra at 1.1 ms, 3.4 ms, 5.7 ms, 10.2 ms, 21.6 ms, and 103 ms. Spectrum before mixing (black line) and final state spectrum (green line). b) Second derivative spectra of a) (solid lines) and results of a three-state exponential fit (dots, plotted only up to 1670 cm-1). Line colouring same as in a). c) The three basis spectra, resulting form the fit....

## Biological Physics In Silico

The following set of notes outlines the work that my colleagues and I have been doing for the past 10 years which have exploited the opportunities that that silicon micro to nanomachining technologies provide in biological physics. This work started with my graduate student Wayne Volkmuth and has grown to include the efforts of a great many people, including but being limited to the following faculty Tom Duke (University of Cambridge Physics), Ted Cox (Princeton Molecular Biology), Harold...

## DSVdt vt1t MtS2t123

S1(t) is the likelihood of being in the bound state and S2(t) 1 S1(t) is the likelihood of being detached. When pulled by an elastic linkage Ks(f) at constant speed v, force and time become equivalent statistical variables connected through the dynamical transformation df Ks(f)v dt. Thus, the likelihood of bond survival to a particular time can be described in terms of survival to a particular level of force 7,10 , i.e. dS1 df Mf) + Mf ) S1(f ) rf (f) + Mf ) rf (f) (1.24) which reveals the...

## Sackmann1 and R Bruinsma2

Cell adhesion is controlled by a complex interplay of short range (lock-and-key) forces mediated by cell surface receptors, a phalanx of (short and long range) non-specific (generic) interactions and, last but not least, membrane elasticity. The physical basis of cell adhesion is explored by the design of simplified model systems mimicking cell and tissue surfaces enabling local measurements of cellular shape changes and adhesion forces by microinterferometry. Cell adhesion can be understood as...

## X

Oscillations induced by a team of motors in series with a spring. is the geometric mean of two rates the typical kinetic rate of the motor a and the rate of viscous relaxation of the filament 1 rvisc K Q. Interestingly, the frequency of oscillation can be significantly faster than the cycle time of an individual motor. There is, however, an upper limit to the frequency, since the dynamical instability is eliminated if the external spring is stonger than the total effective elasticity...

## Lectinlike Domain

Of tight cell-cell contacts thus requires the expulsion of these repellers from the adhesion zone. Secondly, the cell adhesion molecules are randomly distributed within the plasma membrane and the formation of tight adhesion zones by receptor segregation is a diffusion controlled process 3 . Thirdly, long term modulations of adhesion associated with adhesion induced cell signaling have to be considered. Examples are the transfer of receptors from cytoplasmic storage compartments to the plasma...

## P xnxi

And hence the predictive information reduces to The maximum possible predictive information in this case is the entropy of the distribution of states at one time step, which in turn is bounded by the logarithm of the number of accessible states. To approach this bound the system must maintain memory for a long time, since the predictive information is reduced by the entropy of the transition probabilities. Thus systems with more states and longer memories have larger values of pred. Problem 10...

## Slowly growing end

Fig. 5. a) Schematic view of actin as living macromolecule. The filaments are double stranded and exist in a dynamic equilibrium with monomers. They exhibit a fast growing end (also called barbed or plus end) where the rate of monomer association is ten fold higher than the dissociation rate (kon koff 10) while at the opposite end (pointed or minus end) the rate of monomer dissociation is higher (kon koff 0.3). b) At stationary equilibrium the growth rate at the barbed end equals the...

## Course T

CELL ADHESION AS WETTING TRANSITION * Physik Department E22, James-Franck-Stra e, D-85748 Garching b. M nchen, Germany ** Universiteit Leiden, Instituut-Lorentz voor Theoretische Natuurkunde, Postbus 9506, NL-2300 RA Leiden, The Netherlands 2 Mimicking cell adhesion 292 3 Microinterferometry A versatile tool to evaluate adhesion strength 4 Soft shell adhesion is controlled by a double well interfacial potential 294 5 How is adhesion controlled by membrane elasticity 297 6 Measurement of...

## Tmotor Medicine

As expected, we find that the isotropic part is stable and converges exponentially fast toward the steady state value e*, and that the symmetry breaking part is always unstable and grows exponentially fast with a time scale ro t(1 + 2- f-) . Note that tq grows linearly with the bead radius, just like t, and is of the same order of magnitude. Now we know that symmetry-breaking fluctuations are amplified, but where do they come from Could thermal fluctuations be sufficient The typical fluctuation...

## Zenk

The third character in our story is a gene a transcriptional regulator of the immediate-early gene (IEG) family. It is variously known by incomprehensibly different names in different species from mice to human zif268, EGR-1, NGFI-A and krox24. The avian version was named by Claudio Mello by the acronym of the previous names ZENK. I will refer to it as ZENK henceforth, though everyone calls it by the proper name in their own favorite animals. ZENK is a transcriptional regulator of the zinc...

## Aw G w yw215

The real part, G'(w), (called the storage modulus) determines the response in phase with the excitation and is the frequency dependent shear elastic modulus. The imaginary part G''(w) represents the out of phase component and is called loss modulus since it characterizes the energy dissipation during one cycle (cf. Eq. (2.19)). G''(w) is related to the shear 3 For more general time dependent shear strains one has to consider that the momen-taneous stress depends on the pre-history of...

## A

Sign convention for computing Wr. If you compute this integral, you find that the writhe of a spiral with N spiral turns and a pitch angle a equals with the + sign for a right handed spiral and the sign for a left handed spiral (try to prove this yourself). What is the Lk We already know that after stretching the belt you obtain N twisting turns. In this stretched state, there are no spatial turns so Wr 0. It then follows from White's Theorem that the linking number must be +N or N....

## V2 P41

This charge density includes both the charge density of the small mobile ions and of the fixed macro-ions. Macro-ions have a low dielectric constant interior, while their charges normally are located on the outer surface in contact with water. Under these conditions, the electrical field just outside the macro-ions is determined by Gauss' Law with a the macro-ion surface charge density. We now can treat equation (4.2) as a boundary condition to the solution of...

## F f ix L high tension321

This equation tells us that when you pull on DNA against the restoring force due to thermal fluctuations, DNA will be stretched out for tensions large compared to kT , the ratio of the thermal energy and the persistence length. This force is about 0.01 pN. That means that if you do force extension measurements using DNA as your leads, as for instance for the protein pop-off case, then for tensions of less than, say, a few pN, you must allow for this entropic elasticity of the DNA strands to...

## Rf Bruinsma

Department of Physics and Astronomy, University of California, Los Angeles, CA 90024, USA, and Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, Postbus 9506, 2300 Leiden, The Netherlands 1.1 The central dogma and bacterial gene expression 3 1.2 Molecular structure 2 Thermodynamics and kinetics of repressor-DNA interaction 16 2.1 Thermodynamics and the lac 2.2 Kinetics of repressor-DNA 3 DNA deformability and protein-DNA interaction 34 3.2 The worm-like 3.3 The RST 4...

## Vzu2el

Fig. 12. a) In mechanical equibrium, the sum of the forces exerted by the motors (grey arrow) opposes the applied load (black arrow). b) If one of the motors binds and undergoes its power-stroke, the force balance is momentarily upset. c) As a consequence, the filaments slide to restore mechanical equilibrium. Fig. 13. Force-velocity relation (black) and efficiency (grey) of muscle. Experimental data (points) are compared with model predictions (lines). Fig. 13. Force-velocity relation (black)...

## Polymerization Forces

The mechanical framework (cytoskeleton) of higher order (eukaryotic) cells consists of three types of protein filaments actin filaments, intermediate filaments, and microtubules 1 . The assembly or polymerization of both actin filaments and microtubules has been implicated in cellular force generation processes. Examples are the pushing forward of membranes by polymerizing actin filaments in the leading edge of crawling cells 2 the propulsion of Listeria bacteria through their host cell, again...

## Mh

A system of identical attachments that fail cooperatively when loaded in parallel can be considered as a single bond with a W-fold increase in the barrier compared to a single bond. The force scale of the compound bond remains the same as for a single bond interaction. (Note The prefactor N is based on the assumption that molecular damping scales with N.) For identical-cooperative bonds in parallel (cf. Fig. 2.2), location of the transition state xp and thermal force scale fp kB T xp...

## L

Conceptual energy landscape for capture and release of components in solution. The prefactor 4nxbD in equation (1.8) represents the well-known Smoluchowski rate for diffusion-controlled aggregation which, for two-spheres (A-B), is given by the product of interparticle separation (xb r_A + rB) at contact and combined particle diffusivity, (D Da + DB). For nanometer-size molecules in water, the Smoluchowski scale for on rate is 109 1010 s-1, whereas typical on rates for macromolecular...

## DS11df 1rf V121 f S11f 1rf [v22 f S2M

DSia df (1 rf) (1, f) Si,2( ) + vi 2(1, f) Si,2( ) Again at any stage of detachment, the rates of transition can depend on existing number n of bonds as well as force and passage of the final transition state v2 u(n, f) is assumed to be terminal for each state of bonding, i.e. v2 u(n, f) 0. Clearly, solving such a system of master equations for many attachments demands tedious numerical computation. But as described Part I, useful analytic approximations (Eqs. (1.18) and (1.19) of Part I) exist...

## Mechanics Of Motor Proteins

Motor proteins are molecular machines that convert the chemical energy derived from the hydrolysis of ATP into mechanical work used to power cellular motility. In addition to specialized motile cells like muscle fibers and cellular processes like cilia, all eukaryotic cells contain motor proteins (Fig. 1). The reason is that eukaryotic cells are large and their cytosols are crowded with filaments and organelles as a result, diffusion is too slow to efficiently move material from one part of a...