It can be demonstrated that dissociation constants for A and P at the reference state, respectively, and I; are the following generalized equation holds true for any reaction mechanism, where s and p denote the number of substrates and products, respectively.

In this way, Equation 30 enables the energetic analysis of any reaction by decomposing it in two contributions: (1) catalysis (how efficient is the enzyme converting substrates into products at the reference state) and (2) binding (how saturated is the enzyme at the reference state).

Greater contributions of the catalytic term suggest a higher enzymatic efficiency in the conversion of substrates to products, but a suboptimal saturation of the enzyme, 1'.

In order to determine the impact of reactant perturbations on the reaction rate, we estimated the reaction elasticities upon an infinitesimal variation in the concentration of substrates and products [2].

Firstly, the shape of the catalytic function is determined only by the mechanism of elementary interactions between substrates and products with one active site of the enzyme (catalytic mechanism).

number of subunits, transitions, allosteric sites and effectors, and possesses an eXpression representing the catalytic mechanism for the conversion of substrates to products, the catalytic and regulatory functions can be written as follows [23],

The classical approach including various graphical representations works well for studying regular enzymes up to a couple of substrates and a couple of products.

The fundamental cycles are found by traversing the edges of a graph connecting substrates to products and translating the paths into linear relations constraining different reversibility sets.

Essentially, all patterns can be considered cycles that transform substrates into products given that AGr<O (Fig.

These cell forces can be measured with traction force microscopy which inverts the equations of elasticity theory to calculate them from the deformations of soft polymer substrates .

Here we have introduced a novel method to reconstruct cellular forces from the deformation of elastic substrates .

Compared to earlier studies that used truss models to evaluate a few stress fiber tensions on pillar arrays [43,44], we have implemented this procedure for cells on flat elastic substrates with hundreds of FAs.

Forces at FAs have been measured with traction force microscopy (TFM) on soft elastic substrates [8—10], pillar arrays [11,12], and fluorescent force sensors [13—18].

Active cable models have been shown to correctly predict shapes of adherent cells on micro-patterned substrates and yield force distributions that are robust with respect to local changes in network geometry or topography [45].

Substrates used in our experiments are isotropic with a Young's modulus of several kPa.

The elastic problem is stated as a boundary value problem (BVP), where cellular traction stress defines the boundary condition at the substrate’s top surface.

Polyacrylamide substrates for traction force microscopy

Polyacrylamide (PAA) substrates containing far-red fluorescent microbeads (Invitrogen, d = 40 nm) were prepared on glass coverslips using previously published methodslo’37.

Data for three representative UZOS-cells on soft elastic polyacrylamide substrates (E = 8.4 kPa).

The common use of such metrics as the OOP and COOP for biological and medical sciences will allow for a quantitative evaluation of tissue engineered substrates from a variety of cell sources.

To make the substrates 25 mm glass coverslips were coated with PDMS (Ellsworth Adhesives, Germantown, WI) and cured for 12 hours in a 60°C oven.

Fabricated substrates underwent one 10 minute pluronics (250g of Pluronics F- 127, Sigma-Aldrich, Inc., Saint Louis, MO) wash and three rinses of phosphate buffer-saline (PBS) (Life Technologies, Carlsbad, CA).

To make isotropic substrates , UV-sterilized PDMS-coated coverslip were coated with FN for 10 minutes and underwent three PBS washes.

These can be divided into three main groups: interactions with structural role (enforcing a proper relative positioning of the substrates ), those stabilizing the positive charge on the Gal-NAc oxocarbenium ion and finally interactions stabilizing the negative charge on the diphos-phate moiety of the UDP leaving group.

The QM region was defined to include the essential parts of the substrates and residues experimentally known to be crucial for reactivity.

Finally, 12 highly conserved residues interacting with the substrates were included (Table 2) as well as six water molecules that were well defined in the crystal structure (B-factors below 20).

Residue Included part Function agreement with available experimental evidence [12] , including the recent X-ray structures based on modified substrates .

The results suggest that, While all sequences sample a similar set of conformational substates , cancer mutants could introduce both local and long-range structural modulations and in turn perturb the balance of p53 binding to various regulatory proteins and further alter how this balance is regulated by multisite phosphorylation of p53-TAD.

82 Fig illustrates that helical substate distributions largely stabilize by the end of 200-ns RE-GA simulations for both the wild-type p53-TAD and its cancer mutants and that the final distributions from the control and folding runs are largely consistent.

On the helical substate level, While all p53-TAD sequences simulated here apparently sample a similar, if not identical, set of partial helices (Fig 7), their occupancies appear to be sensitive to mutations.

We note that the convergence of helical substate distributions is more limited compared to average residue heli-city profiles (82 Fig).

As cells grow and consume substrates, the concentration of substrates in the medium will decrease (green line in Fig.

For biomass increase, cells consume substrates in the medium.

(A) Cells consume substrates for cell growth and the substrate concentration decreases in the medium (green line).