precise control of the 
 adsorption of proteins on solid surfaces 
 is a key to a wide variety of biological and technological applications . proteins are commonly immobilized on surfaces both in microarrays 
 and other studies of protein function and in the 
 creation of biosensors and biocatalysts . the success of these applications depends on proteins maintaining 
 their native state and function when adsorbed to the surface and on 
 the prevention of nonspecific protein binding . protein 
 adsorption also plays an important role in the outcome of biomaterials 
 ( e.g. , biomedical implants , artificial tissue scaffolds , and nanoparticles 
 for drug delivery ) in vivo , as proper protein adsorption contributes 
 to cell adhesion and the integration of the biomaterial with the circulatory 
 system , while the adsorption of undesired proteins can contribute 
 to failure due to immune responses or fouling . surface interactions are 
 also relevant to understanding many diseases , as they are the first 
 step in many biological processes , including blood clotting and the 
 formation of protein aggregates , such as the amyloid plaques found 
 in alzheimer s disease . because of the 
 importance of protein adsorption in these many applications , 
 investigation of the interplay between the folding and adsorption 
 processes and how adsorption impacts protein conformations is highly 
 valuable . experiments , including a variety of spectroscopic methods , 
 have been able to show that surface adsorption can result in changes 
 in the conformation and thermodynamic stability of a protein and that 
 these changes are dependent on a variety of factors , such as temperature , 
 ph , protein concentration , and the hydrophobicities of the protein 
 and surface . however , experiments 
 have not been able to fully address many aspects of the relationship 
 between protein adsorption and conformational changes and are complicated 
 by the complex heterogeneity of interactions between real protein 
 chains and surfaces . therefore , theoretical 
 and computational efforts that often utilize simplified , coarse - grained 
 protein models have been used to supplement experiments and provide 
 a basic understanding of protein adsorption . one minimalist 
 model used to investigate protein folding and adsorption 
 is the hydrophobic - polar ( hp ) model , in which protein monomers are 
 modeled on a lattice as either hydrophobic ( h ) or polar ( p ) beads . within the hp model , the many thermodynamic factors underlying complex 
 processes , such as protein folding and adsorption , are reduced to 
 a few basic terms ( i.e. , enthalpic interactions between chain segments 
 or between the chain and surface and entropically excluded volume 
 interactions ) . one route through which the hp model can be used to 
 understand protein adsorption and/or folding is the study of two transitions , 
 the coil globule and the critical adsorption transitions , that 
 are the result of a balance between these thermodynamic terms . the 
 coil  globule or collapse transition is one of the first steps 
 in the protein folding process and occurs 
 when attractive interactions between hydrophobic protein monomers 
 become strong enough to balance the conformational entropy lost by 
 the protein adopting compact globule conformations . a recent experiment 
 using synthetic polymers containing hydrophobic and polar monomers , 
 mimicking hp model chains , confirmed that attractions between hydrophobic 
 monomers are sufficient to be the driving force of the collapse transition . the critical adsorption point ( cap ) on the other 
 hand marks the transition of a protein which prefers being in solution 
 to being adsorbed on the surface and also involves a balance between 
 entropic and enthalpic effects . the cap is the point at which a polymer just becomes 
 adsorbed to a surface and occurs when the conformational entropy lost 
 by a polymer chain near a surface is offset by attractive interactions 
 with the surface . thus , the thermodynamics and potential conformational 
 changes of the process through which a folded protein adsorbs on a 
 surface , for example , can be understood in terms of these two transitions , 
 as some hydrophobic interactions underlying the collapsed conformation 
 of the protein can unravel to allow for additional chain  surface 
 attractive interactions . over the last quarter century , the 
 hp and other simple coarse - grained 
 models have been successfully used to provide insight into the conformational 
 changes of proteins and other macromolecules during adsorption both 
 in terms of these transitions and in a variety of other ways . first , 
 the adsorption of hp - like chains with various sequence types on surfaces 
 with various patterns has been studied to understand pattern recognition . these studies have revealed that the adsorption of copolymers on 
 heterogeneous surfaces can proceed via an initial nonspecific adsorption 
 similar to the critical adsorption transition , followed by a reorganization 
 in which the surface pattern is recognized by the copolymer , and that 
 such a two - stage adsorption process depends on the chain sequence , 
 surface pattern , and interaction parameters . additionally , 
 moghaddam and chan investigated the adsorption of block copolymers 
 on patterned surfaces and showed that the sharpness of the adsorption 
 transition was enhanced through the introduction of additional either 
 attractive or repulsive chain  surface interactions . however , these studies did not include intrachain 
 interactions and , therefore , could not consider the balance between 
 intrachain and chain  surface interactions that underlies protein 
 adsorption . second , the adsorption of a homopolymer with intrachain 
 interactions ( i.e. , basically , a chain consisting of only the h beads 
 of an hp chain ) has been considered , and it was shown that the presence 
 of the surface promoted chain collapse and increased the internal 
 structural organization ( e.g. , helices and antiparallel sheets ) in 
 the chain . also , chains with strong intrachain 
 interactions were shown to undergo two types of adsorption transitions : 
 a  docking  transition , in which a collapsed chain does 
 not deform upon adsorption , for weak chain surface attractions 
 and a  flattening  transition , in which the chain adopts 
 two - dimensional conformations after adsorption for strong chain  surface 
 attractions . finally , several studies have examined the adsorption 
 of hp chains directly . rybicka and sikorski compared the adsorption 
 of several hp sequences with that of a homopolymer containing only 
 h - type beads on a homogeneous surface . they showed that the collapse of chains weakly adsorbed on a surface 
 was roughly independent of the chain sequence ; however , under strong 
 adsorption , chains underwent a sequence - dependent rearrangement similar 
 to the previously discussed  flattening  transition . studies of hp chains interacting with surfaces have also confirmed 
 the experimental observation that the presence of the surface can 
 significantly alter the lowest energy conformation of a folded protein and have been used to determine 
 conformational pseudophase diagrams of hp chains near a surface that 
 shows how temperature and the strength of attractive interactions 
 impact adsorption and folding . in this work , we seek to increase understanding of the relationship 
 between protein adsorption and conformation change through a systematic 
 examination of the interplay between the collapse and critical adsorption 
 transitions . specifically , we study the protein folding and adsorption 
 processes by determining the temperatures of collapse , tc , and critical adsorption , tcap , transitions for hp chains end - grafted to a solid surface that equally 
 attracts h and p monomers . in contrast with most previous simulations 
 of the adsorption of hp chains that have used a specific short sequence 
 with a well - defined ground state , we use a simple alternating hp sequence and vary the chain length 
 from 10 to 400 , allowing us to investigate the potential influence 
 of chain length on collapse and adsorption . the current study also 
 investigates the behavior of the chain at more intrachain attraction 
 strengths and over a wider temperature range than was considered in 
 previous studies of the relationship between chain collapse and surface 
 adsorption . we show that , while the critical 
 adsorption point can always be observed and is roughly independent 
 of chain length , tcap is affected by the 
 presence of intrachain attractions in some cases . specifically , if tc > tcap ( i.e. , 
 the chain is already collapsed when the adsorption transition is attempted ) , 
 the critical adsorption transition occurs at a higher temperature 
 than a corresponding homopolymer without intrachain attractions , indicating 
 that collapsed chains are more easily adsorbed . in contrast , if tc < tcap ( i.e. , 
 the chain is already adsorbed when the collapse transition is attempted ) , tc is suppressed and it is more difficult to 
 collapse the adsorbed chain than a corresponding chain that is free 
 in solution . finally , we examine how the strength of the hydrophobic 
 intrachain and chain  surface attractions impact chain conformations . our simulation 
 system is embedded in the three - dimensional ( 3d ) 
 simple cubic ( sc ) lattice . a self - avoiding walk ( saw ) other sequences representing 
 different protein types could have been used ; however , since the 
 current study focuses on the interplay between the two transitions , 
 we focus on a generic alternating hp chain that can be easily extended 
 to long chains . additionally , we note that both the collapse and adsorption 
 of an alternating hp sequence have been shown to differ from a homopolymer 
 with intrachain attractive interactions . the protein of length n is composed of n/2 h monomers and n/2 p monomers . bond lengths between monomers fluctuate 
 among 1 , 2 , and 3 lattice constants . the bond can 
 be taken from 26 allowed bond vectors obtained from the set { ( 1,0,0 ) , 
 ( 1,1,0 ) , ( 1,1,1 ) } by symmetry operations of the sc lattice . however , 
 bond crossing is not allowed . in this coarse - grained model , the monomers 
 do not correspond to specific atoms in a polymer but rather to small 
 groups of atoms , and the bonds do not represent specific covalent 
 bonds between two atoms but , instead , the linkages between monomers . 
 the simulation box is a cuboid with sizes lx , ly , and lz in the x , y , and z directions , 
 respectively periodic boundary conditions are employed in the x and y directions , while the z direction is confined by an infinitely large flat surface located 
 at z = 0 . the surface is impenetrable to the polymer , 
 so polymer monomers are restricted to lie in the upper half space 
 ( z > 0 ) . polymer chain lengths studied are in 
 the 
 range of n = 10 to 400 . the simulation box is always 
 large enough to ensure no finite size effects on the simulation results . 
 to this end , the dimensions of the simulation box in all three directions 
 are always larger than the chain length n. the first monomer , which is always an h , is considered to be adsorbed 
 to the impenetrable surface and is grafted at the center of the z = 1 layer . then the 
 chain is subjected to brownian motion achieved by the dynamic monte 
 carlo ( mc ) technique . polymer monomers that are located on the z = 1 layer are considered to be adsorbed to the surface . surface interaction is assigned for all 
 monomers on the z = 1 layer next to the surface . a two - dimensional ( 2d ) sketch of our 3d simulation system is presented 
 in figure 1 . 2d sketch of our 3d simulation model for 
 an end - grafted hp protein 
 model chain . monomers are numbered from 1 to n for a polymer with 
 length n. the first monomer h is grafted to the surface . the nearest neighbor interactions are ehh , ehp , epp , ehs , and eps , as shown . the energy of a conformation 
 is a summation of all nearest - neighbor 
 ( nn ) contact interactions among the chain and all nearest - neighbor 
 contact interactions between the chain and surface . rij is the spatial distance between two 
 nonbonded monomers i and j and zi is the distance of monomer i away 
 from the surface . it is known that the adsorption of a copolymer 
 chain is influenced by the properties of the surface . here we 
 set ehp = epp = 0 , while the value of ehh is negative 
 and varied . therefore , the energy of polymer can be expressed as2where nhh , nhs , and nps represent 
 the nn contact numbers of h  h , h  surface , and p  surface 
 pairs , respectively . |ehs| is used as 
 the unit of energy while |ehs|/kb is the unit of temperature , where kb is the boltzmann constant . h interaction ehh and temperature t. variation in ehh from zero to negative numbers will allow 
 us to investigate the adsorption of the hp chain on the surface in 
 the absence ( ehh = 0 ) or presence of the 
 intrachain hydrophobic interaction . the brownian motion of the 
 polymer chain is attributed to local 
 moves of chain monomers . polymer dynamics is achieved by bond fluctuation , similar to that used for one - site and eight - site 
 polymer models on the sc lattice . for 
 each trial move , a monomer is chosen randomly to move to one of its 
 six nn sites . if the chosen site is already occupied by another monomer , 
 or such a move will violate bond crossing and bond length restriction , 
 the trial move is abandoned . otherwise , the trial move will be accepted 
 with a probability p = min[1 , exp(e / kbt ) ] , where 
 e is the energy difference between new and 
 old configurations . it has been pointed out that the metropolis method 
 may have problems in describing the behavior of hp chains at low temperatures 
 ( kbt < 0.3|ehh| ) in comparison with the wang landau 
 method . at these low temperatures , the 
 sampling efficiency using the metropolis algorithm can be poor , as 
 the polymer can become trapped in low - energy states . as we use the 
 metropolis method in this work , we focus on polymer behavior near tcap and tc , which are higher than 0.3|ehh| . the 
 results of the metropolis and wang  landau methods are very 
 similar for kbt > 
 0.3|ehh| , and ergodicity 
 can be satisfied by a long simulation run using the metropolis algorithm . the time unit is one monte carlo step ( mcs ) 
 during which n  1 trial moves are attempted 
 since the first monomer is always adsorbed . to avoid correlation between 
 two configurations , we measure the chain s statistical properties 
 only after a regular time interval  = n mcs . typically , each simulation is run as long as 1000 , 
 and 5000 independent runs are simulated . we also adopted 
 an annealing process in simulations of chain configuration 
 at different temperatures . simulations begin at a high temperature 
 with the chain in a desorbed state and in a random coil configuration . the temperature decrement 
 step is not a constant but is specially chosen in advance for clearly 
 presenting the collapse and adsorption transitions and for saving 
 calculation time simultaneously . to this end , we first roughly estimate 
 the two transition temperatures using a simulation with a large temperature 
 decrement step and then adopt a small temperature decrement step around 
 the transition temperatures in a second simulation . at each temperature , the final configuration at the previous temperature was used 
 as the initial configuration for the subsequent temperature . every 
 independent simulation run ends at a low temperature far below the 
 cap , where the chain is in a deeply adsorbed state . we at first determine the collapse transition 
 of the alternating 
 hp model chain in a dilute solution . the dependence of the mean square end - to - end 
 distance r on the temperature t is presented in figure 2 for the 
 case where ehh = 1 . the inset 
 shows that the scaling r 
  n at high temperature changes 
 to r  n at low temperature , indicating a collapse 
 transition from a random coil to a compact sphere . r/n has the steepest 
 decrease at t = 0.75 , that is , the temperature at 
 which dr/dt is at a maximum . therefore , we identify a coil  globule 
 transition at tc = 0.75 when ehh = 1 for the hp chain in dilute solution . 
 since the temperature t and ehh are interrelated through the boltzmann factor , a variation 
 in ehh would shift tc according to tc = 0.75|ehh| for the hp chain 
 in dilute solution . here globule transition temperature of the 
 hp chain in the dilute solution in the absence of any surface . dependence 
 of mean square end - to - end distance r on temperature t for the free 
 hp chain with ehh = 1 in dilute 
 solution . the inset presents the log  log plot of r as a function of the chain length n at t = 2 , 1 , and 0.5 ( from top to bottom ) . the straight lines are the best fits with slopes 1.19 , 1.12 , and 0.65 
 for t = 2 , 1 , and 0.5 , respectively . next , we simulate the adsorption of the end - grafted 
 hp chain with ehh = 1 by annealing 
 the chain with the 
 head h monomer grafted on a flat surface and estimate the collapse 
 transition and the critical adsorption transition temperatures . the 
 critical adsorption transition temperature is estimated from the temperature 
 dependence of the mean surface contact number m of the chain . m as a function 
 of chain length at different temperatures is plotted in log log 
 scales in figure 3 . on the basis of the eisenriegler , 
 kremer , and binder ( ekb ) scaling theory , the scaling relation m  n is satisfied at the critical adsorption 
 point tcap . meirovitch and livne have 
 estimated that tcap = 3.44  0.01 
 and the crossover exponent  = 0.530  0.007 for a saw 
 chain with fixed bond length ( b = 1 ) on the sc lattice 
 with mc simulations . the plot of m versus chain length n has a concave 
 upward curve at temperatures below tcap and a convex downward curve at temperatures above tcap . for the present bond - fluctuation saw hp model , we 
 estimate tcap = 1.65  0.02 and  
 = 0.54  0.01 . the results are close to that estimated for the 
 adsorption of a bond - fluctuation saw homopolymer without intrachain 
 attractive interactions , where tcap = 
 1.625 and  = 0.52 have been estimated by using a finite - size 
 scaling formula m c)n ) ] , indicating 
 that hydrophobic interactions have little effect on tcap as long as the attractive interactions with the surface 
 are the same for both h and p monomers . log log plot of 
 the surface contact number m versus 
 chain length n at temperatures t = 1.55 , 1.6 , 1.65 , 1.7 , and 1.75 for an hp polymer with ehh = 1 . the statistical error of each 
 monte carlo datum is smaller than the symbol size . dependence of mean square end - to - end distance r on temperature t for 
 the end - grafted 
 hp chain with ehh = 1 . chain lengths 
 are n = 50 , 100 , 200 , and 400 from bottom to top . the vertical straight lines show the locations of tcap = 1.65 and tc = 0.5 , respectively . the inset presents the heat capacity per monomer for the end - grafted 
 hp chain with n = 200 and n = 400 . globule transition 
 temperature for an end - grafted 
 chain is estimated from the temperature dependence of the mean square 
 end - to - end distance r. 
 figure 4 shows the dependence of r on t for the end - grafted 
 hp polymer with ehh = 1 . at the 
 critical adsorption temperature tcap = 
 1.65 , we find that r 
 tends to be a local minimum , which is in agreement with the results 
 of adsorption of a homopolymer chain . however , unlike the adsorption of a homogeneous saw polymer on a 
 surface where the r increases 
 monotonically as the temperature is lowered below tcap due to the flattening of the chain on the surface , 
 r for the end - grafted 
 hp chain increases when t is lowered from tcap to about t = 1 and then 
 decreases afterward . the sharp decrease of r below t = 1 is a result of 
 the coil in contrast to the coil  globule transition 
 of free chains ( figure 2 ) , the plots of r/n versus t for different chain lengths of end - grafted chains do not 
 cross , and we , therefore , can not use the crossing point to define 
 the coil we can however still find the 
 steepest decrease of r , 
 which takes place at about t = 0.5 and is roughly 
 independent of the chain length . we also find a peak in the heat capacity 
 at t = 0.5 for the hp chain as shown in the inset 
 of figure 4 . we therefore identified this temperature 
 as the collapse transition temperature of a surface - absorbed chain tc = 0.5 . this tc = 0.5 of the end - grafted hp chain is lower than tc = 0.75 for the free hp chain . we therefore 
 conclude that the collapse transition of the hp polymer is suppressed 
 by being adsorbed to the surface . when tc < tcap , the chain 
 undergoes the adsorption transition before 
 the collapse transition can occur . surface adsorption makes it more 
 difficult for the chain to adopt conformations that provide a sufficient 
 number of h  h contacts for collapse to occur , reducing tc from its value in a bulk solution . figure 5 presents the number of h  h contacts for 
 the hp chains in dilute solution and end - grafted on the surface . above tcap of the 
 end - grafted chain , nhh is small and the 
 same for both chains . at temperature tc < t < tcap , nhh of the end - grafted hp 
 chain is slightly larger than that of the free chain , indicating that 
 the adsorption of the chain promotes the formation of h  h pairs . 
 below tc , however , we find 
 that nhh of the end - grafted hp chain is 
 significantly smaller , clearly indicating that surface adsorption 
 prevents the collapse of chain at low temperatures . this reduces tc for the end - grafted hp chain . on the other 
 hand , the critical adsorption of the polymer is not influenced by 
 the collapse transition of the polymer if tc < tcap . from the heat 
 capacity the temperature at the shoulder is consistent with the 
 cap , determined from the location of the minimum of r , for the finite chain . dependence of the number 
 of h  h contacts , nhh , on the temperature t for hp chains 
 in dilute solution and end - grafted on a surface . the length of the 
 hp chain is n = 400 , and the h comparing data in figures 2 and 4 for t < tc , one can notice that r/n in figure 4 increases 
 with n and is much bigger than that of a free hp 
 chain in solution , as shown in figure 2 . the 
 reason is that the adsorbed chain adopts a roughly 2d conformation 
 at t  tcap , and 
 the subsequent coil globule transition driven by the intrachain 
 hydrophobic attraction now occurs within this 2d conformation . as 
 has been previously shown for a homopolymer with intrachain attractions , 
 the collapse of a chain in 2d takes place at a lower temperature than 
 collapse in 3d , since a 2d chain conformation will have less pairwise 
 attraction . as will be shown , we find 
 that the adsorbed chain is anisotropic , since its asphericity parameter 
 a is even bigger than that of an 
 adsorbed hp chain without h  h attraction . since tc  tcap , the chain 
 at tc is already trapped in the random 
 coil state achieved at tcap ; this would 
 probably result in a more anisotropic conformation because the collapse 
 would likely occur at higher density of h monomers . h 
 attractions ( ehh = 2 , 3 , 
 and 4 ) , while the monomer  surface attractions are fixed 
 as ehs = eps = 1 . globule transition of the hp chain when free 
 in solution to higher temperatures , following tc = 0.75|ehh| . therefore , tc occurs at 1.5 , 2.25 , and 3 for ehh = 2 , 3 , and 4 , respectively . these conditions allow us to examine the interplay between the transitions 
 when the collapse transition occurs at a higher temperature than the 
 critical adsorption transition ( ehh = 
 3 and 4 ) and when the transitions occur at approximately 
 the same temperature ( ehh = 2 ) . first , we determine the collapse transition of end - grafted chains 
 when intrachain attractions are stronger than chain surface 
 attractions ( ehh < ehs = eps ) and find that tc is not influenced by the presence of the surface . 
 as shown in figure 6 , a plot of r/n versus temperature 
 for ehh = 2 and 4 shows 
 the same crossover point as expected for the transition temperature 
 of free chains based on tc = 0.75|ehh| . this behavior is different 
 from the case where ehh = ehs = eps = 1 shown 
 in figure 4 , where the chains with different 
 lengths do not cross over with each other . although tc is not influenced by the surface , the conformational 
 size of the chain r is 
 influenced by the attractive surface , as can be observed through comparison 
 of figures 2 and 6 . we next examine the impact of increasing the strength of intrachain 
 attractions on the critical adsorption transition . figure 7 presents the surface contact number as a function 
 of chain length at different temperatures for ehh = 4 . a scaling relation m  n is observed 
 at tcap = 2.55 with an exponent  
 = 0.34 . we find that both tcap and  
 are different from those of ehh = 1 . the results of tc , tcap , and  for the hp chains with different intrachain 
 interactions ehh are listed in table 1 . the tcap for ehh = 2 , 3 , and 4 is 
 obviously affected by the collapse of chain when tc is close to or larger than tcap of the hp chain with weak h  h interactions . the simulation results show that the presence of intrachain interaction 
 shifts the tcap to a higher temperature . dependence 
 of mean square end - to - end distance r on temperature t for the end - grafted 
 hp chain with ehh = 2 ( black ) 
 and 4 ( red ) . the vertical straight lines show the locations 
 of tc = 1.5 for ehh = 2 and tc = 3.0 for ehh = 4 , respectively . log plot of the surface contact number m versus chain length n at temperatures t = 2.3 , 2.4 , 2.5 , 2.55 , 2.6 , and 2.7 for an hp polymer 
 with ehh = 4 . the statistical 
 error of each monte carlo datum is smaller than the symbol size . surface 
 interactions ehs = eps = 1 . at 
 the end of this subsection figure 8 shows the 
 coil  globule transition line and the adsorption / desorption 
 transition line for the end - grafted hp chain with polymer  surface 
 interactions ehs = eps = 1 . there is a specific interaction , named e*hh , at which the two lines intersect . for intrachain 
 interactions stronger than e*hh , as temperature 
 decreases , the hp chain changes from a desorbed 3d coil at high temperature 
 to a desorbed collapsed structure at tc and , finally , to an adsorbed collapse structure at tcap . for interaction strengths below e*hh , the hp chain changes from a desorbed 3d coil at high 
 temperature to an adsorbed 2d coil at tcap and at last to an adsorbed collapse structure below tc . here e*hh is estimated 
 to be about 2.6 times the polymer  surface attraction , and the 
 corresponding temperature is about 2.0 . symbols are estimated from simulation , while 
 lines are guides for the eyes . to further investigate the interplay between the 
 two transition temperatures , figure 9a presents 
 the mean surface contact number m 
 at different temperatures t for different intrachain 
 interactions ehh . at high temperature t > tcap , the chain is in 
 a 
 desorbed state with m = 0 . at low t , one of the ways 
 to observe the tcap is the substantial 
 increase in m as t is lowered . at t = 0 , we have m = n for the case ehh = 0 , indicating that all monomers are adsorbed on the surface , 
 whereas for ehh < 0 , m is less than n due to the collapse 
 of the hp chain , indicating that the conformation of the adsorbed 
 polymer is of a multilayer structure because of the intrachain attraction . the number of h  h contact pairs , nhh , always increases with the decrease of temperature as shown in figure 9b . moreover , we find that nhh increases with |ehh| , whereas 
 m decreases with |ehh| . similar to behavior that has been observed for homopolymers 
 with intrachain attractions , there are 
 less surface contacts but more intrachain contacts as the intrachain 
 attraction increases . this reflects the fact that the adsorbed chain 
 adopts more compact spherical shapes for stronger intrachain interactions . dependence 
 of ( a ) mean surface contact number m 
 and ( b ) the number of h  h contacts nhh on temperature t for different internal 
 interactions ehh . the length of the hp 
 chain is n = 400 . from table 1 , we find that the crossover 
 exponent  in the scaling relation m  n is about 0.5 
 for tc < tcap while it decreases for tc > tcap at strong h  h attraction . for the 
 former case ( tc < tcap ) , the conformation of the chain is a random coil near tcap , and m 
 behaves similarly near tcap as shown in 
 figure 9a , resulting in the same value of the 
 crossover exponent  for tc < tcap . for the latter case ( tc > tcap ) , the 
 contact number of the compact chain at tcap is reduced , since the contact monomers are located on the globule 
 surface , as can be observed by comparing data plotted in figures 3 and 5 . for the same reason , 
 the crossover exponent  is reduced for the case tc > tcap . the reason is that the difference between tc and tcap increases with ehh as shown in table 1 , and the chain becomes more compact at lower temperature below tc . in order to learn more about the conformation 
 of the chain , we 
 have monitored the mean square end - to - end distance r and its two components parallel to 
 the surface rxy and normal to the surface rz at different internal 
 interactions ehh , as shown in figure 10 . different behaviors are exhibited for three different 
 cases : ( 1 ) a chain with no collapse transition when ehh = 0 , ( 2 ) tc < tcap with ehh = 1 , and ( 3 ) tc  tcap with ehh = 2 and 4 . for the first case in the 
 absence of intrachain interaction , a slight minimum in r is found at tcap that is a result of two changes , as a sharp decrease in 
 rz is partially offset by a sharp increase in rxy . as 
 the temperature is further reduced , the increase in rxy outcompetes 
 the decrease in rz , resulting in an overall increase in r. the behavior of r is similar to an earlier finding by exact enumeration 
 of all configurations for a short homogeneous saw chain . for the second case where tc < tcap , r first increases as the temperature 
 is lowered just as in the previous case but then r decreases because of the collapse of the chain . 
 in this second scenario , r 
 exhibits a maximum at a temperature close to tc , a distinct feature absent in the other cases . the maximum 
 is also presented in the plot of rxy as a function of temperature . 
 for the third case where tc  tcap , we find that r , rxy , and rz all decrease monotonically 
 with the decrease of t. the chain is already in a 
 compact state at tcap ; therefore , it deforms 
 little when it adsorbs on a surface , similar to the  docking  
 transition for a compact chain adsorbed on a weak attractive surface . dependence of ( a ) the mean square end - to - end distance 
 r and ( b ) its components 
 parallel and 
 normal to the surface , rxy and rz , respectively , as a function 
 of temperature t for hp polymers with different h  h 
 interactions . l1 , l2 , 
 and l3 are 
 three eigenvalues of the radius of gyration tensor4where si = col(xi , yi , zi ) is the position 
 of monomer i of 
 polymer in a frame of reference with its origin at the center of mass . the asphericity parameter a ranges 
 from zero for 3d spherically symmetric chain conformations , 0.25 for 
 2d circular shapes , and one for rod - shaped . it was found that a  0.391 for a linear rw chain and a  0.431 for a linear saw chain . values a of 
 the hp chain in dilute solution ( i.e. , free hp chain ) and the end - grafted 
 hp chain are calculated . the dependence of a on temperature t is presented in figure 11 for the end - grafted hp chains with different intrachain 
 h  h interactions . plot of the asphericity parameter a 
 vs temperature t for free hp chains with ehh = 1 and end - grafted hp chains with 
 different h the arrows indicate the location of tc and tcap , and the value 
 in parentheses is ehh . for the free hp chain with ehh = 1 , a is about 0.44 at t  tc and decreases steeply at tc = 0.75 . a is about 0.12 at low temperatures ( t < tc ) , clearly showing that the chain is roughly 
 a sphere at temperatures below tc . for 
 the end - grafted hp chain , the behavior of a , like that of size r , is dependent on the intrachain attraction ehh . moreover , the behavior of a is quite complicated due to the competition between tc and tcap in the 
 hp chain . for ehh = 0 , a increases at tcap due 
 to the transition from a 3d random coil to a 2d random coil . for ehh = 1 , a 
 first increases at tcap = 1.65 and has 
 a second increment at tc = 0.5 . the collapse 
 at tc  tcap happens locally and makes the chain configuration more 
 aspherical . for the case with ehh = 2 
 where tc is close to tcap , we find that a begins 
 to increase when the temperature drops below tcap and continues to increase at tc . but , as temperature continues to decrease further below tc , we find that a 
 begins to decrease due to the strong collapse of chain as |ehh| > |ehs| . for ehh = 4 , a 
 decreases at tc because of collapse and 
 then increases at tcap because of adsorption ; 
 finally , a plateaus as the chain 
 becomes frozen at low temperatures . from these four behaviors , we 
 conclude that adsorption of the chain increases a , whereas the effect of collapse is dependent on the strength 
 of intrachain h if the intrachain h  h 
 attraction is weak where we have tc  tcap , 
 the adsorption of the chain increases a 
 and the adsorbed configuration is a random coil . for this case , the 
 collapse at low temperature will induce extra anisotropy and increase 
 a. if the intrachain h  h attraction 
 is moderate where we have tc  tcap , a is increased 
 due to the adsorption as well as collapse of the chain but will decrease 
 at low temperatures below tc . finally , 
 if the intrachain h  h attraction is strong where we have tc > tcap , a first decreases due to the collapse and then increases 
 due to the adsorption of the chain . moreover , for the last two cases , 
 a at low temperature reaches a plateau 
 with a value close to 0.25 , indicating that the adsorbed configuration 
 is roughly a 2d circle . we have 
 studied the interplay between the critical adsorption of 
 a lattice hp protein with alternating h and p monomers and the coil  globule 
 transition with the dynamical monte carlo method . simulations are 
 carried out in the simple cubic lattice where bond length can be fluctuated 
 among 1 , 2 , and 3 lattice units . we find that the 
 critical adsorption temperature tcap is 
 influenced by the presence of intrachain attractions responsible for 
 the collapse transition of the polymer . if the coil  globule 
 transition tc is lower than tcap then tcap for 
 the hp polymer is roughly the same as that of a homopolymer without 
 monomer  monomer attractions , but the coil it is therefore 
 more difficult for a surface absorbed hp polymer chain to go through 
 the coil . 
 on the other hand , if the intrinsic coil  globule transition 
 temperature tc is higher than tcap , the tcap for 
 the hp polymer occurs at a higher temperature than a homopolymer without 
 monomer  monomer attraction ; that is , a collapsed chain can 
 be more easily adsorbed . the conformational properties of the end - grafted 
 hp chain are strongly influenced by the pairwise h first , 
 the hp model itself is limited in that it does not consider several 
 factors , such as desolvation effects , that have been shown to be relevant 
 to the behavior of real proteins , such as the cooperativity observed 
 during the folding of many proteins . second , the 
 sequence we have studied is the hp polymer with a fully alternating 
 sequence in which the surface interactions of h and p monomers are 
 treated as the same . this is a significant simplification and probably 
 does not represent the real experimental situation very well . in most 
 applications , a further extension of our study is to treat the surface interactions 
 of h and p monomers differently . however , the overall conclusion about 
 the mutual impact on the coil  globule transition and the critical 
 adsorption transition would probably still be valid .
an 
 end - grafted hydrophobic - polar ( hp ) model protein chain with 
 alternating h and p monomers is studied to examine interactions between 
 the critical adsorption transition due to surface attraction and the 
 collapse transition due to pairwise attractive h  h interactions . 
 we find that the critical adsorption phenomenon can always be observed ; 
 however , the critical adsorption temperature tcap is influenced by the attractive h 
 h interactions 
 in some cases . 
 when the collapse temperature tc is lower than tcap , the critical 
 adsorption of the hp chain is similar to that of a homopolymer without 
 intrachain attractions and tcap remains 
 unchanged , whereas the collapse transition is suppressed by the adsorption . 
 in contrast , for cases where tc is close 
 to or higher than tcap , tcap of the hp chain is increased , indicating that a collapsed 
 chain is more easily adsorbed on the surface . 
 the strength of the 
 h  h attraction also influences the statistical size and shape 
 of the polymer , with strong h 
 h attractions resulting in adsorbed 
 and collapsed chains adopting two - dimensional , circular conformations .